Enfin

T Chamarande
email: theo.chamarande@univ-grenoble-alpes.fr

S Mathy

The least cost design of 100% solar power microgrids in Africa: sensitivity to meteorological and economic drivers and

Keywords: conceptualization and methodology: T, C, , B conceptualization and methodology:

Je souhaite tout d'abord remercier Sandrine et Benoit qui m'ont encadré pour cette thèse et m'ont accompagné durant ces années, tout en me laissant la liberté d'aller explorer des pistes parfois éloignées de leurs disciplines. J'ai eu beaucoup de chance de vous avoir comme encadrants, vous avez toujours était présents, bienveillants et pertinents dans vos remarques. C'était un plaisir de travailler avec vous et j'espère que l'on pourra continuer à travailler ensemble à l'avenir ! Je remercie Schneider Electric d'avoir soutenu cette thèse, Nicolas et Benoit pour leurs contributions à ce travail, Angela et Géraldine pour leur accueil à Nairobi, et surtout Sheila pour son aide précieuse lors de notre terrain au Kenya.

Un immense merci à Emilie de m'avoir guidé, que ce soit pour mener des entretiens, pour m'initier aux méthodes qualitatives, ou pour trouver les meilleurs endroits où faire son terrain ! Ma thèse n'aurait pas été la même sans ton apport, j'ai vraiment apprécié de travailler avec toi et je suis convaincu que nos échanges continueront d'influencer mes recherches dans les années à venir. Merci aux collègues de l'IGE et du GAEL pour leur accueil, leurs conseils, et pour toutes ces discussions intéressantes autour d'un café, d'un repas, ou d'un potager. Je souhaite en particulier remercier Brice d'avoir toujours pris le temps de nous aider à gérer les questions du quotidien. Je remercie les services techniques, informatiques et administratifs de l'IGE et du GAEL sans qui la recherche ne serait pas possible, et notamment Christophe pour son implication dans le stage Gaël et ses bons conseils pour se mettre à la voile. Un grand merci à Philippe et Mauro de m'avoir accompagné dans mon premier encadrement de stage, et à Gaël d'avoir été un stagiaire si simple à encadrer du fait de son autonomie, de son implication et de sa sympathie. Merci à Sandra et Isabelle de m'avoir fait confiance pour mes premières expériences d'enseignement et à tous les enseignants qui m'ont inspiré et m'ont donné envie d'avancer tout au long de mes études. Merci beaucoup à Emeric et Philippe de m'avoir donné goût à la recherche pendant mon stage de fin d'étude et de m'avoir conseillé dans le choix de ma thèse.

Merci aussi à toutes les personnes avec qui j'ai pu échanger sur mes recherches et enrichir mes travaux, en particulier à Benjamin, Oskar et Robin d'avoir pris du temps pour participer à mon comité de thèse.

Un énorme merci aux vedettes du bureau 310 et d'ailleurs, pour tous ces moments passés ensembles. Merci d'avoir agrémenter la décoration du bureau en étalant vos serviettes mouillées, maillots de bain, et parfois un peu de terre sur le sol après avoir pratiqué un sport canin. Merci, à Antoine, Thomas, Jean-Luc, enfin quel que soit ton prénom, d'avoir été un co-bureau génial depuis le meilleur poste de surveillance du courrier de l'UGA jusqu'au bureau avec la meilleure vue de la MCP, à Eva, pour ton humour, tes petits pots surgelés, tes très bons goûts cinématographiques, et toute la motivation que tu m'as transmise pendant ces années (c'était vraiment sympa de rester plus longtemps pour soutenir les copains !), à Hanna pour les pauses bien méritées, les soirées cuisine-chichas, les randos, et la sortie ski de fond qui m'a fait faire du stop pendant un mois, à Momo pour les cafés du dimanche au soleil et les discussions sans les mots « ski », « escalade » ou « montagne », à Léo pour les spritz, les dingueries en vélo, les victoires à la pétanque et les photo-montages/e-mails douteux, à Alix, pour les blagues plus ou moins drôles et les podcasts bizarres qui nous ont bien distraits pendant les repas, à Alex pour les aprems jeux et la découverte des pates aux fraises et de Raphael Roan, à Claudia, pour toutes ses histoires, des sorcières boliviennes aux petits bruits de couloir, à Clara d'assurer la relève pour ces prochaines années, à Lola, pour la déco carte postale et ma dose d'énergie du jeudi au GAEL, à Gaël et Manon, pour les balades en montagne avec supplément visite du renard, pour tous ces fous rires et ces supers week-end en votre compagnie.

Merci aussi aux amis de la Normandie à la Corse en passant par Paris, Lyon, Marseille et le Grand Est de m'avoir permis de changer d'air le temps d'un week-end ou d'une semaine et d'avoir continué à me supporter pendant ces années de thèse. Entre les cures de soleil au F, les vacances du Nouvel An avec l'Ankou ou la Quinquenouille, les huitres normandes les pieds dans l'eau, et les soirées dans la vallée de la Saulx, on a encore bien profité pendant ces années.

Thesis abstract:

Ensuring universal access to reliable, sustainable, and affordable energy by 2030 would require electrifying 600 million people in sub-Saharan Africa. In rural areas, mini-grids (MGs) based on decentralized electricity production (solar, diesel, hydro, etc.) and isolated from the national grid are one of the most interesting ways to achieve this objective at low cost, and there are several thousand MG projects already completed or under study on the African continent. Furthermore, this electrification must be compatible with the global pathways of carbon neutrality within a few decades in order to respect the Paris Agreement by limiting global warming below 2°C. This thesis evaluates the potential of hybrid MGs, based on solar PV, batteries, and a diesel generator, to electrify rural areas in Africa while satisfying both constraints: low electricity costs and low greenhouse gas emissions.

In a first chapter, we evaluate the minimum levelized cost of energy (LCOE) that can be achieved with 100% solar MGs. To do so, we simulate the operation of fictitious MGs on the whole African continent using meteorological data (irradiance, temperature) and idealized electricity demand profiles. We then show the strong sensitivity of the configurations (PV panel capacity, battery capacity) that minimize the LCOE to the characteristics of the solar resource and its temporal co-variability with the electricity demand.

Even though these 100% solar MGs do not use fossil fuels, their carbon footprint (CFP) is not zero. The indirect CO2 emissions from the solar equipment and batteries are not negligible and in the second chapter we quantify their CFP which amounts to about 200𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ. Moreover, the costs associated with these systems are much higher than those obtained with hybrid MGs using diesel. Our results show that including a diesel generator in the energy production reduces the cost of electricity production by about 30%, while doubling the carbon footprint. Thus, it is not currently possible to minimize both the costs and the emissions of MGs, but some configurations can be identified that offer interesting trade-offs between these two objectives.

In practice, cost minimization is prioritized by MG developers over emissions minimization. In a third chapter, we propose to evaluate different possible public policies (subsidies, taxes) to reduce the CFP of the economic optimum. In particular, we evaluate their effectiveness by estimating the economic value of a ton of CO2 avoided. Through the examples of Kenya, Senegal, Nigeria and Madagascar, we show that it is important to take into account the heterogeneity of the solar resource and of the economic contexts when defining the objectives of CFP reduction and the means of achieving them.

In the last chapter, we conduct a qualitative analysis based on documents, interviews and observations collected during the thesis, mainly during a fieldwork in Kenya, to better understand the institutional framework in which MGs are developed. This allows to observe how the modes of financing and regulation constrain the sizing of MGs and to identify potential obstacles to the implementation of public policies to reduce their CFP.

Finally, we conclude that MGs can be a solution for affordable electrification with low GHG emissions, but for this, many efforts still need to be made to finance these infrastructures, ensure their sustainability and decarbonize the production chains of their components.

Résumé de la thèse :

Garantir un accès universel à une énergie fiable, durable et à un coût abordable d'ici 2030 demanderait d'électrifier 600 millions de personnes en Afrique subsaharienne. Dans les zones rurales, les miniréseaux (MR) basés sur une production d'électricité décentralisée (solaire, diesel, hydroélectrique, etc.) et isolés du réseau national constituent une des pistes les plus intéressantes pour atteindre cet objectif à faibles coûts, et on dénombre plusieurs milliers de projets de MR déjà réalisés ou à l'étude sur le continent Africain. En outre, cette électrification doit être compatible avec les trajectoires mondiales de neutralité carbone d'ici quelques décennies pour respecter l'Accord de Paris en limitant le réchauffement climatique en dessous de 2°C. Cette thèse évalue le potentiel des MR hybrides, basés sur du solaire PV, des batteries et un groupe électrogène diesel pour électrifier des zones rurales en Afrique tout en satisfaisant ces deux contraintes : un faible coût de l'électricité et de faibles émissions de gaz à effet de serre (GES).

Dans un premier chapitre, nous évaluons le coût actualisé de l'énergie (CAE) minimum que l'on peut atteindre avec des MR 100% solaire. Pour cela, nous simulons le fonctionnement de MR fictifs sur l'ensemble du continent Africain à partir de données météorologiques (rayonnement, température) et de profils de demande électrique idéalisés. Nous montrons alors la forte sensibilité des configurations (capacité PV, capacité de batteries) qui minimisent le CAE aux caractéristiques de la ressource solaire et de sa co-variabilité temporelle avec la demande électrique.

Table of contents

List of abbreviations:

• AMDA: Africa Mini-grids Developers Association New York, 2015, all United Nations Member States adopted a common Agenda to end poverty, improve health and education and reduce inequalities while preserving the ecosystems and tackling climate change [START_REF]UN Sustainable Development Goals[END_REF]. This agenda consists in 17 Sustainable Development Goals (SDGs) with 169 targets to be achieved by 2030, from ending hunger (SDG 2.1) to enhancing a sustainable urbanization (SDG 11.3), or from climate change mitigation (SDG 13.2) to the promotion of economic growth (SDG 8.1). As it covers a large diversity of aspects with ambitious aims, this framework leads to potentially conflicting goals. For instance, depending on how it is done, promoting the industrialization, and developing large transborder infrastructures (SDG 9) may affect the preservation of ecosystems (SDGs 14 and 15). Achieve food security (SDG2) may require large amount of water for irrigation and wide extension of agricultural lands, potentially leading to impact on access to clean water (SDG6), on climate change (SDG13) due to land use change, and on biodiversity (SDG 15) [START_REF] Griggs | An integrated framework for sustainable development goals[END_REF].

Thus, some trade-offs may be considered between objectives and a way to visualize them is the "doughnut economy" representation (cf. Figure 1). This concept was developed by the economist Kate Raworth in her 2017 books [START_REF] Raworth | Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist[END_REF], bringing together the planetary boundaries and the social foundation to perceive the suitable space for humanity. Many of these social foundations match the SDGs (access to water, food, health, education, etc.) and the planetary boundaries embrace SDGs related to climate change (SDG 13) and ecosystems (SDGs 14 and 15) while adding criteria on the ozone layer depletion, the air pollution or the nitrogen and phosphorus loading. As one illustration of the numerous challenges existing to stay in the "middle of the doughnut", this thesis explores, through the example of mini-grids (MGs) for rural electrification in Africa, how to find trade-offs between energy needs and climate change mitigation. [START_REF] Raworth | Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist[END_REF] In this introductory chapter, we will first recall the global context (universal energy access, development of renewable energy and climate change mitigation) in which these MG are developed and the reasons why they are presented as a solution to these challenges. It also describes the current state of development of mini-grids and the different stakeholders involved. It finally presents the specific issues considered within this context in this thesis.

Energy transition and rural electrification in Africa

This first section presents the global objectives of the energy sector regarding climate change mitigation and universal access to energy with a focus on Africa and its electrification pathways.

Climate change and the energy sector

At the Conference of the Parties (COP) 21 in Paris, world leaders agreed to set long-term climate goals in order to "substantially reduce global greenhouse gas emissions to limit the global temperature increase in this century to 2°C while pursuing efforts to limit the increase even further to 1.5 degrees" [START_REF]Nationally determined contributions under the Paris Agreement », United Nations, Synthesis report[END_REF]. Different global emissions trajectories with intermediate targets tailored to each sector make it possible to achieve this overall climate target of the Paris Agreement (cf. Figure 2). The energy sector is the main responsible of the greenhouse gases (GHG) emissions and it must be net-zero emissions before 2050 to keep the global warming below 1.5°C.

Figure 2 : Reduction of CO2 emissions required by different sector to limit global warming to 1.5°C [START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF] Moreover, the cost of renewable energy production relying on wind and solar have been steeply decreasing in the last years (cf. Figure 3) making them the feasible mitigation option with the highest potential for GHG reduction (cf. Figure 4). With cost of energy production divided by more than five in ten years for solar photovoltaic (PV) and by two for wind power [START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF], these technologies are indeed already cost competitive in most of the cases compared to fossil fuels (oil, coal, natural gas) that still represents more than 80% of the world energy supply.

Figure 3: Evolution of renewable energy production costs [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF] Figure 4 : Global potential of GHG emissions reduction for the energy supply [START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF] At the heart of the Paris Agreement are the "Nationally Determined Contributions" (NDCs). In their NDCs, countries communicate actions they will take to reduce their greenhouse gas emissions in order to reach the goals of the Paris Agreement. This bottom-up approach makes it possible to take into account the heterogeneity of the development potential of decarbonized energies in each of the countries, the economic potential, and in particular the economic development priorities, but also the national prospects for the co-benefits of climate policies in terms of, for example, reducing pollution, employment, preserving biodiversity, etc.

As Figure 5 shows using the Index of Human Development, in the case of developed countries, the main goal is to decrease their large level of GHG emissions without reducing the level of development. Their mitigation objectives are indexed on a given past emission level. On the contrary, looking at Africa, India, and a part of Southern Asia where GHG emissions per capita are much lower, the challenge is to increase their development level by controlling the evolution of GHG emissions. Thus, in developing countries, mitigation objectives are usually defined as GHG emissions reduction compared to a business-as-usual scenario, or as a carbon intensity reduction of the energy mix, allowing to integrate the inertia of societies and also the needs for some regions to develop and build the social foundations as expressed in the "Doughnut". Another specificity of mitigation objectives for developing countries is that a part of their targets is conditional to financing, capacity building or technology transfers from other countries. For instance, in Madagascar, a target is set to 14%1 of GHG emissions reduction, but this target is completely determined by these international supports [START_REF]Compare climate targets | Climate Watch[END_REF]. In the case of Senegal, a conditional 30% reduction of GHG emissions is stated, but there is also an unconditional target of 7% reduction [START_REF]Compare climate targets | Climate Watch[END_REF]. Other countries like Kenya specified their unconditional contributions in terms of funding. A conditional objective of 32% is stated and it is estimated that around 18 billion of US dollars are required to achieve this goal, but Kenya intends to bear unconditionally 21% of these investments, the rest being subject to international support [START_REF]Compare climate targets | Climate Watch[END_REF]. As stated previously, the energy sector is at the heart of climate change mitigation objectives, but it is also one of the major aspects that governs the level of development by allowing many services for the population (water and food supply, health and education facilities, communication and transportation infrastructures, …). Thus, to better understand the challenges surrounding climate change objectives for the Global South, it is required to address the issue related to energy access in those regions.

Energy access and electrification

Following United Nations data, around 2.4 billion people still use inefficient and polluting cooking systems and more than 730 million people live without electricity in the world [START_REF]UN Sustainable Development Goals[END_REF] (cf. Figure 6). These populations are mainly located in Southern Asia and in Sub-Saharan Africa where the fast demographic growth (1.3 billion inhabitants today, more than 2 billion by 2050 [8]) could increase these figures even higher if electrification is not accelerated.

Figure 6 : Number of people without access to electricity by country [9] To tackle this challenge, the United Nations dedicated one of their 17 SDGs to energy access: "SDG7: Ensure access to affordable, reliable, sustainable and modern energy for all by 2030" [START_REF]UN Sustainable Development Goals[END_REF].

Traditional uses of energy are still widespread. Biomass (wood, charcoal or dung) for cooking is associated with health issues due to air pollution, deforestation and high workloads to gather the combustible, which is most of the time done by women [10]. The lack of electricity makes people use inefficient, polluting and expensive fuels such as kerosene for lighting [START_REF] Lee | Appliance Ownership and Aspirations among Electric Grid and Home Solar Households in Rural Kenya[END_REF], and prevent them from using many appliances such as refrigeration systems that are essential for food conservation and some health facilities [START_REF] Babalola | Solar powered vaccine refrigerator for rural off-grid areas in Nigeria[END_REF]. These problems mainly affect people living in rural areas as more than 80% of the unelectrified population and around 75% of the people without clean cooking live in these areas.

Improving the development of clean cooking requires further research, but in this thesis, we decided to focus only on electricity access in rural areas. As more than the three-quarters of all the people without access to electricity are in Africa (cf. Figure 7) [13], this thesis will also focus on the African continent. A large part of the literature related to rural electrification aims at evaluating the impacts of electricity access for the development of communities. Many studies tried to estimate them via economic indicators such as the number of unemployed people, the people revenues or the business creations [START_REF] Pueyo | The impact of solar mini-grids on Kenya's rural enterprises[END_REF]- [START_REF] Sedai | Electrification and welfare for the marginalized: Evidence from India[END_REF]. Some studies consider more social aspects around the level of education, the population health and safety, the inequalities reduction, the access to information or the gains in time obtained with electric mills, water pumping or electric cooking [START_REF] Lee | Electrification and Economic Development: A Microeconomic Perspective[END_REF], [START_REF] Falk | Drinking Water Supply in Rural Africa Based on a Mini-Grid Energy System-A Socio-Economic Case Study for Rural Development[END_REF]- [START_REF] Wassie | Socio-economic and environmental impacts of rural electrification with Solar Photovoltaic systems: Evidence from southern Ethiopia[END_REF]. These empirical studies usually show positive results but their effects for a given community depend largely on the quality of the electricity access [START_REF] Acheampong | Empowering the powerless: Does access to energy improve income inequality?[END_REF], [START_REF] Bajo-Buenestado | The effect of blackouts on household electrification status: Evidence from Kenya[END_REF], [START_REF] Azimoh | Electricity for development: Mini-grid solution for rural electrification in South Africa[END_REF].

Different levels of access to energy:

There are indeed differentiated energy service levels behind the concept of access to energy. Different tools and indicators were elaborated to better define the different qualities of electricity access. Among them, the Multi-Tier framework [START_REF]Electricity | Multi Tier Framework[END_REF], developed by the Energy Sector Management Assistance Program (ESMAP) from the World Bank, measures the electricity access with six different levels named "Tier" (cf. Figure 8).

Figure 8 : Multi-Tier Framework [START_REF]Electricity | Multi Tier Framework[END_REF] This Tier Framework summarizes the measures of technical criteria like the power capacity, the availability of the electricity, its reliability or its quality but also criteria on the payment, the security and the affordability of the electricity. This framework is often used in the literature [START_REF] Narayan | Exploring the boundaries of Solar Home Systems (SHS) for off-grid electrification: Optimal SHS sizing for the multi-tier framework for household electricity access[END_REF]- [START_REF] Dagnachew | The role of decentralized systems in providing universal electricity access in Sub-Saharan Africa -A model-based approach[END_REF] but it is sometimes replaced by simpler indicators which focus on fewer aspects of electricity access. For instance, some studies or countries regulations use different measurements of the availability or the reliability of electricity like the SAIDI and the SAIFI2 [START_REF] Ferrall | Measuring the reliability of SDG 7: the reasons, timing, and fairness of outage distribution for household electricity access solutions[END_REF], [START_REF] Ayaburi | Measuring "Reasonably Reliable" access to electricity services[END_REF] or like the level of service quality [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF].

The capacity of the system (its power and energy), as defined in the Multi-Tier framework, largely influences the type equipment that can be used by the community. Despite the large diversity of rural communities, it is possible to find common bases of electric devices that will most of the time be acquired by users as a priority. For instance, when they get access to electricity, non-electrified households first seek to use lights and charge their mobile phone, and then, use the radio or TV if the power capacity is sufficient [START_REF] Lee | Appliance Ownership and Aspirations among Electric Grid and Home Solar Households in Rural Kenya[END_REF], [START_REF] Richmond | Electrification and appliance ownership over time: Evidence from rural India[END_REF]. These are household's appliances but to get the most out of electrification, communities will often require productive devices such as mills, water pumps or refrigeration systems.

By detailing the type of appliance used by the population, the Multi-Tier framework gives a richer characterization of the electricity access current state: describing the proportions of the population falling in each of the different tier categories is much more informative and useful picture of paths toward universal electricity access than a single and global electricity access rate (cf. Figure 9). [START_REF]Kenya -Multi-Tier Framework (MTF) Survey -ENERGYDATA.INFO[END_REF] It also helps to better describe the electrification objectives stated by policymakers and to improve projections of future energy consumption and the infrastructure they need to invest in.

Sustainable electrification pathways for Africa

Following the SDG n°7, all African countries aim at universal access by 2030. However, the energy demand projections may largely vary, depending on the nature of the energy access (Tier level) that is targeted, and the constraints imposed by GHG mitigation objectives (cf. Figure 10). Following the Joint Research Center of the European Commission [START_REF] Pappis | Energy projections for African countries[END_REF], the energy demand for Africa would double by 2065 in a reference scenario. But to stay below +2°C (resp. +1.5°C) of global warming, the increase of energy demand should be limited to about 50% (resp. 15%). Such a more moderate increase in demand may result either from improved energy efficiency or from a lower quality and level of electricity access: the energy demand for a Tier-5 level of access is twice the one for a Tier-4 level. To help policy makers design the deployment of future energy systems in Africa, there is a growing literature on the elaboration of national scenarios that reconcile economic and human development with energy needs under the constraints of GHG emission targets.

Figure 10 : Examples of energy demand projections for Africa depending on the climate objective (left) [START_REF] Pappis | Energy projections for African countries[END_REF] and for residential electricity in Sub Saharan Africa depending on the Tier level (right) [START_REF] Dagnachew | The role of decentralized systems in providing universal electricity access in Sub-Saharan Africa -A model-based approach[END_REF] Currently, the African continent has very low emissions compared to the rest of the world (less than 3% of global energy-related emissions [13]) and still needs to develop its infrastructure to achieve the SDGs (cf. Figure 5). With business-as-usual scenarios like the reference scenario in Figure 10, the development of African economies and their growing population by 2030 would lead to around 3700Mt3 of CO2,eq, i.e. around 10% of current global GHG emissions [START_REF] Atkins | Gap Analysis Report : African Nationally Determined Contributions (NDCs)[END_REF]. Energy efficiency measures to limit the energy demand could moderate these emissions. To implement a long-term decarbonization strategy however, one main lever is the development of renewable energy. Fossil fuels represents more than 50% of the energy consumption of the continent (90% if including traditional biomass that comes with a large part from deforestation) and around 80% of the electricity production [13]. Despite some exceptions with large hydroelectric or geothermal potentials like in Ethiopia or Kenya, many countries still rely on coal and oil to produce electricity leading to high CO2 emissions per kWh generated (cf. Figure 11). For now, major emitters in Africa are located in the North of the continent and in South Africa but several countries such as Senegal and Mozambique have discovered large reservoir of hydrocarbons in their countries and plan to harvest them to support their economic development [10], [13].

Figure 11 : Estimation of the carbon intensity of electricity [𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ] in Africa (2019) [START_REF]Carbon intensity of electricity[END_REF] (a bit underestimated compared to [START_REF] Takahashi | IGES List of Grid Emission Factors[END_REF])

Given the low responsibility of Africa in historical and current GHG emissions, and the slow deployment of renewable energy, whether it is in Africa or in Europe [START_REF]Renewables 2022 -Analysis and forecast to 2027[END_REF] the use of the African fossil fuels to foster the development of the continent is subject to debate [START_REF] Ayompe | Trends and drivers of African fossil fuel CO2 emissions 1990-2017[END_REF]- [START_REF] Dagnachew | Trade-offs and synergies between universal electricity access and climate change mitigation in Sub-Saharan Africa[END_REF]. Twelve African countries, including Nigeria and South Africa, have already pledged to reach net-zero GHG emissions by 2050 -2060 [13], and implemented policies to limit their emissions [START_REF] Mulopo | A mini-review of practical interventions of renewable energy for climate change in Sub-Saharan Africa in the last decade (2010-2020): implications and perspectives[END_REF], (e.g., the instauration of a carbon tax in South Africa in 2019 [START_REF] Nong | Development of the electricity-environmental policy CGE model (GTAP-E-PowerS): A case of the carbon tax in South Africa[END_REF]). Electrification of current and future use of energy is at the center of these lowcarbon development pathways, and the International Energy Agency estimates a 75% increase of the African electricity consumption by 2030 that should be supplied by the installation of renewable production capacities [13].

To reduce the impact of this future electricity consumption, 100% renewables scenarios have indeed been designed in the scientific literature for different African regions or countries like South Africa [START_REF] Barasa | A cost optimal resolution for Sub-Saharan Africa powered by 100% renewables in 2030[END_REF], [START_REF] Oyewo | Pathway towards achieving 100% renewable electricity by 2050 for South Africa[END_REF]. These scenarios mostly rely on solar energy: e.g., around 50% of solar PV and 31% of wind for Sub-Saharan Africa, the remainder being hydropower (8%), biomass (8%) and geothermal energy (3%) [START_REF] Barasa | A cost optimal resolution for Sub-Saharan Africa powered by 100% renewables in 2030[END_REF]. These high proportions of solar and wind energy in the electric mix come with high needs for flexibility means such as storage to deal with the intermittency of renewable energies. If some countries could consider large hydropower reservoirs as storage [START_REF] Danso | Assessing hydropower flexibility for integrating solar and wind energy in West Africa using dynamic programming and sensitivity analysis. Illustration with the Akosombo reservoir, Ghana[END_REF]- [START_REF] Sterl | Smart renewable electricity portfolios in West Africa[END_REF], other countries such as

Nigeria and South Africa are putting the nuclear option on the table to limit the massive development of renewable energy: around 3GW for Nigeria are planned for 2030 [START_REF] Aliyu | Current status and future prospects of renewable energy in Nigeria[END_REF].

Most studies on the development of a low-carbon power system in Africa are confined to the national grid based on large power plants to increase decarbonized power generation capacity [START_REF] Lin | Towards low carbon economy: Performance of electricity generation and emission reduction potential in Africa[END_REF]- [START_REF] Oyewo | Contextualizing the scope, scale, and speed of energy pathways toward sustainable development in Africa[END_REF]. However, as explained in section 1.1.2, most people concerned by electrification are located in rural areas where the grid infrastructure does not exist. Thus, the centralized energy systems may not be the best solution for these remote locations.

Options for rural electrification

Different systems allow to bring electricity to rural populations depending on the community needs, the remoteness of the villages and the local energy sources available. This section gives some insights on some electrification possibilities and how they can be selected by countries.

National grid vs. decentralized solutions

As mentioned in [START_REF] Korkovelos | A Retrospective Analysis of Energy Access with a Focus on the Role of Mini-Grids[END_REF], economies of scale obtained with large power plants and progresses made in transmission over long distances allow to supply electricity to densely populated areas at a low cost. However, for a lot of villages and small cities with low population density in far from the grid areas, two other types of systems could be used: MG and stand-alone systems.

Stand-alone systems consist in small production systems (a few PV panels and batteries for Solar Home Systems (SHS 4 , cf. Figure 12), or a diesel genset smaller than 5kW) dedicated to one building like a school, a dispensary, or a household. It is the most cost-competitive system for remote places with a very low population density, but it is also often used by people connected to a grid as a back-up if the grid is not reliable. Many governmental programs have used SHS to electrify schools or dispensary [START_REF] Energy | KOSAP[END_REF]- [START_REF]USAID-Power Africa Solar Home System Kick-Starter Program for Malawi | GOGLA[END_REF], and it is quite easy for people in rural areas to find SHS on the market [START_REF] Trompette | Frugal Energy and the Global Markets of Pico Solar Systems[END_REF]. MGs produce more energy than SHS and thus, a higher Tier level for the population (usually above Tier 3 [START_REF]Beyond Connection -Energy Access Redefined[END_REF]). It is well adapted to small cities with hundreds of households and productive use of energy (mills, welding stations, water pumping) [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF]. A MG usually consists of one power plant (<1MW) directly connected to the distribution lines (<33kV) [START_REF] Louie | Off-grid electrical systems in developing countries[END_REF].

On-grid MGs are MGs which are connected to the national grid. They are mainly used by industries or critical installations to increase the reliability of their electricity supply or to decrease the cost of their electricity bills [START_REF] Hartono | Review of microgrid technology[END_REF]. Even if connected to the national grid, they can usually operate in islanded mode, i.e., in the event of a grid failure, the MG is able to supply energy autonomously. Off-grid MGs (cf. Figure 13) are not connected to the national grid, they need to locally fulfil the electric demand with the local production.

The design of MG systems therefore requires a good knowledge of the local resources to produce energy and of the electric demand, especially of their temporal variability to ensure the adequation between production and consumption all the time. The design of off-grid MG projects will be detailed below in the next section 1.2.2. Selecting the best electrification option in terms of costs, reliability, environmental impact, user's preference, etc. is not an easy task. It requires to identify the most suitable solution among standalone systems, a MG and grid extension considering the local technical and socio-economic constraints. To help countries defining their electrification strategy and guide their investments in these different options, many planification tools have been developed mostly with the objective of electricity cost minimization [START_REF] Kemausuor | Decentralised Energy Systems in Africa: Coordination and Integration of Off-Grid and Grid Power Systems-Review of Planning Tools to Identify Renewable Energy Deployment Options for Rural Electrification in Africa[END_REF]- [START_REF] Mentis | A GIS-based approach for electrification planning-A case study on Nigeria[END_REF]. These tools rely on a large number of data and assumptions (cf. Figure 14), for instance related to:

• existing and already planned infrastructures (transmissions lines, power plants)

• socio-economic data to estimate the electricity demand (population density, location of specific buildings like health centers, schools or mines) • technical and economic characteristics of the equipment (efficiencies, lifetimes, costs) • hydro-meteorological and land use variables for renewable production (wind speed, temperature, solar irradiance, water discharge, protected areas)

Figure 14 : Illustration of the methodology used by the Joint Research Center of the European Commission for the planification of the rural electrification in Kenya [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF] Given the diversity of data used in these models, their development and use require an interdisciplinary approach to integrate both engineering, socio-economic and environmental aspects, and to evaluate the effects of simplifying assumptions in each discipline on their results. The planification models are indeed quite computationally intensive, hence the relatively low levels of details for some parts of the model. Such simplifications may sometimes lead to a rather crude design, but they give a relatively good first guess of the distribution for the different electrification options.

Even if planning results may be sensitive to these numerous assumptions, it seems indeed that at the first order, the distance from the grid and the energy demand, which is linked to the population density strongly influence the choice between national grid, MG and stand-alone systems (cf. Figure 15). A lot of studies with different socio-economic and technical assumptions indeed show that MGs are a promising solution to accelerate the electrification of African remote rural areas at a low cost [13], [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF]- [START_REF] Puig | An action agenda for Africa's electricity sector[END_REF]. For instance, following the International Energy Agency, more than one third of the future electric connections by 2030 in Africa would rely on MGs and this figure reaches 65% of the new connections for communities currently located more than 20km far from the grid [13]. It represents more than 200 million inhabitants and requires around 300 MW that needs to be installed each year between 2021 and 2030, most of them relying on solar PV [13].

Figure 15 : Estimation of the least cost solution for the electrification of Sub-Saharan Africa between stand-alone systems, national grid extension and MGs. MGs seem to be the best options for communities relatively far from the grid (>10km) with high demand (urban or rural-high demand). Looking at the map, such communities can be found almost all over Sub-Saharan Africa (excluding Southern Africa) with high densities in the Sahel and in Madagascar [13].

Sizing MGs

Projects begin with the identification of potential sites where MGs could be viable, with a good resource and with a potentially high electric demand. The identification, done by public institutions, or by some MG developers, is typically made with some dedicated planning tool (e.g. Geosim IED [START_REF]IED SOLUTIONS -GEOSIM[END_REF], cf. section 1.2.1).

Once the sites have been identified, a detailed assessment is done on the field.

Figure 16 : Sizing process following a guide from the German Cooperation (GIZ) [START_REF]What size shall it be ?[END_REF] International institutions (e.g. ECREEE, ESMAP, GIZ 5 ) have edited many guides to help MG developers in designing their projects. As shown in the one from the GIZ (cf. Figure 16), the major step on site is to evaluate the electric demand of the community. A load curve that gives the future electric consumption (in kW) as a function of time is elaborated through population surveys (identification of the current source of energy (kerosene, candles, wood, electricity via Solar Home Systems or diesel generator), the electric devices they would like to have, the money they spent in energy, their revenues and economic activities, etc.) This allows estimating the desired electricity consumption as well as the population's ability (ATP) and willingness to pay (WTP). Socio-economic factors are also considered to anticipate the potential growth in the electric demand due to population increase, economic development, or lifestyle changes.

The issue of demand estimation has been the subject of numerous publications with specific questions related to the accuracy of these surveys [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Louie | Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability[END_REF], the methods to estimate WTP and/or ATP [START_REF] Sievert | Willingness to pay for electricity access in extreme poverty: Evidence from sub-Saharan Africa[END_REF]- [START_REF] Lee | Experimental Evidence on the Demand for and Costs of Rural Electrification[END_REF] the dependency of estimates to factors such as education level [START_REF] Ayodele | Willingness to pay for green electricity derived from renewable energy sources in Nigeria[END_REF] or payment options [START_REF] Barry | Pay-as-you-go contracts for electricity access: Bridging the "last mile" gap? A case study in Benin[END_REF], the possibility to estimate the dynamics of the electric demand evolution in communities [START_REF] Blunden | Fortis Unum: Clustering mini-grid networks to widen energy access and enhance utility network resilience[END_REF] [START_REF] Riva | Modelling Endogenous complexities in rural electrification : on the local dynamics of groth and the planning of off-grid systems[END_REF]. In all cases, estimating the demand is time consuming and comes with high uncertainties. Many assumptions are made to simplify this process, sometimes to the point of using typical load profiles for productive and domestic uses to give a rough estimation of the load curve. The impact of these assumptions on the reliability of the system or on the economic viability of MG projects was to our knowledge disregarded to date.

Once established, the load curve is used to size the different components of the system, i.e., the capacity of the genset, the capacity of the renewable power and of the batteries to install. Several datasets are available for this. For instance, timeseries of the potential renewable power production over the year can be extracted from the Global Solar Atlas [START_REF] Esmap | Global Solar Atlas[END_REF], Renewable Ninja [START_REF]Renewables.ninja[END_REF], PVsyst [START_REF]PVsyst -Logiciel Photovoltaïque[END_REF] or from local data. Different methods are also available to size the different system components. Some organizations like the IEA [START_REF]IEA PVPS : Mini-réseaux hybrides PV-diesel pour l'électrification rurale[END_REF], ECREEE [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF] or the IEEE 6 [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF] propose simple rules. These rules are easy to use but they do not allow sizing optimization. The optimization can be achieved thanks to different tools and software [START_REF] Sinha | Review of software tools for hybrid renewable energy systems[END_REF], going from relatively simple online application (GIZ Mini-Grid Builder [START_REF]Mini Grid Builder | Web based mini grid tool[END_REF] or NREL REopt [START_REF]REopt Evaluates Centralized and Decentralized Microgrids in Sub-Saharan Africa | NREL[END_REF]) to highly detailed tools (RET Screen [START_REF]Government of Canada[END_REF]). They use the load curve, an estimation of the power production, and technical, environmental and/or socio-economic parameters to find the system configuration 7 with the best performances8 for a set of indicators. The two performance indicators mostly used are the reliability (% of the energy demand supplied) and the cost of electricity [START_REF] Nadal | Accounting for techno-economic parameters uncertainties for robust design of remote microgrid[END_REF]- [START_REF] Azoumah | Sustainable electricity generation by solar pv/diesel hybrid system without storage for off grids areas[END_REF]. Other indicators may also be considered such as the revenues increase for the population, jobs potentially created, GHG emissions or land use requirements [START_REF] Das | Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh[END_REF]- [START_REF] An | Optimal energy management for grid connected microgrid by using dynamic programming method[END_REF]. HOMER is the most popular of such software and allows to minimize the cost of electricity while ensuring a certain level of reliability [START_REF] Stiel | Feasibility Study of Energy Storage Systems in Wind/Diesel Applications Using the HOMER Model[END_REF]- [START_REF] Micangeli | Energy Production Analysis and Optimization of Mini-Grid in Remote Areas: The Case Study of Habaswein, Kenya[END_REF].

Numerous models and methods have been also developed by researchers to help the design of MGs. In many papers, researchers use simple representations of the MG functioning and focus on the improvements of optimization algorithms or of the dispatching of energy sources and the load management to increase systems performances [START_REF] Micangeli | Energy Production Analysis and Optimization of Mini-Grid in Remote Areas: The Case Study of Habaswein, Kenya[END_REF]- [START_REF] Frimpong | A Comprehensive Review of Nature-Inspired Search Techniques Used in Estimating Optimal Configuration Size, Cost, and Reliability of a Minigrid HRES: A Systemic Review[END_REF]. Some others present models with a more accurate modeling of components or a higher resolution of simulations to get closer to the real functioning of MG [START_REF] Hoang | An advanced protection scheme for mediumvoltage distribution networks containing low-voltage microgrids with high penetration of photovoltaic systems[END_REF]- [START_REF] Cicilio | uGrid: Reliable Minigrid Design and Planning Toolset for Rural Electrification[END_REF]. Stochastic modeling were also developed by integrating the uncertainties on the electric demand estimation or on the renewable resource to evaluate how they impact the sizing [START_REF] Louie | Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability[END_REF], [START_REF] Fioriti | Stochastic sizing of isolated rural mini-grids, including effects of fuel procurement and operational strategies[END_REF]. In all cases, the design output is conditioned on a number of parameters to be chosen before the optimization is carried out. The configurations chosen by MG developers may not be always the optimal ones but apart from very few studies [START_REF] Nadal | Accounting for techno-economic parameters uncertainties for robust design of remote microgrid[END_REF], this important issue was mostly disregarded. The robustness of the sizing would be worth focused analyses.

These studies mostly focus on the sizing of the production and the storage systems, but similar research works can be found on the optimization of the distribution grid, and manuals exist to assist developers [START_REF] Louie | Off-grid electrical systems in developing countries[END_REF], [START_REF] Cicilio | uGrid: Reliable Minigrid Design and Planning Toolset for Rural Electrification[END_REF], [START_REF]Energies | Free Full-Text | A New Hybrid Technique for Minimizing Power Losses in a Distribution System by Optimal Sizing and Siting of Distributed Generators with Network Reconfiguration[END_REF].

Finally, the optimized configuration for the power plant and for the distribution grid allows estimating the electricity tariffs. This tariff has to ensure the economic viability of the MG and ability to pay of the population. This compromise shows again the importance of cost optimization in the sizing, hence the common objective of most of the model to minimize electricity cost.

Different sources of energy for MG in Africa

Historically, the electrical production of isolated MGs relied on diesel genset or sometimes hydroelectricity [START_REF] Nygaard | Market for the integration of smaller wind turbines in mini-grids in Kenya[END_REF], [START_REF] Klunne | Small hydropower in southern Africa -an overview of five countries in the region[END_REF]. With the cost decrease of solar PV panels and wind turbines [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], MG production systems tend to hybridize by including these sources of energy. These renewable sources have the advantage of reducing the dependency to fossil fuels and the environmental impacts related to them. However, they usually come with a large variability that needs to be managed by flexibility means [START_REF] Engeland | Space-time variability of climate variables and intermittent renewable electricity production -A review[END_REF], [START_REF] François | Statistical analysis of electricity supply deficits from renewable energy sources across an Alpine transect[END_REF]. With low penetration rate of renewables in hybrid MGs, the diesel genset can manage the stability of the MG. But increasing the part of renewables in the system requires batteries to deal with the high variability of the electric production and the potential energy droughts, i.e. periods of low resource [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], [START_REF] Seyedhashemi | The Impact of Low-Resource Periods on the Reliability of Wind Power Systems for Rural Electrification in Africa[END_REF], [START_REF] Raynaud | Energy droughts from variable renewable energy sources in European climates[END_REF]. Thus, the characteristics of the renewable resources (mean values, temporal variability, cf. section 1.2.4) and some parameters related to the energy conversion system such as the costs are needed to evaluate the potential of these resources.

Some studies have already evaluated the potential for hydro MG [START_REF] Szabó | Sustainable energy planning: Leapfrogging the energy poverty gap in Africa[END_REF], [START_REF] Korkovelos | A Geospatial Assessment of Small-Scale Hydropower Potential in Sub-Saharan Africa[END_REF] identifying many sites that could be interesting, but they often neglected the large seasonal and inter-annual variabilities of this resource [START_REF] Sterl | A spatiotemporal atlas of hydropower in Africa for energy modelling purposes[END_REF] because of a lack of detailed discharge data. Moreover, each location has its own constraints (terrain, water use, etc.) and requires tailor-made solutions resulting in a wide diversity of project costs. The difficulty to have standardized systems for hydropower and its relatively high development costs make the real potential of this resource for MG hard to estimate for an electrification planning at a country scale.

Regarding wind power, a few projects of wind MG hybridized with diesel have been installed recently and different studies tried to estimate the potential for this resource on the continent [START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF], [START_REF] Sterl | A new approach for assessing synergies of solar and wind power: implications for West Africa[END_REF]. Nevertheless, the current trend among manufacturers is towards higher and more powerful wind turbines which allow economies of scale and higher production but are less adapted to MGs for rural electrification [START_REF] Enevoldsen | Examining the trends of 35 years growth of key wind turbine components[END_REF]. Looking at the resource, the spatial variability of wind speeds requires data at a fairly fine resolution to capture sites with the best resource and avoid smoothing effects due to averaging on a too large area. The wind resource is indeed very sensitive to relief, land use features, coastal effects, etc. which often make the resource very variable from one place to the other. High resolution wind atlas have been simulated to give a better view of this spatial variability [START_REF] Hansen | Wind Atlas for South Africa (WASA) -Best practice guide for application of WASA[END_REF]. The temporal variability of the wind resource may also be an obstacle for some regions. In the Horn of Africa, for instance, the production is rather high but very seasonal, with long periods of low to very low resource [START_REF] Seyedhashemi | The Impact of Low-Resource Periods on the Reliability of Wind Power Systems for Rural Electrification in Africa[END_REF], [START_REF] Fant | Characterizing wind power resource reliability in southern Africa[END_REF]. All in all, and apart from very specific regions the potential for wind power in Africa is low to very low compared to solar energy. The costs for wind turbines are additionally still rather high. This makes this resource not really attractive in most SSA regions. [START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF], [START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF] (cf. Figure 17). [START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF]) or by solar PV and storage (right [START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF]), the same load profiles are considered for both studies. The costs for a diesel only MG in these studies is mostly estimated between 0.2€/kWh and 1€/kWh [START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF] Solar energy seems conversely very well adapted for MGs in many regions in Africa. The installation costs of PV panels have been divided by 5 in 10 years [START_REF]Renewable Power Generation -Costs in 2020[END_REF] making PV cost-competitive with diesel (cf. Figure 17) and this technology can be easily used from very low power to hundreds of kW. The availability of solar resource data at high spatial and temporal resolution, especially thanks to satellite estimation, allows to derive solar atlas enough accurate to have a good estimate of the solar PV potential [START_REF] Pillot | Satellite-based assessment and in situ validation of solar irradiation maps in the Republic of Djibouti[END_REF]. The main disadvantage of the solar resource is that it does not produce at night. Thus, MGs based on solar PV must include storage systems, like batteries, or another source of energy, usually diesel, to supply electricity when PV is not producing.

These different sources of energy can be mixed in the production system of a MG, but it appears that hybrid MGs using solar PV, diesel and batteries is the most widespread production system recently installed for rural electrification in Africa [13], [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]. As many studies showed [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], [START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF]- [START_REF] Esan | Reliability assessments of an islanded hybrid PV-diesel-battery system for a typical rural community in Nigeria[END_REF], this choice is usually based on a compromise between reliability, simplicity, and affordability but sometimes also on the consideration of environmental aspects as solar PV allows to decrease the GHG emissions of diesel MGs [START_REF] Das | Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh[END_REF], [START_REF] Nsafon | Integrating multicriteria analysis with PDCA cycle for sustainable energy planning in Africa: Application to hybrid mini-grid system in Cameroon[END_REF], [START_REF] Ullah | Multi-criteria decision-making model for optimal planning of on/off grid hybrid solar, wind, hydro, biomass clean electricity supply[END_REF]. For these reasons, our study will only consider off-grid MGs using solar PV, batteries, and diesel.

The variability of climate, technical and socio-economic contexts

As mentioned in the last sections 1.2.2 and 1.2.3, the renewable resource plays an important role in the sizing of MGs. The solar resource varies quite strongly over the African continent, the annual solar irradiance in Sahel is for instance 70% higher than in Central Africa (cf. Figure 18). This resource does not only differ in average, but also on its temporal variability: the seasonality of the solar irradiance is higher in Libya or in South Africa than in Democratic Republic of Congo (cf. Figure 18). This variability is expected to significantly determine the characteristics of MGs. A few works only have explored such a variability and the reasons for this variability [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], [START_REF] Sterl | A new approach for assessing synergies of solar and wind power: implications for West Africa[END_REF], [START_REF] Danso | Understanding regional climate variability for solar energy development in West Africa[END_REF]. Deeper investigations would be of interest to improve our understanding of determinant design factors and improve in turn decision making. The electric demand supplied by MGs may also be very diverse depending on the size of the community, the uses of energy, or the local climate. A clear distinction is usually made between load profiles with a large share of domestic uses or with a large share of productive uses. Nevertheless we observe common shapes for their related load profiles [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF]. Some papers show seasonal variations of the load profiles that are usually linked with the predominance of the agricultural activities in rural villages (water pumping, variable revenues, time at home, …) [START_REF] Riva | Modelling Endogenous complexities in rural electrification : on the local dynamics of groth and the planning of off-grid systems[END_REF], [START_REF] Hartvigsson | Using system dynamics for long term bottom-up electric load modeling in rural electrification[END_REF], [START_REF] Falchetta | Hydropower dependency and climate change in sub-Saharan Africa: A nexus framework and evidence-based review[END_REF]. Real electric consumption presents also stochastic variations affecting the shape and the total energy consumption of load profiles from one day to another [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Mandelli | Effect of load profile uncertainty on the optimum sizing of off-grid PV systems for rural electrification[END_REF]. Similarly, medium to long term dynamics of the energy demand due to a wide range of factors may lead to significant evolutions of the load profiles over time [START_REF] Blunden | Fortis Unum: Clustering mini-grid networks to widen energy access and enhance utility network resilience[END_REF], [START_REF] Riva | Modelling Endogenous complexities in rural electrification : on the local dynamics of groth and the planning of off-grid systems[END_REF], [START_REF] Hartvigsson | Using system dynamics for long term bottom-up electric load modeling in rural electrification[END_REF]. Such spatial variations and temporal evolutions may have significant impact on MGs: the storage requirements for a solar MG are likely to be highly correlated to the electric demand. They may also influence the performance of the MG (costs, GHG emissions, etc.).

These performances are usually estimated using parameters related to costs, efficiencies, lifetimes, or environmental impact of equipment but these parameters are very variable. As an example, following a benchmark study from the World Bank ESMAP [START_REF] Bank | Benchmarking study of solar PV mini grids investment costs[END_REF], the costs associated of PV panels varies from less than 200 US$/kWp to more than 1000 US$/kWp (cf. Figure 19) and the same variations can be found in the literature [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF], [START_REF]Africa Minigrid Developers Association[END_REF]. Similar variations can be found for the battery related costs, and the diesel costs are very different from a country to another [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF][END_REF]. The lifetime of the components, especially of the batteries, is also very sensitive to the temperature and humidity conditions [START_REF] Narayan | Estimating battery lifetimes in Solar Home System design using a practical modelling methodology[END_REF]- [START_REF] Barré | A review on lithium-ion battery ageing mechanisms and estimations for automotive applications[END_REF] and to the way they are used and maintained [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], [START_REF] Gustavsson | Lead-acid battery capacity in solar home systems-Field tests and experiences in Lundazi, Zambia[END_REF]. A large part of the literature around MG considers study cases where almost all these parameter values are known for a specific project, but it is difficult to generalize their results to other projects [START_REF] Das | Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh[END_REF], [START_REF] Micangeli | Energy Production Analysis and Optimization of Mini-Grid in Remote Areas: The Case Study of Habaswein, Kenya[END_REF], [START_REF] Cartland | Performance Analysis of a Hybrid of Solar Photovoltaic, Genset, and Hydro of a Rural-Based Power Mini-Grid: Case Study of Kisiizi Hydro Power Mini-Grid, Uganda[END_REF], [START_REF] Rangel | An optimisation tool for minimising fuel consumption, costs and emissions from Diesel-PV-Battery hybrid microgrids[END_REF]. If some studies tried to have a more general approach by including a sensitivity analysis or a geospatial analysis like in electrification planning, they usually consider variations from one or two parameters at a time (fuel cost, solar resource, load) [START_REF] Zigah | Are Mini-Grid Projects in Tanzania Financially Sustainable?[END_REF]. But to what extent can MG performances be modified when considering variations of several parameters at once? And what are the main parameters that impact these performances and the optimal MG configurations?

Developing MGs in a global change context

The current landscape of MG in Africa is the result of the large diversity of stakeholders involved in the electrification of rural areas. This section gives some insights of this MG landscape to better understand the challenges surrounding the MG sector in terms of governance, economic viability and funding.

A brief insight of the solar-hybrid MG market

Only a few recent studies tried to evaluate the number of MG installed in Africa, and due to the scarcity of data and the differences in MG definitions, the resulting figures have to be considered with caution. More than two thousand solar and hybrid MG are estimated to operate in 2020 in Sub-Saharan Africa [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]. Hydro and diesel-only MG are estimated to be even more numerous [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]. From the 385 MG (diesel-only MG excluded) identified in West Africa, more than 90% use solar PV , half combine solar and diesel (ECREEE9 [START_REF] Antonanzas-Torres | State-of-the-Art of Mini Grids for Rural Electrification in West Africa[END_REF]) (cf. Figure 20). The power of 100% solar PV MGs is usually quite low (<20kW). It is up to 100kW for hybrid systems. Diesel only systems were historically favored for large projects (>500kW) (e.g. in Kenya for small cities [START_REF] Nygaard | Market for the integration of smaller wind turbines in mini-grids in Kenya[END_REF] or in West Africa for some industries like mining [START_REF] Zhuang | Towards a New Approach in Evaluating the Practical Economic Performance of Off-Grid Storage-Less Hybrid Energy System With Integrated Solar Forecast[END_REF], [START_REF] Kadri | Hybrid Diesel/PV Multi-Megawatt Plant Seasonal Behavioral Model to Analyze Microgrid Effectiveness: Case Study of a Mining Site Electrification[END_REF]) but with decreasing PV costs, they tend to integrate even more PV production [START_REF] Nygaard | Market for the integration of smaller wind turbines in mini-grids in Kenya[END_REF], [START_REF] Zhuang | Towards a New Approach in Evaluating the Practical Economic Performance of Off-Grid Storage-Less Hybrid Energy System With Integrated Solar Forecast[END_REF], [START_REF] Singho Boly | Energy Management Strategies for PV/Diesel Hybrid Systems in Remote Areas: Effects of "Flexy-Energy" Strategy[END_REF]. This increase of the solar energy proportions in these larger systems faces challenges to ensure the same reliability as diesel MGs despite the variability of the solar production and the lower flexibility to adapt the installed solar power production. The trend for PV development is heavy : ESMAP estimates that more than 4000 MG are already planned for Africa, especially in Senegal, Nigeria and Tanzania [START_REF] Esmap | Mini Grids for Half a Billion People: Market Outlook and Handbook for Decision Makers[END_REF] with mostly hybrid MGs in the 50 -100kW power range to be able to supply productive use of energy.

The promotion of productive energy uses:

To increase the economic viability of MGs, a lot of reports and articles advocates for the development of productive uses of energy that allow income generating activities or public services (schools, dispensary, water pumping) in the community [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF], [START_REF] Avila | Evaluation of solar powered agricultural technologies for productive-use applications : a modeling approach[END_REF]- [START_REF] Sackey | The need for agricultural productive uses in the national electrification plan of sub-Saharan African countries-a call to action for Ethiopia[END_REF]. This enthusiasm for productive uses of energy relies on multiple observations. In many rural communities, people have very low revenues and can often not afford electricity. By investing in productive uses of energy with the help of microcredit schemes or NGOs10 [START_REF] Robert | Village development framework through self-helpgroup entrepreneurship, microcredit, and anchor customers in solar microgrids for cooperative sustainable rural societies[END_REF], they can increase the productivity of their agricultural and/or manufacturing processes, and thus, generate more revenues to pay for the electricity [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF]. The potential financial gains from the development of businesses using productive uses of energy attract more private investors than electrification of households [START_REF] Pueyo | The impact of solar mini-grids on Kenya's rural enterprises[END_REF]. Productive uses of energy usually consume much more energy than domestic uses of households leading to higher revenues for the electricity supplier who can reinvest in the system. All these aspects may contribute to the economic development of the community and reduce the risk of project failure, especially for the private MG developers.

The influence of the owner:

Whereas most MG installations were developed by communities, NGOs or public agencies, they are today mostly developed and owned by private companies [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]. The development of the MG market leads to a diversity of business and governance models with for instance community-owned, public and private systems. Some studies assessed the different pros and cons of these models, and try to evaluate how they may influence the development of the MG and/or the community [START_REF] Gill-Wiehl | Beyond customer acquisition: A comprehensive review of community participation in mini grid projects[END_REF]- [START_REF] Pueyo | The Quest for Scalable Business Models for Mini-Grids in Africa: Implementing the Keymaker Model in Tanzania[END_REF]. Among the open issues, an important one is the possibility to find a development model that eases community engagement or that allows improving MG maintenance and thus sustainability.

The economic viability of the MG may also differ between these models. Public MGs usually allow lower electricity tariffs than private MGs, but their development is highly dependent on the funds allocated by the government or international institutions. Community-owned MGs seem to rely more on large subsidies from NGOs with a willing to supply an affordable electricity to users. Private MGs may rely less on subsidies, usually resulting in higher electricity cost. Depending on the regulation, they can be more flexible in the pricing to better fit to the local specificities and needs [START_REF] Zigah | Are Mini-Grid Projects in Tanzania Financially Sustainable?[END_REF], [START_REF] Ackah | Ghana's Transition to Renewable Energy Mini-grids: An Assessment of Ownership, Management and Performance Dynamics[END_REF], [START_REF] Guillou | Mini-Grids at the Interface: The Deployment of Mini-Grids in Urbanizing Localities of the Global South[END_REF].

These differences raise questions on the definition of regulations regarding subsidized or costreflective tariffs and how such regulation may support, or conversely hinder, the development of private MGs.

Difficulties to fund solar MG

While the International Energy Agency estimates that around 19 billion US$ are required each year to deploy MG in Africa [10], only 300 million US$ on average are currently invested each year in this sector [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]. MG investments represents less than 1% of the investments in the electricity sector in Africa [START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF]. Considering the public funds allocated to electrification in the past years, governments need to rely on private investors to reach their ambitious electrification goals [START_REF] Ackah | Ghana's Transition to Renewable Energy Mini-grids: An Assessment of Ownership, Management and Performance Dynamics[END_REF]. However, off-grid MG projects are associated with numerous risks that can make private developers reluctant to finance rural electrification.

The risks behind MG projects:

Risks are related to the estimation of the demand (cf. section 1.2.2), to the obtention of licenses, to the potential competition with the national grid, or to political issues . Many articles advocate that a clear regulatory framework on grid arrival 11 , licensing and tariff-design is required to reduce risks, especially for the private MG developers. The recent development of planning tools could help public institutions to define the areas where MGs are preferred over national grid extensions, and thus deliver licenses and/or concessions to private companies for these areas. By rapidly assessing the profitability of MGs in different locations, these tools may also help private developers to constitute large portfolios of MGs and diversify their projects to dilute the risks. If at the beginning, private developers were small companies or start-ups, international companies such as Engie or Shell are now investing in the MG market with the ability to quickly develop these portfolios [START_REF]State of the Global Mini-grids Market Report 2020[END_REF], [START_REF]Financing Clean Energy Transitions in Emerging and Developing Economies[END_REF].

Planning tools may help to reduce some risks but not all. For instance, they do not integrate the complexity of interactions between the different stakeholders of electrification. The possibility to improve decision-making tools is a key challenge for next years. This especially requires a better understanding and description of the political, financial, and regulatory environments in which MG are developed.

Raising private funds with subsidies:

As often suggested, public funds can also be used as a lever to reduce risks for MG developers via public-private partnerships, and thus attract more funds from the private sector [START_REF]State of the Global Mini-grids Market Report 2020[END_REF], [START_REF] Pueyo | The Quest for Scalable Business Models for Mini-Grids in Africa: Implementing the Keymaker Model in Tanzania[END_REF]. For now, many electrification programs rely on Development Finance Institutions (DFI) such as the African Development Bank (AfDB), the AFD (Agence Française de Développement) or the Renewable Energy Performance Platform (REPP). These institutions give these funds via grants, which represented 37% of the MG finance sector in 2019 (cf. Figure 21), or they lend it to MG developers. The grants are usually given via two systems: result-based financing (RBF) and up-front grants. With the up-front grants, the money is sent to the developer before the installation of the MG whereas in an RBF scheme, the money is sent when the system is installed and users are connected. Regarding the loans given to MG developers, most of them come from DFIs or foundations because MG projects are considered too risky investments by commercial banks and traditional investors. These loans from the DFIs target only large projects i.e., portfolios of several tens of MGs, and usually takes months of discussion to assess the bankability of the projects. Thus, the difficulties to access debt lead to much higher proportions of equities in MG projects financing and to a lower attractivity for investors (cf. Figure 21). 2019) [START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF]. Unlike debt, equity corresponds to the value that belongs directly to the company/corporate or to the project.

The funding environment of MG developers influence the design of the systems to be installed. Solar MG are much more capital intensive than those with diesel genset only. This reinforces the difficulty of financing in a context of multiple and varied risks and where developers are usually looking for shortterm profitability. A lower capacity to invest at the beginning of the project favor a large share of diesel genset which have lower investment costs than solar PV and batteries. These financial constraints tend to favor diesel MGs over solar ones. In this context, one important challenge for next years/decades is thus to find socio-economic and/or policy levers that would foster MG less damaging to the environment.

Mobilizing climate finance for a low-carbon electrification

To date, conciliating affordability for low revenues population, compatibility with climate change objectives and attractivity for private investors seems out of reach. In countries with domestic fossilfuel production (Nigeria, Angola, Algeria, etc.), fossil fuels are subsidized for the consumers to have a lower cost than international markets [START_REF] Mcculloch | Fuel subsidy reform and the social contract in Nigeria: A micro-economic analysis[END_REF]. Reducing these subsidies, or completely re-establish the international market prices, as it was done in Madagascar [START_REF] Couharde | Fossil Fuel Subsidies, Income Inequality, and Poverty: Evidence from Developing Countries[END_REF], may be hard to implement because of potential strong opposition from the population or politicians [START_REF] Houeland | Contentious and institutional politics in a petro-state: Nigeria's 2012 fuel subsidy protests[END_REF], [START_REF] Onyeiwu | Fuel subsidies in Nigeria: they're bad for the economy, but the lifeblood of politicians[END_REF].

However, when succeeding to implement them, such subsidy reduction may be a way to find funds for the development of solar MG while stopping to favor diesel consumptions. For instance, in Kenya, diesel is not subsidized; on the contrary diesel taxes are relatively high (around 40% [START_REF] Ngare | THE EFFECT OF FUEL PRICES ON FOOD PRICES IN KENYA[END_REF]), and solar power is subsidized by tax exemption on imported solar products12 [START_REF] George | Review of solar energy development in Kenya: Opportunities and challenges[END_REF].

Given their high potential for climate mitigation (cf. section 1.1.1), a large share of climate funds is expected be used to develop solar energy in the world. Following the IPCC, yearly mitigation investment flows should be multiplied by a factor three to six by 2030 to respect the Paris Agreement (cf. Figure 22) [START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF]. This gap is even larger for Africa that needs to increase these investments by a factor five to twelve despite their economic vulnerabilities and indebtedness. Thus, international cooperation mobilizing funds from the developed countries towards these regions is critical. For now, the MG sector has not been able to take advantage of climate funds [START_REF]Financing Clean Energy Transitions in Emerging and Developing Economies[END_REF]. The rollout of MG relying on a large share of diesel is indeed hardly compatible with the use of climate finance but, if climate funds tend to increase, it would be possible to use a part of it to invest in solar components and limit the diesel consumption of future MGs. Mechanism such as renewable energy certificate market or carbon trading have already been investigated by some studies to finance electrification systems [START_REF] Kimera | A concept of dynamic pricing for rural hybrid electric power mini-grid systems for sub-Saharan Africa[END_REF], [START_REF] Gujba | Financing low carbon energy access in Africa[END_REF] or reduce the costs of electricity for rural communities [START_REF] Falk | Socio-economic impacts and challenges associated with the electrification of a remote area in rural Tanzania through a minigrid system[END_REF]. Using climate funds to develop MGs with low GHG emissions is likely key to allow a sustainable and climate compatible development of rural African areas electrification.

Shadow carbon pricing to efficiently use climate funds

Given the limited amount of funds available, it is important to adopt an approach that optimizes the allocation of funding to projects according to pre-defined criteria (economic efficiency of mitigation actions, equity and justice issues, contribution to local development, etc.). Several proposals have been made in this sense [START_REF] Mathy | Proposal for a poverty-adaptation-mitigation window within the Green Climate Fund[END_REF], [START_REF] Cui | Exploring the Schemes for Green Climate Fund Financing: International Lessons[END_REF].

Considering the economic efficiency of mitigation actions, governments13 , firms, and institutions (the European Investment Bank ) often use shadow carbon pricing [START_REF]Shadow price of carbon in economic analysis -Guidace note[END_REF]. The shadow carbon pricing help reorient investment decisions, anticipate future pricing or future changes in the carbon price, or account for indirect impacts on emissions (e.g., when public infrastructure investments affect emissions). The World Bank employs a shadow price (referred to as the "social value of carbon") for the economic analysis of its operations and projects. GHG reduction options, whose marginal cost is lower than the carbon price, must be carried out as a priority. In other words, if an investment allows to decrease GHG emissions at a lower cost than the shadow carbon price, it has to be done. For instance, if we consider a shadow carbon price of 40 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 and a potential project that allows to avoid one million tons of CO2 by investing ten million of US$ (marginal cost equal to 10 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 ), this project must be carried out. Thus, the carbon reference value also makes it possible to prioritize investments and plan them over time.

This value is expected to increase over the years, as the least costly reduction potentials (options with the lowest marginal GHG reduction costs) will be deployed first, and mitigation actions will progress to reduction options with higher marginal reduction costs. The High-Level Commission on Carbon Prices (HLCCP) led by Stern and Stiglitz [START_REF]Shadow price of carbon in economic analysis -Guidace note[END_REF] identifies indicative corridors of such carbon prices that can be used to guide the design of carbon-pricing instruments and other climate policies, regulations, and measures to incentivize climate action to deliver on the ambition of the Paris Agreement and support the achievement of the Sustainable Development Goals. The value defined by the High-Level Commission on Carbon Prices (between 40 and 80 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 in 2020) will be used by IBRD 14 and IDA 15 for the future evaluation and choice of MG projects alternatives. Reducing the diesel consumption of MGs is one of these mitigation options but to our knowledge, the efficiency of this option has not been quantified for now in Africa.

The carbon footprint of MG-based electrification

Many studies have estimated the GHG emissions reduction allowed by integrating solar PV in diesel systems [START_REF] Cartland | Performance Analysis of a Hybrid of Solar Photovoltaic, Genset, and Hydro of a Rural-Based Power Mini-Grid: Case Study of Kisiizi Hydro Power Mini-Grid, Uganda[END_REF], [START_REF] Szabó | Mapping of affordability levels for photovoltaic-based electricity generation in the solar belt of sub-Saharan Africa, East Asia and South Asia[END_REF]- [START_REF] Schöne | Model-based techno-economic evaluation of power-tohydrogen-to-power for the electrification of isolated African off-grid communities[END_REF]. Such estimates are typically carried out ex post, once the cost optimal system configuration has been identified. (e.g., with HOMER, cf. section 1.2.2). They allow highlighting co-benefit of introducing solar PV on the MG GHG emissions.

Published studies usually focus on real villages and compare hybrid to genset only configurations.

Upscaling at the country or even continental scale is rarely considered except in a few studies. The European Joint Research Center tried to estimate for instance the GHG emissions for least-cost configurations of around 300 hybrid MGs in sub-Saharan Africa (cf. Figure 23) [START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF]. In almost all studies, the MG CFP is estimated from the direct GHG emissions of diesel consumption. Except for a very few studies [START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF], [START_REF] Ortega-Arriaga | Grid versus off-grid electricity access options: A review on the economic and environmental impacts[END_REF], the CFP of renewable energy sources is thus disregarded. The CFP of any given system theoretically refers to all direct and indirect GHG emissions generated over the system lifetime. For instance, the carbon footprint of a MG must include the GHG emissions related to the extraction of materials, the manufacturing, the operation and the disposal or recycling of all the equipment that are used to supply the demand. The CFP of hybrid MG may be much larger than that estimated in previous publications, potentially making the co-benefits of solar PV not as interesting as currently thought. Better estimates are definitively worth to better inform MG actors.

Including indirect emissions of energy systems:

For now, NDC objectives consider only the territorial GHG emissions, which correspond to the GHG emissions of what was produced over the national territory, and of the national direct emissions related to the combustion of fossil fuels. These territorial emissions (or production-based emissions) do not include the indirect emissions related to the products that are imported. These indirect emissions are however included in the consumption-based emissions.

Thus, to see the importance of these indirect GHG emissions related to the imported products, we can look at the difference between production-based and consumption-based emissions for the different regions of the world (cf. Figure 24). For instance, the consumption-based GHG emissions of Europe are 20% 16 higher than the production-based GHG emissions as a large part of the products used in Europe are imported from other regions of the world (e.g., Eastern Asia). This gap between production-and consumption-based GHG emissions would grow due to the development of low-carbon energy infrastructure whose raw materials and products are mostly imported from a small number of countries. Such growing gap would indicate that some regions are decarbonizing their energy systems by exporting their emissions to other regions of the world without significantly modify their consumption habits

Figure 24: GHG emissions for different regions of the world [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. On the contrary to consumption-based GHG emissions, production-based GHG emissions does not include the positive (resp. negative) GHG emissions related to imported (resp. exported) products.

A growing literature estimates the indirect emissions and material consumptions of different global energy transition scenarios through lifecycle analyses that include material extraction, manufacturing, installation and recycling of all equipment [START_REF] Vidal | Modelling the material and energy costs of the transition to low-carbon energy[END_REF], [START_REF] Hertwich | Integrated life-cycle assessment of electricity-supply scenarios confirms global environmental benefit of low-carbon technologies[END_REF]. Such studies could allow to compare the carbon footprint to develop all the infrastructure and new renewable energy systems to the global carbon budget left to respect the Paris Agreement. A large part of the equipment to be used in these new energy systems are indeed produced in countries with high carbon intensity of the energy mix, leading to higher indirect emissions for this equipment. It is especially true for solar PV and Li-ion batteries that will be used in electric vehicles or for energy storage (cf. Figure 25). For instance, the carbon footprint of a PV system made in France with a low carbon electricity system is around the half of the one of a PV system made in China where more than 60% of the electricity comes from coal power plants [191], [START_REF] Besseau | INCER ACV -Impacts environnementaux de la filière photovoltaïque & évaluation des incertitudes[END_REF]. Further researches would be required to evaluate how the development of renewable industry supplied by decarbonized electricity mix could decrease the indirect GHG emissions of the energy transitions.

Figure 25 : Repartition of PV cells production in the word [START_REF] Masson | Trends in photovoltaic applications 2022[END_REF] and lithium-ion batteries production of the main manufacturers for the year 2016 and projection to 2020 [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF].

Very different carbon footprints can be obtained among renewable energies: from 4 to 80 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ (mean value: 12 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ) for wind power and from 5 to 220𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ (mean value: 40𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ) for solar PV [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF]. These values per kWh correspond to averages, but a large variability can be observed depending on the local renewable resource and the lifetime of the installation [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF]. Moreover, most of CFP estimates consider grid-connected power plant and they do not include the CFP of storage facility needed to deal with the variability of these renewable energies. Thus, these CFP values cannot be used as such to estimate the carbon footprint of MGs where the solar PV production may be stored or curtailed to ensure the adequation between production and consumption. Again, a better estimate of the CFP of MGs is likely required, including that of storage and of potentially oversized production capacities. This would allow a much more relevant estimate of the real climate mitigation potential of solar MGs.

Thesis objectives

This thesis evaluates the potential of isolated MGs based on solar PV, batteries, and diesel genset to electrify rural areas in Africa while satisfying two constraints: a low cost of electricity and low carbon footprint (CFP).

In Chapter 2, we first consider the a priori least CFP MG configuration, i.e., a configuration where electricity is produced with solar PV only. We estimate the LCOE costs of different 100% solar PV MG configurations for a fictitious village located at different locations in Africa. As explained in sections 1.2.2 and 1.2.4, the costs may depend on a lot of parameters and variables (local resource, electric demand, costs, etc.). Our work aims to answer to the following questions: What are the least-cost configurations for 100% solar MGs in Africa, and how sensitive are they to modification of these parameter values?

As the MG developers usually size their MGs following economic considerations (cf. section 1.2.2), we observed that most of the MG installed in the recent years consists of solar hybrid MG using diesel (cf. section 1.3.1). In Chapter 3, we quantify and compare the costs of electricity and the carbon footprint of different hybrid MG configurations. We especially consider the following questions:

▪ How different are hybrid and 100% solar MGs in terms of costs and CFP?

▪ How do the cost and the carbon footprint of hybrid MGs vary when increasing the proportion of solar energy? ▪ What is the contribution of indirect GHG emissions of batteries and solar PV on these carbon footprints? ▪ To what extent can we conciliate a low carbon footprint and low cost of electricity? ▪ How sensitive are our results to the different contexts (climate, technical, socio-economic)? MG development is subject to both objectives of GHG emissions reduction or limitation (cf. section 1.3.4) and financial constraints (cf. section 1.3.2). Chapter 4 explores some strategies that governments and international institutions could follow to reduce the carbon footprint of MG-based electrification without hindering the search of an affordable electricity. We especially consider different economic incentives they could design to reach their climate mitigation objectives. We also estimate how efficient could be these instruments in terms of carbon value (cf. section 1.3.3). These questions are explored and illustrated with examples of public policies for four contrasted African countries: Kenya, Senegal, Nigeria and Madagascar.

The implementation and success of such public policies may be hindered by a variety of obstacles and limitations. If the sizing method presented in section 1.2.2 is actually guided by the search of an economic optimum, it does not integrate the uncertainties and risks surrounding MG project (cf. section 1.3.1). Chapter 5 explores how MG developers and other stakeholders of MG projects deal with these risks, and how it impacts the sizing of these MG. We also consider how the financial and regulatory frameworks can affect the leeway of these different stakeholders. These analyses will be illustrated with results from a field study in Kenya.

Summary of the methods used in this thesis

The four chapters mentioned correspond to four manuscripts, published (Chapter 2), in revision (Chapters 3 and 5) and to be submitted (Chapter 4) in international scientific journal 17 . Each of these articles has its own methodology section, but here are some details on common methodological choices. Figure 26 summarizes the main aspects of MG sizing that are explored in the thesis.

Figure 26: Main aspects of MG sizing involved in this thesis

To be able to compare the results for many different climate and socio-economic contexts, Chapters 2 to 4 rely on the modelling of fictitious MG with different locations, load profiles, costs, etc. (cf. Table 1). This approach allows us to present results that are more general than what can be found in many analyses centered on specific study cases.

The functioning of MG is simulated at a 15-min resolution over several years with timeseries of solar irradiance and temperature to estimate solar PV production, and typical load profile with different temporal pattern (productive/domestic, seasonality). Only a few solar irradiance measurements stations allow to have multiple year of data with an infra-day resolution in Africa [START_REF] Driemel | Baseline Surface Radiation Network (BSRN): structure and data description[END_REF], [START_REF] Ird | AMMA-CATCH: a hydrological, meteorological and ecological observatory on West Africa[END_REF]. Thus, to allow an estimation at any location, we use satellite estimation of the solar irradiance (Heliosat SARAH2 [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF]) and meteorological reanalysis (ERA5 [START_REF] Hersbach | The ERA5 global reanalysis[END_REF]) for the temperature data to be able to cover the whole continent with a relatively high temporal resolution over many years. The results of these simulations are used to compute different MG performance indicators, especially the levelized cost of energy (LCOE) and the carbon footprint (CFP). Given the scope of our study, we decided not to detail many aspects of MG. In particular, we focus on the costs and carbon footprint of the production and storage system, but the distribution grid is not considered in our studies.

The methodology used in Chapter 5 is very different from Chapters 2 to 4 as it consists of a qualitative analysis with semi-directed interviews mostly during a field study in Kenya. This chapter is the result of a collaboration with Emilie Etienne, another PhD student who is sociologist, and give an example of how interdisciplinary research may help to tackle challenges related to access to energy in Africa. Multiple technical configurations can be proposed to deliver a given electricity service for a given community in a given location. In this first analysis, we consider 100% solar MGs made up of PV panels and batteries only. Hybrid MGs combining PV, battery and genset will be considered in the next chapters. The solar resource is known to be rather high in Africa. It is however expected to vary a lot in time, requiring thus some storage facility to be able to satisfy the demand in periods when the resource is too low (cf. section 1.2.4). The optimal configuration, i.e., the one that minimize the cost of electricity, is thus expected to depend on the resource characteristics. It is also expected to depend on a number of other features, including socioeconomic ones such as the load profile or the costs of components which are very variable (cf. section 1.2.4). The goal of this chapter is to answer two questions:

• What are the least-cost configurations (PV and storage capacities) for 100% solar MGs in Africa and what is their LCOE? • How sensitive are these configurations to modifications of the meteorological and socioeconomic parameter values? Innovation compared to previous works: Our works goes therefore a step further than the works published in the recent years where the sensitivity to these parameters, fixed to arbitrary values, is always disregarded. In addition, it gives a normalized description of the LCOE configuration of 100% MGs in Africa and disentangle the effects of meteorological and socio-economic factors that drive the MG best configuration.

In the present work, the MG sizing is carried out through the economic optimization of the LCOE. The CFP of the MGs is disregarded. The present analysis will be put in perspective in the next chapter where both the LCOE and the CFP of the MGs are considered in the design.

All aspects of this study are detailed below in the form of an article: T.

Introduction

The seventh Sustainable Development Goal of the United Nations is to "ensure access to affordable, reliable, sustainable and modern energy for all" [START_REF]UN Sustainable Development Goals[END_REF]. Almost 550 million inhabitants do not have access to electricity in Sub-Saharan Africa and this number will increase with the fast demographic growth in this area [10]. Most of them are located in rural areas and in many cases, an affordable and sustainable electricity supply could help improving living conditions and developing local economies [START_REF]UN Sustainable Development Goals[END_REF]. Fostering electricity access there requires large electrification programs, such as SE4all (Sustainable energy for all), the International Solar Alliance, the Terawatt Initiative or the Power Africa plan [START_REF] Seforall | Sustainable Energy for All[END_REF]- [202].

Such programs require governments and stakeholders (investors, researchers, manufacturers, …) to be guided toward the most interesting electrification strategy -which is expected to be region dependant [START_REF] Puig | An action agenda for Africa's electricity sector[END_REF]. In the recent years, a number of works have then estimated the cost-optimal options for different regions worldwide [START_REF] Azimoh | Electricity for development: Mini-grid solution for rural electrification in South Africa[END_REF], [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Nfah | Simulation of off-grid generation options for remote villages in Cameroon[END_REF], [203], [START_REF] Alfaro | Improving rural electricity system planning: An agent-based model for stakeholder engagement and decision making[END_REF]. The choice, typically to be made between grid extension and mini-grid (MG) installation, is often based on the levelized cost of electricity (𝐿𝐶𝑂𝐸) [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF], [START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF], [203], [START_REF] Ainah | Development of Micro-Grid in Sub-Saharan Africa: an Overview[END_REF], [START_REF] Khodayar | Rural electrification and expansion planning of off-grid microgrids[END_REF].

The 𝐿𝐶𝑂𝐸 of a MG depends on many different features. It relies first on the technical configuration, e.g. the type of energy source or mix (e.g. diesel, photovoltaic, wind, hydroelectricity) and the required storage capacity of battery if any. Different MG configurations with different energy mix are then typically compared to identify the least-cost one. The cost-optimal configuration is expected to vary from one site to the other. When the MG is based on renewable sources, this configuration depends on the available resource and its variability (seasonality, day-to-day variability, and low resource periods). This has been illustrated for 100% photovoltaic solar MGs by Huld et al. [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF] and Plain et al. [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF].

The cost-optimal configuration for a site also depends on the socio-economical features of the system, for instance, the temporal profile expected for the electricity load, mainly determined by the different types of uses expected for the system. In a photovoltaic (PV) MG with batteries, less storage capacity is needed if the nocturnal load decreases, which is typically found when productive uses increase compared to domestic ones [9]. For a given PV installed capacity, a lower storage capacity results in a lower 𝐿𝐶𝑂𝐸. The cost-optimal configuration also depends on the relative costs of the different technical components of the MG, e.g., costs of PV panels, converters, batteries.

A potentially critical problem for the identification of the cost-optimal configuration is that many features come with large variabilities, uncertainties or spatial disparities. The cost-optimal MG configurations, which have been estimated in a number of previous works, especially regarding electrification planning, are obtained using mean values for PV and battery costs. However, large costs variations are observed from one region to the other resulting from different country regulations, distribution circuits or local terrain constraints [START_REF] Bank | Benchmarking study of solar PV mini grids investment costs[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF]. Looking at a specific location, part of the unit costs can be well estimated but some other can come with large uncertainties: this is for instance expected to be the case for installation costs related to civil engineering, transportation or for maintenance costs related to the lifetime of the components, especially batteries as highlighted by [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], [START_REF] Gustavsson | Lead-acid battery capacity in solar home systems-Field tests and experiences in Lundazi, Zambia[END_REF].

On the other hand, the costs of the different MG components can also significantly evolve with time, because of changes in country-specific costs due to regulations and taxes [START_REF] Nygaard | Measures for diffusion of solar PV are aligned in technology action plans for 6 countries in the African region[END_REF] and/or because of learning by doing: the large deployment and maturation of photovoltaic panels for instance led its price to be divided by almost 4 in 5 years [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], [START_REF] Bollinger | Learning-by-Doing in Solar Photovoltaic Installations[END_REF], [START_REF]Predicting the costs of photovoltaic solar modules in 2020 using experience curve models[END_REF]. These costs evolutions are expected to depend on the component of the MG. Learning rates for instance, defined as the relative unit cost reduction when doubling the installed capacity, were estimated around 23% for PV panels, 12% for on-shore wind turbines and between 6% and 9% for lithium batteries [START_REF] Rubin | A review of learning rates for electricity supply technologies[END_REF], [START_REF] Nykvist | Rapidly falling costs of battery packs for electric vehicles[END_REF]. These evolutions are in turn expected to change the cost ratio between the components.

To our knowledge, the sensitivity of the cost-optimal configurations to cost hypothesis has not been characterized so far. Our first objective is to evaluate, for a generic 100% solar MG project in rural sub-Saharan Africa, the sensitivity of the cost-optimal MG configuration to the costs of the main MG technical components, namely the battery and the PV panels. In particular, this will allow to assess how the lowest cost MG configurations targeted for electrification or obtained in existing studies are modified with alternative component cost assumptions.

On the other hand, determining cost-optimal configurations is not straightforward. This is typically achieved with computation demanding simulations of the MG behaviour under a rather large number of different MG configuration scenarios requiring ad-hoc weather data, namely long time series of local weather and ad-hoc simulation models [START_REF] Ciller | Optimizing Off-Grid Generation in Large-Scale Electrification-Planning Problems: A Direct-Search Approach[END_REF]. Such a simulation-based design process is not accessible to all operators especially in the context of a government or rural electrification agency tender where the profitability of MGs over large areas needs to be estimated quickly. [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF], [START_REF] Léna | Mini-réseaux hybrides PV-diesel pour l'électrification rurale[END_REF] or stand-alone PV systems [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF].

The second objective of this paper is to test the possibility for simple rules for the pre-sizing of 100% PV MG systems. In Africa, the solar resource is indeed abundant and the large reduction in PV costs observed in the last decades makes such systems potentially highly competitive. 100% PV MGs produce moreover low greenhouse gases and air pollutant emissions compared to diesel generator and are not subject to fuel price volatility and supply difficulties [START_REF] Akinyele | Techno-economic and life cycle environmental performance analyses of a solar photovoltaic microgrid system for developing countries[END_REF]- [START_REF] Cader | Global cost advantages of autonomous solar-battery-diesel systems compared to diesel-only systems[END_REF]. This makes 100% PV MGs also very attractive as they will help countries to achieve the Nationally Determined Contributions (NDCs) they committed to fulfil during the 2015 Paris' Agreement [START_REF]Nationally Determined Contributions (NDCs)[END_REF]. However, contrary to solar / diesel hybrid MGs, where the electricity production can be adjusted at any time with less or more genset production, the quality service level that can be achieved with a 100% solar system, i.e. its ability to satisfy the demand at any time, fully depends on its design. To ensure reliable energy with such systems, the development of robust sizing rules is thus obviously key.

Section 2.3 details the data and hypothesis considered for the study as well as the methodology used to estimate the least cost MG configuration. The robustness of the least cost configuration to cost variations and their effects on the 𝐿𝐶𝑂𝐸 is presented for different shapes of load profiles in section 2.4. This section also presents and evaluates simple rules to design the storage capacity and the size of the PV field of 100% PV mini-grids. Results are discussed in section 2.5 and the main conclusions are summarized in section 2.6.

Methodology

In the following, we consider a fictious MG system, where the power production, obtained from PV panel only, can be temporarily stored in batteries. The analysis is carried out for 200 different locations randomly selected in Africa (cf. Figure 28). Some of them will be used for illustrative purpose when relevant.

For each location, the MG configuration is optimized to achieve a prescribed level of quality service with the lowest possible 𝐿𝐶𝑂𝐸. The optimization is obtained thanks to simulations of the system behavior over a multiple year period. For any PV capacity/ storage capacity configuration, we simulate the PV production from local weather data and the storage cycles required to best meet a given demand profile, prescribed for the whole simulation period. The different steps of the simulations/optimization process are described in the following.

Load profiles

Load profiles for microgrid projects are difficult to estimate, even with surveys [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF]. We consider two hypothetic daily load profiles, representing domestic and productive uses (Figure 29). These profiles are derived from generic profiles considered in previous publications [START_REF] Plain | Micro-réseaux d'électricité 100% solaire et isolés en Afrique[END_REF]. The domestic use profile is characterized by two peaks (morning + evening) and a quite low demand during the day. Conversely, the electricity demand only occurs during working hours during the day for the productive profile. Seasonal variations in demand may occur especially for agricultural activities like irrigation or postharvest processing which are common in many rural areas of Africa [START_REF] Williams | Load characteristics of East African microgrids[END_REF]. For the sake of simplicity, we model the seasonal profile of the energy demand as a sinusoidal function of time.

𝐷 ̅ 𝑑 = 𝐷 ̅ (1 + 𝐴 cos (2𝜋 𝑑 -𝑑 𝑚𝑎𝑥 365 )) (1)
Where 𝐷 ̅ 𝑑 [𝑊ℎ] is the daily energy demand of calendar day 𝑑, 𝐷 ̅ [𝑊ℎ] is the annual mean daily energy demand, A is the half amplitude of seasonality and dmax is the calendar day for the maximum. In the following A is set to 0.5 and four seasonal profiles are in turn considered with a maximum daily demand occurring in January, April, July, or October respectively. In addition, we also consider a non-seasonal profile, i.e., a profile where the daily electricity demand is the same throughout the year (cf. Figure 30).

PV power production

The solar PV production in the MG is simulated at 15-min resolution for the 2008-2015 period using satellite derived solar irradiance from Heliosat SARAH2 [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF] and temperatures from ERA5 meteorological reanalyses [START_REF] Hersbach | The ERA5 global reanalysis[END_REF]. Irradiance data are available with a 0.05°x0.05° spatial resolution and ERA5 data with a 0.5° grid.

The electrical power delivered by the system (PAC [W]) at a given time (t) is estimated from Global Tilted Irradiance (𝐺𝑇𝐼 [𝑊/𝑚²] : global irradiance over an inclined panel) and module temperature Tm [°C] with the model of Lorenz et al. [START_REF] Lorenz | Regional PV power prediction for improved grid integration[END_REF]. The model is described in equations ( 2) to (4):

𝑃 𝐴𝐶 = 𝜂 • (1 + 𝛼 (𝑇 𝑚 -25°𝐶)) • 𝐶 𝑃𝑉 • 𝐺𝑇𝐼 1000 𝑊/𝑚² (2)
Where 𝐶 𝑃𝑉 [𝑊 𝑝 ] is the peak power of installed PV panels, 1000𝑊/𝑚 2 corresponds to the irradiance at standard conditions, α is the sensitivity of panel efficiency to the module temperature 𝑇 𝑚 . The panel efficiency (𝜂) accounts for inverter efficiency and for losses of the PV production system. Global tilted irradiance, the irradiance received by PV panels, is calculated as:

𝐺𝑇𝐼 = 𝐷𝑁𝐼 • cos(𝜃) + 𝐷𝐻𝐼 (3)
Where Direct Normal Irradiance (DNI: solar energy that reaches the surface in a straight line from the sun) and Diffuse Horizontal Irradiance (DHI: solar energy that has been scattered by particles in the atmosphere before reaching the surface) are derived from GHI based on the empirical method from Sandia National Laboratory [START_REF] Maxwell | A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal lnsolation[END_REF] and where  is the "effectiveness" angle, a function of solar angles (azimuth and zenith) and solar panel inclination and orientation. In the present work, PV panels are assumed facing south in the northern hemisphere and facing north in the southern hemisphere. As a rule of thumb, the tilt angle (inclination) is set equal to the latitude of the location [START_REF] Bahrami | The effect of latitude on the performance of different solar trackers in Europe and Africa[END_REF].

The panel efficiency is typically considered to be a decreasing function of the module temperature. The sensitivity of the panel efficiency to temperature is here set to that of crystalline silicon cells (𝛼 = -0.0035 /°𝐶 ). The temperature of the module (𝑇 𝑚 ) is estimated as a function of the ambient temperature (𝑇 𝑎𝑚𝑏 ) and GTI, expressed as:

𝑇 𝑚 = 𝑇 𝑎𝑚𝑏 + 𝛾 • 𝐺𝑇𝐼 (4)
Where  is a parameter related to the mounted type of the system (roof integrated, free standing, …).

We consider a mean value: γ = 0.04 °C. m 2 /W.

Storage simulation

The storage/discharge cycles in the batteries of the MG are simulated as follows: the battery is charged when (1) the power production from PV panels is higher than the demand and when (2) the state of charge is below 100%. The battery is discharged when (1) production is lower than demand and when (2) the state of charge is higher than a minimum value set to 20% of the storage capacity. The same efficiency (𝜂 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 = 0.95 [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF]) is applied for charge and discharge sequences.

The sizing curve for a given quality service level

In our MG configuration, the demand is only supplied by the PV panels production and/or the batteries discharge. The multiscale variability of the solar resource makes it difficult to satisfy the demand at any time, one main challenge being to deliver electricity during periods with no solar resource (night) and with low solar resource (e.g. winter) (cf. [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF]). Satisfying the demand at any time would require provisioning significant storage and /or significant extra PV production capacity. This may in turn lead to costly and unaffordable systems. Following [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], the design thus typically requires a compromise between the costs of the system and its reliability. In other words, a not fully reliable system, i.e. a system where the demand is not always fully satisfied, is targeted which allows reducing its size and thus its costs [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF]. In this work, the systems are designed to achieve a prescribed reliability level; namely the hourly demand must be met 95% of the time. In other words, production may be lower than demand for 5% of the hours over the simulation period. This reliability level is based on the criteria of the Tier 5 in the multi-tier framework developed by ESMAP [START_REF]Beyond Connection -Energy Access Redefined[END_REF].

Different storage / PV panel configurations can produce the same level of quality service. The optimal design is identified to minimize the 𝐿𝐶𝑂𝐸.

If a configuration is found suitable for a prescribed quality service level, configurations obtained by either increasing the PV capacity (the surface area of the PV panel array) or the storage capacity are also suitable. A minimal storage capacity is needed for each possible PV capacity. Conversely, a minimal PV capacity is needed for each possible storage capacity. The set of the least equipment configurations allowing for a prescribed level of quality service defines what we will refer to as the "sizing curve" for this level.

In the following, to ease the comparison between sites, the sizing curve is normalized using the annual mean power demand 𝐷 0 . The sizing curve will next describe the relationship between the (normalized) storage capacity S and the (normalized) PV production capacity 𝐶 𝑃𝑉 required to satisfy a demand 𝐷 0 with the prescribed level of quality service. Thus, the storage capacity 𝑆 [ℎ𝑟𝑠 𝑒𝑞 ] is expressed in hours of equivalent demand (1 ℎ𝑟𝑠 𝑒𝑞 corresponds to the energy amount to supply one hour of electricity at the annual mean demand power 𝐷 0 ).

Due to the multiscale variability of the solar resource, PV panels do not always produce power at their rated power. The PV capacity 𝐶 𝑃𝑉 0 [𝑊 𝑝 ], that would be required to produce over the whole period, an energy amount exactly equal to the total energy of a constant demand D0 is thus greater than D0. It is actually proportional to the inverse value of the so-called capacity factor CF of the PV panels for the considered site: 𝐶 𝑃𝑉 0 = D0 / CF. Note also that the PV capacity 𝐶 𝑃𝑉 [𝑊 𝑝 ] required to achieve the desired level of quality service for a constant demand equal to D0 is expected to be even larger than the "reference" capacity 𝐶 𝑃𝑉 0 discussed above. This needed PV "oversizing" is actually required to allow for enough production during the periods of low solar resource. In the following, the ratio 𝑥 = 𝐶 𝑃𝑉 /𝐶 𝑃𝑉 0 is named the oversizing ratio of the PV system. It is dimensionless. For the seek of normalisation and comparison between locations, the sizing curve will finally relate the normalized storage capacity S and the oversizing ratio x. This normalized sizing curve obtained for a configuration where a level of quality service 𝑄 is further referred to as the SQ(x) function.

For any given location considered in the following, the sizing curve is identified from simulations. For a given normalized (PV capacity (oversizing ratio), storage capacity) configuration, a simulation consists of simulating 1) PV production, 2) storage operations (charge, discharge) over the whole period, and of 3) estimating the corresponding quality service level of the system. For different PV capacities in turn, simulations are used to identify the storage capacity value required to achieve the target quality service level (dichotomic identification).

LCOE calculation and cost optimal mini-grid configuration

The least 𝐿𝐶𝑂𝐸 MG configuration is finally identified from the SQ(x) curve as follows. For each (PV capacity, storage capacity) configuration, we use a simple economic modelling to estimate the total costs over the whole project lifetime and then the 𝐿𝐶𝑂𝐸 of the system. The total costs of the project, TC in [€], have the following expression: 𝑇𝐶 = 𝐶 𝑆 𝛼 𝑆 + 𝐶 𝑃𝑉 𝛼 𝑃𝑉 [START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF] where 𝐶 𝑆 and 𝐶 𝑃𝑉 are the installed storage [𝑊ℎ] and PV capacity [𝑊 𝑝 ] respectively and where 𝛼 𝑆 [€/𝑊ℎ] and 𝛼 𝑃𝑉 [€/𝑊 𝑝 ], the full unit costs of storage and PV respectively, simply read:

𝛼 𝑆 = 𝐶𝑜𝑠𝑡 𝑆 . ( ∑ 1 (1 + 𝑑) 𝑘𝐿 𝑆 𝑖𝑛𝑡( 𝐿-1 𝐿 𝑆 ) 𝑘=0 + ∑ 𝑃 𝑂&𝑀,𝑆 (1 + 𝑑) 𝑘 𝐿 𝑘=1 ) (6)
𝛼 𝑃𝑉 = 𝐶𝑜𝑠𝑡 𝑃𝑉 .

(

∑ 1 (1 + 𝑑) 𝑘𝐿 𝑃𝑉 𝑖𝑛𝑡( 𝐿-1 𝐿 𝑃𝑉 ) 𝑘=0 + ∑ 𝑃 𝑂&𝑀,𝑃𝑉 (1 + 𝑑) 𝑘 𝐿 𝑘=1 ) (7)
where 𝐶𝑜𝑠𝑡 𝑆 [€/𝑊ℎ] and 𝐶𝑜𝑠𝑡 𝑃𝑉 [€/𝑊 𝑝 ] are the unit investment cost associated to storage and PV panels respectively, where 𝐿, 𝐿 𝑆 , 𝐿 𝑃𝑉 are the project, storage and PV panel lifetime respectively [𝑦𝑟𝑠] and where 𝑑 is the discount rate [-] 18 . The second term of each equation is related to the full cost contribution to cover maintenance and operation of the system where 𝑃 𝑂&𝑀 is a proportionality coefficient between investment and cover maintenance costs [-] (maintenance and operation costs are assumed to be time invariant and proportional to investment costs of each components).

Note that the total costs of the project can be also expressed as: The LCOE depends thus on 2 technical design variables, the normalized storage capacity 𝑆 𝑄 and the PV oversizing factor 𝑥. For any given value of 𝑥, the sizing curve 𝑆 𝑄 (𝑥) gives the normalized storage capacity required to achieve the target quality service level. The 𝐿𝐶𝑂𝐸 can also thus be expressed as a function of 𝑥 only.

𝑇𝐶 =
Two limiting configurations from the sizing curve are to be noticed. When 𝑥 tends to infinity, i.e., when the PV production capacity tends to infinity, the storage capacity tends to a minimum strictly positive value. Whatever the production capacity, a non-zero storage is indeed needed to move part of the diurnal production to the nocturnal electricity demand. As a result also, when 𝑥 tends to infinity, 𝐿𝐶𝑂𝐸 thus tends to be a linear increasing function of 𝑥. If the battery system was perfect (with no energy losses in storage/discharge cycles), the other limiting configuration would roughly correspond to 𝑥 = 0.95. This would correspond to the configuration where all the production could be used to satisfy 95% of the demand. This configuration would obviously require that a huge (and unrealistic) storage capacity is available (e.g., seasonal storage) to allow for the temporal redistribution of the production from resource rich periods to resource poor ones. In practice, the minimum value of the oversizing ratio 𝑥 is greater than 0.95 because of storage losses that result from smaller than 1 storage efficiency. As mentioned above, for this minimum 𝑥 value, the storage gets a typically very large value.

In practice, the minimum value for 𝐿𝐶𝑂𝐸 is therefore reached for 𝑥 = 𝑥 * > 0. [START_REF] Cuesta | A critical analysis on hybrid renewable energy modeling tools: An emerging opportunity to include social indicators to optimise systems in small communities[END_REF] = 0 [START_REF] Lee | Appliance Ownership and Aspirations among Electric Grid and Home Solar Households in Rural Kenya[END_REF] The optimal 𝑥 * value follows the equation:

𝜕𝑆 𝑄 𝜕𝑥 (𝑥 * ) = - 𝛼 𝑃𝑉 𝛼 𝑆 . 𝐶𝐹 = - 𝑟 𝐶𝐹 with 𝑟 = 𝛼 𝑃𝑉 𝛼 𝑆 (12)
The optimal oversizing value 𝑥 * and the optimal storage value 𝑆 * = 𝑆 𝑄 (𝑥 * ) depend only on 𝐶𝐹 and on the full cost ratio 𝑟.

It is not possible to derive an analytical expression for 𝑆 𝑄 (𝑥). 𝑆 𝑄 (𝑥) depends on the storage efficiency, the shape of the load profile, the temporal variability structure of the local solar resource and the chosen quality service level. As mentioned previously, 𝑆 95 (𝑥) was here estimated for each location by simulations.

Statistical distributions of costs for PV and batteries

The full costs of batteries and photovoltaic panels vary from one country to another due to different political, regulatory, or institutional contexts, from one region to another due to local constraints and specific transport costs depending on access facilities. In addition, each type of investor has its own profitability objectives and its own perceptions of the risks inherent in each project. This leads to the use of specific discount rates that strongly impact the LCOE [START_REF] Bank | Benchmarking study of solar PV mini grids investment costs[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF], [START_REF] Hansen | Review of solar PV policies, interventions and diffusion in East Africa[END_REF], [START_REF] Vartiainen | Impact of weighted average cost of capital, capital expenditure, and other parameters on future utility-scale PV levelised cost of electricity[END_REF]. The costs of batteries and photovoltaic panels are also expected to decrease over time as a result of learning by doing [START_REF] Bollinger | Learning-by-Doing in Solar Photovoltaic Installations[END_REF], [START_REF] Rubin | A review of learning rates for electricity supply technologies[END_REF], [START_REF] Candelise | The dynamics of solar PV costs and prices as a challenge for technology forecasting[END_REF]. Cyclical effects may also occur, e.g., pressures on equipment production capacity or on materials that may drive prices up more or less temporarily.

In the following, we explore how robust the optimal design is to economic hypotheses. To do this, we rely on a statistical distribution of full costs estimated via Monte-Carlo simulations. For storage, the values of the different variables in Eq. ( 6) (storage costs, battery lifetime, project lifetime, discount rate, proportionality coefficient for O&M costs) are randomly sorted from their respective statistical distributions allowing in turn to give one estimate of the storage full costs. This simulation process is repeated 10'000 times to produce a probability density function (PDF) of the full costs for storage. The same process is applied for calculating PV full costs. Due to the lack of information and for the sake of simplicity, the different variables in Eq. ( 6) (resp. Eq. ( 7)) are assumed independent and the PDF of each variable is modelled with a normal distribution. The mean and variance of each PDF (cf. Table 2) have been estimated so that the 10 th and 90 th of the PDF correspond to the range of values given by the IRENA (International Renewable Energy Agency) for 2015 and 2025 [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF]. These estimations are based on a bottom-up analysis of the different technologies implied in PV and storage systems and an estimation of the learning cost curve for these technologies. Due to the lack of information, the PDFs for the O&M costs proportionality coefficient and the discount rate are assumed to be the same for both periods. [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF] and the storage ones from [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF]. Discount rate and Proportionality coefficient for operation and maintenance are obtained from [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF]. The PDFs of the full costs for each unit of storage or PV (𝛼 𝑆 and 𝛼 𝑃𝑉 ) and the PDFs of the cost ratio 𝑟 resulting from the Monte Carlo simulations are presented in Figure 31. As highlighted in the figure, the full costs for both PV and storage are expected to decrease with time. The full costs for PV are however expected to decrease faster leading to a shift of the cost ratio distribution to lower ratio values. 2.4 Results

Sizing curve for a 95% quality service level

For the sake of concision, the following sections (2.4.1 to 2.4.3) only present results obtained for the non-seasonal demand profiles. Results for the seasonal demand profiles are presented in the Supplementary Material (cf. SM Figure 80 to Figure 91).

Figure 32 shows the S95(x) sizing curves obtained with the two daily load profiles of Figure 29, for 6 locations in contrasted climates (see SM Figure 80 and Figure 81 for other locations). Whatever the location and the load profile, the storage need is very sensitive to the oversizing value when the latter tends to 1. The large to very large storage needs obtained for an oversizing value close to one depend on the location and on the demand profile. When the size of PV panels is just enough to produce the yearly energy demand (i.e. 𝑥 = 1) in average over the year, large to very large storage capacity is needed where the seasonality of the solar resource or of the demand is significant (cf. SM Figure 80 and Figure 81). This allows to balance the energy from summer to winter or vice-versa (cf. Libya or South Africa). Much smaller storage values are needed for locations where the resource seasonality is small, as this is typically the case near the equator (cf. Central African Republic or Ivory Coast) (cf. Figure 32). This seasonal footprint is largely due to the latitude of the location, but this is not always the case. A significant resource seasonality is also observed in a number of equatorial locations because of significant seasonal variations of the nebulosity (cf. Uganda or Republic of Congo). As mentioned previously, the storage capacity is expected to tend to a minimum value for large oversizing values (cf. illustration in Figure 33). The limiting value per unit of energy demand highly depends on the type of use. Whatever the location, it is larger for domestic uses than for productive ones (cf. Figure 33). It is actually always smaller than 16 hours in the first case and smaller than a few hours in the other. The storage is thus almost only required to deal with the sub-daily resource / demand mismatch, e.g., to move the energy produced during the day to the evening/night-time in the domestic case. Another interesting point is that this minimum required storage value is almost always already reached for rather small PV oversizing values (values below 2.5) (cf. results for the 6 locations of Figure 32). For larger oversizing values, the required storage capacity decreases but the decrease is small and almost always less than one hour at mean demand power. For many locations, the storage is thus used for long temporal scale redistributions only when the oversizing value is small to very small.

For small oversizing values (below 1.5), the storage requirements are modified in a case of a seasonal demand. A larger seasonal resource / demand mismatch leads to a larger storage requirement (cf. SM Figure 80 and Figure 81). For large oversizing values (above 2.5), the storage requirement almost no more depends on the demand seasonality.

Least-cost configurations

This section presents the least cost configurations obtained for the 200 locations with different demand profiles, a 20 years project lifetime and a cost ratio 𝑟 = 1. The case of 𝑟 = 1 is close to the most unfavourable cost configuration for PV for 2025 (𝑟 = 1 actually corresponds to the 99 th percentile of the cost ratios distribution for this period). Estimating the oversizing values for 𝑟 = 1 gives thus almost the minimum possible value of the optimal oversizing. In other words, the oversizing of a given project is very unlikely to be smaller than this value, whatever the cost-ratio configuration for the 2025 cost conditions. The PV optimal oversizing values as a function of latitude varies between 1.1 and 2 without major differences between the two daily load profiles. The optimal oversizing values are higher for regions with a high nebulosity (near the equator) or a high seasonality (north and south of Africa). The lowest values for optimal oversizing are obtained in the Sahelian part (around 15°N). Adding seasonality to the demand profile increases the optimal oversizing values but most of them stay below 2.1 (cf. SM Figure 82 and Figure 83). This increase is larger when the peak demand occurs during the low resource period, which modify the shape obtained in Figure 34. When the peak demand occurs in the northern summer, the optimal oversizing values are lower in the north and higher in the south.

The required (normalized) storage capacities for the domestic profile are around 15 to 18 hours depending on the location (Figure 34). They are around 4 to 7 hours for the productive profile. Even with a cost ratio that favours large storage capacities (𝑟 = 1), these values are relatively close to the minimal storage requirements from Figure 33. As for the optimal PV oversizing values, the optimal storage capacities are increased when adding seasonality to the demand, especially for the domestic load profile (cf. SM Figure 84 and Figure 85). The demand / resource seasonal mismatch has a similar effect: when the peak demand occurs in northern summer, the optimal storage values are lower in the north and higher in the south. Note that whatever the type of use and seasonality, the required storage is smaller than 24 hours. The storage capacities for the domestic load profile could be perceived high for electrochemical storage, however these storage levels can be found in existing solar MGs and they are much lower than what is proposed by the IEEE rule [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF]. The 𝐿𝐶𝑂𝐸 values found here are in the same order of magnitude as the ones calculated by Nerini et al. [203] or by Szabo et al. in [START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF]. They are also logically higher than the 𝐿𝐶𝑂𝐸 for electricity delivered by national grids with values below 0.1US$/kWh for Zambia to 0.6US$/kWh for Liberia but below 0.35US$/kWh for most of the countries in Sub-Saharan Africa [START_REF] Trimble | Financial Viability of Electricity Sectors in Sub-Saharan Africa[END_REF]. The 𝐿𝐶𝑂𝐸 values we obtain are very sensitive to the sub-daily demand profile (cf. Figure 36). The 𝐿𝐶𝑂𝐸 for a productive profile can be two to three times lower than the one for a domestic profile. This logically follows the much lower storage requirements that are two to three times lower in the productive case whereas PV capacities are similar in both demand configurations. The 𝐿𝐶𝑂𝐸 evolution with the latitude is similar to the one found for the optimal oversizing values.

If the 𝐿𝐶𝑂𝐸 is much less sensitive to the seasonality of the demand than to the sub-daily profile, a seasonal demand leads, for most locations, to larger oversizing values and storage capacities and, in turn to larger 𝐿𝐶𝑂𝐸 values (cf. SM Figure 86 and Figure 87).

Sensitivity of the optimal configurations to cost ratio

As mentioned previously, the least-cost configuration depends on the cost ratio r. The PV oversizing level and the storage capacity of the least cost configuration is presented as a function of r for the six locations in Figure 37. Note that the variation range of cost ratios explored in the figure is larger than the variation ranges of the 2015 and 2025 distributions. For the sake of clarity, the 90% range of the 2015 and 2025 distributions is highlighted by the yellow and cyan vertical bands.

Figure 37 : Least LCOE configurations (normalized PV capacity (continuous lines; left scales); normalized storage capacity (dotted lines, right scales)) as a function of cost ratio (PV full costs / storage full costs, log scale) for six locations and for the domestic (blue lines) and the productive (red lines) load profiles. The 90% confidence interval of the cost ratio distribution is presented for 2015 (yellow vertical band) and 2025 (cyan vertical band). The green band corresponds to the overlap of cyan and yellow bands. All configurations allow for a 95 th quality service level.

Larger r values (i.e., larger PV/S cost ratios) logically lead to smaller PV oversizing values and larger storage capacities.

For both variables, the range of the optimal design values is rather small. Considering the 200 locations, while the cost ratio varies by a factor of 8 (from 0.25 to 2), the optimal oversizing coefficient only varies by a factor 1.5 for the domestic profile and of 1.7 for the productive one, for 90% of the locations. The ratio between the largest and the smallest possible PV oversizing value is always smaller than 2.

The robustness of the sizing of the storage capacity is even larger. Whatever the type of use, its variation range is often less than 10%. For both variables, the variation range is even smaller when the cost ratio is kept in the 90% variation range of the 2025 distribution (cyan vertical band). The optimal configuration is actually much more sensitive to the daily load profile than to the cost hypothesis. Even if optimal storage capacities and oversizing values are higher when adding seasonality to the demand, the robustness of the optimal configuration is similar to the one described here (cf. SM Figure 90 and Figure 91).

As shown in Figure 31, the cost ratio r is expected to decrease in the coming years, which will further favour cost-optimal configurations with higher PV oversizing [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF]. In a longer term however, the cost ratio could increase again to values above 1 due to the learning-by-doing effects which are still expected to be significant for storage technologies [START_REF] Vartiainen | Impact of weighted average cost of capital, capital expenditure, and other parameters on future utility-scale PV levelised cost of electricity[END_REF]. Considering the lower sensitivity of the optimal configuration in the right-side of the oversizing curves in Figure 37, this would lead in turn to an increased robustness of the optimal sizing.

The possibility for simple pre-sizing rules

As highlighted in previous sections, the optimal configuration reveals to be rather robust to cost assumptions and to almost only depend on the characteristics of the solar resource, the demand and their co-variability. This suggests that it might be possible to find simple sizing rules that would avoid the computationally demanding simulations of any simulation-based optimization process.

We assess here the possibility for such a set of rules. These rules have been identified and tested from all the optimal configurations obtained, with the simulation methodology presented in section 2.3, for the 200 locations of Figure 28, the ten different load profiles presented in section 2.3.1 and four different cost ratios (namely 0.3, 0.5, 0.8 and 1 corresponding respectively to the quantiles 5%, 50%, 95% and 99% of the cost ratio distribution for 2025). The rules have been first identified/calibrated from half of the locations and their validity has then been assessed on the other half. The evaluation consists in comparing, for each location and each demand profile/cost ratio, the estimated optimal configuration and the reference one, i.e., the optimal configuration obtained with simulations. The detailed procedure to apply these rules can be found in Supplementary Material (cf. section 8.1.1).

Two indicators are used for this evaluation: the normalized mean bias error (eq. ( 13)) and the normalized root mean square error (eq. ( 14)).

𝑛𝑀𝐵𝐸 = 1 𝑌 ̅ ∑ 𝑌 -𝑌 𝑒𝑠𝑡 𝑛 𝑛 𝑖=1 (13) 𝑛𝑅𝑀𝑆𝐸 = 1 𝑌 ̅ √ ∑ (𝑌 -𝑌 𝑒𝑠𝑡 ) 2 𝑛 𝑖=1 𝑛 (14)
With 𝑌 and 𝑌 𝑒𝑠𝑡 the design values obtained for the considered variable (e.g., storage capacity, PV production capacity) for the reference configuration and with the simple rules respectively and 𝑌 ̅ the mean reference value obtained for the 𝑛 =100 evaluations stations.

The rules apply for the normalized PV oversizing factor and the normalized storage capacity. As mentioned in the "Method" section, the actual PV panel area and the storage capacity required for a given location can be simply obtained with those normalized variables from the mean daily demand and from the mean capacity factor of solar panels to be expected for the location. Whereas the mean capacity factor can be easily extracted from already published data sets (e.g. [START_REF] Esmap | Global Solar Atlas[END_REF]), the mean daily demand has to be typically estimated from local surveys.

As mentioned previously, the required PV oversizing factor is related to the resource / demand temporal mismatch. An indicator of this mismatch is the standard deviation (𝜎 𝐷𝑖𝑓𝑓 ) of the daily power differences that can be estimated each day between the mean electricity demand and the mean PV production. This standard deviation obviously depends on both the mean daily difference and on the temporal variations of the difference. For the sake of simplicity, 𝜎 𝐷𝑖𝑓𝑓 is here estimated from the time series of differences between the normalized daily demand (normalized by the mean annual daily demand D0), and the normalized daily PV production for this day (production achieved without any oversizing of the PV panel area (𝑥 = 1) and normalized by D0).

As shown in Figure 38, the variation range of 𝜎 𝐷𝑖𝑓𝑓 depends on the seasonal profile of the demand. In the case of a non-seasonal profile, 𝜎 𝐷𝑖𝑓𝑓 simply refers to the coefficient of variation of the solar resource, which derives from the joint effects of the seasonality of the Top Of Atmosphere (TOA) radiation and of the day-to-day variations of the atmosphere characteristics (e.g. nebulosity, aerosols).

In locations with both small TOA radiation seasonality and low day-to-day weather variability (e.g. in the Sahel and a part of Angola), low values of 𝜎 𝐷𝑖𝑓𝑓 are obtained (< 0.25).

In the case of a seasonal demand profile, the power difference variability is modulated. When the peak demand occurs in the high solar resource season, the value of 𝜎 𝐷𝑖𝑓𝑓 can significantly decrease. For instance, a high energy demand in July in the Maghreb area makes 𝜎 𝐷𝑖𝑓𝑓 decrease from 0.35 to 0.2.

When the peak demand occurs in the low resource period, 𝜎 𝐷𝑖𝑓𝑓 is expected to increase. In Maghreb, it can be higher than 0.5 for a high winter demand.

Figure 38 : Optimum oversizing 𝑥 * as a function of 𝜎 𝐷𝑖𝑓𝑓 , the normalized standard deviation of the daily production/demand differences (differences estimated each day between the mean production and the mean demand for this day (the production is estimated with an oversizing factor of 1) and normalized by D0). Results are presented for 5 different seasonal profiles of the demand (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). This graph presents the optimum oversizing value for 𝑟 = 1 and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles).

As highlighted in Figure 38, regardless of the seasonality of the demand, the relationship between 𝜎 𝐷𝑖𝑓𝑓 and the optimal oversizing 𝑥 * turns out to be strong, and a linear relation is expected to be a relevant first-order approximation.

𝑥 * 𝑒𝑠𝑡,𝑟=1 = 0.83 + 2.12𝜎 𝐷𝑖𝑓𝑓 [START_REF] Lee | Electrification and Economic Development: A Microeconomic Perspective[END_REF] The nMBE and the nRMSE of this model stays respectively below 0.05 and 0.1 for each load profile (cf. SM Figure 93). The global nRMSE for all categories is 0.07 which is quite good for such a simple rule.

The optimal normalized storage capacity was found to mainly depend on the sub-daily resource/demand mismatch (cf. Figure 39). It thus depends on the actual power production and in turn on the oversizing factor chosen for the system. For the storage capacity, the sizing rule is then based on the statistical distribution of the normalized nocturnal energy difference 𝐸 𝑛𝑜𝑐𝑡 [ℎ] estimated each day between the load profile and the PV production profile of this day, where the PV production is obtained with the optimal oversizing 𝑥 * 𝑒𝑠𝑡 estimated by the previous rule (eq. ( 15)) and both production and demand are normalized by D0.

For any given day, this normalized nocturnal energy difference reflects the energy that must be delivered by the storage during night-time. The normalized nocturnal energy difference is calculated between mid-time and mid-time the day after using equation [START_REF] Bahaj | The Impact of an Electrical Mini-grid on the Development of a Rural Community in Kenya[END_REF].

𝐸 𝑛𝑜𝑐𝑡 (𝑑) = ∑ 𝑃 𝑛𝑜𝑐𝑡 (𝑡) • 1ℎ𝑟 ℎ=12 ℎ=-12 (16)
Where 𝑃 𝑛𝑜𝑐𝑡 [-] is the normalized nocturnal power difference for each day 𝑡 defined as:

𝑃 𝑛𝑜𝑐𝑡 (𝑡) = { (𝐷(𝑡) -𝑃 𝐴𝐶 𝑥 * (𝑡))/𝐷 0 , 𝐷(𝑡) -𝑃 𝐴𝐶 𝑥 * (𝑡) ≥ 0 0, 𝐷(𝑡) -𝑃 𝐴𝐶 𝑥 * (𝑡) < 0 (17)
Where 𝑃 𝐴𝐶 𝑥 * [𝑊] is the power produced by PV panels with the optimal oversizing 𝑥 * 𝑒𝑠𝑡 obtained from equation [START_REF] Lee | Electrification and Economic Development: A Microeconomic Perspective[END_REF] and 𝐷 [𝑊] is the power demand. The sizing rule for the optimal normalized storage capacity 𝑆 95 * is considered as:

𝑆 95 * 𝑒𝑠𝑡,𝑟=1 = 0.93 𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 ) 𝜂 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 + 0.14 (18)
Where 𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 ) [ℎ] is the 75 th percentile of the normalized nocturnal energy difference distribution and 𝜂 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 [-] is the storage efficiency. Seasonality with a maximum in January; April, July and October respectively). This graph presents the optimum storage capacity values for 𝑟 = 1 and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles).

As highlighted previously in the manuscript, the storage requirement depends mainly on the load subdaily profile. If all hours would have to be satisfied (𝑄 = 100%), the storage requirement would be related to the maximum nocturnal energy difference. In this work, we set a quality service 𝑄 = 95%, which means that 5% of the hours can be unsatisfied. In this configuration, the 75 th quartile of the nocturnal energy difference distribution turns out to be a very good predictor of the storage requirement.

For the storage capacity, the good order of magnitude is reached with this simple rule whatever the load profiles. If relative errors are much higher for the productive profile than for the domestic one (as a result of smaller absolute values of the required storage), absolute errors are most of the time lower than 1 hour of storage. The estimations for the optimal storage are very satisfactory with a global nRMSE below 0.04.

The level of quality service obtained with the estimated design does not always fit the level initially targeted (between 𝑄𝑆 = 92% and 𝑄𝑆 = 96% for 90% of the locations, cf. SM Figure 92). An overestimated (underestimated) optimal storage capacity leads to a higher (lower) level of quality service and the same applies for the optimal oversizing factor. As the storage capacity is estimated from the estimated oversizing factor, the storage/PV under-and overestimations often compensate themselves. All in all, these compensations allow to have a good estimation of the 𝐿𝐶𝑂𝐸 (cf. Figure 40).

Pre-sizing rules for other cost ratios

The above results refer to a cost ratio of 𝑟 = 1. As highlighted previously, the storage optimal capacity was found to be almost independent on the cost ratio value (cf. SM Figure 91 and Figure 94). Whatever the actual cost ratio value, the storage capacity estimated with equation ( 18), calibrated for 𝑟 = 1, is very satisfactory. The global nRMSE of estimates remains below 0.06.

Results obtained for the PV optimal oversizing conversely significantly depend on the cost ratio value. Smaller cost ratios lead to more favourable configurations for PV and thus to higher oversizing values (cf. SM Figure 90 and Figure 93). An efficient way to account for this in the pre-sizing rules is to multiply the optimal oversizing estimated for 𝑟 = 1 by a constant factor 𝑓(𝑟). This factor was estimated to be equal to 1.5, 1.2 and 1.1 for cost ratios equal to 0.3, 0.5 and 0.8 respectively.

𝑥 * 𝑒𝑠𝑡,𝑟 = 𝑓(𝑟) . 𝑥 * 𝑒𝑠𝑡,𝑟=1 (19)
When no correction is considered, i.e. when the relation ( 15) is used for the pre-design of the PV optimal oversizing for any value of the cost ratio, the global nRMSE is 0.18. With the correction introduced in equation ( 19), it decreases to 0.08, which becomes also very satisfactory.

Using equations ( 18) and ( 19), the level of quality service stays between 93% and 97% for 90% of all configurations (cf. SM Figure 92).

A detailed description of nMBE and nRMSE related to optimal oversizing factors, optimal storage capacities and LCOE estimation for each cost ratio and load profiles can be found in SM Figure 95. Even if the deviations between the estimated and the reference optimal configurations for the storage, the PV oversizing and the level of quality service can be non-negligible, the errors obtained for the 𝐿𝐶𝑂𝐸𝑠 are small whatever the cost ratios and the load profiles (global nRMSE around 0.02, cf. Figure 41).

Influence of the load profile choice

As highlighted here and in some other publications, the load profile has an important influence on the optimal MG configuration. On the other hand, the load profile to be expected for a rural community is very uncertain a priori (cf. [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Louw | Determinants of electricity demand for newly electrified low-income African households[END_REF], [START_REF] Lee | Investigating the Necessity of Demand Characterization and Stimulation for Geospatial Electrification Planning in Developing Countries[END_REF]). Having a good estimate of the load profile is thus obviously a key challenge and an important design issue. This however not modifies the relevance and impact of our analyses. On the one hand, an interesting finding of our work is indeed that the design is almost not sensitive to cost hypothesis. Our results additionally suggest that this applies whatever the load profile. Analyses with an intermediate daily profile (50% domestic/50% productive) give for instance similar (intermediate) results (cf. SM Figure 97 and Figure 98). On the other hand, the simple design rules proposed here are expected to apply whatever the daily/yearly load profile. The characteristics of the load profile are indeed considered both (1) in the mean power difference between production and demand, that is used to estimate the optimal oversizing factor, and (2) in the mean nocturnal energy difference, that is used to calculate the optimal storage capacity.

Influence of technical/economic hypothesis and choices

Our results were obtained under a set of technical choices and economic hypothesis. How they might influence the optimal configuration, the LCOE and the robustness of the sizing rule would need to be studied.

For instance, the targeted level of quality of service is expected to impact the optimal configuration. A lower level would decrease the storage requirements and /or the PV installation size and would decrease in turn the battery and/or PV costs [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], [START_REF] Lee | Cost versus reliability sizing strategy for isolated photovoltaic microgrids in the developing world[END_REF]. The way the quality of service is defined is also expected to impact the design. This would probably be an issue for specific research.

Similarly, unit costs of PV and storage are expected to depend on PV panels and battery efficiency, on the minimum state of charge of the battery below which the battery should not fall. The possible effects of some of these features on the design are easily predictable. A higher value for the minimum battery state of charge would logically increase the storage requirement and in turn the storage costs.

A smaller PV efficiency would similarly increase the required surface of PV panels and in turn PV costs.

A modification of unit costs and of their respective variation ranges would change the PV/battery cost ratio and its variation range. If the influence of such modifications would be worth investigating, our results are not expected to be significantly modified. Results obtained in Figure 37 are very similar when the variation range of r is extended to the range [0.1 , 3]: the robustness of the optimal configuration to modifications of the cost ratio is slightly smaller on the range [0.1 , 0.25] but it is larger on the range [2 , 3] (cf. SM Figure 98).

A more detailed modeling could be also considered to account for auxiliary costs such as costs of civil engineering, cost of the distribution grid and costs of distribution losses, etc. (cf. [START_REF] Lacirignola | LCA of emerging technologies: addressing high uncertainty on inputs' variability when performing global sensitivity analysis[END_REF]). Some of those auxiliary costs are not expected to modify the optimal configuration of a 100% solar MGs and are not expected to modify the pre-sizing rules discussed above. They would just result in the introduction of a fixed cost and increase in turn the 𝐿𝐶𝑂𝐸 by a constant value. Another issue could be the influence of economies of scales, with lower unit costs for larger project sizes [START_REF] Goodrich | Residential, Commercial, and Utility-Scale Photovoltaic (PV) System Prices in the United States: Current Drivers and Cost-Reduction Opportunities[END_REF], or the influence of the component lifetimes, which are very sensitive to maintenance quality, local weather conditions, charge/discharge cycles for the battery, degradations, etc. [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], [START_REF] Gustavsson | Lead-acid battery capacity in solar home systems-Field tests and experiences in Lundazi, Zambia[END_REF].

Comparison with other sizing rules

As stated in the introduction, some international organizations propose rules or guidelines to design isolated MGs in Africa.

In all cases, the load profile of the community has to be estimated based on the different appliances (light bulb, TV, fridge, …) to be used and on their respective consumption profiles. This allows in turn estimating the mean daily demand and the nocturnal energy consumption of the whole system.

The Institute of Electrical and Electronics Engineers (IEEE) [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF] proposes a rule to size 100% PV systems that can be compared to our rule. The PV array is sized using the mean daily demand and solar resource for the worst month (high monthly demand and low resource). For the storage capacity, the IEEE recommends 5 to 7 days of autonomy to deal with sequences of low resource days. This leads to much larger 𝐿𝐶𝑂𝐸𝑠 (with storage capacities at least 5-8 times larger than the ones estimated in the present work).

Contrary to the IEEE, the International Energy Agency (IEA) [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF] and the ECOWAS Centre for Renewable Energy and Energy Efficiency (ECREEE) [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF] give rules to design hybrid PV/diesel MGs. In such a configuration, the level of service quality that can be achieved is no more an issue, as the genset can supply the missing solar production at any time.

Similarly to the IEEE rule, the rule proposed by ECREEE [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF] uses the mean daily demand and solar resource for the worst month to size the PV array but they recommend a smaller storage capacity corresponding to 2 times the value of the nocturnal energy consumption.

For the IEA [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], the design recommendations take the form of general guidelines: the installed PV capacity should be able to supply more than 20% of the daily energy demand and the storage capacity should be large enough to supply the nocturnal energy demand apart from the evening peak power that should be supplied by the diesel genset. A large part of the demand is thus expected to be supplied by the genset making the design of the PV / storage components rather simple.

The two previous rules apply to hybrid PV / diesel systems. They are not necessarily suited for remote locations where fuel supply is not reliable enough or for MGs operators who want to use only decarbonized technologies. The rules we propose in the present work apply to 100% solar systems that could fit with the above constraints/objectives. Our results show that a 95% level of quality service can be reached with such systems, without any diesel generator and with smaller storage capacities than those proposed by the ECREEE. Our work additionally shows that the least cost configurations for such systems, very robust to a set of economic hypotheses, have to be adapted from one location to the other depending on the local climate features and on the sub-daily demand profile.

Our rules do not replace a more accurate sizing of a MG that could be done with HOMER [START_REF] Energy | KOSAP[END_REF] or any similar optimization software. It only aims at pre-assessing the regions where 100% PV MGs have a potential by quickly estimating the cost of power generation and compare it with other energy sources or other electrification solutions (national grid, solar home systems) for rural electrification planning.

The sites for which this comparison favours a 100% PV MGs will need to be studied in more detail.

Conclusion

The optimal configuration and the 𝐿𝐶𝑂𝐸 of autonomous PV + battery systems is expected to depend on cost hypotheses. The robustness of the least cost configuration to cost assumptions is investigated for 200 African locations. The simulation-based design is carried out to achieve a prescribed level of quality service, namely to supply energy for 95% of the hours.

Whatever the shape of the load profiles (domestic or productive), we show that different storage / PV oversizing configurations are suited to achieve a prescribed level of quality service. The large storage requirements usually recommended can be reduced by oversizing the PV production capacity. In most of the cases, an oversizing coefficient of 2.5 is enough and the storage energy requirements are close to the value that allows to deal with the sub-daily resource/demand mismatch.

The least-cost configuration that allows to achieve a given level of quality service depends, among other drivers, on relative costs of PV and battery, but the sensitivity to the cost ratio is not large. The robustness of the configuration is thus rather good. When the cost ratio varies with a factor 8, the variations of the optimal oversizing factor are most of the time not larger than 70%, while the one for the required storage capacity are often smaller than 10%. The required storage capacity is thus highly robust to cost ratio variations.

The 𝐿𝐶𝑂𝐸 for a productive load profile is two to three times lower than the one for a domestic load profile. This is an incentive for mini-grid designer to integrate as much productive uses as possible when assessing the electricity demand of a community. This definitively also calls scientists and practitioners to collect, share and publish demand data for a better knowledge of the temporal profile of the demand and its possible evolution through years.

All in all, the optimal (PV capacity / storage) configuration almost only depends on the characteristics of the solar resource, the electricity demand and their co-variability. This allows to propose simple rules for a rapid but reliable design. The goal of these rules is not to find the accurate optimal configuration for one specific site, it is rather to evaluate quickly the cost of electricity from solar MGs over a large area. Such estimation can then be used to compare solar MGs to different electrification solutions in a preliminary planning. The optimal oversizing factor can be estimated using the standard deviation of the mean daily power difference between the solar power production and the power demand. The required storage capacity can be calculated using the 75 th percentile of the daily nocturnal energy difference between the load profile and the solar power production. These rules give a good estimate of the optimal configurations whatever the load profile (domestic or productive, seasonal or not) and the cost ratio (between 0.3 and 1) considered.

The approach used in this work and the results offer further research perspectives. A least 𝐿𝐶𝑂𝐸 criterion was used to determine the optimal configuration. It could be interesting to compare the results for this criterion obtained with our rule and with the ones proposed by the IEEE, the IEA and the ECREEE. This comparison should also consider the environmental impact of the MGs (for instance, the greenhouses gases emissions, the land use or the toxicity to human health and to ecosystems) and modified rules could be derived by including these criteria in the optimization.

The methodology presented here was applied to identify the optimal (PV capacity/storage) configuration of 100% PV MGs. It could also be used for MGs based on other variable energy sources such as wind or hydroelectricity that are also promising renewable energy sources in many regions worldwide (e.g. [START_REF] Seyedhashemi | The Impact of Low-Resource Periods on the Reliability of Wind Power Systems for Rural Electrification in Africa[END_REF]). For wind power and hydroelectricity, the important civil engineering works to be produced and the large variety of terrain configurations to be found would likely result in a large variability of installation and in turn equipment costs. The robustness of the optimal design configurations is expected to be in turn rather low.

The demand profiles considered in this article are constant from one year to the other, however the evolution of the electricity demand during the lifetime of the MG could change the performance of the system. A better knowledge of the processes involved in the evolution of the electricity demand are necessary to choose the most suitable profile on which the sizing rules must be applied.

Key messages:

• To achieve a given level of service quality, 100% PV MGs have to be oversized and require significant storage capacity, • Many different storage/PV capacity configurations allow to achieve a given target level of service quality, • The least-cost configuration is relatively robust to economic assumptions (e.g. costs of the different MG components), but highly sensitive to the co-variability of the solar resource and the electric demand • The least-cost configuration is typically determined with long times series simulation of multiple battery/solar capacity configurations. It can be however also estimated with simple sizing rules based on characteristics of this resource / demand co-variability • These rules can accurately estimate the levelized cost of electricity for different load profiles and economic assumptions

3 Sizing hybrid mini-grids: a trade-off between the LCOE and the CFP

Context and objectives

Actually, most of the MGs installed are hybrid MGs relying on both solar (PV and battery) and genset power production to be able to supply 100% of the energy demand. Many authors highlight indeed the necessity to have a very reliable electricity supply to benefit from the positive effects of rural electrification, especially when supplying productive use of energy [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF]. Increasing the level of service quality close to 100% lead to prohibitive costs for 100% solar PV MGs (cf. section 2.3.4 and SM Figure 99), which is not the case when adding a diesel genset to supply of a few percent of the consumption.

On the other hand, hybrid MGs lead to non-zero direct greenhouse gas emissions due to fuel combustion, whereas MGs considered in the previous chapter do not. If we consider the carbon footprint of the equipment, how does the comparison between 100% solar MGs and hybrid MGs evolves? The aim of the following chapter is to quantify the LCOE and CFP of different MG configurations, ranging from a MG using only a diesel genset to an almost 100% solar MG 19 , in order to shed light on the following questions:

• What is the CFP of different MG configurations and how does it vary across the continent?

• How the indirect GHG emissions affect the CFP of MGs?

• What reductions in LCOE and CFP can be achieved by integrating solar PV into MGs?

• To what extent is it possible to combine a low CFP and a low LCOE for hybrid MG?

Introduction

According to the International Energy Agency, more than 40% of the Sub-Saharan African population does not have access to electricity [13]. Achieving the sustainable development goal n°7 i.e., ensuring a universal access to a reliable, affordable, and sustainable energy by 2030, would require electrifying around 90 million people on this subcontinent each year [START_REF]UN Sustainable Development Goals[END_REF]. To reach this objective at the lowest cost, the International Energy Agency estimates that one third of these future electricity connections would be met by mini-grids (MGs), the two other thirds relying on grid extension and solar home systems [13].

This electrification must be compatible with the objective of the Paris agreement to limit global warming to below 2°C and as close as possible to 1.5°C [START_REF]Nationally Determined Contributions (NDCs)[END_REF]. Global pathways likely limiting warming to 2°C require to reach net-zero CO2 emission around 2070-80 (and as soon as 2050 to limit warming to 1.5°C) and the power generation sector is the first sector that will have to be completely decarbonised [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. Some African countries like Namibia or Nigeria have submitted very ambitious National Determined Contributions (NDCs) to the Paris Agreement aiming net-zero emissions by respectively 2050 and 2060 [START_REF]Nationally Determined Contributions (NDCs)[END_REF]. In this context, MGs based on solar PV are a promising solution as a large reduction of GHG emissions is typically obtained when replacing a diesel generator by solar PV and batteries [START_REF] Nsafon | Integrating multicriteria analysis with PDCA cycle for sustainable energy planning in Africa: Application to hybrid mini-grid system in Cameroon[END_REF], [START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF], [START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF], [START_REF] Breyer | Profitable climate change mitigation: The case of greenhouse gas emission reduction benefits enabled by solar photovoltaic systems[END_REF]. These systems have indeed been promoted by international institutions with several hundred millions of US$ invested each year in Africa during the last decade [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF].

Many different MG configurations hybridizing solar PV, diesel genset and batteries are able to supply the production required for a given community. The configuration retained by developers is often the one that minimizes the levelized cost of electricity (LCOE) [START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF], [START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF], [START_REF] Boadzo | A study on dairy farm-based hybrid renewable energy systems in South Africa[END_REF]. This cost-optimal configuration is also typically considered for planning studies at the regional level seeking to identify the best rural electrification option between solar home systems, MGs and grid extension [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF], [START_REF] Nerini | A cost comparison of technology approaches for improving access to electricity services[END_REF].

Given the goals to achieve carbon neutrality for the power sector, the planification of rural electrification should include the greenhouse gases (GHG) emissions associated to these solutions. If some studies already evaluated these GHG emissions for MGs, they only consider the direct emissions related to fuel consumption, assuming that solar PV and batteries do not emit any GHG [START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF], [START_REF] Rangel | An optimisation tool for minimising fuel consumption, costs and emissions from Diesel-PV-Battery hybrid microgrids[END_REF], [START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF], [START_REF] Elkadeem | Sustainable siting and design optimization of hybrid renewable energy system: A geospatial multi-criteria analysis[END_REF]. However, as highlighted in [START_REF] Akinyele | Development of photovoltaic power plant for remote residential applications: The socio-technical and economic perspectives[END_REF], the indirect GHG emissions of solar PV and batteries due to material extraction and component manufacturing is not negligible and may make the full CFP of such systems not as attractive as usually considered (CFP: including both direct and indirect emissions [START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF], [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF], [START_REF] Frischknecht | Life Cycle Inventories and Life Cycle Assessments of Photovoltaic Systems[END_REF], [START_REF] Varlet | Comparative life cycle assessment of lithium-ion battery chemistries for residential storage[END_REF]). To reach a real carbon neutrality of the power sector, these indirect (or embodied) emissions must be included as they may represent a large part of future global emissions (section 2.3 of [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]).

As they are expected to be key for rural electrification of many regions worldwide [13], our work focuses on hybrid solar/diesel MGs. We especially aim to quantify, for a variety of climate conditions and socio-economic contexts in Africa, the LCOE and the CFP of different MG configurations. These estimates are obtained thanks to the simulations of the MG functioning over multiple years at an infrahourly resolution to account for the temporal variations of weather and demand. The simulations allow identifying and characterizing the configurations with the least CFP and LCOE values, but also the trade-offs between these criteria, and the CFP reduction that could be obtained for different levels of carbon pricing.

This analysis is carried out for more than 90 locations spread over the continent, giving some insight on the dependence of results to climate conditions. A sensitivity analysis to the numerous technical, economic, and environmental parameters involved in the sizing process is finally carried out to identify the main factors affecting the sizing of MGs and the robustness of our main conclusions.

Methods

We considered fictitious hybrid MGs using solar PV, diesel genset and batteries to supply typical load profiles for 93 different locations over Africa. We simulated the functioning of these MGs over two years using meteorological data to estimate the solar PV production and simple dispatch rules for the batteries and the genset to ensure that the electrical consumption is fully supplied. These simulations are performed for a large range of configurations (PV panels and storage capacities) to compute the LCOE and the CFP and determined the ones that minimize these criteria. The following presented the different steps of these simulations and calculations.

MG modelling

PV production

The solar PV production is estimated at 15 min resolution using the global horizontal irradiance (GHI) from Heliosat SARAH 2 [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF] and the air temperature from ERA5 reanalysis [START_REF] Wamukonya | Socio-economic impacts of rural electrification in Namibia: comparisons between grid, solar and unelectrified households[END_REF]. These data are taken on two years (2008 and 2009) for 93 locations (Figure 44). First, the decomposition model of the Sandia National Laboratory [START_REF] Maxwell | A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal lnsolation[END_REF] is used to compute the direct (DNI) and the diffuse (DHI) irradiances from the global horizontal irradiance (GHI) and solar angles. Then, the global tilted irradiance (GTI) is calculated using equation [START_REF] Wamukonya | Socio-economic impacts of rural electrification in Namibia: comparisons between grid, solar and unelectrified households[END_REF].

𝐺𝑇𝐼 = 𝐷𝑁𝐼 • cos(𝜃) + 𝐷𝐻𝐼 (20)
Where 𝜃 is the "effectiveness" angle, a function of solar angles and panel inclinations and orientation.

For this study, we assume that PV panels have a tilt angle equal to the latitude [START_REF] Bahrami | The effect of latitude on the performance of different solar trackers in Europe and Africa[END_REF] and are oriented towards the south (resp. north) in northern (resp. southern) hemisphere. Then, the estimated solar PV production is estimated using equation [START_REF] Wassie | Socio-economic and environmental impacts of rural electrification with Solar Photovoltaic systems: Evidence from southern Ethiopia[END_REF] as in [START_REF] Lorenz | Regional PV power prediction for improved grid integration[END_REF]:

𝑃 = 𝜂 𝑃𝑉 • (1 + 𝛼 (𝑇 𝑚 -25°𝐶)) • 𝐶 𝑃𝑉 • 𝐺𝑇𝐼 1000 𝑊/𝑚² (21)
Where 𝐶 𝑃𝑉 [𝑊 𝑝 ] is the peak power of installed PV panels, 1000𝑊/𝑚 2 corresponds to the irradiance at standard conditions, 𝛼 is the sensitivity of panel efficiency to the module temperature 𝑇 𝑚 which is computed using equation [START_REF] Bajo-Buenestado | The effect of blackouts on household electrification status: Evidence from Kenya[END_REF] and 𝜂 𝑃𝑉 , the panel efficiency that accounts for inverter efficiency and losses of the PV production system.

𝑇 𝑚 = 𝑇 𝑎𝑚𝑏 + 𝛾 • 𝐺𝑇𝐼 (22)
Where 𝑇 𝑎𝑚𝑏 is the ambient temperature and  is a parameter related to the mounted type of the system (roof integrated, free standing, etc.). We consider a mean value: γ = 0.04 °C. m 2 /W and for the sensitivity of the panel efficiency to temperature, we take the value for crystalline silicon cells: 𝛼 = -0.0035 /°𝐶 [START_REF] Lorenz | Regional PV power prediction for improved grid integration[END_REF].

Demand data

Figure 45 shows three different daily load profiles that are estimated from the literature for a fictitious community [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Louie | Off-grid electrical systems in developing countries[END_REF], [START_REF] Mandelli | Novel LoadProGen procedure for micro-grid design in emerging country scenarios: application to energy storage sizing[END_REF], [START_REF] Li | Microgrid Load and LCOE Modelling Results[END_REF]. The mean power demand 𝐷 ̅ is the same for the three profiles to allow comparisons of the results. The hybrid load profile is a mix between a load profile for productive uses and one for domestic uses of electricity. The productive uses consume mostly during the day, whereas a domestic load profile is characterized by a high peak demand in the evening and electricity consumption at night. In African rural areas, electricity can be used for agricultural activities like irrigation or post-harvest processing [START_REF] Williams | Load characteristics of East African microgrids[END_REF], which implies that the load profile is different from one season to another. To account for these seasonal variations, we use sinusoidal yearly load profiles with an amplitude chosen at half of the mean yearly electricity demand (cf. Figure 46 and equation ( 23)). Four yearly load profiles are used to account for different periods of high demand, and we also consider a yearly profile without seasonality, i.e., the daily demand is the same throughout the year.

𝐷 𝑑 = 𝐷 ̅ (1 + 𝐴 cos (2𝜋 𝑑 -𝑑 𝑚𝑎𝑥 365 )) (23)
Where 𝐷 𝑑 [𝑘𝑊] is the daily mean power demand of calendar day 𝑑, 𝐷 ̅ [𝑘𝑊] is the annual mean power demand, A=0.5 is the half amplitude of seasonality and dmax is the calendar day for the maximum. Thus, 15 different load profiles are considered, but for the sake of simplicity we present results for the hybrid load profile without seasonality. The other load profiles are used in the sensitivity analysis in Discussion section 3.5.1.

As we will show later, the seasonality of demand, but also more generally the demand/production covariability, has a significant effect on the results. To characterize this mismatch in the following, we will use two indicators as in [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF]. The first one, 𝜎 𝑑𝑖𝑓𝑓 , is used to characterize the daily temporal mismatch of the solar resource and the electric demand and is defined as stated in equation ( 24):

𝜎 𝑑𝑖𝑓𝑓 = 1 𝐷 ̅ √ ∑ (𝐷 𝑑 -𝑃 𝑑 0 ) 2 𝑁 𝑑𝑎𝑦𝑠 𝑁 𝑑𝑎𝑦𝑠 𝑑 (24)
Where 𝑁 𝑑𝑎𝑦𝑠 is the number of days for the whole period, 𝐷 𝑑 is the demand for day d and 𝑃 𝑑 0 is the mean PV production that would be obtained for day d for a system with a PV capacity

𝐾 𝑃𝑉 0 [𝑘𝑊 𝑝 ],
where 𝐾 𝑃𝑉 0 is the capacity that would be required to produce over the whole period, an energy amount exactly equal to the total energy of a constant demand 𝐷 ̅ . As reported in [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF], 𝐾 𝑃𝑉 0 is proportional to the inverse value of the so-called mean capacity factor CF of the PV panels for the considered site:

𝐾 𝑃𝑉 0 = 𝐷 ̅ /𝐶𝐹.
𝜎 𝑑𝑖𝑓𝑓 depends both on the seasonal profile of the demand and of the variations of the solar resource which derives from the top-of-atmosphere (TOA) radiations and from the atmosphere characteristics (e.g., nebulosity, aerosols).

The second index, the nocturnal energy (𝑁𝐸), is used to describe the infra-day mismatch between the solar resource and the power demand. It is based on the statistical distribution of the nocturnal energy difference 𝐸 𝑛𝑜𝑐𝑡 [𝑘𝑊ℎ] estimated each day between the load profile and the PV production profile of this day 𝑃 0 (𝑡). For any given day, this nocturnal energy difference reflects the energy that must be delivered by the storage or the genset during night-time. The nocturnal energy difference is calculated between mid-time and mid-time the day after using equations below.

𝐸 𝑛𝑜𝑐𝑡 (𝑑) = ∑ 𝑃 𝑛𝑜𝑐𝑡 0 (𝑡) • 1ℎ𝑟 ℎ=12 ℎ=-12 (25)
67

Where 𝑃 𝑛𝑜𝑐𝑡 0

[𝑘𝑊] is the nocturnal power difference for each hour 𝑡 defined as:

𝑃 𝑛𝑜𝑐𝑡 0 (𝑡) = { 𝐷(𝑡) -𝑃 0 (𝑡), 𝐷(𝑡) -𝑃 0 (𝑡) ≥ 0 0, 𝐷(𝑡) -𝑃 0 (𝑡) < 0 (26)
The nocturnal energy indicator is then taken as the 75 th percentile of the 𝐸 𝑛𝑜𝑐𝑡 (𝑑) distribution: 𝑁𝐸 = 𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 (𝑑)). For more details on these two indicators of the temporal mismatch between solar resource and electric demand, please refer to [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF].

Battery storage and dispatch of energy

A simple modelling is used for battery storage with the same efficiency for charge and discharge: 𝜂 𝑠𝑡𝑜 = 0.95. We assume that the storage can only be charged by a solar PV production higher than the demand, so the genset cannot be used to charge the batteries. If PV production is higher than the demand and storage is full, the production is curtailed. If the PV power is below the demand, both the genset and the batteries can supply the demand. To reduce genset consumption, the energy dispatch rule is to maximize the genset efficiency, i.e., it is used as close as possible to its nominal power. The battery is, therefore, mainly used during the lowest consumption hours. The hours of the sequence that cannot be supplied with the storage are supplied by the genset (Figure 47). The power to be produced by the genset for each time of the simulation period gives the total fuel consumption for the period, and in turn the direct emissions of the genset. The fuel consumption 𝑓 𝑐𝑜𝑛𝑠𝑜 (𝑡) [𝐿] at time t is estimated as:

𝑓 𝑐𝑜𝑛𝑠𝑜 (𝑡) = 𝐸 𝑔𝑒𝑛 (𝑡) 𝐻𝑉 𝑓 * 𝜂 𝑔𝑒𝑛 ( 𝑃 𝑔𝑒𝑛 (𝑡) 𝐾 𝑔𝑒𝑛 ) (27)
Where 𝐸 𝑔𝑒𝑛 (𝑡) [𝑘𝑊ℎ] is the electrical energy to be supplied by the genset at time t, where 𝑃 𝑔𝑒𝑛 (𝑡)[𝑘𝑊] and 𝜂 𝑔𝑒𝑛 [-] are the genset power and efficiency, and 𝐾 𝑔𝑒𝑛 its nominal power, and where 𝐻𝑉 𝑓 = 10𝑘𝑊ℎ/𝐿 is the heating value of diesel. Following [START_REF] Stiel | Feasibility Study of Energy Storage Systems in Wind/Diesel Applications Using the HOMER Model[END_REF], [START_REF] Ayele | Renewable Energy to Support Local Development in Peru[END_REF], the genset efficiency is considered as a function of its load factor

𝑃 𝑔𝑒𝑛 (𝑡)
𝐾 𝑔𝑒𝑛 (cf. SM Figure 100). To make sure that the electric demand is always supplied, the genset nominal power is set to the maximum value of the electric load profiles, e.g., 𝐾 𝑔𝑒𝑛 ≈ 3𝐷 ̅ for the domestic load profile without seasonality (cf. Figure 45).

LCOE and CFP calculation

Following subsections present how the LCOE and the CFP of a given MG configuration are calculated.

CFP calculation

The CFP is calculated per kWh of supplied energy. It encompasses the emissions related to the whole lifecycle of the components, from the mining of the material needed and the manufacturing to the end-of-life of the components.

𝐿 𝑔𝑒𝑛 = 𝐿 𝑔𝑒𝑛,ℎ𝑟𝑠 𝐹 𝑢𝑠𝑒 /𝐿 (29)
Finally, the carbon footprint by 𝑘𝑊ℎ of energy supplied 𝐶𝐹𝑃 is given by equation [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF]:

𝐶𝐹𝑃 = 𝐶𝐹𝑃 𝑡𝑜𝑡 𝐸 𝑠𝑢𝑝𝑝𝑙𝑦 (30)
Where 𝐸 𝑠𝑢𝑝𝑝𝑙𝑦 [𝑘𝑊ℎ] is the energy supplied over the project lifetime.

Values taken for the different parameters used in this calculation are given in Table 3 and correspond to mean values estimated by Besseau in [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF]. The sensitivity of our results to the values considered there will be discussed in section 3.5.1.

LCOE calculation

We do not include the cost related to the distribution system in the 𝐿𝐶𝑂𝐸 calculation. As for the CFP, total system costs are estimated using costs by unit of installed component and by litre of diesel fuel consumption (cf. equation ( 31)).

𝐶 𝑡𝑜𝑡 = 𝐾 𝑏𝑎𝑡 𝛼 𝑏𝑎𝑡 + 𝐾 𝑃𝑉 𝛼 𝑃𝑉 + 𝐾 𝑔𝑒𝑛 𝛼 𝑔𝑒𝑛 + 𝐶 𝑓𝑢𝑒𝑙 ∑ 𝐹 𝑐𝑜𝑛𝑠𝑜,𝑦𝑟 (1 + 𝑑) 𝑦𝑟 𝐿 𝑦𝑟=1 (31)
Where 𝐶 𝑓𝑢𝑒𝑙 [$/𝐿] is the cost of 1𝐿 of fuel, 𝐹 𝑐𝑜𝑛𝑠𝑜,𝑦𝑟 [𝐿] is the fuel consumption for one year; 𝑑 is the discount rate and 𝛼 𝑏𝑎𝑡 [-], 𝛼 𝑃𝑉 [-] and 𝛼 𝑔𝑒𝑛 [-] are the costs related to installation, replacement and maintenance of the components over their lifetime as shown by equations ( 32), ( 33) and [START_REF] Pappis | Energy projections for African countries[END_REF].

𝛼 𝑏𝑎𝑡 = 𝐶 𝑏𝑎𝑡 . ( 1 -(1 + 𝑑) (𝐿+𝐿 𝑏𝑎𝑡 ) (1 + 𝑑) 𝐿 -(1 + 𝑑) (𝐿+𝐿 𝑏𝑎𝑡 ) + ∑ 𝑃 𝑂&𝑀,𝑏𝑎𝑡 (1 + 𝑑) 𝑘 𝐿 𝑘=1 ) (32) 𝛼 𝑃𝑉 = 𝐶 𝑃𝑉 . (1 + ∑ 𝑃 𝑂&𝑀,𝑃𝑉 (1 + 𝑑) 𝑘 𝐿 𝑘=1 ) (33)
𝛼 𝑔𝑒𝑛 = 𝐶 𝑔𝑒𝑛 . ( 1 -(1 + 𝑑) (𝐿+𝐿 𝑔𝑒𝑛 ) (1 + 𝑑) 𝐿 -(1 + 𝑑) (𝐿+𝐿 𝑔𝑒𝑛 ) + ∑ 𝑃 𝑂&𝑀,𝑔𝑒𝑛 (1 + 𝑑) 𝑘 𝐿 𝑘=1 ) (34)
Where 𝐶 𝑏𝑎𝑡 [$/𝑘𝑊ℎ], 𝐶 𝑃𝑉 [$/𝑘𝑊 𝑝 ], 𝐶 𝑔𝑒𝑛 [$/𝑘𝑊] are respectively the installation costs associated to 1𝑘𝑊ℎ of installed batteries, 1𝑘𝑊 𝑝 of installed PV and 1𝑘𝑊 of genset; and 𝑃 𝑂&𝑀,𝑏𝑎𝑡 [-], 𝑃 𝑂&𝑀,𝑃𝑉 [-] and 𝑃 𝑂&𝑀,𝑔𝑒𝑛 [-] are proportionality coefficients between investment and maintenance costs related to each component (maintenance and operation costs are assumed to be time invariant and proportional to the investment cost of each component). The mean values considered for the different parameters are given in Table 4 [114], [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF]. The sensitivity of the results to the values considered there will be discussed in section 3.5.1.

Table 4 : Parameters values for the LCOE calculation, lifetimes of components are given in Table 3 [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF], 𝐶 𝑃𝑉 and 𝐶 𝐵𝑎𝑡 also include the costs for inverters.

𝐶 𝑏𝑎𝑡 [$/𝑘𝑊ℎ] 𝐶 𝑃𝑉 [$/𝑘𝑊 𝑝 ] 𝐶 𝑔𝑒𝑛 [$/𝑘𝑊] 𝐶 𝑓𝑢𝑒𝑙 [$/𝐿] 350 1900 500 1 𝑃 𝑂&𝑀,𝑏𝑎𝑡 [%] 𝑃 𝑂&𝑀,𝑃𝑉 [%] 𝑃 𝑂&𝑀,𝑔𝑒𝑛 [%] 𝑑 [%] 3 2 10 10
Finally, the LCOE is computed using equation [START_REF] Atkins | Gap Analysis Report : African Nationally Determined Contributions (NDCs)[END_REF]:

𝐿𝐶𝑂𝐸 = 𝐶 𝑡𝑜𝑡 ∑ 𝐸 𝑠𝑢𝑝𝑝𝑙𝑦 (1 + 𝑑) 𝑘 𝐿 𝑘=1 (35)

Least LCOE or CFP configurations and envelope curve

By setting a configuration (𝐾 𝑏𝑎𝑡 , 𝐾 𝑃𝑉 ), we can simulate the functioning of the MG and compute the diesel consumption required over the project lifetime such as 100% of the electricity demand is supplied. Then, using this diesel consumption and this configuration (𝐾 𝑏𝑎𝑡 , 𝐾 𝑃𝑉 ) values, we calculate the LCOE and the CFP associated to this configuration. We do so for a large range of configurations i.e., a range of couples (𝐾 𝑏𝑎𝑡 , 𝐾 𝑃𝑉 ) that could have a storage capacity in the range 1 to 20 hours of mean demand equivalent [ℎ𝑟𝑠 𝑒𝑞 ] with a step of 0.5ℎ𝑟𝑠 𝑒𝑞 , and a PV capacity in the range of 0 to 2.5 𝐾 𝑃𝑉 0 with a step of 0.01 as in [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF]. One ℎ𝑟𝑠 𝑒𝑞 of storage corresponds to 𝐷 ̅ × 1 ℎ𝑟 = 𝐷 ̅ 𝑘𝑊ℎ and it has been found that, in a 100% PV MG configuration, a storage capacity equivalent to 15 to 20ℎ𝑟𝑠 𝑒𝑞 allow to satisfy more than 95% of the demand, whatever the location in Africa (e.g. [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF]). To ease the comparison between sites, we use a normalized PV capacity in the following corresponding to the ratio 𝐾 𝑃𝑉 /𝐾 𝑃𝑉 0 .

Two configurations are used: the LCOE* configuration that minimizes the LCOE and the CFP * one that minimizes the CFP of the MG. These configurations can be estimated by selecting from the simulated configurations, the couple (𝐾 𝑏𝑎𝑡 , 𝐾 𝑃𝑉 ) with the minimum LCOE or CFP. The LCOE and CFP values obtained for all simulated PV capacity/storage configurations can be presented in a (CFP, LCOE) graph. As illustrated in Figure 48 for a given location, not all (LCOE, CFP) MG combinations are possible. As an example, it is not possible here to have a LCOE below 0.37 and a CFP below 200𝑔 𝐶𝑂 2 /𝑘𝑊ℎ. Thus, by selecting the lowest LCOE value obtained for each value of CFP, it is Diesel only possible to draw a curve that defines the limit between the (LCOE, CFP) values that are possible and the ones that are not. In the remainder of this paper, we will refer to this curve as the envelope curve.

We can notice that this curve consists of two parts: a first part from the diesel-only configuration to the LCOE* configuration where an increase of the PV capacity allows to reduce both the LCOE and the CFP, and a second part from the LCOE* configuration to the CFP* one, which corresponds to the pareto front between the LCOE and the CFP. Keeping these two parts, and not only the second one, allows to see how the progressive integration of solar energy modifies the LCOE and the CFP values.

Results

Carbon footprint vs. GHG direct emissions of a mini-grid

For the sake of simplicity, one location in Angola (-12.5°N; 17.5°E) is selected to illustrate this section, but similar results are obtained for other locations. Figure 49 shows a comparison between the envelope curve and another envelope curve that considers only direct emissions for this location. This latter curve only considers GHG emissions produced by the genset consumption of diesel. It does not include indirect emissions from PV panels and batteries. When disregarding indirect emissions, a 100% solar system appears as a zero emission MG. Yet, indirect emissions are far from negligible. Even with a 100% solar system, they reach ~200𝑔 𝐶𝑂 2 /𝑘𝑊ℎ, which is almost 20% of the CFP of a 100% genset MG configuration. Note that for high shares of solar in the mix, the rate of CFP solar contribution increase is higher than the rate of solar production share increase because part of the solar overproduction is curtailed when storage is full. The CFP* configuration corresponds then to a compromise between lower diesel consumption and higher CFP due to higher solar and/or batteries capacities. So, in the CFP* configuration, there is still diesel to supply a very small part of the energy (<1%). The distribution of this diesel consumption over the year is available in Supplementary Material (cf. SM Figure 101).

Spatial variability of LCOE* and CFP*

The LCOE* and CFP* values obtained for the least-cost and least-CFP configurations obviously vary across the African continent (Figure 51). 102). In all regions, the genset still supplies a few percentages of the energy in the CFP* configurations, up to 6-8% in some specific locations (cf. Figure 51, bottom). For the LCOE* configurations, the renewable fraction, i.e., the percentage of supplied energy from solar PV, is much lower (50% to almost 80% lower) and presents much more spatial variability than for the CFP* configurations These spatial differences are closely related to the characteristics of the solar resource and the covariability between the resource and the power demand as seen in Figure 52. The better the solar resource, the lower the cost associated to the PV production. In LCOE* configurations, the storage capacity is typically low (typically smaller than 5 hrs, cf. SM Figure 103), and the main compromise is between the cost of solar PV and the one of diesel consumption. LCOE* configurations are thus mainly driven by the mean capacity factor of the solar resource.

In CFP* configurations, diesel consumption is negligible, and the storage capacities are much larger than for LCOE* configurations (cf. SM Figure 103). The sizing of these MGs relying almost exclusively on solar PV and batteries is mainly driven by the co-variability between the solar resource and the power demand, especially by the days with low resource as explained in [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF], [START_REF] Chamarande | The least cost design of 100 % solar power microgrids in Africa: Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules[END_REF]. Thus, the least CFP values are better correlated to the co-variability between resource and demand (cf. section 3.3.1.2) than to the mean capacity factor.

Figure 52 : Least LCOE (bottom) and least CFP (top) for all locations with a hybrid demand profile as a function of the mean capacity factor CF (left) and the co-variability (right). Color corresponds to the absolute distance from the equator [°]. NB:

These graphs are subject to changes depending on economic and CFP assumptions (cf. SM Figure 104 and Figure 105).

The characteristics of the solar resource also influence the distance between the LCOE* and the CFP* configurations (cf. Figure 53). Switching from LCOE* to CFP* configuration allows a reduction of 45% to 55% of the CFP but at the cost of an increase in LCOE between 15% and 40%. Logically, it is for sites with a higher mean capacity factor and lower co-variability that the LCOE* configuration is closest to the CFP* configuration. On the contrary, for sites with a lower mean capacity factor, the distance between both configurations is greater. For these sites, the CFP reduction potential compared to the LCOE* configuration is thus higher.

For locations with similar mean capacity factor, a higher co-variability leads to higher LCOE and lower CFP relative changes. The locations with higher variabilities are typically located far from the equator. Their solar resource has a higher seasonality, which requires higher PV capacity to deal with period of low solar resource. This higher variability leads to higher LCOE and CFP of the CFP* configurations (cf. SM Figure 102). Apart from few locations, the increase of LCOE required to move from the LCOE* to the CFP * configuration is higher than 20%. This increase can be considered as prohibitive in the context of rural electrification, as the population of this area cannot afford high electricity tariffs. However, many other MG configurations can serve as compromise between the CFP* and the LCOE* configurations. These configurations are explored in the next subsection. The CFP reduction achieved with only a 5% (resp. 10%) increase of the least LCOE value is between 25% to 40% (resp. 40% to 50%) in most locations. A 20% increase of the LCOE allows in many locations to almost reach the least CFP values, with some exceptions far from the equator and in Central Africa (in the equatorial zone). LCOE relative changes to achieve 30% CFP reduction are much lower (<10%) and less sensitive to the latitude than the ones to reach the least CFP values (between 17% and 50%).

Previous results are obviously expected to depend on the techno-economic and CFP assumptions retained for the analysis. This sensitivity is discussed hereafter.

Discussion

Dependence to techno-economic and CFP parameters

The envelope curve depends on multiple factors, such as the solar resource, the load profile and the parameters (cost, CFP, lifetime) related to each component. Those values are highly variable depending on the context of installation and the components chosen [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF]. For instance, the cost of fuel in Nigeria is around 0.6$/L, whereas it is around 1.3$/L in Rwanda [START_REF][END_REF]. The CFP of a 𝑘𝑊 𝑝 of PV produced with a decarbonized electric mix is half of the one produced with an electric mix with a high proportion of coal [START_REF] Besseau | INCER ACV -Impacts environnementaux de la filière photovoltaïque & évaluation des incertitudes[END_REF]. Figure 56 shows how this curve is modified with other solar PV and fuel cost assumptions. Figures related to other parameter assumptions are given in the Supplementary Material (cf. SM Figure 107 and Figure 108). The large variations associated to diesel-only configurations in Figure 56 (configurations on the right border of the graphs) only depend on the fuel cost. This parameter keeps a large impact on the rest of the curve apart from the CFP configurations and is the main driver of the LCOE* configuration. The cost of solar PV also plays an important role on the LCOE * configuration but has the largest impact on the LCOE of the CFP * configurations (configurations on the left border of the graphs).

We performed a sensitivity analysis on the costs (𝐶 𝑏𝑎𝑡 , 𝐶 𝑃𝑉 , 𝐶 𝑓𝑢𝑒𝑙 ), the CFPs (𝐶𝐹𝑃 𝑏𝑎𝑡 , 𝐶𝐹𝑃 𝑃𝑉 , 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 ) and the lifetimes (𝐿 𝑏𝑎𝑡 , 𝐿 𝑃𝑉 , 𝐿 𝑓𝑢𝑒𝑙 ) related to each component, the discount rate d and the load profile to see how these parameters influence the envelope curve. A value of CFP sensitivity (resp. LCOE sensitivity) to a given parameter X is estimated from the relative slope of the CFP(X) relationship (resp. LCOE(X) relationship) when modifying only this parameter X. For instance, a value of 0.3 for the CFP sensitivity to the fuel cost 𝐶 𝑓𝑢𝑒𝑙 means that an increase of 𝑥% of 𝐶 𝑓𝑢𝑒𝑙 leads to a 0.3𝑥% increase of the least CFP. More details on the method are given in the Supplementary Material (cf. SM 8.2.2). One value of sensitivity is computed for each scenario of location, demand profile, discount rate and parameters related to component (cost, CFP and lifetime) resulting in distributions of sensitivity values associated to each parameter. These distributions are given for the LCOE and CFP of the CFP * and LCOE * configurations in Figure 57. For both the LCOE* and the CFP* configurations, the highest sensitivity is obtained for the capacity factor of the solar resource (CF), followed by the co-variability between the solar resource and the power demand, especially the nocturnal energy demand (NE). A more productive profile needs less storage because the consumption is higher during the day when solar PV produces, so it reduces costs and CFP. The reverse is obtained for a more domestic profile. This is coherent with results described in the results section (cf. Figure 52 and Figure 53).

The CFP* values are obviously not impacted by costs conditions. Similarly, the LCOE* values are not impacted by CFP conditions. For the CFP* (resp. LCOE*) configuration, the sensitivity of the LCOE (resp. CFP) values to lifetimes and costs (resp. CFP) reflects the relative contribution of each component to the total cost (resp. CFP). For instance, the impact related to the cost of PV panels in the LCOE of the CFP* configuration is slightly higher than the one of the batteries (cf. SM Figure 109).

The CFP and LCOE sensitivities of the CFP* configurations are higher than the ones related to the LCOE* configurations. These latter configurations are based on a compromise between solar PV, batteries, and diesel, whereas the CFP* configurations use very little diesel. Thus, the LCOE* configurations can easily adapt to costs variations and lead to lower sensitivities of the LCOE.

Even if some parameters seem to have a lower sensitivity, their importance may not be negligible on the LCOE and CFP values. As an example, the LCOE and CFP sensitivities to battery lifetime or discount rate are very small compared to the capacity factor. However, the capacity factor ranges from 0.14 to 0.21 (x1.5) over the continent, whereas battery lifetime ranges from 2 to 10 years (x5) (due to maintenance issues, temperature and humidity conditions, or overuse [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF]) and discount rate from 8% to more than 30% (x4) (due to type of funding or risks level [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF]). For the configuration considered in the Results section 3.4, a small or moderate increase in LCOE relative to LCOE* can achieve a significant reduction in CFP (cf. Figure 58).

This result, however, does not necessarily hold for all possible costs, CFP, lifetimes, and load profile scenarios. Among the different scenarios considered for the sensitivity analysis, a 10% LCOE increase leads to a CPF reduction higher than 40% in only 20% of the cases (cf. Figure 55). This result may seem disappointing at first. Note, however, that the CFP distance between LCOE* and CFP* configurations depend a lot on the scenario and that for certain scenarios this distance limits the possibility for emissions reductions. A 10% increase of LCOE would, for instance, lead to a CFP reduction lower than 20% in around 30% of the cases. But these 30% decrease to 12% if we remove the configurations in which the CFP distance between the CFP* and the LCOE* is below 20% (cf. SM Table 11). Thus, even if this mean CFP reduction (20%) is quite lower than the one presented in the result section (40%), it is still significant for most of the scenarios considered here.

Note that the configurations that only allow small CFP reduction correspond to low fuel costs (cf. SM Figure 110). For a domestic profile, low CFP reduction potentials correspond to small lifetime and high cost for batteries. For productive and hybrid load profiles, it corresponds to high PV costs and high discount rate. However, scenarios with a low fuel cost, a high cost for PV and a high discount rate do not automatically lead to a small CFP reduction. In our analysis results, only 50% of these scenarios lead to a CFP reduction below 20% for a 10% LCOE increase (cf. SM Table 12). More details can be found in SM Table 12 and SM Table 13.

All in all, a significant CFP reduction can be obtained with moderate additional costs in most of the cases. When this is not the case, this is typically because the CFP distance between the LCOE* and CFP* configurations is already small.

Influence sizing choice

MG developers typically look for the LCOE * configurations to increase profitability and supply electricity at the lowest cost [START_REF]What size shall it be ?[END_REF], [START_REF]IEA PVPS : Mini-réseaux hybrides PV-diesel pour l'électrification rurale[END_REF], [START_REF] Mukoro | A review of business models for access to affordable and clean energy in Africa: Do they deliver social, economic, and environmental value?[END_REF]. Reducing the CFP of MGs compared to this economic optimum implies an increase of the investment costs, whereas access to capital is a well identified obstacle for developers [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF], [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF]. Incentives are needed to favour the development of low CFP MGs.

We evaluate the ambition of the necessary incentives by referring to the shadow carbon price. This method of investment analysis adds a virtual surcharge to the price of carbon emissive projects to supports less emissive projects. It is actually a corporate commitment for all IBRD/IDA investment project financing that are subject to GHG accounting (IBRD: International Bank for Reconstruction and Development, IDA: International Development Association).

The carbon shadow prices required to move the LCOE* configurations to lower CFP configurations are estimated in this section. It is defined as the carbon price that would be necessary to be charged for direct and indirect emissions to ensure that the CFP* configuration, or configurations that reduce the CFP by a certain level (determined a priori) compared to the LCOE* configuration, minimize the LCOE. This is achieved by introducing into the LCOE calculation equation (see section 3.3.2.2) a carbon price (SPC [$/𝑡 𝐶𝑂 2 ,𝑒𝑞 ]) on the diesel consumption and on the CFP of the different components (cf. equation ( 36)). The updated LCOE, to be minimized, reads then as follows:

𝐿𝐶𝑂𝐸 𝑆𝑃𝐶 = 𝐿𝐶𝑂𝐸 + 𝐶𝐹𝑃 * 𝑆𝑃𝐶 (36)
Figure 59 shows the values of the carbon shadow price corresponding to specific levels of CFP reductions. The carbon shadow prices needed to go from the LCOE * to the CFP * configuration are huge, reaching several thousands 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 (cf. Figure 59 left). To give orders of magnitude, to limit warming to 2°C, the carbon shadow price for 2030 estimated by the IPCC (2022) would need to be between 60𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 and 120 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 , and to limit warming to 1.5°C, around 170-290𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. Smaller but still significant CFP reductions are achievable with these shadow prices. A shadow price of 120𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 is sufficient to reduce by more 10% the CFP of the LCOE * configuration, and at 290𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 , this reduction goes between 30 and 40% (cf. Figure 59 right and SM Figure 111). Such values are already used; for instance the current carbon shadow price of the European Investment Bank, which has already invested in energy projects in Senegal and Kenya, was 80𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 in 2020 [START_REF]Climate Bank Roadmap[END_REF]. These shadow prices can be implemented through various public policy tools, including carbon taxes and subsidies, for example, from international funders like the Green Climate Fund, which finances low-carbon projects [START_REF] Green | GCF at a glance[END_REF]. Other funding agencies or even country governments could subsidize MGs with reduced CFP, as it is currently done to lower the cost of electricity [START_REF]SEforALL Africa Hub[END_REF].

Conclusion

Renewable energies are usually considered to be emission-free, but they are not if indirect emissions are considered.

We show that the indirect emissions of PV panels and batteries have a non-negligible contribution to the CFP of MGs with high shares of solar production. They increase the CFP by 15% for systems for which 60% of the demand is supplied by solar energy. Indirect emissions set a threshold of MG CFP below which it is not possible to go, even with 100% solar MG. In Africa, with the mean costs, lifetimes and CFP values for the present time, this threshold varies from 180𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ to 250𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ for a hybrid load profile depending on the location.

Beyond the energy efficiency and the energy mix used for the extraction of materials, manufacturing processes and disposal of solar PV and batteries, this threshold depends on the mean solar resource and the co-variability between the resource and the electrical demand. Regions with higher resource seasonality (Maghreb, South of Mozambique) or with lower solar resource (Central Africa) would have more difficulties to reach a lower CFP level than in the Sahelian region, where the resource is abundant.

When compared to a genset-only configuration, the least LCOE genset/solar/battery configuration allow decreasing both the LCOE (by around 15%) and the CFP (by more than 50%) of the MG. Moving further to the least CFP configuration increase the LCOE. The increase is high (often >20%) considering the low ability to pay of many rural communities in Africa. Smaller LCOE allow significant CFP reduction. In many cases, a 5% LCOE increase is enough to reduce the CFP of the least LCOE configuration by more than 25%, and a 10% LCOE increase by more than 40%.

These results obviously depend on a number of factors, such as the electric demand profile, costs, CFP and lifetimes of each MG component. These factors should be carefully estimated to insure a relevant assessment of MG CFP. Special attention should be paid to parameters with high impacts and high uncertainties, such as the electric load profiles [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Louie | Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability[END_REF], [START_REF] Mandelli | Effect of load profile uncertainty on the optimum sizing of off-grid PV systems for rural electrification[END_REF], or the batteries and project lifetimes that were sometimes observed below two [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], [START_REF] Gustavsson | Lead-acid battery capacity in solar home systems-Field tests and experiences in Lundazi, Zambia[END_REF] and six years [START_REF] Semis | Livrable 2: Rapport d'état des lieux avec les données quantitatives et qualitatives sur l'état de fonctionnement de l'ensemble des ERILs et GDTs[END_REF], [START_REF] André-Bataille | Publication d'une étude de capitalisation de 16 projets d'électrification rurale à Madagascar[END_REF] respectively. The results are also sensitive to the discount rate, which varies greatly depending on project risks and profitability expected by the investors [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF].

Attracting investors in the MG sector is still a challenge [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF], but given the CFP reductions obtained for moderate shadow carbon prices, our results show that climate funds could find interest in MG projects. Following the International Energy Agency [255], MGs are expected to supply around 160TWh in 2040. A 20% reduction of the CFP for the future installed system would lead to more than 13𝑀𝑡 𝐶𝑂 2 ,𝑒𝑞 avoided each year, being more than the yearly GHG emissions of a country such as Gabon (excluding land use change) [256]. Such estimates, although rough, show how important it is to guide MG developers toward low CFP configurations using incentives or regulatory framework. These issues call for more investigations to design suitable policies.

Key messages:

• The indirect emissions of GHG associated to solar power production (PV panels, battery) are not negligible for solar/genset mini-grids • Whatever the location, introducing solar PV in a genset-only MG is valuable for both its LCOE and CFP: in most cases, the least LCOE hybrid configuration allows at least a 20% reduction in LCOE and at least a 60% reduction in CFP.

Introduction

The seventh sustainable development goal (SDG) of the United Nations requires to conciliate a large increase of an affordable energy production to ensure universal access by 2030 with a lower environmental impact of the energy systems [START_REF]UN Sustainable Development Goals[END_REF]. On the one hand, around 730 million of people are indeed lacking access to electricity in the world [START_REF]UN Sustainable Development Goals[END_REF] and more than 80% of them are currently located in Sub-Saharan Africa [13]. On the other hand, among environmental impacts, global pathways likely limiting global warming to 1.5°C require achieving net zero greenhouse gases (GHG) emissions by 2050, with full decarbonization of power systems as a priority [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF].

According to the International Energy Agency, mini-grids (MGs) will play a key role in accelerating the electrification in rural African areas and in reconciling the affordability and sustainability criteria of SDG 7 [13]. A large literature already shows that MGs can supply energy at a lower cost than national grids in many regions [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF], [START_REF] Mentis | The benefits of geospatial planning in energy access -A case study on Ethiopia[END_REF], and the abundance of the solar resource in Africa allows to significantly reduce the carbon footprint (CFP) of these MGs [START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF], [START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF]. However, most of the currently operating MGs rely on both solar and diesel [START_REF]Africa Minigrid Developers Association[END_REF].

Many configurations of solar PV, batteries and diesel genset can indeed supply the energy needed for a community. MG developers can select the configuration to be installed according to different criteria such as the cost of electricity, the carbon footprint or the reliability. In most cases, they seek to minimize the levelized cost of electricity (LCOE) in order to supply electricity at an affordable cost [START_REF]What size shall it be ?[END_REF], [START_REF] Gambino | Methodology for the Energy Need Assessment to Effectively Design and Deploy Mini-Grids for Rural Electrification[END_REF]. These least-cost configurations generally achieve significant CFP reduction compared to a genset [START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF], [START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF], [START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF], but larger CFP reductions should be sought to move towards carbon neutrality.

Some international institutions like the Green Climate Fund invested hundreds of millions of US dollars in low-carbon MGs [START_REF] Green | Energy generation and access[END_REF]. Other programs subsidize 100% solar MGs such as the US$100 million Green Mini Grid Program [START_REF] Hunt | 5 years on from the launch of Green Mini-Grids Africa -what's been achieved, and what have we learned? | Mini-Grids Partnership[END_REF]. National public policies may also be used: South Africa implemented a carbon tax in 2019 to slow the increase in national GHG emissions [START_REF]Carbon Tax | South African Revenue Service[END_REF]. While these examples show a willingness to decarbonize the MG sector, these figures are small compared to the US$190 billion required each year for the energy sector following the IEA [13]. In a financially constrained context such as the MG sector, it seems interesting to estimate what would be the costs to reduce the CFP of MGs.

This reduction cost could be expressed as the economic cost to avoid a ton of CO2, eq. Such reduction cost allows to compare its value to the one calculated for other climate mitigation options, or to estimate the level of carbon tax to foster the rollout of low-carbon systems. Some studies investigated this carbon cost for low-carbon development pathways of different African countries (Ivory Coast [START_REF] Assoumou | Côte d'Ivoire's electricity challenge in 2050: Reconciling economic development and climate commitments[END_REF], Nigeria [START_REF] Dioha | Exploring the energy system impacts of Nigeria's Nationally Determined Contributions and low-carbon transition to mid-century[END_REF], Eritrea [START_REF] Van Buskirk | Analysis of long-range clean energy investment scenarios for Eritrea, East Africa[END_REF]). However, these values refer to the entire energy or electricity system of the country, and the models do not consider off-grid solutions for rural electrification. A few studies integrate the possibility to use MGs in electrification pathways and estimate the carbon tax required to favor renewable MGs over national grid or diesel genset, or to decrease MG emissions with energy efficiency measures [START_REF] Dagnachew | Trade-offs and synergies between universal electricity access and climate change mitigation in Sub-Saharan Africa[END_REF], [START_REF] Deichmann | The economics of renewable energy expansion in rural Sub-Saharan Africa[END_REF]. But these studies do not detail the different hybrid MG configurations, and thus, they do not include the numerous trade-off configurations between costs and GHG emissions (cf. Chapter 3). Such trade-off configurations could significantly reduce the CFP with moderate additional costs (cf. Chapter 3). What would be the cost of carbon for these trade-off configurations?

As highlighted by some studies [START_REF] Dagnachew | Trade-offs and synergies between universal electricity access and climate change mitigation in Sub-Saharan Africa[END_REF], [START_REF] Finon | Carbon policy in developing countries: Giving priority to non-price instruments[END_REF], implementing a carbon tax in the electricity sector of developing countries would increase the cost of electricity for a low-affordability population. Other policies such as subsidies or standards could be imagined reducing the CFP of MGs. But how efficient would be these policies in terms of cost per tCO2 avoided? And how would they share the costs of CFP reduction among the different stakeholders of MGs?

This article aims to help design public policies to reduce the carbon footprint (CFP) of hybrid MGs combining solar PV, batteries, and diesel generators for rural electrification in Africa. One of the original features is to include indirect emissions during the manufacture of solar panels and batteries in addition to direct diesel emissions. To do this, we simulate the sizing of fictitious MG in four countries chosen for their contrasted solar resources end economic context for hybrid MG development: Kenya, Senegal, Nigeria, and Madagascar. In addition to the simulation of individual MGs to estimate how policies could differently affect the CFP of MG, our approach also differs from the literature by including the indirect emissions related to solar PV and batteries (which are not negligible (cf. Chapter 3)) into the calculation of the CFP of MG.

Section 4.3 describes the method used to construct the marginal cost curve for reducing the CFP at a MG level. We first analyze (section 4.4.1) the impact of the variability of the solar resource and of the diesel cost on the dispersion of the marginal costs of carbon between MGs. We also explain how this dispersion impacts the definition of carbon footprint reduction targets at national level. We then compare different tax and subsidy strategies in terms of the costs of carbon (section 4.4.2), as well as the distribution of these costs between MG project stakeholders (section 4.4.3). The robustness of the results obtained is discussed in section 4.5 in the light of the uncertainties relating to the socioeconomic context and the ease of financing these MGs.

Methods

This study is based on the simulation of fictitious hybrid MG configurations using solar PV, batteries and diesel genset. We evaluate the LCOE and CFP of a large range of configurations (share of PV production and storage capacities) to find the CFP of the least LCOE (LCOE*) configuration. The following gives a summary of the methodology for the simulation of MG, (see details in (cf. Chapter 3)) and the methods to evaluate the impact of subsidies and taxation over MG sizing.

Fictitious MG in four countries

We selected four countries as examples for our study: Kenya, Senegal, Nigeria and Madagascar. These countries were chosen for their diversity in terms of surface area, solar resources (cf. Figure 61), and differences in diesel prices which are similar in Kenya, Senegal and Madagascar, but much lower in Nigeria due to local fossil fuel resources and government subsidies [START_REF] Mcculloch | Fuel subsidy reform and the social contract in Nigeria: A micro-economic analysis[END_REF]. To account for the variability of the solar resource within the countries, we considered fifteen or so MGs evenly distributed in each country, i.e., 60 MGs in total (cf. SM Figure 112). The solar PV production for each location is computed using the global horizontal irradiance (GHI) from Heliosat SARAH 2 [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF] and the air temperature from ERA5 reanalysis [START_REF] Wamukonya | Socio-economic impacts of rural electrification in Namibia: comparisons between grid, solar and unelectrified households[END_REF] at 15 min resolution on a two years period (2008)(2009).

The electric demand for all the MG consists in typical load profiles derived from the literature [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Louie | Off-grid electrical systems in developing countries[END_REF], [START_REF] Mandelli | Novel LoadProGen procedure for micro-grid design in emerging country scenarios: application to energy storage sizing[END_REF], [START_REF] Li | Microgrid Load and LCOE Modelling Results[END_REF]. Only a hybrid load profile (i.e., combining domestic and productive uses) with an annual mean power demand 𝐷 ̅ (cf. Figure 62) is used throughout the result section. The domestic load profile has the higher peak power demand and nighttime consumption, whereas the productive load profile has a much higher daily consumption (the dependence of the results to these profiles is discussed in section 4.5.1). The economic, technical, and environmental parameters values (cf. SM Table 15) and all the equations used for these calculations are detailed in Chapter 3.

Marginal cost curves for CFP reduction

As illustrated in Figure 63 for one location in Kenya, a large panel of configurations exists between the LCOE* configuration and the CFP* configuration. In this example, the CFP of the LCOE* configuration can be reduced by around 50% with a 10% increase of the LCOE and a 3% increase of the LCOE is enough to decrease the CFP by 25%. As shown in Chapter 3, this behavior is found almost all over the continent.

It is then possible to calculate the additional cost required to reduce the CFP (including direct and indirect emissions) compared with the LCOE* configuration. This is considered through a shadow carbon price (SPC) (cf. section 3.5.2) taken into account in the LCOE:

𝐿𝐶𝑂𝐸 𝑆𝑃𝐶 = 𝐿𝐶𝑂𝐸 + 𝐶𝐹𝑃 * 𝑆𝑃𝐶 (37)
Considering incremental SPC values, the envelope curve and the corresponding LCOE* configuration are modified. The higher the SPC value, the higher the reduction of the CFP of the least LCOE configuration. This is illustrated on a study case for a fictitious MG in Kenya (-4°N; 38.5°E) in Figure 64. Note that a certain level of CFP reduction can be achieved provided an adequate SPC value is fixed. The value of SPC that is required for a given objective of CFP reduction is called the marginal cost of carbon. It is illustrated for the considered location in Figure 65. Such theoretical marginal cost curves help designing public policies which can take different forms (norms, subsidies or tax). In the following section, we estimate such curves for the 60 MGs.

Results

How to define CFP reduction objectives at the national level?

The four countries considered in the following have different characteristics regarding their solar resource (cf. Figure 61) and as fuel is subsidized in Nigeria, its price is particularly low. This impacts the mean CFP of the LCOE* configurations (cf. Table 5) in each country. This mean CFP is estimated with the mean of the CFP values obtained for the LCOE* configurations identified for the different locations considered in the country (14 for Senegal, 15 for Madagascar and Kenya, 16 for Nigeria). The parameters used for this identification are described in SM Table 15.

The mean CFP is below 470g 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ except for Nigeria where it exceeds 720g 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ. This obviously results from the low fuel cost there, a context which even leads to LCOE* configurations without PV production. The average CFP values obtained for the other countries differ because of the specific solar resources. For example, it is higher in Senegal than in Madagascar.

Within each country, the CFP value differs from one location to the other. The within country differences tend logically to be larger for larger countries as a result of potentially larger spatial differences in the solar resource. For instance, CFP values do not vary a lot in Senegal due to its rather small surface. Specific geographic features can obviously also boost the local variability of the resource. The diversity of climates in Madagascar, due to its island nature is for instance much higher than that in Kenya whereas the surface of both countries is similar.

Table 5 : Some characteristics of the countries studied. The mean capacity factors and their standard deviations are computed only on the locations selected. Surface area values are taken from the World Bank [START_REF]World Bank Open Data[END_REF] and fuel costs from the German cooperation (GIZ) report [START_REF][END_REF]. The characteristics of the solar resource in each location impact also the marginal cost curve for this location (cf. Figure 66). A larger spatial variability of the solar resource directly translates to larger differences between the marginal cost curves to be obtained for different locations in a given area. This variability is expected to influence the implementation of national policies for MG CFP reduction.

Kenya

To achieve a national CFP reduction target, a country can set a standard, i.e., a certain emission level by kWh not to be exceeded, whatever the MG project in the country. It can alternatively set a target to be achieved on average by setting the same marginal costs of CFP reduction for all MG projects within the country.

In countries with a homogenous solar resource, the marginal cost curves for CFP reduction would be very close to each other. A standard would then lead to similar marginal costs for all MGs. On the contrary, if the solar resource is very heterogeneous within a country, the marginal costs when implementing a standard would be very different between the MGs.

The total cost for a country would be lower with an average CFP reduction at the national level, as it allows an equalization of the marginal reduction costs, i.e., using the same marginal cost for all MGs.

For example, imposing a CFP value of 350g 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ for each MG (i.e., imposing a standard) leads to marginal cost between 47 and 88 US$/t 𝐶𝑂 2 ,𝑒𝑞 in Senegal and between 85 and more than 550US$/t 𝐶𝑂 2 ,𝑒𝑞 for Madagascar. Considering an average objective for the country, the marginal cost value for all MGs would be 70US$/t 𝐶𝑂 2 ,𝑒𝑞 in Senegal and 205US$/t 𝐶𝑂 2 ,𝑒𝑞 in Madagascar. In the case of Senegal, the total costs of the policy with a standard are less than 10% higher than with an average objective and a uniform tax, whereas in Madagascar this cost difference is more than 40%. (cf. Table 6). Such issues have to be considered when designing the CFP reduction objectives of public policies. Taking a mean CFP value objective allows to share the efforts between each project to obtain the same final CFP results as shown in Figure 67. Both strategies increase the LCOE of all the projects but using a standard leads to small increases (%) for locations with the best solar resource and much higher increases where the resource is lower (%). In countries with heterogenous solar resource, a standard would strengthen the cost disparities between projects, with much higher LCOE increase for some MG projects. For instance, a few projects in Madagascar (cf. Figure 67) would face a LCOE increase higher than 50% in the case of a standard, whereas the LCOE increase for the same projects would be lower than 25% when using an average CFP reduction objective and a uniform CFP tax. These results both in terms of total cost and cost distribution legitimize to adopt an average target at the level of all MGs in a country. From a more practical point of view, it is necessary to assess how these objectives could be achieved through public policy tools such as subsidies on equipment (batteries and solar panels) or a tax on diesel. In this context, in the next section we compare these incentives that can be effectively implemented to reduce CFP.

How efficient are equipment subsidies or a fuel tax?

Low-carbon incentives already exist in the energy sector in Africa. Many MG projects in Africa benefited from subsidies for initial investments (mostly solar panels and batteries) [START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF], and, in a few countries like Kenya, solar components are exempted from importation taxes to foster the development of solar energy [START_REF] George | Review of solar energy development in Kenya: Opportunities and challenges[END_REF]. Fuels are usually taxed in Africa (e.g., South Africa [START_REF]Treasury on Carbon Tax on Fuel | South African Government[END_REF], Senegal [START_REF] Michaelowa | Etude d'opportunité sur la mise en place d'un instrument de tarification carbone au Sénégal[END_REF] or Kenya [START_REF]Petroleum Development Fund Act -Chapter 426C[END_REF]). In some countries, especially ones with domestic fossil-fuel productions (e.g., Nigeria [START_REF] Mcculloch | Fuel subsidy reform and the social contract in Nigeria: A micro-economic analysis[END_REF]), fuels are subsidized, but reducing these subsidies, as it was done in Madagascar [START_REF] Couharde | Fossil Fuel Subsidies, Income Inequality, and Poverty: Evidence from Developing Countries[END_REF], can be seen as a fuel tax. In this section, we consider three different strategies of incentive:

-Solar PV panels subsidies -Battery subsidies -Fuel tax

To compare the economic efficiency of these different strategies, we estimate the mean cost of carbon avoided. It corresponds to the total costs of the subsidy (or the tax) divided by the number of tons of carbon avoided during the project lifetime (cf. equation ( 38)). ) is the difference between the CFP of the LCOE* configuration without any incentive and the CFP of the LCOE* configuration with the incentive.

𝐶 𝑐𝑎𝑟𝑏𝑜𝑛

The mean cost of carbon avoided for different targets of CFP reduction is illustrated in Figure 68 for the four countries and the three strategies. Figure 68 also highlights the maximum possible CFP reduction in each country. For the fuel tax and subsidy context considered for the illustration, results are similar for Senegal, Madagascar and Kenya but differ significantly for Nigeria. None of the three policies can incite MG developers to select the least CFP configurations, whatever the level of subsidy or tax considered.

Figure 68 : Mean cost of carbon avoided for the three strategies of fuel tax, PV subsidy and storage subsidy. These results are obtained with the parameter values from SM Table 15. The CFP reduction is expressed as the relative change compared to the initial mean CFP of the least LCOE configuration for each country. The red dashed line corresponds to the maximum CFP reduction that can be reached for the country. This maximum CFP reduction is estimated by taking the average of the least-CFP configuration for each MG within a country.

For subsidies on PV or on batteries, the cost of avoided carbon is a function that first decreases, then increases, depending on the mean CFP reduction to be achieved. As low CFP reductions are easy to reach with integration of PV production (cf. Chapter 3), the mean CFP decreases faster than the cost of subsidies increases. When reducing the CFP, the installed PV and battery capacities increases, leading to higher costs associated to each additional percent of subsidy. Moreover, each additional percent of CFP reduction requires even larger increase of PV and/battery capacity. For large levels of CFP reduction, the costs of subsidies increase therefore faster than the decrease of the CFP, increasing in turn the mean cost of avoided carbon. Note that very large subsidies on battery (>80%) would favor battery development at the expense of PV panel capacity, having in turn counterproductive effects on the CFP.

While batteries are the least costly solution for CFP reductions of up to around 30%, the taxation of diesel is more efficient to reach higher levels of CFP reduction. Increasing the level of fuel taxation logically reduces diesel consumption and in turn the MG CFP. For high CFP reduction levels however (e.g., 40% reduction or more), the diesel consumption becomes very small and further increasing fuel taxation has roughly no more effect.

For smaller CFP reduction levels (e.g., around 30-35%), the least cost strategy is the fuel tax (around 50% tax level). It is however probably not the easiest to implement. Given the low revenues of the population to electrify and the current difficulties of MG developers to attract investors, this strategy may come up against the population acceptability, willingness, and ability to pay. Moreover, implementing a fuel tax that only applies to electricity generation and not to transport is likely difficult.

A strategy based on subsidies is not without its obstacles. Subsidies require government spending, which must be financed either by taxation or by the deficit. MG component manufacturers may first pocket all or part of the subsidy (windfall effect) and reduce in turn the policy's impact. Some governments are often reluctant to give public funds to private MG developers. However, these subsidies could also be implemented using external funding, independently from governments via international organizations such as development finance institution or funds for climate mitigation. These questions show that the way in which costs are shared between MG developers, funders, public institutions and users is an important issue for the effective implementation of these policies.

Sharing the costs of CFP reduction among stakeholders: an important issue

In this section, we keep the fuel taxation strategy and consider two new strategies to illustrate how the costs of a CFP reduction policy can be shared. To do so, we decided to set a common objective of 35% of CFP reduction for each country. They are:

-The "Tax" strategy: it is a fuel taxation only strategy, the same as in the previous section. The tax is paid by the operator of the MG who would transfer it to users though higher tariff of electricity. -The "Sub" strategy consists in subsidies only, for both PV panels and batteries (it differs from the previous strategies as it combined the subsidies on PV and on batteries). In this case, the subsidy cost is borne by public institutions or by international funds for development or climate, but as a result, the electricity tariff could be lower. -The "Bonus/Malus" strategy consists of a combination between fuel taxation and subsidies for solar PV and batteries. It allows to share the cost between the MG developers and operators, users, public institution and/or international funds.

In addition, we compare these strategies to a business as usual ("BAU") strategy, a strategy without any policy for CFP reduction.

The level of subsidies/taxations required in each strategy to ensure a mean 35% CFP reduction for each country is summarized in Table 7. As presented in the previous section, fuel taxation levels required to reach the -35% objective are between 45 and 55% and subsidies on batteries are more efficient than subsidies on PV for the "Sub" strategy. These levels of taxations and subsidies are reduced when combined in the "Bonus/Malus" strategy.

In Figure 69, we compare the impacts of each strategy on the investment costs (CAPEX), the operational costs (OPEX) and the LCOE.

strategies ("BAU"," Tax", "Sub" and "Bonus/Malus"). These costs are only referring to the configuration changes without the effect of subsidies and taxation on the final costs. The LCOE modifications only related to the configuration change correspond to the height of the blue and yellow bars. The means are computed as the average costs for the 14-16 MG in each country. The red bar extension corresponds to the effect of fuel taxation (cost increase) and the red frame corresponds to the effect of subsidies (cost reduction). Green bars correspond to the LCOE values, including subsidies and taxation effects.

Any policy strategy is expected to a change in the "optimal" MG configuration, i.e., in the capacity of PV panel and batteries and in the share of PV/genset production. Considering only the effects of the configuration change (i.e., without equipment and fuel costs modifications), the average LCOE increases by around 5% compared with the BAU case.

In the "Tax" strategy, this increase is reinforced by the effect of the rise in the cost of diesel, resulting in an increase in LCOE of around 10 to 20% compared with the BAU strategy. On the contrary, in the "Sub" and "B/M" strategies, subsidies compensate the additional costs related to the configuration changes. The "Sub" (resp. "Bonus/Malus") strategy allows to decrease the LCOE by 5% to 17% (resp. 3% to 10%).

The three strategies logically increase the CAPEX compared to the BAU case because of increased PV and storage capacities. The CAPEX increase depends on the initial MG configurations of the BAU case.

It is here for instance +37% for Kenya to +100% for Nigeria. The more BAU MG relies on diesel, the larger is the relative increase of CAPEX. The CAPEX increase is partially compensated by an OPEX decrease due to the reduction of the genset use.

As tax only targets the diesel consumption, it does not amplify the CAPEX increase due to configuration change, but it increases the OPEX and the LCOE. In the other strategies, the CAPEX increase due to configuration change is partially covered by subsidies and OPEX decrease due to the reduction of the costs for batteries replacement.

As explained in section 4.4.1, these changes can be very different from one MG to the other, even within a same country. Figure 70 presents the CAPEX, OPEX and LCOE variations for each MG and strategies. Implementing the « Tax » strategy leads to very high LCOE increase (+27%) for the MG running exclusively on diesel and lower LCOE increase (+8%) of MG with high penetration of solar. The "Sub" strategy decreases likewise the cost for MG with a large share of solar and has almost no effect on the LCOE of the ones relying mostly on the genset. If these costs change are transferred to the electricity tariffs, this would increase the inequalities of access to electricity by favoring communities where the solar resource is better to the detriment of the communities with a lower resource. But such inequalities could be reduced by implementing a tariff equalization among the communities.

The costs of policies such as those discussed above could be optimized. In all cases however, one challenge of such policies could be to share the costs of CFP reduction policies among stakeholders and among the diverse MG projects in a same country. Depending on the strategy chosen, the stakeholders who bear the costs of the policy are very different. Thus, it seems important to design the policy following the desired cost sharing, instead of focusing only on maximizing the economic efficiency (i.e., cost minimization) of the policy.

Discussion

Governments or funders could adopt different strategies to incite MG developers to reduce the CFP of their systems. As illustrated previously, costs for the CFP reduction could be shared in different ways between the state, the funders, the users, and the developers. The most impacting policy strategy is expected to depend on many features, including solar resource and variability, population needs, socio-economic constraints. These characteristics are subject to large uncertainties. In the following, we explore how robust the policies could be in such a context.

The robustness of public policy

Due to the large variability of these characteristics, it is hard for the designer of the public policy to estimate the values of the different parameters to calculate the LCOE and the CFP. As examples, the CFP values of solar PV and batteries are highly dependent on the manufacturing processes and difficult to estimate [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF]; installation and maintenance costs can differ a lot from one location to another depending on local constraints and climate, location accessibility, etc. Load profiles are also very variable due to the diversity of communities and their electricity uses.

Given the difficulty of accurately estimating all parameters required to determine cost and CFP [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Bank | Benchmarking study of solar PV mini grids investment costs[END_REF], we evaluate the robustness of the different policy strategies to different scenarios of costs and load profiles (socio-economic alternatives). We assume here that the policy maker uses the assumptions of section 4.3 and SM Table 15 to calibrate its policy to reach a relative CFP reduction of -35%, the level of subsidies and taxes are thus the same as Table 7. But we consider four scenarios where the socio-economic context is actually different from what the policy maker expected. These four scenarios are presented in Table 8 and differs by the load profiles, costs, and CFP. Two scenarios ("Domestic" and "Productive") rely on the same costs and CFP values as in the "Reference" scenario but have different load profiles. Due to its larger consumption during the night, the "Domestic" scenario is less favorable to solar energy than the "Productive" scenario that has a larger consumption during the day.

The "Best for ren" scenario consists in lower costs and CFP for solar PV and batteries, and higher cost and CFP for diesel production. Thus, this scenario is more favorable to renewable energy than the "Reference" scenario. Inversely, the "Worst for ren" scenario consists of higher costs and CFP for solar PV and batteries, and lower costs and CFP for diesel production.

Figure 71 gives the mean CFP obtained in the BAU strategy for the different scenarios. As expected, scenarios that are less favorable to solar energy ("Worst for ren" and "Domestic") lead to configurations with a larger share of diesel and much higher CFP values (usually more than 50%) than in the "Reference" scenario. The CFP reductions achieved with the different strategies for these scenarios are presented in Figure 72.

Considering scenarios with costs and CFPs alternatives, results are different depending on the countries. Apart from Nigeria, the "Best for ren" scenario leads to relatively low CFP reduction: the initial CFPs of the BAU case are already low (cf. Figure 71), it is thus difficult to further reduce the CFPs.

In Nigeria, the BAU CFP stays relatively high with the "Best for ren" scenario, hence the larger CFP reductions obtained in Figure 72.

On the contrary, no CFP reduction is obtained in Nigeria with the "Worst for ren" scenario. The "Reference" scenario is already much more favorable to diesel production, and this is amplified by the assumptions of the "Worst for ren" scenario to the point that the development of solar energy is blocked. For the other countries, especially for Madagascar and Kenya, the large share of diesel in the LCOE* configurations of the BAU case gives a larger margin for CFP reductions when applying subsidies or taxes, resulting in larger CFP reductions.

Looking at the electric demand profile alternative, the "Productive" scenario leads to similar results as the "Best for ren" scenario as it also favors solar energy: the CFP of the BAU case is already low, thus the CFP reduction achieved is also low. As for the "Domestic" scenario, CFPs of the BAU case are high (cf. Figure 71) but integrating more solar energy requires larger storage capacities due to the higher night-time consumption, hence the difficulty to reduce the CFP. We now analyze the impact of the different public policy strategies according to socio-economic assumptions. The sensitivity of the CFP reduction to the socio-economic scenario is quite similar for the three strategies, but policy costs (the total amount of the tax and the total amount of the subsidies at the national level) for each strategy depend on socio-economic assumptions (cf. Figure 73). The lower diesel consumptions in the "Best for ren" and "Productive" scenarios lead to lower costs related to fuel taxes. On the contrary, "Worst for ren" and "Domestic" scenarios favor larger diesel consumption and lead thus to higher costs related to the tax. This cost increase is very high (more than 200%) in Senegal and Kenya where the share of genset is low in the "Reference" scenario.

Apart from Nigeria, the subsidy costs are almost always equivalent or lower than in the "Reference" scenario. In the "Worst for Ren" scenario, the PV and batteries capacities installed are much lower leading to a lower cost for the subsidies. In the "Best for Ren" scenario, larger PV and batteries capacities are installed but their costs per unit is lower, these effects compensate in the total cost for subsidies. For the "Domestic" and "Productive" scenarios, the opposite variations of the installed capacities (less solar and more storage or the opposite) lead to subsidy costs that compensate. Finally, in a context favorable for solar energy ("Best for Ren"," Productive"), even if the CFP reduction objective is not achieved, the absolute values of MG CFP are already close to the least CFP values, and the costs for subsidies are usually lower than what expected. Thus, it only leads to benefits for the developers who can decrease their generation cost of electricity.

In the "Worst for ren" and "Domestic" scenarios, the policies may not be sufficient to achieve the CFP reduction objectives and the strategies with taxes would lead to very high increase of the tax costs that are borne by the MG operator and/or the users. Thus, it seems better to use the "Sub" strategy to avoid these potential negative effects of the strategy using taxes.

Note that if the "Best for ren" and "Worst for ren" scenarios are constrained by a global economic context, the different stakeholders of MG project could work on the electric demand profile to head towards a more advantageous scenario. The "Domestic" scenario could, for instance, be avoided by promoting the productive uses of energy as many papers already suggest for lowering the LCOE and increase the income generating activities [START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF], [START_REF] Lukuyu | Building the supply of demand: Experiments in mini-grid demand stimulation[END_REF], [START_REF] Agenbroad | Minigrids in the money : Six ways to reduce minigrids cost by 60% for rural electrification[END_REF]. Such policies to foster productive uses of energy would also help MG developers to attract funds for the development of MG project, which are currently difficult to finance.

The impact of the financial framework

In Sub-Saharan Africa, access to capital for MG development is quite difficult due to risks associated to the rentability / reliability of the projects (possible future competition with future grid extensions, ability to pay of low-income populations, possible instability of political context and lack of clear policies, etc.) [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF], [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF], [START_REF] Williams | Enabling private sector investment in microgrid-based rural electrification in developing countries: A review[END_REF]. Most funds go then to grid connected projects, less risky and having usually shorter payback time. Attracting investors may require increasing the profitability of the projects. However, this is not always possible due to low-income levels and regulations that may limit electricity tariffs for MGs in order to avoid excessive differences with the national grid.

Accessing to funds is additionally not always easy as some institutions prefer result-based financing, providing funds only after all users have been connected. Financing the CAPEX of MG projects can thus be difficult, leading MG developers to select a trade-off between CAPEX and LCOE instead of the LCOE* configuration [START_REF] Fioriti | Coupling economic multi-objective optimization and multiple design options: A business-oriented approach to size an off-grid hybrid microgrid[END_REF]. The LCOE* configuration may in fact have a fairly high CAPEX, while other configurations could reduce this CAPEX while slightly increasing the LCOE. If the difficulty to access capital is not correctly identified when designing the policies, the CFP reduction envisaged by the strategies may not be achieved.

To simulate the potential impact of the difficulty of accessing capital on the reduction in CFP, we use various assumptions for the discount rate used in the calculation of LCOE. An increase of d means that funders are more reluctant to invest capital and the access to capital is more difficult for MG developers. Figure 74 shows how these variations of discount rate affect the mean CFP of the LCOE* configurations for the different strategies. A higher discount rate would increase the relative share of capital costs in the project's costs and vice versa. For this reason, higher discount rates lead to LCOE* configurations with more fuel and higher CFP. Without any policy and considering our cost assumptions, a discount rate higher than 0.25 leads to diesel-only configurations for almost all MGs, no matter the country. Above this discount rate value, the strategies with taxations, especially the "Tax", seem more robust to discount rate variations than the "Sub" strategy. Between d=0.1 and d=0.25 and apart from Nigeria, the three strategies ("Tax", "Sub" and "B/M") do not achieve the objective of 35% CFP reduction but stay close to 30% CFP reduction.

On the other hand, lower discount rate would lead to MGs with lower CFP. In the BAU case, going from d=0.1 to d=0.03 as in Europe [START_REF] Victoria | Early decarbonisation of the European energy system pays off[END_REF] decreases the CFP by around 20% (30% in Nigeria). Combined with the other strategies, such a discount rate reduction leads to a mean CFP close to the least CFP values that can be achieved in Kenya, Senegal and Madagascar. Moreover, decreasing the discount rate also leads to a decrease in the LCOE of MG, between 15% and 20% by going from d=0.1 to d=0.03 (cf. SM Figure 114). A large literature already highlighted the need to decrease the risks related to electrification projects and reduce the obstacles to investments [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF], [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF], [START_REF] Williams | Enabling private sector investment in microgrid-based rural electrification in developing countries: A review[END_REF]. This could be done, for instance, by defining clear regulations on electricity tariffs setting and concurrence with the national grids, by supporting productive use of energy and anchor customer or by stimulating local investors.

Conclusion

This paper illustrates various strategies of public policies to lower the CFP of MG using economic incentives. These strategies consist in subsidies on solar PV or batteries and/or fuel tax to drive MG developers towards low CFP configurations.

By simulating 60 fictitious MG scattered over four countries (Kenya, Senegal, Nigeria, and Madagascar), we show that the marginal carbon costs to reduce the CFP of MGs differs between countries but also within a country between individual MG projects because of the diversity of their solar resource. In a country like Nigeria, diesel price is so low that genset-only configurations are the configurations with the lowest LCOE value for some locations. In countries with very distinct climate zones like Madagascar, the marginal cost of carbon varies a lot between locations. On the contrary, in countries with rather homogenous climate conditions and especially solar resources, as in Senegal, the marginal cost of carbon does almost not vary in space. These specific features should be considered when defining national CFP reduction objectives, as a mean CFP reduction objective for the whole country allows this diversity to be used: further CFP reductions can be achieved where it is cheaper, and these high CFP reductions can compensate for lower ones where conditions are less favorable.

Then, we compared the mean cost of carbon avoided when implementing different incentive strategies to reduce the CFP of MGs. We showed that subsidizing solar PV is not the more cost-efficient way to decrease emissions, and that, depending on the CFP reduction objective targeted, subsidies on battery or fuel taxation should be preferred (<150US$/𝑡 𝐶𝑂 2 ,𝑒𝑞 with our parameter values). When applied alone, none of these strategies can achieve the maximum CFP reduction. Combining these strategies allow to share the costs of the policy among the different MG stakeholders.

Subsidizing PV panels and batteries will reduce both the CFP and the LCOE whereas a tax on fuel will increase the LCOE. On the one hand, costs of subsidies are borne by development finance institutions or by the state that may transfer these costs to the population via taxes or tariff equalization. On the other hand, costs of taxes are borne by the MG operator who can report this cost increase on the users. A bonus/malus strategy that subsidizes solar equipment (PV and battery) and partially covers these costs by using revenues from a fuel tax could be an interesting trade-off. Designing CFP reduction policies cannot be only based on the search of the more efficient tools in terms of cost, but it should consider how the costs would be distributed between the stakeholders, and between the different MG projects as well.

The CFP reduction obtained with the three strategies ("Tax", "Sub" and "Bonus/Malus") proposed in this work are highly dependent on a good identification of the initial context (cost for each component and load profiles). In a context that is more favorable for solar energy than expected (low costs for solar and batteries or productive load profile), low CFP reductions are obtained because the CFP of the LCOE* configurations are already low without subsidies or taxation. In a more unfavorable context for solar energy, CFP of LCOE* configurations are higher, and the CFP reduction are lower than expected. When taxes are implemented in such scenarios, the costs related to these taxes can double or even triple for the MG operators, whereas the costs related to subsidies are usually lower than expected.

Thus, the "Sub" strategy seems more robust when the socio-economic context of the MG is not well known. Moreover, it allows to partially compensate the CAPEX increase due to the integration of more solar energy.

Going towards MG configurations with lower CFP requires indeed to increase the CAPEX, which is hard to fund in the current MG financial context. In addition to the design of incentives on PV, battery and fuel costs, it is possible to reduce the CFP of MGs by decreasing the risks associated to MG projects.

We show that combining one of the strategies proposed in this article with a very low cost of capital almost allows to reach the least CFP values for some countries. On the contrary, the lack of clear regulations and the search of high profitability on the short-term tend to reduce the integration of solar energy and lead to higher MG CFP.

Even if we tried to have a diversity of climate and economic contexts with our four country examples, further research is required to extend our analysis to more countries with different contexts to see how our results are generalizable. Moreover, the different costs and CFP assumptions should also be more specific to each country.

This paper only touches upon the importance of the environment in which MG are developed, and other articles already shows the complexity surrounding the development of MG for rural electrification in Africa [START_REF] Njoh | Implications of institutional frameworks for renewable energy policy administration: Case study of the Esaghem, Cameroon community PV solar electrification project[END_REF]- [START_REF] Falchetta | The role of regulatory, market and governance risk for electricity access investment in sub-Saharan Africa[END_REF]. The design of suitable policies needs to integrate this complexity by considering aspects such as the low affordability of newly electrified populations, the difficulties to finance projects both at the beginning and on its whole lifecycle, the current regulations, and institutional practices. For instance, assuming that MG developers always select the LCOE* configuration seems a very simple hypothesis and improvements have to be done in understanding what are MG developer practices when sizing MG.

Finally, the work presented here with fictitious MGs is a first step to illustrate how to quantify and optimize economic incentives to reduce MG CFP considering economic efficiency (cost minimization) and distributive impacts among stakeholders. This approach needs to be followed up by one that is closer to real conditions on the field: locations selected on the basis of the areas that really need electrification and the amount of energy potentially consumed in these regions. Results for each country are obviously dependent on the solar resource of the selected locations and the average of the MG CFP should be weighted by the estimated energy consumption of each MG. Better defining MG locations and the energy that has to be supplied could also allow to better estimate the costs and load profile differences between locations.

Key messages:

• The solar resource variability and the different economic context imply large heterogeneity in the efforts required to reduce the CFP of MGs between projects • Setting a national CFP reduction objective should be preferred to a CFP standard for all MGs • Fuel taxation and battery subsidies are more efficient incentives to reduce the CFP of MGs than subsidies on PV panels • Depending on the strategy chosen, the stakeholders who bear the costs of the policy are very different, potentially leading to acceptability challenges • Reducing the investment risks associated to MG projects is a major potential lever to reduce their CFP 104

5 Institutional constraints of mini-grid sizing

Context and objectives

Designing such CFP reduction policies also requires knowing the different constraints each stakeholder, in particular the MG developers and operators, have to face during the whole lifetime of MG projects. Even if, in theory, some strategies seem to be more efficient in terms of cost per ton of CO2 avoided or better in terms of cost sharing, their practical feasibility from each stakeholder's point of view must be assessed. For instance, if subsidies on solar components may decrease the costs for developers and users, it may be hard for African governments to find funds to subsidize these infrastructures. Moreover, governments could be reluctant to give these funds to private MG developers.

In such cases, governments could prioritize the reduction of the risks related to MG project by defining clear regulations or supporting local investors to develop income generating activities related to agriculture or crafts (cf. section 1.3.1). Again, reducing the investment risks requires to better understand the broader context of MG project development for rural electrification. In this context, we here focus on the following questions:

• How do MG developers and other stakeholders of MG project deal with these risks, and how does it impact the sizing of these MGs? • How do the financial and regulatory frameworks affect the leeway of these different stakeholders?

In the following analysis, we let behind the simulation of fictitious MGs and the quantifications of their LCOE and CFP to adopt a qualitative approach using interviews, document analysis and field observations in Kenya. All aspects of this study are detailed below in the form of an article: T. Chamarande

Introduction

"Sizing is more of an engineering problem" said one representative of an African regulatory energy authority, evading our question related to the role of the public sector in isolated mini-grids21 (MGs) sizing. Academia, public authorities, funding agencies, indeed tend to consider MGs sizing mostly through technical lenses that need to align with economic constraints, to electrify as many people as possible with the least costs. 600 million Sud-Sahara Africans are lacking electricity [13]. In rural areas, only 25% of them have access to electricity [13]. The decreasing costs of photovoltaic (PV) panels [START_REF]Renewable Power Generation -Costs in 2020[END_REF] makes solar off-grid systems cost-competitive in rural areas [13], [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF], [START_REF] Mentis | A GIS-based approach for electrification planning-A case study on Nigeria[END_REF] compared with grid extension. International programs such as Sustainable Energy For All [START_REF] Seforall | Sustainable Energy for All[END_REF], the Green MG Program [START_REF]SEforALL Africa Hub[END_REF], Power Africa [281], Lighting Africa [282] favor three kinds of solar solutions to reach the seventh Sustainable Development Goal (SDGs) of the United Nations [START_REF]UN Sustainable Development Goals[END_REF], dedicated to energy: Solar Home Systems (SHS) and stand-alone systems for scattered households and single users such as schools, and MGs for large and dense villages. MGs can supply relatively large amount of energy for productive activities such as welding, pumping, or milling compared with SHS and stand-alone systems. In addition, MGs might foster energy justice compared with large grid-utility solar plants [START_REF] Sareen | Bridging socio-technical and justice aspects of sustainable energy transitions[END_REF]. Therefore solar MGs have become a mainstream option for rural electrification: more than two thousand MGs have been installed in Sub-Saharan Africa [START_REF]State of the Global Mini-grids Market Report 2020[END_REF] and the International Energy Agency estimates that MGs are the best option to electrify more than 200 million people by 2030 in this continent [13].

Proper MG sizing is crucial: enough capacity must be installed to ensure a reliable electricity supply for users, but not too much to minimize generation costs and electricity tariffs. International institutions and academics have published many guides to calculate the number of PV panels and batteries to electrify a community with minimal costs [START_REF] Louie | Off-grid electrical systems in developing countries[END_REF], [START_REF]What size shall it be ?[END_REF], [START_REF]IEA PVPS : Mini-réseaux hybrides PV-diesel pour l'électrification rurale[END_REF], [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF], [START_REF] Gambino | Methodology for the Energy Need Assessment to Effectively Design and Deploy Mini-Grids for Rural Electrification[END_REF], [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF], [START_REF]Energy Sector Management ASsistance Programme[END_REF]. All these guides present similar steps. First, the MG developer estimates the electrical demand to draw a load curve, with visits and on-site surveys in the community. These tools assess electricity-intensive activities, existing alternatives such as SHS or diesel generators (genset) and potential users' ability and willingness to pay. The developer also quantifies solar radiation and shading patterns to supply this demand [START_REF] Esmap | Global Solar Atlas[END_REF]- [START_REF]PVsyst -Logiciel Photovoltaïque[END_REF]. Finally, the developer collects financial data such as the costs for physical assets (PV panels, inverters, distribution grid, etc.), for operation and maintenance, for capital, etc. These data feed numerical models, ranging from simple Excel calculation sheets to highly detailed software such as the well-known HOMER software [START_REF]REopt Evaluates Centralized and Decentralized Microgrids in Sub-Saharan Africa | NREL[END_REF], [START_REF]Government of Canada[END_REF], [START_REF]HOMER Pro -Microgrid Software for Designing Optimized Hybrid Microgrids[END_REF], [START_REF]Mini Grid Builder | Web based mini grid tool[END_REF]. A large academic literature explains how to increase the accuracy of these simulations, how to reduce computational time or to improve results robustness [START_REF] Micangeli | Energy Production Analysis and Optimization of Mini-Grid in Remote Areas: The Case Study of Habaswein, Kenya[END_REF], [START_REF] Abada | An innovative approach for the optimal sizing of mini-grids in rural areas integrating the demand, the supply, and the grid[END_REF], [START_REF] Frimpong | A Comprehensive Review of Nature-Inspired Search Techniques Used in Estimating Optimal Configuration Size, Cost, and Reliability of a Minigrid HRES: A Systemic Review[END_REF], [START_REF] Cicilio | uGrid: Reliable Minigrid Design and Planning Toolset for Rural Electrification[END_REF], [START_REF] Fioriti | Stochastic sizing of isolated rural mini-grids, including effects of fuel procurement and operational strategies[END_REF], [START_REF] Chaware | Design and Optimization of Mini-grid PV System for Developing Country[END_REF]. Most of these models look for the "optimal sizing", i.e. the configuration with the least levelized cost of electricity, but some include other indicators such as investment costs or environmental impacts [START_REF] Das | Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh[END_REF], [START_REF] Nsafon | Integrating multicriteria analysis with PDCA cycle for sustainable energy planning in Africa: Application to hybrid mini-grid system in Cameroon[END_REF], [START_REF] Ullah | Multi-criteria decision-making model for optimal planning of on/off grid hybrid solar, wind, hydro, biomass clean electricity supply[END_REF], [START_REF] Fioriti | Multiple design options for sizing off-grid microgrids: A novel single-objective approach to support multi-criteria decision making[END_REF]. A MG business model is eventually built from these estimations.

Considering the abundant literature on this topic, sizing MG seems quite well understood. Nonetheless, numerous MGs have a shortened lifetime compared to the theoretical 20 years lifespan, with a critical threshold around six years [START_REF] Semis | Livrable 2: Rapport d'état des lieux avec les données quantitatives et qualitatives sur l'état de fonctionnement de l'ensemble des ERILs et GDTs[END_REF], [START_REF] André-Bataille | Publication d'une étude de capitalisation de 16 projets d'électrification rurale à Madagascar[END_REF]. Sizing is stressed as a major risk [START_REF] Hazelton | A review of the potential benefits and risks of photovoltaic hybrid mini-grid systems[END_REF]: undersized MGs deteriorate rapidly as electricity over-consumption damages components such as batteries [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], while oversizing may impair MG financial viability [START_REF]Hybrid Mini-grids for rural electrification : Lessons learned[END_REF]. Referring to the sizing of a MG in Kenya, one of our interviewees declared that "we were very lucky because reality appeared quite close to our estimation". Building on multiple sizing tools and decades of feedback, how can we understand that sizing is merely a matter of "luck"? How does "reality" and "estimation" interact with each other, through tools, uncertainties, constraints and adjustment strategies?

We answer this question by mobilizing insights from management studies that we briefly introduce in our literature review (section 5.3). After describing our methodology and the Kenyan context (section 5.4), we detail how developers face constraints to design MG (section 5.5). In 5.5.1, we show how these constraints merge uncertainties around demand estimation, funding and regulatory aspects. Sub-section 5.5.2 analyzes how public and private developers adapt their methods and business models to deal with uncertainties and conflicting constraints. In the last results sub-section 5.5.3, we discuss strategies to recover the equilibrium between electricity production, consumption and economic viability in under and oversize situations. We discuss results in section 5.6: we conclude that MG design is mostly considered as a one-shot issue due to unsuitable regulatory and funding context, resulting in transferring most risks on developers and operators, with a knock-on effect on rural endcustomers.

Risks and uncertainties management in the literature

MGs are expected to play a key role in Africa's electrification but they receive only 1% of electricity investments [START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF]. Whereas large grid-connected production plants attract private investors and lenders, the MG sector still relies heavily on grants from foreign governments and Development Finance Institutions. Scholars have identified multiple barriers for MG investments, such as the high level of risks (mostly related to technical, financial, social aspects), the low profitability and the lack of clear regulatory framework [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF], [START_REF] Williams | Enabling private sector investment in microgrid-based rural electrification in developing countries: A review[END_REF], [START_REF] Falchetta | The role of regulatory, market and governance risk for electricity access investment in sub-Saharan Africa[END_REF], [START_REF] Hazelton | A review of the potential benefits and risks of photovoltaic hybrid mini-grid systems[END_REF]. Gregory and Sovacool [START_REF] Gregory | Rethinking the governance of energy poverty in sub-Saharan Africa: Reviewing three academic perspectives on electricity infrastructure investment[END_REF] show for example the complexity of the electrification financial context with fifteen issues that negatively impact investors. They advocate for financial, political, and technological governance schemes to be implemented by governments and funding agencies.

A large literature analyses risk management of investment projects. These methods are based on real options [START_REF] Cuervo | Photovoltaic power purchase agreement valuation under real options approach[END_REF], [START_REF] Markham | The application of real options to renewable energy investments in South Africa: the case of solar energy technology for small businesses and individual homeowners[END_REF], adaptive pathways [START_REF] Prasad | Irrigation development under uncertainty: A call for adaptive investment pathways[END_REF], [START_REF] Gibberd | Anticipating and Preparing for Future Change and Uncertainty: Building Adaptive Pathways[END_REF], or stochastic dynamic modelling [START_REF] Lara | Electric power infrastructure planning under uncertainty: stochastic dual dynamic integer programming (SDDiP) and parallelization scheme[END_REF]. Building on the idea that as the project progresses, uncertainties decrease but so do available options (cf.

Midler curve [START_REF] Reverdy | Antimanuel de management de projet[END_REF]), these methods look for the best timing to take irreversible decisions such as investments. As an example, uncertainties on MG sizing disappear after the system installation, while the relative irreversibility of such action reduces the possibility to adapt the electric production to the demand. These approaches rely on the quantification of the uncertainties surrounding the project, thus requiring a good knowledge of the "known unknows" [299]. Those "known unknows" refer to identified risks and their impacts, such as the arrival of the grid for a MG project that can be anticipated to some extent [START_REF] Gentil | Les « agencements organisationnels » des situations perturbées : la coordination d'un bloc opératoire à la pointe de la rationalisation industrielle[END_REF].

On the contrary, those methods are not suitable for "unknows unknown" such as 100-year storms, because their low probability of occurrence usually exclude them from risk analysis [299]. These events act as "surprises" [START_REF] Bechky | Expecting the Unexpected? How SWAT Officers and Film Crews Handle Surprises[END_REF], whose causes and consequences can hardly be anticipated. However, specific forms of organization or project management can help to cope with "surprises", such as parallel projects [299], "agile" methods [START_REF] Geraldi | The Titanic sunk, so what? Project manager response to unexpected events[END_REF] or "resilient" management [START_REF] Gentil | Les « agencements organisationnels » des situations perturbées : la coordination d'un bloc opératoire à la pointe de la rationalisation industrielle[END_REF]. The idea is to rely on wellestablished partnerships and communication to quickly respond [START_REF] Bechky | Expecting the Unexpected? How SWAT Officers and Film Crews Handle Surprises[END_REF], [START_REF] Geraldi | The Titanic sunk, so what? Project manager response to unexpected events[END_REF]. Those methods have burgeoned in software development and computing, but they may also be used for infrastructure building through incremental design with frequent tests and evaluation by future users [START_REF] Sakikhales | Using Agile Project Management and BIM for Improved Building Performance[END_REF].

These coping strategies also require a common goal among stakeholders and cooperation in adversity. Still, a lot of projects, such as private MG, gather entities with (potentially) competing objectives.

Cooperation issues have been widely studied in the literature referring to the stakeholders' theory.

Ward and Chapman (2008) [START_REF] Ward | Stakeholders and uncertainty management in projects[END_REF] stressed for example how multiple stakeholders increase the level of uncertainties, as each stakeholder influences the project based on hidden vested interest. Methodologies exist to identify stakeholders and to define ways to deal with their expectations [START_REF] Ward | Stakeholders and uncertainty management in projects[END_REF], [START_REF] Olander | Stakeholder impact analysis in construction project management[END_REF], as stakeholders' identification is not always straightforward. Analyzing the MG ecosystem in Kenya, we define five main stakeholders: MG developers, operators, MG user, regulators, and funders.

MG developers refer to the primary organization (usually a private company, a Non-Governmental Organization (NGO), or a public utility) who initiates the project up to the MG commissioning. They look for seed funding, design the MG, obtain the licenses from the regulators and install the MG. They handover the MG to the operator. This second actor (usually a private actor, public utility or community-based organization) sells electricity to the customers and maintains the system in working order, thanks to so-called "cost-reflective tariffs". Thirdly, customers, or MG users, consist of households, small businesses, or community services (health center, school, public lighting, etc.) connected to the MG. The fourth type of stakeholders is made of regulators. Regulators refer to national public institutions overseeing the MG compliance with norms and standards related to electricity tariffs, quality of service electricity or environmental impacts. In Kenya, the main one is EPRA, the Energy and Petroleum Regulatory Authority. Finally, funders gather both public and private institutions providing grants, equities or loans for the MG [START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF]. In practice, a unique entity can have more than one role, being for example the MG developer, operator and partial funder through equity.

MG ecosystems is thus made of stakeholders with different roles and objectives. In the Kenyan MG sector, what kind of risks do these stakeholders face? How do the nature of the risk, but also organizations schemes and financial constraints, shape risk management and anticipation strategies for each stakeholder?

Methodology and Kenyan context

Kenya is a particularly interesting country to study MG, thanks to its long-term experience with MG and its variety of MG actors. Up to the 1990s, electrification was mostly a public matter. The Republic of Kenya promoted electrification of rural areas to foster economic activities: basic infrastructures such as electricity was presented as a way to develop so-called "rural trade and production centers", with the final objective to slow migration from rural areas to urban areas [306]. The national electricity company Kenya Power and Lighting Company (KPLC) directed both urban and rural electrification. In 2004, the Ministry of Energy acknowledged the little progress in rural electrification rates and announced the creation of Rural Electrification Authority (REA) to speed up electrification. At the same time, the Ministry recognized off-grid technologies as suitable options for rural electrification. These technologies were already prevalent in the country, with an estimation of 200,000 SHS nationwide, installed by private actors thanks to "aggressive marketing" [307]. In line with the privatization trend promoted by international aid agencies and donors worldwide [START_REF] Sergi | Institutional influence on power sector investments: A case study of on-and off-grid energy in Kenya and Tanzania[END_REF] and enacted in 1997 through the Electricity Power Act, the Ministry of Energy announced a framework for "independent power distributors" in areas far away from the grid.

The period after 2006 consolidated private and international actors for rural electrification, with major programs such as Lighting Africa (World Bank) in 2014 and the implementation of international companies such as Powerhive or Powergen in the country. The public sector was also consolidated with the 2019 Energy Act that created the Rural Electrification and Renewable Energy Corporation (REREC) to replace the Rural Electrification Authority (REA) and the Energy and Petroleum Regulatory Authority (EPRA) instead of the Energy Regulatory Commission (ERC). EPRA supervises the sector and is in charge of developing MGs regulations22 .

To understand this broad sector, we conducted 75 interviews with Kenyan and international actors, as well as on-site surveys in seven Kenyan MG sites mostly in April/Mai 2022. MGs were chosen according to 3 criteria: a longevity of at least 5 years to grasp demand evolution and operators' strategies to cope with sizing challenges (cf. section 5.5.3), a diversity of MG operators and developers (public sector, international cooperation agency, community cooperative, NGOs, international private company) and an installed capacity between 8kW and 650kW. Interviews targeted the whole ecosystem of MG, from users to international funding agencies, including operators and developers, MG managers, public institutions, NGOs and experts (cf. Table 9), using a snowball sampling approach. Interviews were mostly conducted in English with some exceptions in French and Spanish, following semi-structured guides adapted to the type of interviewee. Interviews last between 30 minutes and 2 hours and were mostly done face-to-face, with a few phone or video calls. Interviews were transcribed and analyzed using an abductive coding approach on QSR International's NVivo [START_REF]Best Qualitative Data Analysis Software for Researchers | NVivo[END_REF]. We first indexed elements on large thematic categories. Based on this initial coding, we formulated middle-range theories regarding MG sizing methods, interactions between actors as well as strategies to adjust sizing in the long term. We then tested the consistency of these theories through a second coding of interviews, with analytical codes. We also triangulated interviews with official documents such as the counties development plan, the Kenyan Energy Acts 2012 and 2019, the draft MG regulations. Besides, we attended or watched recordings of EPRA public events and conferences from international institutions.

Results

5.5.1

Revealing the constraints around MG sizing: when demand, funds and regulation are unstable

The demand estimation conundrum

According to most of the sizing guides [START_REF]What size shall it be ?[END_REF], [START_REF]IEA PVPS : Mini-réseaux hybrides PV-diesel pour l'électrification rurale[END_REF], [START_REF] Cadilla | Micro-réseaux photovoltaïques hybrides -Guide de conception et Calcul[END_REF], [START_REF] Ashton | IEEE Recommended Practice for Sizing Stand-Alone Photovoltaic (PV) Systems[END_REF], [START_REF]Energy Sector Management ASsistance Programme[END_REF], three elements are needed to estimate the load curve required for MG sizing: the number of users, the number and types of appliances and the time slots when these appliances are used. Household surveys estimate who wants to connect, what kind of appliances he/she would like to use and when. Each of these elements are compared with the user's ability to pay, indirectly estimated based on current households' energy expenses, monetary revenues, future income, etc.

In addition to usual challenges associated with household surveys such as social desirability, which may lead users to overestimate their ability to pay for electricity, demand estimation for non-electrified users faces specific issues. The first one refers to the demand for a good that does not yet exist, and which encompasses several aspects of life such as daily activities (cooking, lighting, etc.), leisure (TV, sound systems, etc.), collective and productive uses (school, irrigation, shops, etc.) [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Rahut | A ladder within a ladder: Understanding the factors influencing a household's domestic use of electricity in four African countries[END_REF], [START_REF] Blodgett | Accuracy of energy-use surveys in predicting rural mini-grid user€consumption[END_REF].

The second issue deals with rural users' ability to pay: current and future incomes are tricky to calculate when they depend on a mix between fluctuating daily jobs, small-scale agriculture, occasional remittances from family, and so on [START_REF] Lee | Experimental Evidence on the Demand for and Costs of Rural Electrification[END_REF], [START_REF] Poblete-Cazenave | A model of energy poverty and access: Estimating household electricity demand and appliance ownership[END_REF], [START_REF] Bhandari | Rural electrification in Africa -A willingness to pay assessment in Niger[END_REF]. The third difficulty is linked with understanding the attractiveness of the MG compared with alternative sources of energy (local biomass, coal, paraffin, SHS, etc.). Users may prefer these energy sources or alternate them with the MG depending on their price, flexibility, reliability, in a phenomenon known as "fuel stacking" [START_REF] Lee | Appliance Ownership and Aspirations among Electric Grid and Home Solar Households in Rural Kenya[END_REF], [START_REF] Masera | From Linear Fuel Switching to Multiple Cooking Strategies: A Critique and Alternative to the Energy Ladder Model[END_REF]. The last issue is survey extrapolation: surveys are typically conducted over a few days and as such, they hardly grasp demand variabilities at different time scales [START_REF] Mandelli | Novel LoadProGen procedure for micro-grid design in emerging country scenarios: application to energy storage sizing[END_REF]. Some weekdays may require more electricity due to religious events or market days, some months might experience a peak or a decrease in electricity demand due to harvest periods, rural-urban migrations or climatic conditions, among others [START_REF] Bahaj | Electrical Minigrids for Development: Lessons From the Field[END_REF]. Similarly, users' ability to pay depends on seasonal expenses such as school fees, holidays or celebrations. In the longer term, the economic characteristics of the community might also change. These demand variations are critical for MGs given that energy production and consumption should match at all times [START_REF] Louie | Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability[END_REF], [START_REF] Mandelli | Effect of load profile uncertainty on the optimum sizing of off-grid PV systems for rural electrification[END_REF].

As Riva shows [START_REF] Riva | Modelling Endogenous complexities in rural electrification : on the local dynamics of groth and the planning of off-grid systems[END_REF], the dynamics of electric demand are related to many factors that cannot be fully measured or predicted. If the MG is functioning well, small entrepreneurs from other villages may relocate in the MG's perimeter, creating a "service center" [START_REF] Guillou | Mini-Grids at the Interface: The Deployment of Mini-Grids in Urbanizing Localities of the Global South[END_REF] while non-connected villagers might change their mind and eventually connect to the MG. Furthermore, electricity tariffs may evolve due to regulatory constraints and impact the demand (cf. section 5.5.1.3). All these factors lead to large uncertainties on the effective electric demand and its evolution, and thus impact the sizing and the funding strategies for MGs.

Fundraising requires existing funding

In Kenya, the median capital cost for MGs is estimated at 2,102 US$/kW [START_REF] Esmap | Mini Grids for Half a Billion People: Market Outlook and Handbook for Decision Makers[END_REF]. A private MG for an offgrid in rural villages in this country typically ranges from 10kW up to 60kW, representing an initial investment ranging from 21,020 US$ to 126,000 US$ [START_REF] Nygaard | Market for the integration of smaller wind turbines in mini-grids in Kenya[END_REF], [START_REF]Africa Minigrid Developers Association[END_REF]. MG developers rarely have enough equity to self-fund physical assets: they must look for external funding such as grants and commercial debt.

As one of the SDGs, access to electricity attracts huge international aid funding: more than $1.3 billion have been committed for MG investments [START_REF] Esmap | Mini Grids for Half a Billion People: Market Outlook and Handbook for Decision Makers[END_REF]. In Kenya, development agencies from Germany, the United Kingdom and France (Green MG program [START_REF]SEforALL Africa Hub[END_REF]), the World Bank (KOSAP project [START_REF] Energy | KOSAP[END_REF]) are some of the international actors who fund MGs. These actors often earmark MG budgets before their site are identified: developers must then find a site that matches funding instead of adjusting funding to the site characteristics.

Other kinds of subsidies like result-based financing (RBF) are disbursed after achieving performance indicators such as the number of connected households. Developers must cover the costs and risks associated with physical assets, licensing, customer engagements, and so on, before being paid back. As such, RBF moves the risks to the developers, since the funding agency will not disburse anything until the developer proves that households have been connected to the MG.

Lastly, commercial debt can be difficult to access because of the perceived risks associated with MGs.

MGs indeed are still a new kind of infrastructure, developers are relatively recent players, the sector is still looking for economically viable models [START_REF] Mukoro | A review of business models for access to affordable and clean energy in Africa: Do they deliver social, economic, and environmental value?[END_REF], and Kenyan MG regulations are still under development. For these reasons, MGs may be considered as risky investments [START_REF] Hazelton | A review of the potential benefits and risks of photovoltaic hybrid mini-grid systems[END_REF] and lenders expect evidence of developers' engagement to build their financial credibility. That is why lenders often expect developers to spend their own funding before approving loans: Developing a MG thus requires pre-existing equity to leverage further funding or to be able to wait until funds are disbursed. Financial skills are also necessary to navigate among funding temporalities and funding requirements, and to reassure banks on the project feasibility. Yet, even when developers manage to obtain funding, uncertainties remain in terms of capital cost due to inflation, profitability required by investors, regulations changes, in particular regarding tariffs [START_REF] Agutu | Accounting for finance in electrification models for sub-Saharan Africa[END_REF], [START_REF] Falchetta | The role of regulatory, market and governance risk for electricity access investment in sub-Saharan Africa[END_REF], [START_REF] Charles | Risks on the rural electrification project implementation performance in Mukurwe-Ini Sub-county, Nyeri County, Kenya[END_REF]. This leads us to examine another critical element for the MG design: compliance with evolving regulations.

"

Negotiating license and tariff approval among stakeholders

In Kenya, MGs are approved and supervised by different layers of public agencies. In this section, we detail the regulatory constraints on two critical initial stages in MG deployments, licensing and tariffs settings.

The MG developer needs the validation of the targeted community, the relevant county and the Ministry of Energy before building the MG [START_REF]The Energy[END_REF]. In practice, Kenyan authorities seem keen to approve as many sites as possible. Our interviewees from REREC and two counties stress strategies to attract MG investors rather than to discourage them, in a context of ambitious electrification goals with modest public budget. In some cases, counties may facilitate community engagement for developers, building on their existing relationships with village leaders. Counties' approval is also compulsory for land issues when developers target communal land. In addition to contributing to electrification, private developers might be perceived as a source of funding by counties: during a public consultation for MG regulations in July 2021, a county representative pleaded for counties to receive a share of MGs' electricity fees. This request happened as counties have been given new mandates: the new Constitution of 2010 devolved some electricity responsibilities to counties, but they face limited budget, staff and skills to implement them [START_REF] Volkert | Electrification and devolution in Kenya: Opportunities and challenges[END_REF]. The request was nonetheless discouraged by the regulator for fear that additional fees would be passed on to customers tariffs.

Tariffs are indeed the second major topic of negotiations between regulators on the one hand, and the MG operators and developers on the other hand: while these latter typically look for tariffs that would ensure the maximum profitability, EPRA is also concerned by tariffs equity in the country. EPRA requires the communities' approval as well regarding tariffs. The regulator estimates the MG's costs and the corresponding so-called "cost-reflective tariff" [START_REF]Standard Tariff Application Model for Minigrids[END_REF], thanks to an Excel tool created with the German cooperation agency GIZ 23 . EPRA also benchmarks existing and proposed MG tariffs. The Excel calculation sheet and the benchmark are not only useful to estimate tariffs, but also to reduce tensions regarding tariffs settings thanks to their perceived neutrality. The negotiation of tariffs can indeed be bumpy and continue after the MG is already operating, as reported in the case of two Kenyan MGs. EPRA may also ask for substantial tariff reduction, as reported by one operator who was requested to halve its tariff after the MG was already providing electricity.

While EPRA typically demand low tariffs to "protect" communities, they see their role as protectors of the private sector as well. EPRA "protects both sides", as this regulator representative explains:

"When we go for community engagement, we also take the opportunity to explain to them why their [MG] tariff is relatively higher than the KPLC tariff. Because in some cases, somebody will ask, "Why are they [users connected to the public system] paying Ksh.20 and we are paying Ksh.70?" So we explain to them why, so that they also accept the tariff because it could be higher, but it's the best option. And then we try to compare with the other alternatives that they were using before the MG developer comes in". (interview with an EPRA representative, April 2022).

This interviewee highlights the public discourse about private MG tariffs: they are high compared with the public sector harmonized tariffs, but they remain the "best option" compared with "alternatives" such as SHS or diesel generators. In the next section, we explain how constraints between MG demand estimation, fundraising and regulation are often both contradictory and simultaneous.

Juggling simultaneously with demand, funding and regulation settings

Tariff setting is at the heart of tensions between funders, developers, operators, regulators and electricity users. Demand estimation comes at a time when users are expressing wishes for a good they are not familiar with, and for which tariffs are not yet stabilized. Demand estimation, in turn, influences the design of the MG including sizing and financial arrangements: sizing, tariffs and funding are interdependent and simultaneous. Moreover, tariffs are constrained by national players, as the regulator arbitrates between profit maximization for private actors, and tariffs as close as possible to the national operator KPLC's to foster national equity among customers [START_REF] Bandi | The paradox of mini-grid business models: A conflict between business viability and customer affordability in rural India[END_REF]. This tension between profitability and social goals also appears when operators are legally required to connect all willing customers, even those who are not profitable.

Regulators and funders impose other concomitant constraints on license approval and funding requirements. The regulator usually asks for the funding scheme of a MG before licensing, while funders typically demand a valid license as a proof of developers' credibility before funding disbursement. These charges evict small players, as highlighted by Sareen in Portugal [START_REF] Sareen | Metrics for an accountable energy transition? Legitimating the governance of solar uptake[END_REF]. In the next section, we present the strategies to ease those constraints: we first clarify that constraints are more salient for private actors than for the public, and then we explain how private stakeholders adapt their methods and business models around these constraints.

5.5.2 Navigating through constraints and uncertainties

Public MG have more leeway than private ones

Before diving into strategies to ease constraints, a distinction must be made between public and private actors. For public MGs, uncertainties regarding tariffs, licensing and fundraising are less salient or even inexistent [START_REF] Williams | Enabling private sector investment in microgrid-based rural electrification in developing countries: A review[END_REF], [START_REF] Dagnachew | Actors and governance in the transition toward universal electricity access in Sub-Saharan Africa[END_REF]. Firstly, public MG tariffs are known from the start since the same tariffs apply for the Kenyan grid and public MGs. Secondly, license approvals follow a different process as public MGs and national grid are both managed by KPLC, with no competition risks. Lastly, regarding fundraising, government agencies can access larger subsidies and cheaper credit facilities than private companies. Thus, the main uncertainty for public MGs comes from the demand estimation, but this uncertainty is alleviated compared with private MGs. Since the public sector chooses first the areas to electrify, they select the most profitable sites, namely richer users and densely populated areas. The higher number of potential users smooth the consumption profile and approximates the mean typical load profiles that are often used for sizing assumptions, with no need to perform extensive household surveys.

Moreover, even though KPLC has a profitability objective, in practice, the rural electrification sector is heavily subsidized, with mechanisms such as a levy that transfers 5% of nationwide electricity bills for rural electrification 24 . As subsidies compensate for losses, the public sector can afford MGs with a large share of costly gensets. These agile diesel-based MGs can adapt easily to almost every consumption profile, reducing demand estimation uncertainties.

On the contrary, in the private sector, subsidies are cautiously distributed: on the one hand, the State does not want to extend the levy to private actors as it considers that public money should not be used for private actors; and on the other hand, cooperation agencies seek to reduce subsidies to promote a market-based approach with competition among developers [START_REF] Etienne | Fiabilité et accountability de l'électricité solaire hors-réseau au Sénégal[END_REF]. The quote below illustrates how an ex-member of a cooperation agency internally negotiated funding for a new MG project by justifying the need for blended subsidies and loans to support developers while maintaining a market-approach:

"We reached 70 MG but here again, it was a mixture of loans and subsidies because it was absolutely useful. But we needed to justify that we would not distort the market" (interview with an ex-employee of a cooperation agency, May 2022; translated from French by the authors).

In the next section, we go back to private developers to analyze how experience and intuition are mobilized to cope with unstable parameters.

Experience and intuition to arbitrate between uncertain parameters

Even though recognized sizing software such as Homer (cf. Figure 76) exist, several developers we interviewed elaborate their own. These "home-made" models are improved continuously using feedback from previous projects, comparing estimated and effective demand. Sizing models are also a way to explore assumptions related to the cost of capital and discount rate, ratio of equity and debt, operation costs (especially fuel cost) and so on [START_REF] Homer Energy | HOMER® Pro Version 3.7 User Manual[END_REF]. Developers can visualize how different assumptions affect the MG sizing. The models do not have "any judgment" according to one of our interviewees: the developer is the only one who can assess whether the MG sizing seems relevant based on his or her "experience" and "intuition".

Figure 76 : Illustration of HOMER Pro Software [START_REF] Homer Energy | HOMER® Pro Version 3.7 User Manual[END_REF] This hands-on knowledge builds on several years working in MG sizing, of "failures" and "successes" as described by one interviewee. Some experts declared that walking in a village is enough to grasp its economic potential and the appropriate MG sizing. Furthermore, MG sizing typically also aims at ensuring electricity reliability: as developers anticipate unforeseen events such as long cloudy periods or demand peak based on their experience, they often size MGs with security margins. In that sense, experience allows developers to move from "unknown unknows" to "known unknows", building on previous failures [START_REF] Perros | Lost learnings: Breaking the silence of failure in the energy and development sector[END_REF]. Security margins can consist in installing more batteries for a 100% solar MGs, or in adding a back-up diesel generator. The genset reduces the impact of demand uncertainties as it can easily be turned off and on, or used at a share of its capacity, to avoid power interruption.

The genset versatility is thus a way to adjust electricity production to a varying demand and climaterelated "known unknows". Nonetheless, genset are costly to operate and maintain in the long run compared with renewable energy sources, whose capital expenditures (CAPEX) are high, but operation expenditures (OPEX) are low. How do developers and operators balance short term and long-term costs, considering funding characteristics? In a broader way, how do they adapt their business models?

In the next section, we show how some developers and operators manage to circumvent constraints through diversification of funding sources, complex financial arrangements, and innovative tariff schemes.

Customized private business models to circumvent constraints

Developers face conflicting constraints when choosing the size and energy sources for MGs. The security margin described previously may lead to oversize renewable electricity production instead of relying on gensets, especially as funders prefer to invest in CAPEX than in OPEX. Moreover, funders such as the German cooperation or the Green Climate Fund specifically promote renewable energy because of their lower carbon footprint. For these reasons, MGs might be oversized and renewable energy-oriented. On the contrary, subsidies rarely cover all the investment costs and the developers must find other funding through debt and equity. Investors usually expect a fast return on investment (3 to 5 years), which is difficult to achieve with capital-intensive renewable sources.

To solve this time-related issue, developers often have no choice but to combine different funding sources, as illustrated by the company Powerhive who has installed 21 MGs in Kenya. This USA-based company managed to raise equity through investors, obtained grants from the Green MG program to fund physical assets, and smaller grants for specific electricity-related programs such as electric vehicles (see section 5.5.3.1). Table 10 illustrates how the company fundraises every year, with different actors, and for varied MG-related expenses. This kind of strategy is nonetheless time-intensive and requires specific skills and high-level international profile 25 . Actors such as the African MGs Developers Association (AMDA) support developers to design their financial plans and achieve subsidies. One of our interviewees, a former GIZ employee, considered that initial costs, and in particular feasibility studies before licensing, should be covered by subsidies as they do not always result in a successful MG. Still, small developers, and especially national ones, find it difficult to enter the MGs' market. In Kenya, most MGs developers were created abroad: Powerhive, Renewvia and Powergen are originally from the USA, while TTA is from Spain and RVE.SOL is from Portugal. Solinc, a national company, installs solar panels but does not develop rural MGs: they focus on less risky commercial and industrial uses. Other Kenyan actors (Dream EP, Nirav Agencies Ltd, etc) are listed by Nygaard [START_REF] Nygaard | Market for the integration of smaller wind turbines in mini-grids in Kenya[END_REF] but we could not find information regarding their recent activities. Moreover, many funding opportunities reach millions of dollars and evict small players who cannot prove their credibility with a substantial project portfolio [START_REF] Dagnachew | Actors and governance in the transition toward universal electricity access in Sub-Saharan Africa[END_REF]. From funders' perspectives, a MG portfolio indeed decreases financial risks, as developers and operators can balance losses between their pool of (un)successful MG.

Another strategy to decrease risks relies on complex financial arrangements to separate OPEX from CAPEX. Specific financial structures split the entity that owns the physical capital (production and storage system) from the teams operating the MG: way, funders invest in the entity with a lower risk (physical capital), and developers can easily sell this entity when needed. International companies with existing teams may buy MG physical assets to develop their own MG portfolio. Thus, developers may specialize in physical assets using their design experience and large subsidies program, and then sell their MG portfolio to operators. That way, MG developers achieve a fast return on investment without bearing the risk of long-term operation of MG. This de-risking mechanism could end in an institutionalized separation between developers and operators of MG, with consequences on sizing and MG longevity (see section 5.5.3.4).

The last strategy these latter can use is related to in-kind donations and tariff setting. They can negotiate donations or services from the community to lower costs: one operator explained that public lighting is granted for free in exchange for free land for the MG. Regarding tariffs, they must be approved by the community and the regulator (see section 5.5.1.3). Still, one operator we interviewed got around the regulation through a "bundle" system. The customer can pay a fixed cost (a "bundle") to buy electricity credits for a given period of the day, or a whole week. In certain cases, the operator also sells a service (charging a phone, using a mill…) instead of selling electricity. These strategies are further explained in the next section about strategies to match electricity demand and production.

Coping with unsuitable sizing

Stimulate the demand for electricity

MGs are over-sized when the electricity demand is structurally lower than the capacity of the system. Over-sizing may have several causes: users who appeared willing to connect to the MG changed their mind, people did not buy as many appliances as planned, users restricted their desire for electricity due to economic difficulties, and so on [START_REF] Tesfamichael | Eager to connect, cautious to consume: An integrated view of the drivers and motivations for electricity consumption among rural households in Kenya[END_REF] (see section 5.5.1.1). On the other hand, the project design itself may have incorporated over-sizing to take advantage of physical assets subsidies (see section 5.5.2.3) or to anticipate a future demand growth. When a MG appears to be oversized, we identify three strategies to increase demand: enhance the desire for electricity, foster productive uses of energy and set appealing tariffs.

The first strategy looks to recruit new MG customers or incentivize electricity consumption among existing customers [START_REF] Mukoro | A review of business models for access to affordable and clean energy in Africa: Do they deliver social, economic, and environmental value?[END_REF]. This strategy often involves marketing campaigns and community engagement approaches, sometimes relying on "ambassadors" as described by one operator. These "ambassadors" are villagers who are particularly enthusiastic about electricity and who promote electricity uses. Some of them sell electrical appliances on behalf of the operator, and benefit from transaction fees for successful sales. New customers may be found in the same locality or in the vicinity, and buy electricity as a service (phone charging for example). Operators sometimes closely follow-up customers, enquiring why they did not buy electricity credits recently through automatic SMS or home visits. This is an attempt to better understand customers' needs and constraints. From the users' point of view, however, these reminders can be perceived as a pressure to be a "good customer", that is to say a frequent and high-level electricity user.

The second strategy is gaining strength among the donors and operators ecosystem, through the socalled "productive uses of energy" [START_REF] Falchetta | Harnessing finance for a new era of decentralised electricity access: A review of private investment patterns and emerging business models[END_REF]. A vast literature details how productive use of electricity could solve the viability challenge of MG operators while favoring local economic development [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF], [START_REF] Avila | Evaluation of solar powered agricultural technologies for productive-use applications : a modeling approach[END_REF]- [START_REF] Robert | Village development framework through self-helpgroup entrepreneurship, microcredit, and anchor customers in solar microgrids for cooperative sustainable rural societies[END_REF], as expressed by one of the funding agency we interviewed.

"The whole business of rural electrification is based on the fact that you're going to bring something to supply a light bulb or charge a phone assuming that electricity will develop the village economically. We are going to make people richer, so they are going to consume more and this is how you will make profits". (interview with an employee of a funding agency, May 2022; translated from French by the authors).

Productive uses of electricity are diverse: activities made possible by extending lighting time (e.g., tailors working after sundown), new activities directly related to electricity (e.g., printing services) or activities with enhanced productivity (e.g., solar-based water pumping for agriculture) [START_REF] Cholez | Les problématiques clés en matière de développement des activités économiques dans le cadre de projets d'électrification. Une revue de la littérature grise et académique[END_REF]. Operators sometimes ally with partners to develop productive uses of energy. IKEA Foundation and the UK cooperation agency funded for example Powerhive to develop a chicken rearing project entitled "Kuku poa" ("nice chicken" in Swahili).

Finally, the bundle system developed by one operator (see section 5.5.2.3) is a way to increase consumption and to displace it throughout the day. Customers might buy weekly bundles, day-light bundles, and so on. Daylight tariffs are cheaper to encourage consumption when the overall demand is low. The biggest customers, defined as "residential premium", also enjoy more attractive tariffs.

All those strategies deal with the demand-side of electricity: we found no example, neither in Kenya nor in the literature, where the capacity of a MG was deliberately decreased to cope with oversizing. This may be due to funding constraints, costs to move the infrastructure to another location, or the preference for demand-based strategies. This leads us to another demand-based strategy for a reverse scenario, where the MG appears to be undersized compared with demand.

Limit the demand for electricity

If the demand for electricity cannot be fulfilled by the MG, the MG is considered undersized. The causes are multiple and might be related to the demand for electricity (increase of connected users or increase in users' consumption) or to the MG capacity. The MG might have been designed to electrify only a share of the community at first or its capacities might have decreased over time due to aging components, vandalism, misuses, etc. [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF] Considering the demand-side, technical devices such as power limiters, or connections capping are ways to limit electricity consumption to match the MG capacity. They are particularly critical when users have the perception that the MG capacity is "infinite" and can bear heavy appliances such as welding machines, as the national grid does. If agreed by the regulator, tariffs increase can be another way to discourage electricity consumption. No matter the methods, electric consumption's monitoring is needed to know when and how to apply those strategies.

In smart MG, this monitoring is mostly performed remotely by the company headquarters. The manager of the MG in the village may not have access to the monitoring data or to the theoretical maximum number of connections the MG can supply. This lack of information makes it difficult for the local manager to know when and to what extent connection demands should be rejected. Moreover, village MG managers often live in the electrified community and might find it touchy to refuse someone a MG connection. The same applies with power limitation: how easy is it to refuse your neighbour the use of his or her electricity appliances? Local managers are thus embedded in a "manager dilemma", to protect both their community and the sociotechnical system [START_REF] Laurent | Sémantique populaire du détournement dans les associations de développement en pays mossi (Burkina Faso)[END_REF].

In addition, the regulator can interfere in the connection process: operators are sometimes obliged to accept every new customer as long as they can pay for connection fees. Regulators can also block the electricity tariffs, preventing the operator from tailoring tariffs according to demand. In such cases, the remaining demand limitation strategy consists in promoting efficient appliances, with a limited effect according to one of our interviewees. A last option, more ambitious, is then to increase the production capacities thanks to system modularity.

Modulate the electricity capacity

System modularity consists in expanding or decreasing the existing MG capacity. As mentioned in section 5.5.3.1, we have found no examples of MG capacity decrease that is why this section focuses solely on MG capacity expansion.

Installed MGs, when equipped with smart meters and inverters, produce detailed data regarding effective electricity demand, reducing the large uncertainties mentioned previously (cf. section 5.5.1.1). It is then easier to estimate the capacities needed to match the demand. This demand-gap from an existing site, based on real-life data, reveals a good economic potential for the MG. The financial risk for investors is lower compared with the project initial stage, where "known unknows" and "unknown unknows" are larger. Operators and developers may then refinance their debt at a lower interest rate. Moreover, decreasing cost for PV and batteries components make it cheaper to wait a few years before expanding the system. These elements show that modularity could be a promising solution to deal with demand uncertainties and financial constraints: a developer could initially design small projects when funds are expensive and risks are high, and then increase the system capacities after a few years, benefiting from detailed data and lower cost for components and debt financing.

In practice, we met two operators who increased the capacities of their MGs, thanks to subsidies: they added more solar panels and batteries. On the contrary, many projects do not have funds to replace faulty components (see section 5.5.3.4), and even less to expand the MG capacity. The most common modularity strategy relies on diesel generators. When the consumption exceeds expectations, operators increase the production of gensets beyond initial plans. As a result, operation and maintenance costs increase while the genset lifetime decrease. This genset-based strategy can be considered as an adverse coping strategy, which jeopardizes the sociotechnical equilibrium of MGs. In the next section, we go further into adverse wait-and-see strategies.

Wait-and-see strategies, hoping for the best

"Operational sustainability" refers to the possibility to cover OPEX through tariffs [START_REF] Aresti | Rethinking Access to Energy Business Models: Ways to Walk the Food-Energy-Nexus Talk in Sub-Saharan Africa[END_REF]. This includes the ability to replace faulty components such as batteries and inverters thanks to electricity fees. In practice, operators often face financial difficulties to replace MG components. This seems to be the result of a gap between optimistic business designs and intertwined technical, economic and social challenges. For example, while lead-acid batteries (cf. Figure 77) are supposed to last around 8 years, they often last less due to hot temperatures or overuse (see section 5.5.3.2). In that context, assuming that batteries will last as long as in laboratory conditions can be assimilated to an "optimistic bias" [START_REF] Reverdy | Antimanuel de management de projet[END_REF]. When batteries fail before planned, the operator might not have gathered enough funds to replace them. Besides, users might pressure the operator to decrease tariffs as happened in two MGs that we studied, leading to lack of funds to replace components. One MG we studied also experienced financial fraud, as the electrician tampered with the payment system.

Project governance also plays a central role in MGs maintenance. The four well-functioning MGs that we studied were the ones with one single entity to develop and operate the system. On the contrary, damaged MGs had more complex governance schemes with separated developer and operators. In case of trouble, the operator sometimes blames the developer for a so-called poor MG design, while the developer may blame the operator (or users) for a so-called poor MG management. Agreement in this blame game is difficult to find, although operators and developers sometimes eventually agree to look for external funding from international aid agencies. This strategy is nonetheless bleak and lengthy.

In the meantime, the MG keeps degrading. In one of the MGs we studied in Kenya, only a few batteries had been replaced thanks to funding from the international agency who initially subsidized the infrastructure. It was not possible to replace the whole lead-acid battery row due to financial limitations, although it is technically recommended to do so. In another Kenyan MG, the system was delivering a few hours of unreliable electricity per day, due to battery problems as well. We observed the same situation in Senegal, where half of a 100 MGs' program is not working any longer [START_REF] Semis | Livrable 2: Rapport d'état des lieux avec les données quantitatives et qualitatives sur l'état de fonctionnement de l'ensemble des ERILs et GDTs[END_REF]. This wait-and-see strategy does not only technically degrade the MG, but it also damages customers' trust in this technology. As power cuts become more frequent, users tend to disconnect from the MG and buy alternative systems such as diesel generators and SHS (cf. Figure 77). The customers eventually perform by themselves the modularity that the MGs could not realize.

Discussion and conclusion

MG projects involve multiple actors who usually focus on one or a few aspects: funding, tariffs, reliability, sizing, maintenance. Each aspect comes with specific uncertainties. Compared with pluridisciplinary project team focusing on a single common goal, this specialization leads to competing objectives and compartmentalized view of uncertainties [START_REF] Reverdy | Antimanuel de management de projet[END_REF]. Each actor tries to reduce its own uncertainty by applying constraints on other actors [START_REF] Marchal | L'art d'accommoder les incertitudes[END_REF] (cf. Figure 78). It is especially salient with lenders, who require developers to prove their creditworthiness by hiring costly international consulting groups, by spending equity, or by de-risking their project through complex financial schemes. Likewise, the regulator protects itself from the dissatisfaction of the population by imposing low tariffs and high reliability constraints to operators. Funders and the regulator seek to minimize their own risks by transferring the uncertainties on the developer and operators, affecting the viability of a specific project. Even though one interviewee from the International Finance Corporation suggested that risks should be allocated to the actors who are best fitted to deal with them, in practice, developers and operators bear two types of risks. On the one hand, they are responsible for managing daily and long-term risks, but on the other hand, they can also be held accountable in case of problems. This situation goes against ideal uncertainties allocation scenario identified by Ward and Chapman [START_REF] Ward | Stakeholders and uncertainty management in projects[END_REF]. In a MG project, accountability remains thus at an individual organization level, instead of building a collective accountability that can be more suitable in highly uncertain contexts [START_REF] Reverdy | Antimanuel de management de projet[END_REF]. Thus, funders, regulators, developers and operators do not bear the same risks. They also do not hold the same power. Those actors can be divided into stakeholders and influencers, following Donaldson and Preston's theory [START_REF] Donaldson | The Stakeholder Theory of the Corporation: Concepts, Evidence, and Implications[END_REF] : influencers can influence the project, but they do not have any stake, whereas stakeholders have stakes and may not have any influence. In the MG ecosystem, funders and the regulator can be seen as influencers. Funders receive many funding requests and their activity do not depend on a specific project. Regarding the regulator, even if private actors are seen as critical to fasten the electrification pace, KPLC and REREC remain the mainstream electricity actors. In short, MG are at the heart of operators and developers business, while such projects are not vital for funders and the regulator. In addition, funders and regulators have more power as they intervene before sizing and investments materialize.

Developers and operators have developed diverse coping strategies against risks such as multiple MG designing tools and trade-offs (section 5.5.2.2). These methods are well defined for known uncertainties (i.e., "known unknows"), but they may not be adapted to treat "unknows unknown". For instance, betting on multiple potential funders and developing a solution that is location-flexible could increase the project resilience for MG developers, a strategy known as "parallel approach" ([299], cf. section 5.3). Still, this strategy is difficult to implement as each location requires long and costly studies as well as looking for allies in each county and community. On the operator side, resilience may be difficult to build as they arrive quite late in the project, when many decisions are irreversible (cf. section 5.3 and the Midler curve). The installation of the MG is done as a one-shot and modifications of the initial installation is not straightforward: MG commissioning reduces greatly uncertainty but also flexibility to adapt. The only way for the operator to be more "agile" ( [START_REF] Geraldi | The Titanic sunk, so what? Project manager response to unexpected events[END_REF] cf. section 5.3) might be to develop a more integrated approach by developing the project itself. In that sense, the continuity of actors in the project could ease the management of uncertainties and increase the responsivity to "surprises" ([301] section 5.3).

Our research shows that electricity consumption typically increases over time with little possibility to anticipate the scale of this evolution while the MG production capacity usually decreases as components age. Due to these opposing trends, matching production capacity with electricity demand seems to be only a transitional equilibrium before or after an under or oversizing situation. Regulatory and financial environments are ill-suited for these mid-term flexibility needs: tariffs approval by the regulator may slow down or even prevent some demand-side management strategies, while grants and subsidies mostly target the early stages of project design. Unrealized demand anticipations, the perception of equipment replacement and maintenance as sunk costs [START_REF] Florentin | Réseaux techniques. Un tournant patrimonial ?[END_REF] and blame games between developers and operators result in degrading MGs. Eventually, customers are the ones to bear the costs of unreliable MGs by restricting their electricity uses or by investing in more expensive systems like solar home systems and gensets. Adaptation strategies such as demand stimulation or limitation are thus supported by end-users, raising issues of energy justice for poor customers [START_REF] Ojong | Energy Justice and Off-Grid Solar Electrification in Africa: Trends, Narratives and Contestations[END_REF], [START_REF] Trompette | At the Margins of the Grid: The Politics of Off-Grid Electrification in Senegal[END_REF].

Key messages:

• MG sizing goes beyond technical and economic optimization, and is a trade-off between developers, operators, regulators, funders, and users • Equilibrium between the production capacity and the electricity demand is only transitional;

sizing cannot be considered as a "one-shot" and may have to be updated with time • Regulatory and financial environments are ill-suited for mid-term flexibility needs, lowering the possibilities for demand and production capacities adaptation over time • The stakeholders try to transfer the risks of MG projects on each other, especially funders and regulators by imposing constraints on license and funds obtention, modifying thus the MG sizing • Customers are the ones to eventually bear the costs of unsuitable MGs by reducing their electricity use or by investing in more expensive systems

To go one step further

This chapter was not directly focusing on the CFP reduction of MG, but we detailed the environment in which MG projects are developed, and some of the obstacles that may reduce the rollout of MGs with a large share of solar energy. Thus, we give here some complementary results from our qualitative analysis bringing different questions that could be interesting for further research.

Reducing the risk with food security or water access projects

In most of our interviews, the reduction of the MG CFP or the need to have MG with low CFP was not a subject. Even if the promotion of renewable energy is one of the objectives of some public institutions, the priority is the increase of the number of connections and sometimes, even electricity access is not a priority compared to projects related to food security or access to clean water. Nevertheless, projects related to water pumping, agriculture or food transformation could be a way to reduce the cost and the CFP of MG by using the curtailed energy during the day (cf. SM section 8.4) [START_REF] Yamegueu | Potential of microfinanced solar water pumping systems for irrigation in rural areas of Burkina Faso[END_REF]. Developing such projects could also increase the revenues of population, and thus improve their ability to pay for electricity [START_REF] Falchetta | Energy access investment, agricultural profitability, and rural development: time for an integrated approach[END_REF]. Moreover, funding such projects is a way for government to support the development of private developers without directly subsidize them. Such strategy was for instance developed by the operator Powerhive as explained in section 5.5.3.1, but as shown in section 5.5.3.4, operators using this strategy have to be careful with the consumption load profiles of these productive uses and with the evolution of the demand. Characterizing the potential synergies between agriculture and water access projects with energy access projects would be worth investigating.

Increasing the lifetime of projects to reduce the CFP

As stated in section 5.5.3, some MG projects face difficulties to deal with unsuitable, leading in many cases to a shortened lifetime [START_REF] Semis | Livrable 2: Rapport d'état des lieux avec les données quantitatives et qualitatives sur l'état de fonctionnement de l'ensemble des ERILs et GDTs[END_REF], [START_REF] André-Bataille | Publication d'une étude de capitalisation de 16 projets d'électrification rurale à Madagascar[END_REF]. Public policies, especially through subsidies, should accompany the MG project along their lifetime. Subsidizing the batteries could be a good way to increase the proportion of solar energy in MG, and to easier their replacement after some years that seems to be an important issue for operators. Both these effects allow to decrease the CFP of MG, the first by decreasing the use of diesel, the second by increasing the project lifetime. As shown in the sensitivity analysis of section 3.5.1, increasing the lifetime of batteries and of the project allow to reduce quite significantly (cf. section 3.5.1) both the LCOE and the CFP. Thus, working on the longevity of MG is an important lever to allow a low-carbon and affordable rural electrification. This can be done by supporting MG projects and local entrepreneurs, by improving regulation and governance around 123 MG, by training electrical technicians on solar installation, or by easing the access to spare parts and PV components suppliers.

The CFP reduction of public MG: a potential within easy reach

As explained in section 5.5.2.1, private MG projects are more constrained than public MGs regarding the regulations (tariffs, grid arrival, license), the users' affordability and the profitability expectations of the investors. On the contrary, public developers and operators, such as the rural electrification agency and/or the public utility could access to state fund to finance their installations and could thus more easily develop solar energy which is CAPEX-intensive [START_REF] Ouedraogo | Incentives for rural off grid electrification in Burkina Faso using LCOE[END_REF]. Looking at the Kenyan example, some public utilities already have portfolios of MGs running mostly on diesel for which they have years of consumption data, avoiding the risks of demand estimation when installing solar power. Thus, if there is a clear political willing to reduce CFP emissions, a very large proportion of solar energy could be integrated to those public MG. It could be interesting to identify such existing diesel-only MGs owned by public entities in different countries to evaluate the potential CFP reduction that could be achieved with investments from their governments.

6 General conclusions and perspectives

Conclusion

In the introduction, we detailed the importance of considering both the universal energy access and the climate mitigation objectives when addressing rural electrification. Given the carbon neutrality pledges of several African countries [13], [START_REF] Omukuti | Net Zero Commitments by Businesses in Africa : a stocktake[END_REF] and the large number of people living too far from the national grid, renewable-based MGs have a key role to play there. Many issues are related to these renewable MGs regarding their reliability, longevity, financing, environmental impacts, etc. Among all these, the affordability is the main aspect considered by developers and electrification planers in the design of MGs, mostly through the optimization of the LCOE.

This thesis contributes to one of these numerous issues by assessing the potential of isolated MG based on solar PV, batteries and diesel genset to foster electricity access of rural areas in Africa while satisfying two constraints: a low cost of electricity and low carbon footprint. The objective is to answer these questions:

❖ What are the LCOE and CFP of MGs in Africa and what are their drivers? Is it possible to minimize these two criteria at the same time? (cf. section 6.1.1) ❖ What public policies would help to reduce the CFP of MGs? What are the potential obstacles to these policies? (cf. section 6.1.2) ❖ How sensitive are these results to the climate, technical and socio-economic contexts? (cf. section

A robust response to all these questions requires an interdisciplinary approach based, for instance, on:

• Engineering sciences, in particular the modelling of energy systems and electrical engineering to model the operation of a MG and its various components in particular, • Geosciences and environmental sciences, to understand and account for the variability of weather conditions and their impact on the system, • Economics, to assess electricity demand, optimize system costs including environmental externalities, and design policies to reduce these externalities, • Social and management sciences, to understand the interactions between MG stakeholders and the way they manage with uncertainties, risks or institutional rules.

By considering a simplified representation of fictitious MGs, we were able to simulate their operation for any given location, electric demand and configuration. One original aspect of our approach compared to existing literature is the generalization of our results for the different climate and socioeconomic contexts in Africa through the spatialization of our results and detailed sensitivity analysis.

Another original aspect of this thesis is the confrontation of some of our simulation-based results to the field thanks to a qualitative analysis led in collaboration with Emilie Etienne, PhD student in sociology. Our results from these different methodologies show the need for interdisciplinarity to tackle the current global challenges, and advocates for a more integrated approach in research project from their outset.

Minimizing the LCOE or the CFP: conflicting objectives?

Under current conditions and in most locations, integrating solar PV and batteries in a diesel-only configuration can significantly reduce both LCOE and CFP

In chapter 3, we introduced the envelope curve that presents the least possible LCOE obtained for a given level of CFP, going from a genset-only configuration to the least CFP configuration. Using this curve, we show that solar energy is most of the time cost-competitive with diesel, and that integrating solar in diesel MGs reduces both LCOE and CFP. Even if many MGs are still exclusively running on diesel, most of the currently installed MGs consist indeed in hybrid solar/diesel system as MG developers try to minimize their costs. Considering our costs and load profile assumptions, the LCOE minimization usually leads to MG supplying between 50% and 80% of the electric demand with solar energy. These LCOE* configurations reduce then the LCOE by around 15% and the CFP by 50% to 65% compared to a genset-only configuration. These CFP reductions are already high, but if countries want to achieve net-zero emissions of the power sector or at least to go further in low carbon development, MGs installed should have much lower CFP.

The CFP of MG cannot be zero. The lowest CFP values are even relatively high because of indirect GHG emissions.

When the indirect GHG emissions of solar PV and batteries are included in CFP calculations, the CFP of MGs cannot go below a certain threshold estimated around 200𝑔 𝐶𝑂 2 /𝑘𝑊ℎ with our assumptions. This is not negligible to reach net zero emissions 26 . It should also be noticed that the least CFP configurations still use a small proportion of diesel (a few percent of the supplied energy) to ensure that 100% of electricity demand is supplied. Nevertheless, they already allow a very large CFP decrease compared to a genset and a reduction of the dependency to fossil fuels whose supply may be constrained by the international context, as current geopolitical events showed [340]. In theory, it is possible to avoid diesel use with 100% solar MG, but supplying entirely the electricity demand with such systems requires very large storage and solar PV capacities to deal with the periods of very low resource (cf. Chapter 2). In practice, such configurations lead to high CFP values and are not affordable for MGs, or only for small systems.

Oversizing the PV production capacity of 100% solar MGs allows to achieve a quality of service of 95% with a storage capacity close to only one night of energy demand.

A way to decrease the large storage and PV capacities needs for 100% solar MGs is to accept part of the electricity demand will not be met. By allowing 5% of energy not to be supplied, it is possible to reduce the storage capacity requirements close to the value that allows to deal with the sub-daily resource/demand mismatch by oversizing the PV installed capacity (cf. Chapter 2). This oversizing is below 2 for most locations in the case of a very seasonal load profile, and decreases to around 1.6 for load profiles without seasonality. However, the LCOE* values associated with 100% solar MGs are still higher than the LCOE* values obtained with hybrid solar diesel MGs. In addition, lower system reliability can potentially have many negative consequences, as shown in Chapter 5, including the fact that users bear the costs of unreliable MGs. Other articles also point out that the positive effects of electrification can only be achieved with a reliable electricity supply [START_REF] Booth | Productive Use of Energy in African Micro-Grids: Technical and Business Considerations[END_REF].

Reducing the CFP further than the LCOE* configuration could be done at relatively low additional cost.

With our cost and load profile assumptions, the CFP of the CFP* configurations are often half the CFP of the LCOE* configurations, but its LCOE is more than 20% higher. This LCOE increase may not be suitable considering the low affordability of the population to electrify, and subsequently, an affordable low-carbon electrification with MGs seems out of reach. However, many trade-offs configurations are between the LCOE* and CFP* configurations. We show that most of the times, significant CFP reduction from the LCOE* configurations can be reached with moderate additional cost. Thus, even if the CFP* configurations are not reached, a 10% LCOE increase reduces the CFP by more than 30% in the vast majority of climate and socio-economic contexts, and even more than 40% in many cases.

Public policies to reduce the CFP of MG

Significant CFP reduction corresponds to relatively large values of shadow carbon pricing

Introducing a virtual CFP cost in LCOE calculations allows estimating the economic efforts required to shift from the LCOE* configurations towards lower CFP configurations. The curve of the marginal cost of carbon needed to reduce the CFP of a given MG allows to estimate the shadow price of carbon (SPC) needed to arbitrate between investments in favor of less emitting projects. Considering a global SPC around 290 $/𝑡 𝐶𝑂 2 ,𝑒𝑞 27 , as evocated by the IPCC to limit global warming to 1.5°C [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF], the CFP reduction of MGs would be between 30% and 40% with our assumptions (cf. Chapter 3). These CFP reductions drop to less than 20% when considering the SPC estimated to limit global warming to 2°C (120 $/𝑡 𝐶𝑂 2 ,𝑒𝑞 28 ).

Setting a national CFP reduction objective should be preferred to a CFP standard for all MGs

The spatial variations of the solar resource and of the fuel costs imply different CFP reduction costs from one country to another and from one location to another within a country. Thus, as NDCs are defined at the national level, the SPC should be defined at the country scale. The spatial variability of the solar resource may be also significant within a given country, potentially leading to inequalities between MG projects within the country. By setting an average CFP reduction target for the country as a whole, the increase in costs can be spread more evenly between projects and the total costs of the reduction policy can be reduced. This is therefore to be preferred to a CFP standard for each project.

Subsidizing batteries or taxing the fuel are efficient economic incentives to reduce the CFP of MGs

However, the SPC values defined by the governments or other institutions only apply to themselves and do not affect the other MG projects, especially the ones of private developers. Supposing they are guided by economic considerations, different incentives could be designed to incite private developers to select less emitting MG configurations. These incentives could directly affect the costs supported by developers and operators such as subsidies on solar or batteries, or taxation on fuel. The comparative efficiency of these incentives in terms of carbon cost depends on the level of CFP reduction aimed. In the current context, battery subsidies are more efficient than PV subsidies and fuel tax for low CFP reduction targets, while fuel tax is more efficient for higher CFP reduction targets. Indirect ways could also be used to reduce the CFP of MGs, for instance reducing the obstacles and risks related to MG projects (national grid arrival, issue of licenses, access to funding, etc.). By combining these different strategies it is possible to further reduce the CFP of MGs to get closer to the maximum CFP reduction that can be achieved (cf. section 4.5.2).

The design of public policies should emphasize the sharing of costs between MG stakeholders.

A fuel tax is a cost-efficient policy to reduce the CFP, but it seems difficult to implement this strategy alone. It would increase the cost for MG operators leading to an increase of electricity tariffs that may be not affordable for people living in rural areas. Moreover, such fuel tax would certainly cover all fuel suppliers at the national level, impacting also the transport sector. Thus, a fuel tax represents a challenge in terms of acceptability, by both the population and decision makers, if it is not accompanied by a clear redistribution of the tax revenues. Such redistribution could be done by subsidizing the solar components for MG. Combining subsidies and taxations (cf. section 4.4.3) allows to efficiently reduce the CFP of MGs without increasing the LCOE. Subsidies could also be implemented alone, i.e., without any tax, to encourage lower electricity tariffs for MGs 29 . It has the advantage of reducing both the CAPEX and the OPEX 30 , and of sharing the benefits of the subsidy between developers and operators. However, these subsidies require also funds from governments, DFI or other international funds for development and/or climate change mitigation, which are currently relatively limited.

The issues involved in sizing MGs go beyond technical and economic optimization; it is a compromise between stakeholders who are trying to pass on the risks to each other.

The design of public policies must also consider the broader funding and regulatory environment in which MGs are developed. MG projects involve multiple stakeholders (funders, regulators, developers, operators, users) who have to deal with risks and uncertainties. If policies aiming at reducing the risks of MG projects could be a good way to foster the investments in the MG sector and decrease the CFP of MG (cf. section 4.5.2), it may, in practice, only consists of a risk transfer and not of a real risk reduction. Depending on their influence on the project, the stakeholders can indeed report risks on others by imposing constraints, for instance related to the CAPEX for funders, or to the electricity tariffs for regulators. These constraints show that sizing is not only a technical problem, it is the result of negotiations and complex interactions between stakeholders.

The sensitivity of our results to the diversity of contexts

From chapter 2 to 4, we tried to evaluate the sensitivity of our results to the different parameters used in our models (solar resource, load profiles, technical, economic and CFP assumptions for each component). We showed that the sizing and the LCOE and CFP values for hybrid solar/diesel MG were very sensitive to these parameters.

The solar resource variability is one of the main drivers of low-carbon MG configurations.

To significantly reduce the use of diesel (100% solar MG and low CFP configurations), sizing consists mainly of a compromise between the solar capacity and the storage capacity, which is mainly driven by the characteristics of the solar resource and its co-variability with the load profile (cf. chapters 2 and 3). These characteristics and temporal variability differ quite a lot between the different climate regions of Africa, and sometimes also within a country (cf. Madagascar in section 4.4.1), hence the large spatial variations of the LCOE and CFP for these low carbon MGs.

Least-cost configurations of hybrid MGs are very sensitive to the socio-economic context and to the average solar resource.

Many more MG configurations are available when minimizing the costs without constraints on the diesel consumption. In this case, alternative economic assumptions (discount rate and costs for PV panels, batteries and fuel) have similar relative impact to the one of the solar resource or the load profile variations. The PV capacity of the LCOE* configuration is mostly driven by the cost of PV panels and fuel, and by the capacity factor. But the storage capacity of this configuration is very sensitive to almost all parameters (technical, economic, load profile, solar resource). These high sensitivities of the LCOE* configurations to parameter values lead to very different CFP values but to relatively low variations of the LCOE by comparison. Thus, even if we mostly present in this thesis general results with average values for the different parameters, these values must be estimated carefully when sizing a specific MG or designing public policies.

Our contribution to rural electrification players

Our work is obviously not without its limitations. Our methodological developments and analyses could however provide valuable insights to rural electrification stakeholders for the identification and / or choice of development strategies with reduced CFP.

Some contributions that might help…

MG developers:

• Rules for estimating the least cost configuration of 100% solar MGs • Envelope curve to size MG • Estimate the economic value of a ton of CO2 avoided (to apply for carbon credit or climate mitigation funds) • Identify some obstacles to MG development

Electrification planners:

• Rules for estimating the least cost configuration of 100% solar MGs In this thesis, we considered only fictitious MGs to develop our methodology and evaluate main factors that influence the sizing and performance of MGs. This methodology can also be implemented by energy planners in theirs models for rural electrification planning.

Many planning works [START_REF] Dagnachew | The role of decentralized systems in providing universal electricity access in Sub-Saharan Africa -A model-based approach[END_REF], [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF], [START_REF] Mentis | The benefits of geospatial planning in energy access -A case study on Ethiopia[END_REF], [341] focus on the least cost solution. Including the CFP of MGs in those works would give some insight on the CFP of the future electricity mix in the region. Such an estimation should be combined with scenarios for the extension of national grids 31 . This would allow a more relevant identification of the strategy to follow.

Then, the quantification of the CFP for these least-cost electrification scenarios could be compared to least-CFP scenarios in terms of CFP and costs. Such study has to be done to really assess the potential of MGs to allow a low-carbon electrification. Given the storage requirements of MGs, CFP could indeed be lower by having centralized flexibility systems that take advantage of aggregation of electricity demand and renewable production at the national grid level to reduce their variability. The same methodology as the one we presented can be followed to find some trade-offs between the costs and the CFP of different planning configurations, and to estimate a Pareto front and marginal cost of carbon curves that could help to design policies to guide the country electrification.

Economic incentives proposed in our work can be used and extended by subsidies on other renewables or on SHS by taxing coal and/or gas or by regulating the installation of MG or the grid extension depending on the objective to be achieved. Implementing the economic incentives into a planning model for a specific country would make it possible to estimate the overall funding requirements and the total quantity of GHG emissions that could be avoided and/or proposed as carbon credit. It would also be possible to evaluate the spatial distribution of tax and revenues and thus the potential regions or communities that are advantaged compared to others, potentially leading to some conflicts. Note that in some countries such as Kenya, it could be possible to imagine policies at the county/province level to better adapt the incentives to the solar resource and demand variability.

We already show the large dependency of MG configurations and LCOE and CFP values to the covariability between solar resource and electricity demand, especially at the infra-daily scale which is not considered by many planners. We advocate for the integration of this variability into planning models to assess its impact on planning results. The same type of analyses should be done with other parameters such as diesel cost or battery lifetime, that have a relatively high impact on the LCOE and the CFP values (cf. section 3.5.1). To our knowledge, the robustness of planning has not been studied for now and we think this deserves further research. This robustness shall not be assessed only by varying quantitative assumptions, but also by having a qualitative evaluation of the feasibility of proposed planning and of the potential obstacles (regulations, financial context, …) that must be anticipated to reach electrification objectives.

Considering the dynamics of MG projects

As in most planning models, we consider a static system but this is likely not the case, potentially leading to unsuitable designs. This is an important limitation of our work. For instance:

• The demand for energy is expected to evolve with time as a result of demographic and economic growth, or of more and more diverse appliances. Most projects tend to be undersized (and more rarely oversized) after a few years. • Production is also expected to evolve in time. PV panels efficiency decrease with time and battery performances deteriorate, especially when their maintenance is not regularly done and when they are exposed to high humidity and temperatures, and to deep discharge cycles. These deep discharge cycles are often due to a misestimation of the demand, showing that electricity demand, sizing and costs of electricity are interlinked as stated in section 5.5.1.4.

Some authors already tried to characterize the uncertainties surrounding demand estimation [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF], [START_REF] Louie | Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability[END_REF] or to understand and model demand evolution. On the production side, PV panels degradation is usually modelled as a constant rate of efficiency decrease and, to our knowledge, loss of battery performance in African MGs were partially described but not modelled. Considering these evolutions in MG modelling may reveal critical moments and/or factors that could have a large impact on the costs and CFP of MGs, or even on the viability of MG projects. By simulating different scenarios of demand or production evolution, it is possible to assess the robustness of MG configurations. Thus, trade-offs could be identified between the optimal configurations and the more robust ones to improve the sizing of MGs.

Anticipate the critical moments of MG projects could also help operators to avoid them by adapting the production system or taking demand-side management measures. Strategies could then be elaborated, for instance using the real options theory or adaptive pathways [START_REF] Cuervo | Photovoltaic power purchase agreement valuation under real options approach[END_REF]- [START_REF] Gibberd | Anticipating and Preparing for Future Change and Uncertainty: Building Adaptive Pathways[END_REF], to manage some of the risks related to MG. Moreover, public policies could also be designed to support MG operators in those critical moments, for example, by granting subsidies for production system extension or by allowing more flexibility in the electricity tariff design when necessary. These different approaches require to have a better knowledge of the costs and potential obstacles associated with modularity and must also be accompanied by a qualitative analysis of these strategies, their feasibility, and their impacts on the other stakeholders of MG projects.

Towards a more integrated approach

In this thesis, we focused almost exclusively on two indicators: the LCOE and the CFP but other criteria should be considered to design sustainable MG. The CFP is only one of the multiple environmental impacts of energy systems (acidification, ecotoxicity, material requirements, …), and other indicators than the LCOE could be considered as explained in the introduction (employment rate, working hours, cf. section 1.2.2). Some criteria may compete with each other, leading to potential contradiction between the sustainable development goals.

For instance, as water can be scarce and dust deposit very frequent in some African locations (e.g., Sahel), how the water requirements for cleaning PV panels would affect the local access to water (SDG 6)? In regions with strong land competition, would the PV installations replace agricultural lands (SDG 2)? What would be the impact of battery disposal or diesel genset leaks on the local ecosystem (SDG 14 and 15) or on human health (SDG 3)? These questions call for a more holistic view on rural electrification using MGs.

The different sectors (water, food, energy, health, economy, etc.) are indeed interlinked. The demand and resources for each of these sectors are also linked to those of the other sectors. For instance, increasing access to clean water for rural population may need water pumping, thereby increasing energy demand. Ensuring the good health of local population may likewise require energy to supply clean cooking systems and cold storage for vaccines or other medicines. Reducing hunger or malnutrition may use irrigation and equipment for food conservation and transformation, increasing once again the energy consumption. These applications have thus a high impact on the amount and on the shape of the electricity demand. They could also increase incomes of the population, potentially leading to different consumption behaviors related to food, water, etc.

A more integrated modelling representing these sectors and their interactions with the MG model could help to identify potential competing or common interests between sectors, and vulnerabilities in the system, especially considering the effect of climate change on these sectors. Preliminary results show for instance how using the solar curtailed energy of MGs to pump water could decrease the LCOE and CFP of the system (cf. Supplementary Material 8.4) [START_REF] Yamegueu | Potential of microfinanced solar water pumping systems for irrigation in rural areas of Burkina Faso[END_REF]. Given that some policy makers are more interested in access to water or agriculture productivity (cf. section 5.8) and do not consider energy access as a priority, such tool could help them to have a more global view when designing public policies.

The development of such tool is not an easy task due to the complexity of interactions and the multiplicity of the parameters involved in each sector. Nonetheless, a first step can be done with a qualitative analysis by using some causal loop diagram as in [START_REF] Purwanto | Using group model building to develop a causal loop mapping of the water-energy-food security nexus in Karawang Regency, Indonesia[END_REF] to identify potential reinforcing or balancing retroactions. Then, quantitative models dedicated to specific applications could be developed to compare different scenarios or technologies. For instance, irrigation supplied by a solar hybrid MG may increase the agricultural yields, leading to a larger quantity of biomass residues that may serve as combustible to replace partially or entirely the diesel consumption of the MG genset [START_REF] Yamegueu | Experimental Investigation of the Power Quality of Diesel Engines Operating with Straight Jatropha Curcas Oil[END_REF]. Among other energy sources, biomass residues were not considered in our thesis, but this resource must be included in further research on access to energy in rural areas, especially as it could cover both electricity demand and thermal energy demand (e.g., cooking). Thermal energy demand is indeed a large part of energy needs for communities and it worth more investigations to know what the needs are exactly and how they can be fulfilled by renewable energy.

Once again, these suggestions for future research, being the integration of our methodology to planning models, the consideration of MG projects dynamics and uncertainties, or the development of more integrated approach show the need to support the collaboration of researchers from different fields and to rely on interdisciplinary approaches to address current challenges [START_REF] Cader | The Energy Nexus Group -An Interdisciplinary Research Agenda[END_REF], [START_REF] Opoku | Electricity Access, Community Healthcare Service Delivery, and Rural Development Nexus: Analysis of 3 Solar Electrified CHPS in Off-Grid Communities in Ghana[END_REF].

• Compute the full unit costs of PV 𝛼 𝑃𝑉 [€/𝑊 𝑝 ], using equation ( 7 + 0.14 to estimate the useful storage capacity required for your system • Divide this value by the maximum depth of discharge (𝐷𝑂𝐷 = 0.8) and multiply it by the mean demand 𝐷 0 to obtain the optimal storage capacity to install for your system. Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). This graph presents the optimum oversizing values for 𝑟 = 1 and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles).

Supplementary figures

155 Figure 90 : Optimum oversizing 𝑥 * as a function of 𝜎 𝐷𝑖𝑓𝑓 , the normalized standard deviation of the daily production/demand differences (differences estimated each day between the mean production and the mean demand for this day (the production is estimated with an oversizing factor of 1) and both demand and production are normalized by 𝐷 0 ). Results are presented for 5 different seasonal profiles of the demand (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). Each graph presents the optimum oversizing value for a different cost ratio and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles). Parameters for each regression are given in the titles. 92 : Level of quality service obtained for the 200 locations with the estimated optimal configurations using equations ( 18) and [START_REF] Falk | Drinking Water Supply in Rural Africa Based on a Mini-Grid Energy System-A Socio-Economic Case Study for Rural Development[END_REF]. Top boxplots give the distribution for each yearly load profile, cost ratios are gathered. Bottom boxplots give the distributions for each cost ratio, yearly load profiles are gathered.

Figure 93 : Error indicators for optimal oversizing factors estimation for each cost ratio and load profile using equation [START_REF] Falk | Drinking Water Supply in Rural Africa Based on a Mini-Grid Energy System-A Socio-Economic Case Study for Rural Development[END_REF]. (four top graphs) and equation [START_REF] Lee | Electrification and Economic Development: A Microeconomic Perspective[END_REF] (bottom four graphs) 160 18) (bottom four graphs) Figure 95 : Error indicators for optimal LCOE estimation for each cost ratio and load profile using equation ( 18) and [START_REF] Falk | Drinking Water Supply in Rural Africa Based on a Mini-Grid Energy System-A Socio-Economic Case Study for Rural Development[END_REF] 161 5°E) and for a hybrid load profile without seasonality. The 𝐶 𝑃𝑉 graph represent the variation of the Envelope curves when changing the value of 𝐶 𝑃𝑉 , the red colour corresponds to an increase of 50% of the 𝐶 𝑃𝑉 value whereas the blue one corresponds to a decrease of 50% and the purple one is obtained with the reference value of 𝐶 𝑃𝑉 . The area represents the variations of this curve when modifying the other parameters as specified in section 8.2.2. The upper limit of the area is the 90 th percentile of values and the lower limit is the 10 th percentile. The same applies to the other graphs, apart for 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 where variations are only of ±10% and for L with variations of ±33%.

168

Sensitivity analysis

The goal of this sensitivity analysis is to see how variable are the results found in section 3.4 when modifying the discount rate 𝑑, the costs (𝐶 𝑏𝑎𝑡 , 𝐶 𝑃𝑉 , 𝐶 𝑓𝑢𝑒𝑙 ), the CFP (𝐶𝐹𝑃 𝑏𝑎𝑡 , 𝐶𝐹𝑃 𝑃𝑉 , 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 ) and the lifetimes (𝐿 𝑏𝑎𝑡 , 𝐿, 𝐿 𝑔𝑒𝑛,ℎ𝑟𝑠 ) related to each component. For each of these parameters, 3 values are taken: the reference value (cf. Table 3 and Table 4) and variations of ±50% from this reference value (with two exceptions for 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 : ±10% and 𝐿 : ±33%). These variations are representative of the variability for these parameters [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF] Crossland | A socio-technical approach to increasing the battery lifetime of off-grid photovoltaic systems applied to a case study in Rwanda[END_REF], [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF]. The analysis is performed on the 8 locations of the NS transect presented in Figure 44 and for the 15 load profiles presented in section 3.3 (Domestic, Productive, Hybrid with or without seasonality). Thus, it allows us to estimate the sensitivity of the results related to the mean capacity factor and the co-variability indicators between the solar resource and the demand. Combining all these variations give us more than 885 000 scenarios per locations, i.e. in total, we identify around 7 million different least LCOE and least CFP configurations.

To summarize the results of this sensitivity analysis and to better see the impact of each parameter, it is possible to look at the relative difference of CFP and LCOE results when modifying only one parameter. The calculation of the sensitivity for each parameter is made for the 8 N-S transect locations, for each demand profile and for each scenario of cost and CFP related to component. Table 14 gives an example of how to calculate the sensitivity for some scenarios, a location in Angola and a hybrid demand profile without seasonality.

SM related to chapter 5

Some preliminary results about the curtailed energy:

In the previous chapters, we did not present any result regarding the curtailed solar energy. When the batteries are full and when PV production is higher than the electric demand, a part of the production is curtailed. This curtailed energy represents between 5% and 15% for the LCOE* configurations, but it is much higher for the CFP* configurations, sometimes higher than 45% (cf. Figure 115). As explained in Chapter 2, the more the resource is variable, the more the PV system should be oversized, leading to a higher proportion of curtailed energy. Instead of wasting this energy, we could imagine valorizing it with easily dispatchable uses like water pumping with storage. When electric storage is full et PV production is higher than the demand, water could be pumped and stored for future use. If we consider the whole curtailed energy as part of the supplied energy into the LCOE and CFP calculations, their values decrease as shown in Figure 116.

Given the low level of curtailed energy for LCOE* configurations, the decrease of CFP and LCOE values is quite small for these configurations (less than 5%). But in the case of CFP* configurations, this decrease is much larger, reaching almost 50% in some cases. In many cases, the LCOE of CFP* configurations when including curtailed energy goes below the LCOE* values. It is certainly difficult to valorize the whole curtailed energy as if it was part of the electric demand. But we can evaluate what would be the part of this curtailed energy that has to be valorized for the CFP* configurations calculated previously to be cheaper than the LCOE* configurations (cf. Figure 117). We only give here an insight of the potential to use the curtailed energy. But additional analyses would be required to really assess this potential. Historiquement, le déploiement de ces MR s'est principalement appuyé sur des genset ou parfois des turbines hydroélectriques. Du fait de la réduction des coûts associés aux énergies solaire et éolienne [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF], [START_REF] Irena | The Power to Change: Solar and Wind Cost Reduction Potential to 2025[END_REF], des MR basés sur ces énergies deviennent compétitifs en termes de coût de l'électricité.

Cependant ceux-ci doivent inclure des moyens de flexibilité (batteries, genset) pour gérer la forte variabilité associée à ces énergies. Ainsi, il est nécessaire d'avoir une bonne représentation de cette variabilité pour pouvoir évaluer correctement le potentiel des MR basés sur les énergies renouvelables. Malgré une littérature croissante sur le potentiel de l'hydroélectricité ou de l'éolien pour alimenter des MR, il existe actuellement trop peu de données avec une résolution spatiale et temporelle suffisante pour correctement caractériser la variabilité de ces ressources en Afrique Sub-Saharienne. En revanche, de telles données sont disponibles pour l'énergie solaire, notamment grâce aux estimations satellites du rayonnement [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF].

Il est difficile d'avoir des chiffres sur le nombre de MR installés en Afrique mais pour avoir un ordre de grandeur, on estime que plusieurs milliers de MR ont été installés [START_REF]State of the Global Mini-grids Market Report 2020[END_REF]

Méthode 33

Pour réaliser cette étude, nous simulons le fonctionnement d'un MR fictif composé de panneaux PV et de batteries avec une résolution de 15min sur huit années. Ces simulations sont réalisées pour 200 localisations distribuées sur le continent Africain, et pour 10 profils de demande électrique avec des variabilités infra-journalières et saisonnières différentes (domestique/productif, sans saisonnalité ou avec un pic de demande en janvier, avril, juillet ou octobre).

La production PV est simulée à partir de données de rayonnement (Heliosat SARAH2 [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition 2[END_REF]) et de températures (ERA5 [START_REF] Hersbach | The ERA5 global reanalysis[END_REF]) et l'on considère que les panneaux sont orientés vers le Sud (resp. le Nord) dans l'hémisphère Nord (resp. Sud) avec une inclinaison égale à la latitude. Pour le stockage, les batteries se chargent lorsque la production PV est supérieure à la demande électrique et qu'elles ne sont pas pleines. Elles se déchargent lorsque la production PV est inférieure à la demande et que l'état de charge de la batterie est supérieur à 20% (i.e. une profondeur de décharge maximum de 80%). Nous considérons une efficacité de 95% à chaque charge ou décharge.

Dans ce chapitre, le système n'utilise pas de diesel et du fait de la variabilité de la ressource solaire, répondre à 100% de la demande électrique requiert des capacités PV et de stockage très importantes. Nous considérons un compromis entre le coût et la fiabilité du système en acceptant une qualité de service de 95%. Cela signifie que le MR doit pouvoir subvenir aux besoins de la demande pour 95% des heures, pour les 5% restants, la production (PV + décharge de la batterie) peut être inférieure à la demande.

Ainsi, il est possible d'identifier toutes les configurations qui permettent de satisfaire ce critère de 95%. Sachant que si une configuration le respecte, les configurations obtenues en augmentant la capacité de stockage ou la capacité PV sont aussi valides, on peut définir pour chaque capacité PV une capacité minimale de stockage qui permet de répondre à 95% de la demande. On peut ensuite utiliser cette courbe de dimensionnement pour calculer le CAE qui prend en compte les coûts associés à l'installation et à la maintenance du système PV, ceux associés à l'installation, à la maintenance et au remplacement des batteries ainsi que la quantité d'énergie produite sur la durée de vie du projet. On peut alors en déduire l'optimum économique qui dépend principalement du ratio entre les coûts associés au PV et ceux associés au stockage. La variabilité de ces courbes en fonction de la localisation et du profil de demande apparait bien lorsque l'on s'intéresse à l'optimum économique (cf. Figure 120). Une plus forte variabilité de la ressource augmente le surdimensionnement optimal, qu'elle soit due à une saisonnalité importante aux extrémités du continent, ou à une forte nébulosité dans la zone équatoriale. En intégrant de la saisonnalité dans les profils de demande, il s'avère que la co-variabilité entre demande électrique et ressource influence ce surdimensionnement. Pour le stockage, la principale différence provient du profil de demande et de sa co-variabilité infra-journalière avec la ressource solaire. Ces règles ont été identifiées sur la moitié des 200 localisations et testées sur l'autre moitié en prenant en compte les 10 profils de demande (cf. Figure 122). Elles ont été évaluées pour quatre ratio des coûts différents et sont disponibles dans le chapitre 2. Les configurations estimées permettent d'obtenir une qualité de service proche des 95% visés (entre 92% et 96%) et une très bonne estimation du CAE (nRMSE 34 environ égale à 0.02). 123). Ainsi, si l'on choisit une configuration (capacité PV, capacité de stockage), on peut en déduire la consommation de diesel nécessaire pour respecter ce critère de 100% de qualité de service. A partir de ces résultats de simulation, on peut ensuite calculer le CAE et l'EC correspondant à cette configuration 36 . On réitère ces calculs sur un grand nombre de configurations et on place les CAE et EC obtenus pour chaque configuration sur un graphe CAE vs. EC (cf. Figure 124).

Principaux résultats

Conclusion

Principaux résultats

Comme on pouvait le constater sur la Figure 124, il n'est pas possible de réduire l'EC jusqu'à 0𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ, et l'EC minimum est plutôt élevée avec une valeur proche de 200𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ. Cette empreinte est due aux émissions indirectes associées au stockage et au PV, et cette valeur minimum varie en fonction de la localisation (cf. Figure 125). Ces résultats dépendent bien sûr des valeurs considérées pour les paramètres techniques, économiques et environnementaux intervenant dans la modélisation des MR. Nous avons pu montrer 37 que les plus grandes valeurs de sensibilité sont associées aux caractéristiques de la ressource solaire et de sa co-variabilité avec la demande par rapport aux autres paramètres. Néanmoins, même si la sensibilité à ces paramètres est plus faible, leurs gammes de variations pouvant être très étendues 38 , il convient de prendre en compte leurs impacts sur les résultats. Quant aux réductions d'EC permises par des augmentations modérées de CAE, l'ensemble des scénarios testés dans notre analyse de sensibilité donnent des résultats moins optimistes 39 , mais qui ne remettent pas en question notre conclusion. La partie précédente montre que des incitations et politiques publiques sont nécessaires pour que les développeurs orientent leurs choix vers des configurations avec une EC plus faible. Plusieurs outils de politique publique peuvent être mobilisés pour cela, notamment des outils économiques tels que les taxes ou les subventions ou des outils réglementaires tels que les normes. Si une valeur tutélaire du carbone permet d'orienter les choix pour ce qui est des projets publics d'électrification ou ceux financés par certaines institutions internationales, elle n'a pas d'effet direct sur les développeurs privés. C'est pourquoi, nous évaluons l'impact de différentes politiques à destination des développeurs privés et les comparons de leur efficacité, de leur robustesse, et de la répartition de leurs coûts et revenus entre les différentes parties prenantes du projet. Le but est d'apporter des éléments 37 Plus de détails sur l'analyse de sensibilité sont disponibles en section 8.2.2 38 Par exemple, le facteur de charge moyen peut varier de 0,14 à 0,21 (x1,5) alors que la durée de vie des batteries peut varier de 2 à 10 ans (x5) 39 Une augmentation de 5% du CAE permet une réduction de l'EC supérieure à 30% dans un tiers des scénarios testés, et supérieure à 20% dans les deux tiers des scénarios testés. 40 La valeur tutélaire du carbone correspond à une valorisation monétaire des émissions de CO2 fixée par une institution (e.g. un gouvernement) et permettant de prioriser les investissements dans la lutte contre les changements climatiques. Si un investissement permet de réduire les émissions de GES avec une valeur inférieure à la valeur tutélaire, il doit être mis en oeuvre, sinon il n'est pas prioritaire. Pour limiter le réchauffement global à 2°, le GIEC estime une valeur tutélaire du carbone entre 60 et 120 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 .

Conclusion

méthodologiques et des exemples de mise en oeuvre pour aider d'une part les gouvernements à concevoir des politiques publiques de réduction de l'empreinte carbone de l'électrification, et d'autre part, les fonds internationaux qui souhaitent financer des MR ou qui recherchent des leviers d'atténuation des changements climatiques. Nous étudions de telles politiques au niveau de quatre pays contrastés en termes de ressources solaires et de politiques de tarification du diesel : le Kenya, le Sénégal, le Nigéria et Madagascar.

Méthode

La méthode utilisée reprend largement celle utilisée dans la section précédente (cf. section 9.3.1). Nous simulons le fonctionnement de nombreuses configurations de MR fictifs composés de solaire PV, de batteries et d'un groupe diesel. Cette fois-ci, nous ne considérons qu'un profil de demande hybride sans saisonnalité pour la courbe de charge utilisée dans nos simulations. Un profil domestique et un profil productif seront aussi utilisés mais seulement pour évaluer la robustesse des politiques publiques 41 . Pour les localisations, nous avons décidé de mener notre étude sur quatre pays présentant des contextes climatiques et économiques différents : le Kenya, le Sénégal, le Nigéria et Madagascar. En effet, les caractéristiques de la ressource solaire sont assez variées entre les pays du fait de leur géographie et si le prix du diesel est similaire au Kenya, au Sénégal et à Madagascar, il est bien inférieur au Nigéria. Nous sélectionnons environ 15 localisations régulièrement espacées dans chaque pays (soit 60 localisations au total), et nous utilisons les mêmes modèles que dans les sections précédentes pour y estimer la production solaire.

La simulation du fonctionnement du MR suit les mêmes règles que dans la section précédente. Il en est de même des modèles pour le calcul du CAE et de l'EC qui utilisent aussi les mêmes valeurs que dans la section précédente avec une seule différence pour le cas du Nigéria pour lequel le prix du diesel est fixé à 0.6$/L au lieu des 1$/L considéré pour les autres pays. On peut alors obtenir comme précédemment la courbe enveloppe qui relie l'EC de chaque MR à son CAE. En introduisant une valeur carbone sur l'EC, il est possible de modifier l'EC de l'optimum économique : par exemple, la Figure 128 montre pour une localisation au Kenya qu'avec une valeur carbone de 160 𝑈𝑆$/𝑔 𝐶𝑂 2 ,𝑒𝑞 , l'optimum économique devient un MG avec une EC inférieure à 330𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ contre environ 410𝑔 𝐶𝑂 2 ,𝑒𝑞 / 𝑘𝑊ℎ. On peut alors tracer une courbe qui montre le coût marginal qu'il faut donner à la tonne de CO2 évitée pour faire varier l'EC de l'optimum économique (cf. Figure 128). Dans la suite, nous estimons cette Du fait des différences importantes dans la répartition des coûts et des revenus entre les trois stratégies, il semble primordial de s'intéresser en priorité à cette répartition plutôt qu'à la recherche de la solution la plus efficace économiquement lors de la conception de politiques publiques. D'autres critères tels que la robustesse de la politique publique à une mauvaise estimation du contexte initial (profil de demande électrique, coûts des équipements, accès au capital, etc.) doivent aussi être pris en compte, ces aspects sont détaillés dans le manuscrit.

Conclusion

Nous avons présenté dans cette section un exemple de méthodologie pour concevoir des politiques publiques en quantifiant des niveaux de subventions et de taxations pour atteindre un objectif de réduction d'EC. Si l'efficacité de ces politiques est un critère à prendre en compte, la répartition des coûts et des revenus liés à la politique, ainsi que sa mise en oeuvre pratique semblent prioritaires par rapport à la maximisation de l'efficacité. Fixer un objectif moyen au niveau national plutôt qu'une norme unique d'EC que chaque projet doit respecter permet à la fois de gagner en efficacité et de limiter les inégalités entre les projets. En revanche, utiliser une taxe sur le diesel pour atteindre cet objectif peut certes être plus efficace, mais entraînera un surcout sur l'électricité qui se répercutera sur les usagers qui rencontrent déjà des difficultés à payer pour l'électricité. Mettre en place des subventions permettrait au contraire de réduire les tarifs de l'électricité pour les usagers, mais devraient être financées par ailleurs, par exemple via une péréquation des tarifs sur l'ensemble des consommateurs d'électricité ou via des fonds internationaux.

En plus de ces mécanismes de subvention/taxation, d'autres leviers peuvent être envisagés pour réduire l'EC des MR, notamment la réduction des risques liés aux projets de MR et la facilitation de l'accès au capital pour investir dans ces projets. En effet, le contexte, notamment financier, dans lequel sont développés les MR joue un rôle important sur les types de systèmes qui seront sélectionnés par les développeurs. Outre les aspects théoriques évoqués dans cette section, il est nécessaire de mieux comprendre le cadre institutionnel dans lequel ces politiques devraient être implémentées pour anticiper de potentiels obstacles à leur réussite.

Un environnement financier et régulatoire contraignant pour les MR

Cette section résume les résultats du chapitre 5 du manuscrit et reprend les résultats de l'article : T. 45 a été réalisé sur l'ensemble des textes pour associer chaque passage à une thématique assez large. A partir de ce premier codage, certaines hypothèses sur les interactions des acteurs, leurs opinions et leurs méthodes sur certains aspects du dimensionnement et des MR en général peuvent être formulées. Ces hypothèses sont alors testées et approfondies avec un second codage plus précis sur une partie restreinte des textes et en s'appuyant sur des apports théoriques, notamment des sciences de gestion.

Principaux résultats

Dans les sections précédentes, nous considérons la demande électrique comme une donnée d'entrée du modèle qui serait connue précisément et ne serait pas modifiée au cours de la simulation. Utiliser ces profils idéalisés convient pour nos études théoriques mais sur un cas pratique de développement d'un projet de MR, obtenir cette donnée est particulièrement difficile. Plusieurs guides et méthodologies sont entièrement consacrés à l'estimation de la future consommation électrique de la communauté à électrifier, sans pour autant mener à des résultats précis [START_REF] Hartvigsson | Comparison of load profiles in a mini-grid: Assessment of performance metrics using measured and interview-based data[END_REF]. Les grandes incertitudes associées à l'estimation du profil de charge proviennent notamment de la difficulté des sondages à anticiper la demande de personnes qui n'ont pas accès à l'électricité, leurs capacités/volontés à payer pour cette électricité et leurs arbitrages entre différentes sources d'énergie. A cela s'ajoute les incertitudes liées à la variabilité temporelle de la consommation : est-ce que certains usages sont saisonniers ? Y a-t-il des évènements ponctuels particuliers (festivités) ou des tendances à long terme (développement du village) ?

Une mauvaise estimation du profil de charge peut mettre en danger la viabilité technique et économique du MR. Il ne s'agit là que d'un risque parmi d'autres (arrivée du réseau national, vandalisme, instabilités politiques, …), d'où une forte réticence de la plupart des investisseurs et des prêteurs au financement de ce type de projet. Cela s'applique aussi aux institutions qui subventionnent les MR et qui développent des mécanismes pour financer les projets d'électrification en fonction de leurs résultats (result-based financing). Ainsi les développeurs de MR doivent souvent adapter leur dimensionnement aux fonds disponibles et à leurs temporalités.

Pour obtenir leurs licences, les développeurs doivent aussi s'adapter aux contraintes fixées par le régulateur (accord des politiques locaux, preuve de financement, …). Le régulateur peut aussi contraindre le développeur sur la proportion de personnes à connecter ou le tarif de l'électricité. Les différentes contraintes peuvent être interdépendantes et simultanées 46 , créant des tensions entre les acteurs dans le développement du projet. Ainsi, le dimensionnement n'est plus une question 45 Il ne faut pas prendre ici le terme de codage au sens du codage/développement d'un modèle en programmation, il s'agit plutôt d'un « surlignage » multiple pour pouvoir associer chaque portion de texte à un ou plusieurs « codes » (mot ou groupe de mots pour évoquer une thématique, un attribut, etc.) 46 Par exemple, la consommation d'électricité dépend du tarif, mais elle influence le montage financier et le dimensionnement qui eux-mêmes influencent le tarif 196 purement technique mais devient le résultat de compromis entre les développeurs, financeurs et régulateurs.

Dans ces jeux d'acteurs, les développeurs et opérateurs privés sont plus contraints que ceux du public. Ces derniers peuvent en effet compter sur des investissements moins risqués, des licences plus simples à obtenir et des subventions permettant d'utiliser des genset pour s'adapter aux variations de la demande même si cela n'est pas rentable. Au contraire, les développeurs privés doivent adapter leur dimensionnement pour réduire au maximum les coûts tout en gardant de la flexibilité pour gérer cette demande incertaine. Ce compromis entre optimisation et robustesse se base en général sur « l'intuition » et « l'expérience » du développeur. Même s'il utilise des logiciels d'optimisation, il choisit souvent un dimensionnement différent des résultats en fonction de ses succès et échecs passés.

En plus d'adapter leurs méthodes aux incertitudes et aux contraintes financières et régulatoires, les développeurs et opérateurs de MR doivent adapter leur business model. Certains développeurs tentent de diversifier leurs activités (mobilité électrique, aide à la création d'entreprise) pour attirer un maximum de subventions d'institutions internationales pour financer leurs MR. D'autres développent des grands portefeuilles de MR pour attirer les grands investisseurs et espérer les revendre rapidement à un opérateur pour réduire le temps de retour sur investissement. Ces stratégies sont généralement menées par des entreprises internationales et sont difficilement accessibles pour des plus petits développeurs locaux.

Du côté des opérateurs de MR, ceux-ci doivent en particulier s'adapter à des dimensionnements souvent inadaptés à la demande électrique. Dans le cas d'un surdimensionnement (capacité de production supérieure à la demande), les opérateurs vont essayer de stimuler la demande électrique en incitant les usagers à consommer plus d'électricité et à acheter davantage d'équipements électriques, notamment pour des usages productifs de l'énergie. En revanche, lorsque le système est sous-dimensionné (capacité de production inférieure à la demande), l'opérateur peut choisir de limiter la consommation (augmentation du tarif, refus de nouvelles connections, limiteurs de puissance, …) ou d'augmenter la production (installation de nouveaux panneaux/batteries/genset). Ces deux possibilités sont souvent difficiles à mettre en oeuvre à cause des contraintes imposées par le régulateur sur les connections ou les tarifs de l'électricité, et de la difficulté d'accéder aux financements pour étendre la capacité de production ou remplacer certains composants (e.g. batteries, cf. Figure 132, gauche). Lorsque ce sous-dimensionnement se prolonge, les équipements de production/stockage peuvent s'endommager réduisant encore plus la qualité de service du MR. Cela peut finalement mener à la faillite du MR et à la perte de confiance dans cette technologie des usagers qui vont finalement supporter les coûts de la modularité en s'équipant avec des genset et des SHS (cf. Figure 132, droite). Chaque aspect du développement des MR vient avec des incertitudes et des risques. En tentant de minimiser leurs risques, certains acteurs de ces projets les transfèrent aux autres acteurs (cf. Figure 133). Par exemple, les financeurs sécurisent au maximum les fonds investis en utilisant des montages financiers complexes et en augmentant les exigences des garanties demandées pour obtenir un prêt. De son côté, le régulateur peut imposer de faibles tarifs de l'électricité et des exigences élevées de fiabilité pour se prémunir contre un mécontentement de la population. Dans ces cas, les risques sont transférés au développeur et à l'opérateur qui doivent les gérer pour que leurs projets aboutissent. Ainsi, même si le régulateur et les financeurs ont relativement peu d'intérêts pour le développement des MR, ils peuvent influencer fortement les projets et contraindre les développeurs et opérateurs.

La mise en service du MR marque une rupture dans le projet : les risques portés par le développeur disparaissent et de nouveaux risques apparaissent pour l'opérateur. Une fois ce moment passé, la flexibilité pour adapter la production à la demande est considérablement réduite pour l'opérateur. L'environnement régulatoire et financier réduit encore plus cette flexibilité d'adaptation à une évolution souvent imprévisible de la demande, au détriment des usagers qui subissent alors les conséquences de ces transferts de risques successifs.

Conclusion

L'optimisation économique présentée précédemment (cf. sections 9.2 à 9.4) pour diminuer les coûts de l'électricité reste un enjeu majeur du dimensionnement. Cela permet de revendre l'électricité moins chère pour respecter les exigences du régulateur et/ou d'augmenter la rentabilité des investisseurs. Cependant, nous avons bien vu ici que le dimensionnement ne se résume pas à cette seule optimisation des coûts, mais correspond plutôt à un compromis entre les développeurs, les financeurs et le régulateur. Les nombreuses contraintes imposées par le régulateur et les financiers peuvent modifier la taille des systèmes à installer : d'un côté, le régulateur peut imposer un nombre minimum de connexions, de l'autre, la difficulté d'accès aux financements réduit la taille des systèmes. Ces contraintes sur le financement posent des obstacles au déploiement de MR avec une grande part de renouvelable du fait de leurs coûts d'investissement bien plus élevés.

Les business model conçus par les développeurs et opérateurs privés montrent qu'il est compliqué d'être rentable dans le secteur des MR, d'où un recours plus élevé aux subventions que dans le reste du secteur de l'électricité. Pour mener à bien les objectifs d'électrification rurale en gardant un coût abordable, il semble préférable de subventionner le secteur des MR. En subventionnant principalement les batteries et le PV, on peut à la fois réduire le coût de l'électricité et inciter les développeurs à réduire l'EC des MR. Ces subventions pourraient venir de fonds internationaux comme c'est déjà le cas, mais aussi de l'Etat, par exemple via un système de péréquation du tarif de l'électricité qui diminuerait les écarts de tarifs entre zones urbaines et rurales. Ces subventions devraient pouvoir être obtenus à différents moments de la durée de vie du MR pour pouvoir gérer le remplacement des batteries et/ou l'adaptation de la production à l'évolution de la demande électrique et ainsi soutenir la pérennité du système. En effet, une durée de vie réduite pour les MR entraîne aussi des coûts de l'électricité et une empreinte carbone plus élevés, d'où la nécessité d'intégrer cette problématique dans la conception des politiques publiques.

Conclusion et perspectives 9.6.1 Conclusion

Finalement, peut-on dire que les MR sont une solution pour électrifier les zones rurales à un coût abordable avec de faibles émissions de GES ? Nous avons vu que pour des MR 100% solaire, le coût de l'électricité est pour l'instant bien plus élevé que celui de MR hybrides avec du diesel, et souvent plus élevé que les coûts d'extension du réseau. En revanche, bien que l'EC des MR 100% solaire ne soit pas négligeable du fait des émissions indirectes, elle reste tout de même plus faible que celle de la majorité des mix électriques actuels en Afrique et environ deux fois plus faibles que celle de MR hybrides qui minimisent le coût de l'électricité. Nous avons montré que des compromis existent entre minimiser les coûts et minimiser les émissions de GES, permettant de réduire l'EC des optimums économiques en augmentant modérément le CAE. Pour inciter les développeurs de MR à réduire l'EC des systèmes installés, nous avons proposé différentes stratégies de subventions/taxations pour différents pays. Etant donné les difficultés de financement des MR et les contraintes imposées par le régulateur, il semble préférable de privilégier des mécanismes de subventions, notamment sur les batteries, pour réduire à la fois les tarifs de l'électricité pour les usagers et l'EC des MR. Ces subventions doivent être adaptées à chaque territoire et pensées sur l'ensemble de la durée de vie du projet et pas seulement au début pour aider les opérateurs à adapter leur production à l'évolution de la demande. Ainsi, même si les résultats en termes de coût de l'électricité et d'émissions de GES sont moins optimistes que dans la majorité des études évoquées en introduction, les MR sont une solution prometteuse pour électrifier à un coût abordable avec de faibles émissions de GES. Et ils le seront d'autant plus à l'avenir avec la baisse des coûts sur les équipements solaires et les batteries, et la diminution de l'empreinte carbone des mix électriques utilisés dans la production des composants.

En plus des connaissances apportées, cette thèse aura permis de développer plusieurs outils d'aide à la décision qui pourront être réutilisés, notamment par les développeurs et les planificateurs de l'électrification. Les règles de dimensionnement établies à la section 9.2 permettent de réduire le temps de calcul pour estimer les configurations optimales de MR 100% solaire. L'estimation de la courbe enveloppe à la section 9.3 illustre les différentes possibilités de dimensionnement pour trouver des compromis entre CAE et EC. L'estimation des courbes de coût marginal du carbone et les analyses en termes de valeur du carbone faciliteront la mobilisation de financements d'institutions comme le Fond Vert pour le climat, dont les moyens financiers pourraient accélérer l'électrification rurale. La méthodologie développée dans la section 9.4 offre un outil de conception de politiques publiques pour définir des objectifs de réduction d'EC et évaluer des stratégies pour atteindre ces objectifs. Les analyses de sensibilités réalisées dans les sections 9.2 à 9.4 montrent l'importance d'adapter les paramètres des modèles de dimensionnement et de planification au contexte local, ainsi que la nécessité d'évaluer la robustesse des résultats obtenus. L'amélioration de ces modèles passe aussi par une meilleure prise en compte de la variabilité spatiale et temporelle de la ressource solaire et de sa co-variabilité avec la demande électrique, ainsi que par l'intégration des émissions indirectes de GES dans les calculs d'empreinte carbone.

Enfin, ces travaux montrent le besoin de recourir à une approche interdisciplinaire pour pouvoir traiter les questions liées à l'électrification rurale. En nous appuyant sur les sciences de l'environnement, les sciences de l'ingénieur, les sciences de la gestion, l'économie et la sociologie, nous espérons avoir convaincu le lecteur ou la lectrice de la nécessité de telles approches.

Perspectives

Pour correctement répondre à la problématique initiale, les résultats obtenus ici doivent être comparés à ceux que l'on peut obtenir pour d'autres solutions d'électrification (extension du réseau, systèmes individuels). Les travaux présentés dans cette thèse ont vocation à être prolongés et intégrés dans des modèles plus larges de planification de l'électrification rurale [START_REF] Dagnachew | The role of decentralized systems in providing universal electricity access in Sub-Saharan Africa -A model-based approach[END_REF], [START_REF] Mentis | A GIS-based approach for electrification planning-A case study on Nigeria[END_REF], [START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF]. Ainsi, en plus des habituelles optimisations économiques entre extension du réseau, MR et SHS, il sera possible de quantifier l'empreinte carbone de cet optimum économique mais aussi de mener une optimisation de l'empreinte carbone de l'électrification pour comparer les valeurs obtenues. Cela permettra notamment de quantifier les valeurs absolues totales des émissions de GES qui pourraient être évitées à l'échelle d'un pays et les coûts totaux que cela demanderait. De même qu'avec la courbe enveloppe, il sera possible d'estimer un front de Pareto pour proposer différents compromis entre empreinte carbone et coût de l'électricité, et de concevoir des politiques publiques pour atteindre ces compromis.

Pour améliorer ces modèles de planification mais aussi nos propres modèles, il est nécessaire de modéliser les aspects dynamiques du système (évolution de la demande et des systèmes de production) comme le souligne la section 9.5. En effet, nous avons toujours considéré une demande constante au fil des années et nous n'avons pas pris en compte la baisse des performances des équipements solaires et des batteries, alors que ces aspects représentent un enjeu primordial pour la pérennité des MR et qui influence à la fois les coûts et les émissions de GES. On peut aborder ces questions en regardant la robustesse d'un MR lorsque l'on fait évoluer la demande et les paramètres techniques des équipements au cours du temps. Mais il peut être intéressant de pousser plus loin la démarche et d'évaluer des stratégies de modularité des capacités installées et d'adaptation de la demande, par exemple en s'appuyant sur la théorie des options réelles [START_REF] Cuervo | Photovoltaic power purchase agreement valuation under real options approach[END_REF], [START_REF] Markham | The application of real options to renewable energy investments in South Africa: the case of solar energy technology for small businesses and individual homeowners[END_REF].

Enfin, nous avons restreint notre étude à une demande électrique couverte par un système PV avec des batteries et un groupe diesel, mais l'accès à l'énergie ne se résume pas à l'électricité (e.g. la cuisson) et d'autres ressources renouvelables comme la biomasse pourraient remplacer une partie, voire la totalité du diesel. De même si nous avons résumé les performances du MR à deux indicateurs : le CAE et l'EC, d'autres critères doivent être pris en compte dans le choix de ces systèmes qui ont aussi des impacts sur l'occupation des sols, les écosystèmes locaux et l'utilisation d'eau. Ainsi, il pourrait être intéressant de développer une approche plus intégrée qui détaillerait les différents besoins de la communauté (électricité, cuisson, irrigation, réfrigération) et proposerait des solutions pour subvenir à ces besoins en tenant compte des interactions entre secteurs (e.g. liens entre production agricole, disponibilité de biomasse, besoin en irrigation et demande électrique).

1

  Introduction ...................................................................................................................................

  • ATP: Ability to pay • BAU: Business-as-Usual • CAPEX: Capital expenditures • CFP: Carbon footprint • CFP* : configuration that minimize the carbon footprint • DFI: Development Finance Institution • DHI: Diffuse Horizontal Irradiance • DNI: Direct Normal Irradiance • ECOWAS: Economic Community of West African States • ECREEE: ECOWAS Centre for Renewable Energy and Energy Efficiency • EPRA: Energy and Petroleum Regulation Authority • ESMAP: Energy Sector Management Assistance Program • GHG: Greenhouse Gases • GHI: Global Horizontal Irradiance • GIZ: Deutsche Gesellschaft für Internationale Zusammenarbeit (German cooperation) • GTI: Global Tilted Irradiance • IBRD: International Bank for Reconstruction and Development • IDA: International Development Association • IEA: International Energy Agency • IEEE: Institute of Electrical and Electronics Engineers • IPCC: Intergovernmental Panel on Climate Change • KPLC: Kenya Power and Lighting Company • LCOE: Levelized Cost of Energy • LCOE*: configuration that minimizes the levelized cost of energy • MG: Mini-Grid • NDC: Nationally Determined Contribution • NGO: Non-Governmental Organization • O&M: Operation and Maintenance • OPEX: Operational Expenditures • PV: Photovoltaic • RBF: Result-Based Financing • REA: Rural Electrification Authority • REREC: Rural Electrification and Renewable Energy Corporation • SDG: Sustainable Development Goal • SHS: Solar Home Systems • SM: Supplementary Material • SPC: Shadow Price of Carbon • WTP: Willingness to pay 1 Introduction

Figure 1 :

 1 Figure 1 : Illustration of the Doughnut economy developed by Kate Raworth in[START_REF] Raworth | Doughnut Economics: Seven Ways to Think Like a 21st-Century Economist[END_REF]

Figure 5 :

 5 Figure 5 : Current GHG emissions per capita as a function of the Index of Human Development for different regions of the world [6]

Figure 7 :

 7 Figure 7 : Share of the population without access to electricity [10]

Figure 9 :

 9 Figure 9 : Detailed situation of electricity access with the Multi-Tier framework in Kenya in 2020[START_REF]Kenya -Multi-Tier Framework (MTF) Survey -ENERGYDATA.INFO[END_REF]

Figure 12 :

 12 Figure 12 : Diagram of a Solar Home Systems (SHS) to supply a household on Mfangano Island, Kenya

Figure 13 :

 13 Figure 13: Diagram of an off-grid MG using solar PV, batteries and diesel in Kisii, Kenya

Figure 17 :

 17 Figure 17 : Estimation of the LCOE for a 15kWp MG supplied by wind turbines and storage (left[START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF]) or by solar PV and storage (right[START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF]), the same load profiles are considered for both studies. The costs for a diesel only MG in these studies is mostly estimated between 0.2€/kWh and 1€/kWh[START_REF] Szabo | Energy solutions in rural Africa: mapping electrification costs of distributed solar and diesel generation versus grid extension[END_REF]

Figure 18 :

 18 Figure 18 : Left: Mean annual Global Horizontal Irradiance (GHI) over 8 years (2008-2015). Right: Illustration of the solar irradiance variability for three locations. The top graphs show the infra-day variability, the continuous line give the mean GHI whereas the dashed lines give the 10 th and 90 th percentiles of the GHI at this hour over one year. The bottom graph shows the seasonal and inter-days variations of the resource for one year.

Figure 19 :

 19 Figure 19 : Left: Selection of PV MG equipment benchmark costs, 16 MG selected from Africa and Asia [139].

Figure 20 :

 20 Figure 20 : Left: Map of identified MGs in West Africa [156] ; Right: Evolution of the estimated number of MGs in Africa [130]. Both graphs do not include fossil-fuel only MGs.

Figure 21 :

 21 Figure 21 : Repartition of finance instrument types for the different electricity sector in Africa (2019)[START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF]. Unlike debt, equity corresponds to the value that belongs directly to the company/corporate or to the project.

Figure 22 :

 22 Figure 22 : Investment flows required for climate change mitigation to stay below 1.5°C or 2°C[START_REF]Synthesis report of the IPCC sixth assessment report (AR6) -Longer report[END_REF]

Figure 23 :

 23 Figure 23 : Configurations, energy consumption, avoided GHG emissions and project costs for electricity access of refugee settlement in Africa under three different scenarios (Tier 1 to 3)[START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF]

Figure 27 :

 27 Figure 27 : Optimizing the costs of 100% solar MGs and assessing the sensitivity of the optimal configuration

Figure 28 :

 28 Figure 28 : Mean annual Global Horizontal Irradiance (GHI) for the 200 randomly selected locations. The six numbered locations will be used as examples to illustrate some results in the following. They have been chosen for their different resource characteristics (seasonality, day-to-day variability).

Figure 29 :

 29 Figure 29 : Domestic and productive daily load profile

Figure 30 :

 30 Figure 30 : The five seasonal patterns considered for the electricity demand

Figure 31 :

 31 Figure 31 : Probability Density Functions of full PV costs (left), full storage costs (middle) and for the cost ratio r (PV/Storage) (right) as obtained from Monte Carlo simulations for two periods of time (2015 and 2025)

Figure 32 :

 32 Figure 32 : Sizing curves S95(x) (normalized storage capacity S as a function of oversizing factor x) for six locations and for two demand profiles: domestic (blue) and productive (red) without seasonal variations. All MGs configurations allow for a 95th quality service level.

Figure 33 :

 33 Figure 33 : Normalized storage capacities [ℎ𝑟𝑠 𝑒𝑞 ] for the 200 locations obtained with a large oversizing ratio (x = 2.5). (The normalized required storage capacity is the storage capacity [Wh] required per unit of mean power demand (i.e. 250 W) to satisfy the demand 95% of hours in a year. It is expressed in [Wh/W] or in [ℎ𝑟𝑠 𝑒𝑞 ]. Left and middle maps: results for a domestic and a productive daily profile. Right: normalized storage capacities as a function of latitude (blue dots: domestic and red dots: productive, only a part of the abscissa (from 5 to 13) is not shown).

Figure 34 :

 34 Figure 34 : Optimum oversizing 𝑥 * obtained by simulation with a cost ratio r=1 and without seasonality as a function of the latitude for a domestic (blue dots) and a productive (red dots) demand profile.

Figure 35 :

 35 Figure 35 : Optimal normalized storage capacity 𝑆 * obtained by simulation with a cost ratio r=1 and without seasonality as a function of the latitude for a domestic (blue dots) and a productive (red dots) demand profile. Grey dots correspond to the limiting storage capacity requirement presented in Figure 33 for x = 2.5.

Figure 36 :

 36 Figure 36 : Optimal LCOE obtained by simulation with a cost ratio r=1 and without seasonality as a function of the latitude

Figure 39 :

 39 Figure 39 : Optimum normalized storage capacity 𝑆 * as a function of the 75 th percentile of the normalized nocturnal energy 𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 ). Results are presented for 5 different seasonal profiles of the demand (None: No Seasonality; Jan, Apr, Jul, Oct:Seasonality with a maximum in January; April, July and October respectively). This graph presents the optimum storage capacity values for 𝑟 = 1 and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles).

Figure 40 :

 40 Figure 40 : Comparison between optimal LCOE obtained by simulation and configurations estimated by the sizing rule for all load profiles and 𝑟 = 1

Figure 41 :

 41 Figure 41 : Comparison between optimal LCOE obtained by simulation and configurations estimated by the sizing rules for the four cost ratios (0.3, 0.5, 0.8, 1) and all load profiles.

Figure 42 : 57 2. 5

 42575 Figure 42 : Summary diagram of the procedure to apply the pre-sizing rules

Figure 43 :

 43 Figure 43: Optimizing the costs and carbon footprints of hybrid MGs and identifying the potential trade-offsInnovation compared to previous works: This study contributes to the research field around MG by giving a more general view on their CFP over the African continent and a greater emphasis on the CFP in the sizing than what can be found in the existing literature. This is mainly done through: the integration of indirect emissions of GHG into the CFP calculation, the identification of a Pareto front between a CFP optimal configuration and a LCOE optimal configuration, a wider sensitivity analysis

Figure 44 :

 44 Figure 44 : Mean annual GHI over the 2008-2015 period from Heliosat SARAH2. The dots are the locations used in the study. The blue ones give a transect and are used in sections 3.4.3 and 3.5.1. The green one is used in section 3.4.1.

Figure 45 :

 45 Figure 45 : Three daily load profiles used in the study

Figure 46 :

 46 Figure 46 : The five seasonal patterns considered for the electricity demand. 'Mar', 'Jun', 'Sep, 'Dec' account respectively for 'March', 'June', 'September' and 'December' and correspond to the month with the highest demand. 'None' is a yearly demand profile without seasonality.

Figure 47 :

 47 Figure 47 : Simulation of solar, genset and batteries dispatching for one week in January. The top graph corresponds to the first run of the simulation without maximizing genset efficiency, the bottom one corresponds to the improved temporal dispatch of genset and batteries.

Figure 48 :

 48 Figure 48 : Least LCOE (LCOE * ) and least CFP (CFP * ) configurations in a LCOE vs.GHG graph. The black line is the envelope curve. The color gives the normalized PV capacity installed (dark dots refer to configuration with low penetration of solar, and light dots to high penetration of solar) and the size of the dots gives the normalized storage capacity installed. Each U-shape line corresponds to a given storage capacity (only one out of three storage capacities simulated is represented). Each point of each line to a given PV capacity.To each dot corresponds finally a given genset production, i.e., the production required to satisfy the demand all along the period. This graph is obtained for a location in Angola (-12.5°N; 17.5°E) with a hybrid load profile.

Figure 49 :

 49 Figure 49 : Envelope curves considering the whole or only direct emissions for a location in Angola (-12.5°N; 17.5°E) with a hybrid load profile. Dots correspond to the whole CFP, including both direct and indirect emissions; diamonds correspond to the direct GHG emissions only. The least CFP (CFP*), least GHGdirect (𝐺𝐻𝐺 𝑑𝑖𝑟𝑒𝑐𝑡

Figure 50 :

 50 Figure 50 : CFP decomposition for a location in Angola (-12.5°N; 17.5°E) with a hybrid load profile for all configurations of the left-hand side of the envelope curve in Figure 7. The white arrows give indications on how to read the graph : the illustrative configuration has a LCOE around 0.415$/kWh and a CFP around 210gCO2/kWh from which 22% are related to the genset, 54% to the batteries and 24% to solar PV.

Figure 51 :

 51 Figure 51 : Least LCOE (top left) and least CFP (top right) for all locations with a hybrid load profile. LCOE and CFP for a dieselonly configuration are respectively equal to 0.46US$/kWh and 996𝑔 𝐶𝑂 2 /𝑘𝑊ℎ. Renewable fraction (bottom) corresponds to the proportion of the energy demand supplied by solar and batteries.

Figure 53 :

 53 Figure 53 : Relative differences between the LCOE * and the CFP * configurations. The relative CFP change (resp. LCOE change) corresponds to the CFP reduction (resp. LCOE increase) obtained from the LCOE * configuration to the CFP * configuration. Color refers to the mean capacity factor (left) and the first co-variability indicator 𝜎 𝑑𝑖𝑓𝑓 (right; cf. section 3.3.1.2).

3. 4 . 3

 43 Trade-offs configurations between LCOE* and CFP* Looking at Figure 54, the slope of the envelope curve for different locations on a N-S transect is very steep near the CFP* configuration. Near this point, very important LCOE increases are thus required to achieve only small CFP reductions. Conversely, the slope is much lower around the LCOE* configuration. Around this point, significant CFP reductions can be obtained at low or moderate LCOE increase.

Figure 54 :

 54 Figure 54 : Envelope curve for the N-S transect locations (Longitude 17.5°E, cf. Figure 44).

  𝜎 𝑑𝑖𝑓𝑓This highlights the potential for significant reductions of MG CFPs with only moderate additional costs compared to the least cost configuration. Figure55shows the reduction in CFP from the LCOE* configurations that can be achieved for the 96 locations of Figure44with different levels of LCOE increase (Figure55left), and, from another point of view, the increase in LCOE needed to achieve different levels of CFP reduction (Figure 55 right).

Figure 55 :

 55 Figure 55 : Left: Reduction of the CFP from the LCOE* configuration with different levels of LCOE increase. Right: Increase of the LCOE from the LCOE * configuration for different objectives of CFP reduction. In both graphs, "Max" corresponds to the CFP and LCOE relative changes obtained with the CFP * configurations.

Figure 56 :

 56 Figure 56 : Envelope curves for different scenarios of 𝐶 𝑃𝑉 and 𝐶 𝑓𝑢𝑒𝑙 of a location in Angola (-12.5°N,17.5°E) and for a hybrid load profile without seasonality. The 𝐶 𝑃𝑉 graph represents the variation of the envelope curves when changing the value of 𝐶 𝑃𝑉 , the red color corresponds to an increase of 50% of the 𝐶 𝑃𝑉 value, whereas the blue color corresponds to a decrease of 50% and the purple color is obtained with the reference value of 𝐶 𝑃𝑉 . The area represents the variations of this curve when modifying other parameters as specified in section 8.2.2. The upper limit of the area is the 90 th percentile of values and the lower limit is the 10 th percentile. The same representation applies to the other graph for 𝐶 𝑓𝑢𝑒𝑙 .

Figure 57 :

 57 Figure 57 : Distribution of LCOE and CFP sensitivities to each parameter for LCOE* and CFP* configurations. The lines corresponds to the distribution between the 10 th and the 90 th percentile; the square is the value of the median. For the sensitivity related to locations and load profiles, three variables were computed to characterize the variations in solar resource and in the co-variability of this resource and the power demand: the mean capacity factor, the first co-variability indicator 𝜎 𝑑𝑖𝑓𝑓 and the nocturnal energy (cf. section 3.3.1.2). Results are obtained for the 8 locations on the N-S transect.

Figure 58 :

 58 Figure 58 : Cumulative distribution of the CFP reduction from the LCOE* configurations related to all the scenarios of the sensitivity analysis. The different curves correspond to different level of LCOE increase from the LCOE* configuration.

Figure 59 :

 59 Figure 59 : Left, map of SPC, the shadow carbon price to go from LCOE * to CFP * . Right, value of SPC for all locations and for different objectives of CFP reduction. Both graphs are obtained with a hybrid load profile and using the reference values for all parameters.

Figure 61 :

 61 Figure 61 : Mean annual Global Horizontal Irradiance (GHI) for Kenya, Senegal, Nigeria, and Madagascar

Figure 62 :

 62 Figure 62 : Typical load profiles for the fictitious mini-grids. The hybrid load profile is a mix between the productive and the domestic load profile.

Figure 63 :

 63 Figure 63 : Envelope curve for a location in Kenya (-4°N; 38.5°E) and a hybrid load profile. The CAPEX is normalized by its value for a genset only configuration.

Figure 64 :

 64 Figure 64 : Envelope curves for different level of SPC. Red dots show the LCOE* configurations for five SPC: 0, 40, 80, 120 and 160 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 . These graphs refer to a location in Kenya (-4°N; 38.5°E) and a hybrid load profile.

Figure 65 :

 65 Figure 65 : Marginal cost of carbon for a location in Kenya (-4°N; 38.5°E) and a hybrid load profile. The five red dots refer to the value for the LCOE* configurations with the five SPC values taken in Figure 64: 0, 40, 80, 120 and 160 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞

Figure 66 :

 66 Figure 66 : Marginal cost curves of carbon for 60 MG (15 in Kenya, 14 in Senegal, 16 in Nigeria and 15 in Madagascar) and a hybrid load profile. The red dashed curves correspond to the mean curve for the country.

Figure 67 :

 67 Figure 67 : Evolution of the LCOE when using an individual norm of emissions or a uniform CFP tax at the country level. Each point corresponds to an individual MG and MG projects are sorted by increasing LCOE.

Figure 69 :

 69 Figure 69 : Mean costs (blue bars: CAPEX and yellow bars: OPEX) for the different strategies ("BAU"," Tax", "Sub" and "Bonus/Malus"). These costs are only referring to the configuration changes without the effect of subsidies and taxation on the final costs. The LCOE modifications only related to the configuration change correspond to the height of the blue and yellow bars. The means are computed as the average costs for the 14-16 MG in each country. The red bar extension corresponds to the effect of fuel taxation (cost increase) and the red frame corresponds to the effect of subsidies (cost reduction). Green bars correspond to the LCOE values, including subsidies and taxation effects.

Figure 70 :

 70 Figure 70 : Costs (CAPEX, OPEX and LCOE) for each MG (15 in Kenya, 14 in Senegal, 16 in Nigeria and 15 in Madagascar) with the different strategies. The costs represented here include both subsidies and taxation effects.

Figure 71 :

 71 Figure 71 : Mean CFP [𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ] of MG in the BAU strategy for the different scenarios and countries.

Figure 72 :

 72 Figure 72 : Mean CFP reduction compared to the BAU case for the different scenarios, strategies, and countries. The red dashed line corresponds to a 35% CFP reduction objective.

Figure 73 :

 73 Figure 73 : Mean relative change of taxation (top) and subsidies (bottom) costs compared to the "Reference" scenario for the different strategies, scenarios and countries.

Figure 74 :

 74 Figure 74 : CFP of LCOE* configurations for each country and strategy as a function of the discount rate. The discount rate used in the strategy design is 0.1 (dashed line).

Figure 75 :

 75 Figure 75: Understanding the influence of the institutional environment on the sizing of MGs Innovation compared to previous works: The vast majority of studies related to the sizing of MG consider the sizing from a technical point of view only. Thanks to a collaboration with Emilie Etienne, a PhD student in sociology, this study uses an interdisciplinary approach to illustrate how the technical tools and methods are used in practice in real villages. Our work differs also from the literature on the

Figure 77 :

 77 Figure 77: Left: Due to funding difficulties, only 7 batteries have been replaced instead of replacing the whole 12 batteries' row. Right: The barbershop is connected to the MG but is also equipped with solar panels to cope with MG outages. Source: authors, fieldwork in Kenya, May 2022.

Figure 78 :

 78 Figure 78: Summary of risks endured by each type of actors. For a better readability, only the risks that we observed most frequently are represented. The dotted line represents a loose consequence.

•

  Importance to consider the co-variability of solar resources and electricity demand • Robustness of 100% solar MG configurations to economic assumptions • High sensitivity of hybrid MG sizing optimization to socio-economic parameters Policy maker and DFI: • Estimation of the economic value of a ton of CO2 avoided (to know the efficiency of CFP reduction in the MG sector) • Marginal cost of carbon to design CFP reduction objectives • Strategies to reduce the CFP of MG • Methodology to design economic incentives for MG CFP reduction • Identification of some obstacles to MG development 6.2 Perspectives 6.2.1 Apply our methods to rural electrification planning

7 .

 7 Compute cost ratio 𝒓• Compute the cost ratio 𝑟 [-] for your system using equations (12): 𝑟 = 𝛼 𝑃𝑉 𝛼 𝑆 8. Optimal oversizing PV capacity for cost ratio 𝒓 using 𝒙 * 𝒆𝒔𝒕,𝒓 = 𝒇(𝒓) . 𝒙 * 𝒆𝒔𝒕,𝒓=𝟏 • Estimate the correction coefficient 𝑓(𝑟) corresponding to the cost ratio 𝑟. It can be done using the curve in Figure 79 conjectured by the analyses obtained from four cost ratios.

Figure 79 : 9 .• 12 ) 10 .

 7991210 Figure 79: Correction coefficient to apply to the optimal oversizing factor as a function of the cost ratio r • Multiply the oversizing 𝑥 * 𝑒𝑠𝑡,𝑟=1 by this correction coefficient, it gives an estimation of the optimal oversizing value: 𝑥 𝑒𝑠𝑡 * [-]• The estimated optimal PV capacity to install is 𝐶 𝑃𝑉 = 𝑥 𝑒𝑠𝑡 * 𝐶 𝑃𝑉 0 [𝑊 𝑝 ]

Figure 80 :

 80 Figure 80 : Sizing curves S95(x) (normalized storage capacity S as a function of oversizing factor x) for six locations and for five domestic demand profiles (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). All MG configurations allow for a 95th quality service level.

Figure 81 :

 81 Figure 81 : Sizing curves S95(x) (normalized storage capacity S as a function of oversizing factor x) for six locations and for five productive demand profiles (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). All MG configurations allow for a 95th quality service level.

154

 154

Figure 82 :Figure 83 :

 8283 Figure 82 : Maps of the optimum oversizing 𝑥 * obtained by simulation with a cost ratio r=1 and without seasonality

Figure 84 :Figure 85 :

 8485 Figure 84 : Maps of the optimal normalized storage capacity 𝑆 * obtained by simulation with a cost ratio r=1 and without seasonality

Figure 88 :

 88 Figure 88 : Least LCOE configurations (normalized PV capacity (continuous lines; top graphs); normalized storage capacity (dotted lines, bottom graphs) as a function of cost ratio (PV full costs / storage full costs, log scale) for six locations and for the domestic load profiles (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). The 90% confidence interval of the cost ratio distribution is presented for 2015 (yellow vertical band) and 2025 (cyan vertical band). The green band corresponds to the overlap of cyan and yellow bands. All configurations allow for a 95 th quality service level.

Figure 89 :

 89 Figure 89 : Least LCOE configurations (normalized PV capacity (continuous lines; top graphs); normalized storage capacity (dotted lines, bottom graphs) as a function of cost ratio (PV full costs / storage full costs, log scale) for six locations and for the productive load profiles (None: No Seasonality; Jan, Apr, Jul, Oct: Seasonality with a maximum in January; April, July and October respectively). The 90% confidence interval of the cost ratio distribution is presented for 2015 (yellow vertical band) and 2025 (cyan vertical band). The green band corresponds to the overlap of cyan and yellow bands. All configurations allow for a 95 th quality service level.

Figure 91 :

 91 Figure 91 : Optimum normalized storage capacity 𝑆 * as a function of the normalized 75 th percentile of nocturnal energy (𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 )). Results are presented for 5 different seasonal profiles of the demand (None: No Seasonality; Jan, Apr, Jul, Oct:Seasonality with a maximum in January; April, July and October respectively). Each graph presents the optimum storage capacity values for a different cost ratio and for both the domestic and productive load profiles (no distinction is made here between the 2 profiles). Parameters for each regression are given in the titles.

Figure

  Figure92: Level of quality service obtained for the 200 locations with the estimated optimal configurations using equations (18) and[START_REF] Falk | Drinking Water Supply in Rural Africa Based on a Mini-Grid Energy System-A Socio-Economic Case Study for Rural Development[END_REF]. Top boxplots give the distribution for each yearly load profile, cost ratios are gathered. Bottom boxplots give the distributions for each cost ratio, yearly load profiles are gathered.

Figure 94 :

 94 Figure 94 : Error indicators for optimal storage capacity estimation for each cost ratios and load profiles using a modified version of equation(18) that includes the cost ratio : 𝑆 95 * 𝑒𝑠𝑡,𝑟=1 = 0.91 𝑝 75 (𝐸 𝑛𝑜𝑐𝑡 ) 𝜂 𝑠𝑡𝑜𝑟𝑎𝑔𝑒 + 1.13𝑟 -0.75(top four graphs) and

Figure 96 :Figure 97 :Figure 98 :

 969798 Figure 96 : Domestic, productive and mixed daily load profile

8. 2

 2 SM related to chapter 3 8.2.1 Supplementary figures

Figure 99 :

 99 Figure 99 : Least LCOE values obtained for different level of service quality (QS) with 100% solar MG.

Figure 100 :

 100 Figure 100 : Genset efficiency 𝜂 𝑔𝑒𝑛 as a function of its load factor 𝑃 𝑔𝑒𝑛 /𝐾 𝑔𝑒𝑛 . This efficiency is the ratio of the electricity output of the genset on the thermal energy from the fuel.

Figure 101 :

 101 Figure 101 : Distribution of the solar capacity factor (top) and of the genset use timestep (bottom) over the two years used in the simulation

Figure 102 :

 102 Figure 102 : LCOE and CFP of the Least LCOE and least CFP configurations obtained for a hybrid load profile without seasonality. LCOE and CFP for a diesel only configuration are respectively equal to 0.46US$/kWh and 996𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ.

Figure 103 :

 103 Figure 103 : Storage and PV normalized capacities for the least LCOE and least CFP configurations. The right column gives the relative differences between the least CFP and the least LCOE configurations (PV and storage capacities).

165

 165

Figure 104 :

 104 Figure 104 : Least LCOE (bottom) and least CFP (top) for all locations with a hybrid demand profile as a function of the mean capacity factor CF (left) and the co-variability (right). Color correspond to the absolute distance from the equator [°]. This figure is obtained with costs and CFP related to each component that are different from the reference scenario: +50% for 𝐶𝐹𝑃 𝑏𝑎𝑡 , 𝐶𝐹𝑃 𝑃𝑉 , 𝐶 𝑏𝑎𝑡 and 𝐶 𝑃𝑉 ; -10% for 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 and -50% for 𝐶 𝑓𝑢𝑒𝑙

Figure 105 :

 105 Figure 105 : Same figure as Figure 104 but with costs and CFP related to each component that are different from the reference scenario: -50% for 𝐶𝐹𝑃 𝑏𝑎𝑡 , 𝐶𝐹𝑃 𝑃𝑉 , 𝐶 𝑏𝑎𝑡 and 𝐶 𝑃𝑉 ; +10% for 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 and +50% for 𝐶 𝑓𝑢𝑒𝑙

Figure 106 :

 106 Figure 106 : Relative change of CFP and LCOE between the least LCOE and the least CFP configurations. The left map gives the reduction of CFP from the least LCOE to the least CFP configuration. The right map gives the increase of LCOE from the least LCOE to the least CFP configuration.

Figure 107 :

 107 Figure 107 : Envelope curves for different scenarios of costs, CFPs and lifetimes of a location in Angola (-12.5°N,17.5°E) and for a hybrid load profile without seasonality. The 𝐶 𝑃𝑉 graph represent the variation of the Envelope curves when changing the value of 𝐶 𝑃𝑉 , the red colour corresponds to an increase of 50% of the 𝐶 𝑃𝑉 value whereas the blue one corresponds to a decrease of 50% and the purple one is obtained with the reference value of 𝐶 𝑃𝑉 . The area represents the variations of this curve when modifying the other parameters as specified in section 8.2.2. The upper limit of the area is the 90 th percentile of values and the lower limit is the 10 th percentile. The same applies to the other graphs, apart for 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 where variations are only of ±10% and for L with variations of ±33%.

Figure 108 :

 108 Figure 108 : Envelope curves for different load profile of a location in Angola(-12.5°N,17.5°E). Each graph corresponds to a daily load profile: Domestic, Productive and Hybrid and colours account for the seasonality: blue, red, yellow and purple corresponds respectively to a peak consumption in March, June, September and December. The black one is obtained for load profiles without seasonality. The area represents the variations of this curve when modifying all the costs and CFP as specified in section 8.2.2. The upper limit of the area is the 90 th percentile of values and the lower limit is the 10 th percentile.

Figure

  Figure 109 : LCOE decomposition of the Envelope curve for a location in Angola (-12.5°N; 17.5°E) and a hybrid demand profile.

Figure 111 :

 111 Figure 111 : CFP reduction from the LCOE* configuration as a function of the latitude when adding different values of shadow carbon prices (SPC) taken from the IPCC report[START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF].

Figure 112 :

 112 Figure 112 : CFP of the LCOE* configuration for each location in the four countries with a hybrid load profile in the BAU case.

Figure 113 :

 113 Figure 113 : CFP* values for all locations with a hybrid load profile.

Figure 114 :

 114 Figure 114 : LCOE* values for each country and strategy as a function of the discount rate. The reference discount rate used in the strategy design is 0.1 (dashed line).

Figure 115 :

 115 Figure 115 : Proportion of curtailed energy of the CFP* and LCOE* configurations as a function of the co-variability between the solar resource and the electric demand. Results are obtained for the 93 locations simulated in Chapter 3.

Figure 116 :

 116 Figure 116 : LCOE and CFP modifications when considering the total curtailed energy as part of the electric demand, as a function of the mean capacity factor CF. Results are obtained for the CFP* and LCOE* configurations from Chapter 3

For

  most of the Sub-Saharan regions, a valorization of around half the curtailed energy would make the LCOE of CFP* configuration lower than LCOE* values estimated in Figure 48 of chapter 3.

Figure 117 :

 117 Figure 117 : Proportion of curtailed energy required for the LCOE of the CFP* configuration to be lower than the one of the LCOE* configuration (without valorizing the curtailed energy). Results are obtained for the CFP* and LCOE* configurations from Chapter 3

9. 1 . 2

 12 Les mini-réseaux d'électrification Alors que le taux d'électrification est en moyenne de 75% pour les ménages urbains d'Afrique Sub-Saharienne, il n'est que de 25% pour les populations rurales [255]. La problématique d'accès à l'énergie en zone rurale est donc fondamentale. Dans les dernières années, l'électrification s'est principalement faite par l'extension des réseaux électriques nationaux mais de nombreuses études ont montré que des systèmes décentralisés d'électrification permettraient de réduire les coûts d'électrification. En effet, les coûts associés à l'extension des réseaux dans des zones reculées avec des densités de populations relativement faibles sont souvent prohibitifs. Dans ces zones, un groupe électrogène (genset) ou des panneaux solaires photovoltaïques (PV) pourront suffire à électrifier une habitation, une école ou tout autre bâtiment avec une faible consommation électrique, on parle alors de « Standalone system ». Comme le montre la Figure 118, les mini-réseaux (MR) interviennent lorsque la demande est plus élevée, par exemple du fait d'une plus forte densité de population (villages, petites villes) ou d'appareils avec une plus forte consommation (moulins, pompes, …). Ces systèmes se composent d'un ou plusieurs moyens de production (PV, genset, éolienne, turbine hydroélectrique) avec une capacité totale allant de quelques kW au MW, et d'un réseau de distribution qui fonctionne indépendamment du réseau national.

Figure 118 :

 118 Figure 118 : Estimation de la solution d'électrification qui minimise les coûts pour l'Afrique Sub-Saharienne entre des systèmes individuels, des MR et l'extension du réseau [13]

Figure 119

 119 Figure 119 pour six localisations avec des ressources solaires contrastées et deux profils de demande électrique (domestique et productif). On peut y voir que la capacité de stockage nécessaire est énorme pour un surdimensionnement proche de 1, puisqu'elle doit compenser les variations saisonnières de la ressource, d'où les plus grandes valeurs de stockage pour les localisations éloignées de l'équateur (Lybie et Afrique du Sud). Ces valeurs diminuent rapidement lorsque l'on augmente le

Figure 119 :

 119 Figure 119 : Courbes de dimensionnement (capacité de stockage normalisée en fonction du surdimensionnement) pour six localisations et pour deux profils de demande : un profil domestique (bleu) et un profil productif (rouge) sans saisonnalité. Toutes les configurations indiquées sur cette courbe permettent d'atteindre une qualité de service de 95%.

Figure 120 :

 120 Figure 120 : Surdimensionnement optimal (gauche), capacités de stockage optimales normalisées (milieu) et CAE optimal (droite) obtenus par simulation pour deux profils de demande (productif et domestique) sans saisonnalité en fonction de la latitude.Le CAE intègre ces deux effets, d'abord la co-variabilité infra-journalière entre la ressource solaire et la demande qui l'influence fortement (facteur 2 entre les valeurs) du fait des besoins en stockage, et dans une moindre mesure la co-variabilité saisonnière ou inter-journalière (± 10 à 15%). On retrouve globalement des valeurs similaires à celles obtenues dans d'autres études de quantification des CAE pour des MR 100% solaire. Dans le scénario de coûts utilisé ici, la configuration optimale est telle que le stockage est proche du stockage minimum requis avec un surdimensionnement moyen, majoritairement compris entre 1,2 et 1,7. On peut maintenant s'interroger sur les variations de cette configuration lorsque l'on fait varier le ratio des coûts.

Figure 121 :

 121 Figure 121 : Configurations (surdimensionnement et capacité de stockage normalisée) qui minimisent le coût de l'électricité en fonction du ratio des coûts entre solaire et batterie pour six localisations et deux profils de demande (95% de la qualité de service). La bande jaune (resp.bleue) correspond à l'intervalle comprenant 90% des valeurs estimées de ratio des coûts en 2015 (resp. 2025). La bande verte correspond à la superposition des deux bandes (bleu et jaune).La Figure121illustre, sur les six localisations, les variations de configurations optimales en fonction du ratio des coûts. Malgré des variations d'un facteur 8 pour le ratio des coûts, le surdimensionnent optimal ne varie que d'un facteur 1,5 à 1,7 suivant le profil de demande et le stockage optimal d'un facteur 1,1 à 1,3. Ces résultats sont confirmés à l'échelle des 200 localisations. La configuration s'avère ainsi relativement robuste aux variations de coûts.En nous appuyant sur ce résultat, nous établissons des règles de prédimensionnement qui utilisent les différentes échelles de co-variabilité de la ressource et de la demande pour estimer les capacités PV et de stockage optimales. Pour le surdimensionnement optimal, la co-variabilité saisonnière et interjournalière est mesurée par 𝜎 𝐷𝑖𝑓𝑓 , l'écart type de la différence en moyenne journalière entre la production PV normalisée et la demande normalisée. Pour la capacité de stockage optimale, on utilise la distribution de la différence d'énergie nocturne entre la demande et la production calculée chaque nuit de la période considérée.

Figure 122 :

 122 Figure 122 : Estimation du surdimensionnement optimal (gauche) et de la capacité de stockage optimale (milieu) en fonction des caractéristiques de la co-variabilité entre la ressource solaire et la demande électrique. Comparaison entre les CAE estimés par les règles de dimensionnement et les CAE obtenus par simulation (droite). Les résultats sont présentés pour 10 profils de demande (productif et domestique, associés à cinq saisonnalités : sans saisonnalité ou saisonnalité avec un maximum en janvier, avril, juillet ou octobre). Les graphes concernant les configurations (gauche et milieu) montrent les résultats pour un ratio des coûts égal à 1. Celui sur le CAE (droite) regroupe les résultats pour quatre ratios des coûts (0.3, 0.5, 0.8 et 1).

Figure 123 :

 123 Figure 123 : Simulation du solaire PV, des batteries et du groupe diesel pour une semaine début janvier. L'utilisation du genset est optimisée pour maximiser son efficacité.

Figure 124 :

 124 Figure 124 : Configurations qui minimisent le CAE ou l'EC dans un graphe CAE vs. EC. La ligne noire est la courbe enveloppe. La couleur correspond à la capacité PV normalisé (les points noirs ont une faible capacité PV installée, les points clairs ont une capacité PV élevée). La taille des points indique la capacité de stockage normalisée. Chaque courbe en forme de « U » correspond à une capacité de stockage (seulement une capacité simulée sur trois est représentée) et chaque point de cette courbe à une capacité PV. A chaque point correspond aussi une consommation de diesel qui permet de satisfaire l'ensemble de la demande électrique. Ce graphe est obtenu pour une localisation en Angola (-12.5°N; 17.5°E) avec un profil de demande hybride. Ce graphe permet de visualiser l'impact sur le CAE et l'EC d'une augmentation des capacités PV et de stockage. Une courbe enveloppe peut alors être définie. Celle-ci donne pour chaque valeur d'EC, le CAE minimum que l'on peut obtenir. Cette courbe est constituée de deux parties. La première part d'une configuration purement diesel (le point à l'extrême droite du graphe) et va jusqu'à la configuration qui minimise le CAE (le point en bas de la courbe enveloppe, CAE*). Dans cette portion de courbe, augmenter la proportion de solaire permet à la fois de réduire le CAE et l'EC. La deuxième partie, entre la configuration qui minimise le CAE et celle qui minimise l'EC (le point à l'extrême gauche de la courbe enveloppe, EC*) correspond quant à elle au front de Pareto entre l'optimisation du CAE et celle de l'EC. Dans la suite on notera EC* la valeur minimum d'EC et CAE* la valeur minimum de CAE.

Figure 125 :

 125 Figure 125 : CAE (en haut à gauche) et EC (en haut à droite) minimums pour toutes les localisations avec un profil de demande hybride. Le CAE et l'EC d'un groupe diesel correspondent respectivement à 0.46US$/kWh et 996 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ. Fraction de renouvelable : part de la demande électrique satisfaite par le solaire et les batteries correspondantes à ces valeurs (bas).Les valeurs d'EC* les plus élevées sont situées aux extrémités du continent (Maghreb, Afrique du Sud) ainsi qu'en Afrique centrale du fait d'une ressource plus faible et plus variable que dans le Sahara. La répartition géographique des valeurs de CAE* suit le même schéma que celle d'EC*. Quant aux configurations associées à ces valeurs, on peut voir que celles qui minimisent le CAE utilisent le solaire pour subvenir à 50 à 80% de la demande électrique, le restant étant fourni par du diesel. Bien que très fortement réduite, l'utilisation de diesel persiste dans les configurations associées aux EC* ; elle y fournit entre 0,1 et 5% de la demande électrique. En effet, il est parfois préférable de consommer une faible quantité de diesel plutôt que de devoir rajouter des batteries ou des panneaux PV qui ne serviront que très rarement.

Figure 126 :

 126 Figure 126 : Distances relatives entre les deux configurations optimales. La différence relative d'EC (resp. de CAE) correspond à la réduction de l'EC (resp. l'augmentation de CAE) obtenus en passant de l'optimum économique à l'optimum carbone. L'échelle de couleur correspond au facteur de charge moyen (gauche) et à un indicateur de la co-variabilité entre ressource solaire et demande électrique 𝜎 𝑑𝑖𝑓𝑓 .Les configurations EC* permettent de réduire l'EC des configurations CAE* de 45 à 55%, mais requièrent en contrepartie une augmentation des CAE de 10 à 50%. Ces différences relatives sont réduites lorsque le facteur de charge moyen est plus élevé : l'optimum économique est plus proche de l'optimum carbone dans les endroits où la ressource solaire est meilleure. En revanche, une plus grande saisonnalité augmente la différence de CAE sans pour autant augmenter celle d'EC.Etant donné le contexte de l'électrification rurale, les augmentations de CAE observées ici pour passer de l'optimum économique à l'optimum carbone mèneraient à des tarifs de l'électricité prohibitifs pour les populations locales. En reprenant la courbe enveloppe évoquée dans la Figure124, on peut s'intéresser aux compromis existants entre les deux optimums, i.e. à la partie « Pareto » de la courbe enveloppe. La Figure127montre qu'il est possible d'obtenir des réductions significatives d'EC en augmentant de façon modérée le CAE. Par exemple, une augmentation de 5% du CAE permettrait de réduire de plus de 30% l'EC pour presque toutes les localisations.

Figure 127 :

 127 Figure 127 : Gauche : réduction d'EC obtenues à partir de l'optimum économique pour différent niveaux d'augmentation du CAE. Droite : Augmentation du CAE à partir de l'optimum économique pour différent objectifs de réduction de l'EC. Dans les deux graphes, « Max » correspond aux différences relatives maximales, i.e., obtenues en passant de l'optimum économique à l'optimum carbone.

9. 4

 4 Quelles incitations économiques pour décarboner les MR ? Cette section résume les résultats du chapitre 4 du manuscrit et reprend les résultats de l'article : T. Chamarande, S. Mathy, B. Hingray, Designing policies to reduce the carbon footprint of mini-grids in Africa (à soumettre à Energy Policy en juin 2023).

Figure 128 :

 128 Figure 128 : Gauche : Courbes enveloppe pour différentes valeurs tutélaires du carbone. Droite : Courbe de coût marginal du carbone. Dans les deux graphes, les points rouges montrent les optimums économiques pour cinq valeurs du carbone (VC) : 0, 40, 80, 120 et 160 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 . Ces graphes sont obtenus pour une localisation au Kenya (-4°N; 38.5°E) avec un profil de demande hybride.

Figure 131 :

 131 Figure 131 : Coûts moyens (barres bleues : CAPEX et barres jaunes : OPEX) pour les différentes stratégies ("BAU", "Tax", "Sub" et "Bonus/Malus"). Ces coûts se réfèrent uniquement aux changements de configurations, sans tenir compte de l'effet des subventions et des taxes sur les coûts finaux. Les valeurs correspondent aux coûts moyens pour les 14-16 MG dans chaque pays. L'extension de la barre en rouge correspond à l'effet de la taxation des carburants (augmentation des coûts) et le cadre rouge correspond à l'effet des subventions (réduction des coûts). Les barres vertes correspondent aux valeurs de CAE, incluant les effets des subventions et de la taxation.

Figure 132 :

 132 Figure 132 : Gauche : En raison de difficultés de financement, seules 7 batteries ont été remplacées au lieu de remplacer l'ensemble de la rangée de 12 batteries. Source : auteurs, travail de terrain au Kenya, mai 2022. Droite : Le salon de coiffure

Figure 133 :

 133 Figure 133 : Résumé des risques encourus par chaque type d'acteurs. Seuls les risques les plus fréquents que nous avons observés sont représentés, certains ne le sont pas pour une meilleure lisibilité. 1 : Risque sur la production (dégradation de l'infrastructure, pas assez de fonds pour l'entretien ou la modularité). 2 : Risque sur la demande (Instabilité des tarifs suite à un changement de régulation ou à une pression des usagers), arrivée du réseau, consommation trop faible).

Table 1 :

 1 Characteristics of different chapters that include simulation of MG

	Chapter	2	3	4
	Type of MGs:	Solar/batteries	Solar/batteries/diesel	Solar/batteries/diesel
	Number of MGs:	200	93	60
	Regions:	Africa	Africa	Kenya, Senegal, Nigeria, Madagascar
	Performances:	LCOE	LCOE and CFP	LCOE and CFP
	Service quality:	95%	100%	100%
			Hybrid without	Hybrid without
			seasonality	seasonality
	Type of electric load profile simulated	Domestic, productive, and hybrid, with or without seasonality (total: 15 profiles)	+ For the sensitivity analysis: Domestic, productive, and hybrid, with or without	+ For the robustness analysis: Domestic, productive, and hybrid, without
			seasonality (total: 15	seasonality (total 3
			profiles)	profiles)
	Main aspect studied:	Robustness of optimal configuration (solar PV and batteries) for 100% solar MG	Comparison and trade-offs between cost and carbon optimums	Design of economic incentives to reduce the CFP

  International Energy Agency (IEA) and the Institute of Electrical and Electronics Engineers (IEEE) propose such rules for West Africa based on simple estimates of the demand and of the mean solar resource. These rules do however only target solar / diesel hybrid MGs

	(ECREEE),
	Simple pre-sizing rules,
	bypassing the need for simulations, are thus of high interest, for instance to discriminate between
	different solutions (MGs, national grid, Solar Home Systems) or to assess a large portfolio of sites in
	rural electrification planning [203]. ECOWAS Centre for Renewable Energy and Energy Efficiency

Table 2 :

 2 Economic parameters and component lifetimes distribution. The PV related parameters (investment cost and lifetime) are obtained from

  The total 𝐶𝐹𝑃 𝑡𝑜𝑡 [𝑡 𝐶𝑂 2 ] of the MG is estimated from the CFP values of the different MG components 20 : Where 𝐾 𝑏𝑎𝑡 [𝑘𝑊ℎ], 𝐾 𝑃𝑉 [𝑘𝑊 𝑝 ], 𝐾 𝑔𝑒𝑛 [𝑘𝑊] are respectively the capacity installed for the batteries, the PV panels and the genset; 𝐶𝐹𝑃 𝑏𝑎𝑡 [𝑡 𝐶𝑂 2 /𝑘𝑊ℎ], 𝐶𝐹𝑃 𝑃𝑉 [𝑡 𝐶𝑂 2 /𝑘𝑊 𝑝 ], 𝐶𝐹𝑃 𝑔𝑒𝑛 [𝑡 𝐶𝑂 2 /𝑘𝑊], 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 [𝑡 𝐶𝑂 2 / 𝐿] are respectively the carbon footprint associated to 1𝑘𝑊ℎ of installed batteries, 1𝑘𝑊 𝑝 of installed PV, 1𝑘𝑊 of genset power capacity and 1𝐿 of fuel; 𝐹 𝑐𝑜𝑛𝑠𝑜 [𝐿] is the fuel consumption over the lifetime of the project 𝐿 [𝑦𝑟𝑠] and 𝐿 𝑏𝑎𝑡 [𝑦𝑟𝑠] , 𝐿 𝑔𝑒𝑛[𝑦𝑟𝑠] are respectively the lifetime of batteries and genset. We consider a project lifetime of 15 years, so we assume that it is not needed to replace the PV panel.

	𝐶𝐹𝑃 𝑡𝑜𝑡 = 𝐾 𝑏𝑎𝑡 𝐶𝐹𝑃 𝑏𝑎𝑡 (1 +	𝐿 𝐿 𝑏𝑎𝑡	) + 𝐾 𝑃𝑉 𝐶𝐹𝑃 𝑃𝑉 + 𝐾 𝑔𝑒𝑛 𝐶𝐹𝑃 𝑔𝑒𝑛 (1 +	𝐿 𝐿 𝑔𝑒𝑛	) + 𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 𝐹 𝑐𝑜𝑛𝑠𝑜	(28)

The genset lifetime in years 𝐿 𝑔𝑒𝑛 is derived from a lifetime expressed in functioning hours 𝐿 𝑔𝑒𝑛,ℎ𝑟𝑠 [ℎ𝑟𝑠] using equation

[START_REF] Ayaburi | Measuring "Reasonably Reliable" access to electricity services[END_REF]

with 𝐹 𝑢𝑠𝑒

[ℎ𝑟𝑠]

the number of the genset use hours over the whole project lifetime:

Table 3 :

 3 Parameter values used for the CFP calculation. 𝐶𝐹𝑃 𝑃𝑉 and 𝐶𝐹𝑃 𝐵𝑎𝑡 also include the carbon footprint for inverters[START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF].

	𝐶𝐹𝑃 𝑏𝑎𝑡 [𝑡 𝐶𝑂 2 /𝑘𝑊ℎ]	𝐶𝐹𝑃 𝑃𝑉 [𝑡 𝐶𝑂 2 /𝑘𝑊 𝑝 ]	𝐶𝐹𝑃 𝑔𝑒𝑛 [𝑡 𝐶𝑂 2 /𝑘𝑊]	𝐶𝐹𝑃 𝑓𝑢𝑒𝑙 [𝑡 𝐶𝑂 2 /𝐿]
	0.3	1	0.02	2.6x10 -3
	𝐿 [𝑦𝑟𝑠]	𝐿 𝑏𝑎𝑡 [𝑦𝑟𝑠]	𝐿 𝑔𝑒𝑛,ℎ𝑟𝑠 [ℎ𝑟𝑠]
	15	7	25000

  • The configuration with the lowest CFP is often very different from the configuration with the lowest LCOE: for a CFP that is around 50% lower than the configuration with the lowest LCOE, the LCOE is generally 30% higher. • Results are highly dependent on the solar resource available across Africa and the socioeconomic and technical parameters considered. • In almost all cases however, a significant CFP reduction from the least LCOE configuration can be achieved with moderate additional electricity costs. • In most cases, a reduction of at least 20% in the CFP of the least LCOE configuration corresponds to a shadow carbon price close to 200𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞

Table 6 :

 6 Difference of the total policy costs between using individual norm of CFP or an average objective of CFP reduction.Results are obtained to achieve a CFP of 350𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ and are normalized by the total energy supplied. The values are calculated by taking the integral of the marginal cost curves presented inFigure 66.

	Costs [$/kWh] using: Individual norms	Average objective
	Kenya	3.73x10 -3	2.73 x10 -3
	Senegal	1.56 x10 -3	1.43 x10 -3
	Nigeria	38.15 x10 -3	37.07 x10 -3
	Madagascar	14.94 x10 -3	10.61 x10 -3

Table 7 :

 7

	94

Optimal (5% rounded) of subsidies and taxations levels for each strategy with a mean CFP reduction objective of 35%. These values are obtained for the four countries and a hybrid load profile.

Table 8 :

 8

		𝐶 𝑏𝑎𝑡	𝐶 𝑃𝑉	𝐶 𝑓𝑢𝑒𝑙	𝐶𝐹𝑃 𝑏𝑎𝑡	𝐶𝐹𝑃 𝑃𝑉	𝐶𝐹𝑃 𝑓𝑢𝑒𝑙	Load profile
		[$/𝑘𝑊ℎ]	[$/𝑘𝑊 𝑝 ]	[$/𝐿]	[𝑡 𝐶𝑂 2 /𝑘𝑊ℎ]	[𝑡 𝐶𝑂 2 /𝑘𝑊 𝑝 ]	[𝑡 𝐶𝑂 2 /𝐿]
	Reference	350	1900	1	0.3	1	2.6x10 -3	Hybrid
			Variations compared to the "Reference" scenario:
	Worst for ren	+25%	+25%	-25%	+25%	+25%	-10%	Hybrid
	Best for ren	-25%	-25%	+25%	-25%	-25%	+10%	Hybrid
	Domestic	0%	0%	0%	0%	0%	0%	Domestic
	Productive	0%	0%	0%	0%	0%	0%	Productive

Parameters values for the robustness analysis. Parameters not indicated in this table are the same as in section 3.3. "Worst for ren" stand for "Worst for renewables", the same applies to "Best for ren".

grids in Kenya: beyond technical and economic calculations, how does sizing crystallize regulatory, financial and institutional uncertain constraints?

	, E. Etienne, S.
	Mathy, Designing rural isolated mini-grids in Kenya: beyond technical and economic calculations, how
	does sizing crystallize regulatory, financial and institutional uncertain constraints? (submitted in
	Renewable and Sustainable Energy Transition, Special Issue: Governing Renewable Energy Rollouts in
	Financially constrained contexts, March 2023)
	Designing rural isolated mini-

Table 9 :

 9 Interviews' characteristics

	Nb of interviews	Duration [hrs]

  The lenders are very particular about this. They absolutely want you to put money in because if you don't put money in and the project fails, as you didn't put money in, you don't care. So the lenders will say to themselves: "if the project fails and you put in 20 million, you had better make it work because if it fails, I get paid first, and you who put in your money, you won't get it back"." (interview with a funding company representative, translated from French, April 2022).

Table 10 :

 10 Powerhive funding (non exhaustive) indicating what the funding targets as well as its type, amount, date and origin. Source: authors, compiled from on-line media.

	What is being	Loans to buy	Productive	33 electric	MG assets	Investments	Others
	funded:	appliance	uses	vehicles
	Type, amount,	Loans for	Leases and	E-mobility:	Output-	First Solar:	Debt:
	date and	MG users:	loans: 500K	175,176£,	based	undisclosed	3m.
	origin, of	Unknown	US$, 2017	2020	grants:	value, 2013	US$,2018
	funding	value, 2014 (Equity Bank of Kenya)	(USAID/Po wer Africa) Kuku Poa:	(UK Aid, IKEA)	Unknown value, total of 5,4m € for 10 -15	ENEL: 12m US$, Series A round, 2015	Cryptocurre ncy: 23m. US$
			unknown		MG, from	Diverse actors:	expected
			value (less		Powerhive,	20m. US$,	with Sun
			than		Renewvia	Series A round,	Exchange
			300KUS$)		and RVE	2016	SUNEX, 2018
			2022 (Powering Renewable Energy Opportuniti		(Green Mini-Grids program)	Toyota Tsusho: 9.3m. US$ Series B round, 2019
			es)			Kouros: 9.3m.
						US$, Series B
						round, 2019

  109 : LCOE decomposition of the Envelope curve for a location in Angola (-12.5°N; 17.5°E) and a hybrid demand profile.

				CFP reduction from the LCOE* configuration [%]
			10	20	30	40	50	60
		5	7.8	36	71	90	95	97
	Accepted LCOE	10	1.4	12	35	65	84	90
	increase [%]	15	0.20	4.9	18	42	68	81
		20	0.041	2.1	9.9	27	52	71

Table 11 :

 11 CFP reduction from the LCOE* configuration when allowing an increase of LCOE. These numbers refer to the sensitivity analysis (cf. Figure58) and are given in %. Scenarios where the CFP relative change between LCOE* and CFP* is lower than the CFP reduction wanted are excluded. For instance, the 12% (red value in the table) means that, when excluding all the scenarios where the CFP* and LCOE* configurations have a CFP relative difference below 20%, a 10% LCOE increase gives a CFP reduction lower than 20% in 12% of the scenarios. Figure 110 : Proportion of scenarios with the different parameters values for a 10% LCOE increase and a CFP reduction lower than 10%. Scenarios where the CFP relative change between LCOE* and CFP* is lower than 10% are excluded. Left and right legends are different. On the left graph, the 'low', 'medium' and 'high' values corresponds to the value given in section 8.2.2.On the right graph, the colours refer to the load profile characteristics and location of the N-S transect (cf. Figure44). For the Seasonality, from left to right, colours correspond to 'No seasonality', 'March', 'June', 'September', 'December' (month of the highest demand). For the Infra-day load profile, they correspond to 'Domestic', 'Productive', 'Hybrid'. For the Location, they correspond to the 8 locations of the transect (17.5°E) from -27.5°N to 25°N with a step of 7.5°N.

	Combination of parameters

Table 12 :

 12 Proportion of scenarios that give a CFP reduction lower than 10, 15 and 20% for a LCOE increase of 10% for different combination of parameters value. For instance, the 8.0% (red value in the table) means that, on all the scenarios with a low value of 𝐶 𝑓𝑢𝑒𝑙 and 𝐿 𝑏𝑎𝑡 , and a high value of 𝐶 𝑃𝑉 , 8% give a CFP reduction lower than 10%.

	Combination of parameters

Table 13 :

 13 Same table as Table12with a 20% LCOE increase.

Table 14 :

 14 Calculation of the sensitivity of the least LCOE when changing 𝐶 𝑃𝑉 for different scenario. Values in bold corresponds to the relative change of the least LCOE value compared to the mean of these 3 LCOE values. The sensitivity is then the slope of the linear regression between these relative changes and the 𝐶 𝑃𝑉 variations.

  thèse, nous nous intéressons principalement à la question de l'accès à l'électricité pour répondre à ces besoins, qu'ils soient domestiques et/ou productifs.A ces objectifs d'électrification s'ajoutent les objectifs d'atténuation des changements climatiques fixés par les Accords de Paris[START_REF]Nationally determined contributions under the Paris Agreement », United Nations, Synthesis report[END_REF]. Pour ne pas dépasser les 2°C de réchauffement global et rester au plus proche des 1,5°C, des trajectoires globales de réduction des gaz à effet de serre (GES) ont été élaborées avec l'atteinte d'une neutralité carbone d'ici 2050 -2070[START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. Bien que les pays d'Afrique Sub-Saharienne ne représentent qu'une très faible partie (3%) des émissions de GES globales, ceux-ci sont aussi engagés dans l'atteinte de cette neutralité carbone. Parmi eux, une douzaine de pays ont déjà annoncé des échéances pour atteindre cette neutralité, on peut notamment citer l'Afrique du Sud (2050), la Namibie (2050) ou encore le Nigéria (2060)[13].Atteindre cette neutralité nécessite de transformer profondément le secteur énergétique et dans le cas des pays d'Afrique Sub-Saharienne d'intégrer ces contraintes au développement de leur système énergétique. En effet, l'inertie dans le déploiement des infrastructures dans ce secteur demande d'anticiper dès maintenant la réduction de l'utilisation des énergies fossiles au profit des énergies renouvelables. Ainsi, l'électrification doit tenir compte des enjeux liés à l'atténuation des changements climatiques en s'appuyant sur des technologies permettant de limiter ses émissions de GES.

Taking the example of water pumping, it could be interesting to see what the needs are and what would be the water storage capacities to valorize the curtailed energy. As the user can only use this curtailed energy when it is available, its valorization requires an adapted business model, for instance a lower electricity tariffs when using curtailed energy. These results show the advantages of a consumption in adequation with the solar resource, and thus, they incite further research on demand management strategies to reduce both LCOE and CFP of MG. cette

  et qu'environ 4000 MR supplémentaires étaient déjà planifiés en 2019[START_REF] Esmap | Mini Grids for Half a Billion People: Market Outlook and Handbook for Decision Makers[END_REF]. Si l'on s'intéresse aux systèmes récemment installés, il s'agit principalement de MR hybrides utilisant à la fois des panneaux PV, des batteries et un ou plusieurs genset avec des capacités comprises entre 50 et 100kW[START_REF]Africa Minigrid Developers Association[END_REF]. Le choix de ces sources d'énergie est principalement guidé par l'optimisation des coûts du système, notamment pour accroitre la rentabilité des projets dans le cas de financement privé.En effet, les investissements dans les MR restent encore faibles (1%) comparés au reste du secteur électrique, en particulier du fait des risques élevés associés à ces projets, liés par exemple à l'estimation de la demande pour des populations qui accèdent à ce nouveau service[START_REF]Energizing Finance: Understanding the Landscape 2021[END_REF],[START_REF] Hartvigsson | On system dynamics and the viability of mini-grids in rural electrification[END_REF]. De plus, les populations à électrifier ont le plus souvent de très faibles revenus, d'où une limite sur les tarifs de l'électricité qui réduit la rentabilité des investissements. Dans le cas de MR publics, i.e. financés par l'Etat, il s'agit principalement de fournir une électricité à un coût abordable en évitant les déficits. Mais dans le cas de développeurs privés, il est souvent nécessaire de recourir à des subventions pour assurer la viabilité économique des projets. Ces subventions proviennent majoritairement de fonds d'aide au développement comme la Banque Africaine de Développement (AfDB), la Banque Mondiale, ou encore des organismes liés à d'autres pays (AFD, DFID, GIZ32 ).Le but de cette thèse est d'évaluer le potentiel de mini-réseaux hybrides (PV, batteries, diesel) isolés pour électrifier les zones rurales en Afrique en satisfaisant deux contraintes : un coût de l'électricité abordable et de faibles émissions de GES.Il s'agit de voir si les résultats obtenus dans les études mentionnées précédemment sont généralisables à d'autres localisations, d'autres profils de consommation et à d'autres caractéristiques techniques, économiques et environnementales des mini-réseaux. Cela demande de mieux comprendre les principaux facteurs qui influencent le dimensionnement des mini-réseaux et leurs performances (coût de l'électricité et empreinte carbone). Connaître ces principaux facteurs permet aussi de savoir sur quels paramètres il faut agir si l'on veut mettre en oeuvre des politiques publiques pour réduire les coûts et/ou l'empreinte carbone de ces MR. Les quatre chapitres principaux de la thèse tentent de répondre à tout ou partie de ces questions.Dans un premier temps (cf. section 9.2), nous nous intéressons à des mini-réseaux 100% solaire (PV et batteries sans diesel). L'utilisation du diesel étant, a priori, la principale source d'émissions de GES des MR, nous nous focalisons sur le coût de l'électricité associé à ces systèmes. Ce coût a déjà été quantifié à l'échelle du continent pour certains scénarios de coûts des équipements mais la forte variabilité de ces données interroge la robustesse des résultats obtenus. Ainsi, nous évaluons la sensibilité du dimensionnement de ces MR 100% solaire à des variations de coûts, de durée de vie des équipements et de profils consommations. Du fait de l'importance des aspects économiques dans le dimensionnement des MR, nous avons d'abord focalisé nos recherches sur les incitations financières qui permettraient de guider les choix des développeurs de MR vers des systèmes moins émetteurs de GES. Ce travail présente une méthodologie pour élaborer des stratégies de subventions/taxations pour atteindre des objectifs de réduction d'empreinte carbone des MR dans quatre pays offrant une diversité de ressource solaire et de prix du diesel (Kenya, Sénégal, Nigeria et Madagascar).Dans la dernière section (cf. section 9.5), nous tentons d'identifier de potentiels obstacles à ces politiques publiques. Nous tentons en particulier de mieux comprendre l'environnement régulatoire et financier dans lequel sont développés les MR. Pour cela, nous changeons d'approche en appliquant une méthodologie qualitative basée sur l'analyse d'entretiens, réalisés notamment lors d'un terrain au Kenya, avec différents acteurs de l'électrification (bailleurs de fonds, régulateurs, développeurs, opérateurs, usagers, …). Ces travaux montrent comment les développeurs et opérateurs de MR adaptent leurs méthodes et leur business model pour gérer les contraintes et les risques associés à ces projets, et ils nous permettent de questionner la pertinence des différentes stratégies d'incitations financières proposées. 9.2 Robustesse du dimensionnement de mini-réseaux 100% solaire Cette section résume les résultats du chapitre 2 du manuscrit et reprend les résultats de l'article : T. Chamarande, S. Mathy, B. Hingray, The least cost design of 100 % solar power microgrids in Africa : Sensitivity to meteorological and economic drivers and possibility for simple pre-sizing rules, Energy for Sustainable Development, Volume 69, 2022, Pages 211-223, ISSN 0973-0826, https://doi.org/10.1016/j.esd.2022.07.001.Etant donné la diminution rapide des coûts des panneaux PV ces dernières années, les MR 100% solaire semblent une solution prometteuse pour satisfaire les contraintes de coûts de l'électricité abordable et de faibles émissions. Dans cette partie, nous évaluons les coûts de ces MR en nous intéressant à leur dimensionnement, c'est-à-dire au choix de la configuration (capacité PV et capacité de stockage installées) optimale du point de vue économique. En effet, plusieurs configurations de MR permettent de répondre à un même profil de demande électrique. Le choix de la configuration optimale se fait généralement en minimisant le coût actualisé de l'énergie (CAE). Cette configuration et son CAE associé dépendent des caractéristiques de la ressource solaire disponible, du profil de demande électrique ainsi que d'un certains nombres de paramètres techniques et économiques.De nombreuses études ont déjà évalué ces CAE pour des MR 100% solaires, notamment pour pouvoir les comparer aux coûts d'autres sources d'énergie et à ceux d'extension des réseaux nationaux[START_REF] Huld | Geospatial Analysis of Photovoltaic Mini-Grid System Performance[END_REF],[203],[START_REF] Moner-Girona | Decentralized rural electrification in Kenya: Speeding up universal energy access[END_REF]. Cependant la majorité de ces études ne prends pas en compte la forte variabilité des différents paramètres intervenants dans le dimensionnement. Par exemple, dans le cas des coûts associés aux composants (panneaux PV et batteries), on peut observer des variations importantes liées aux contraintes locales d'installations, à leurs circuits de distribution ou encore aux régulations du pays concerné. A cela s'ajoute l'évolution rapide des coûts du fait du déploiement rapide de l'énergie solaire et de la maturité des technologies[START_REF] Bollinger | Learning-by-Doing in Solar Photovoltaic Installations[END_REF],[START_REF] Rubin | A review of learning rates for electricity supply technologies[END_REF].Ainsi, nous présentons ici une étude de la sensibilité des configurations et des CAE associés aux MR 100% solaire. Cette étude montre la relative robustesse du dimensionnement par rapport aux hypothèses économiques, et au contraire, sa forte sensibilité à la ressource solaire et à sa co-variabilité avec la demande électrique. Ces résultats nous permettent d'élaborer des règles simplifiées de prédimensionnement à partir des caractéristiques de la ressource solaire et de la demande électrique.

	9.1.3 Les MR : une solution pour une électrification bas carbone ?

Comme évoqué en section 9.1.2, la majorité des MR installés utilisent du diesel. L'objet de la section 9.3 est de quantifier l'empreinte carbone (EC) de ces systèmes hybrides solaire/diesel pour la comparer à celle des MR 100% solaire. A cette comparaison d'EC, s'ajoutera une comparaison des coûts de l'électricité permettant de montrer la compatibilité, ou non, des objectifs de coûts abordables de l'électricité et de faibles EC. Une analyse de sensibilité vient compléter ces résultats et mettre en évidence les paramètres les plus importants intervenant dans le dimensionnement des MR hybrides.

Ces résultats permettent alors de proposer des exemples de politiques publiques pour réduire l'empreinte carbone des MR. C'est l'objet de la section 9.4.

  La courbe définie par la fonction qui à chaque capacité PV (𝐶 𝑃𝑉 [𝑊 𝑝 ]) associe la capacité de stockage minimum (𝑆 [𝑊ℎ]) pour satisfaire ce niveau de qualité de service sera appelée courbe de dimensionnement. Pour calculer cette courbe, nous fixons une capacité PV et nous identifions par une recherche dichotomique la capacité de stockage minimum en simulant le fonctionnement du MR. Pour faciliter la comparaison entre les sites, nous choisissons de normaliser cette courbe en divisant les capacités de stockage par la demande moyenne D0 [W] et la capacité PV par une capacité 𝐶 𝑃𝑉 0 [𝑊 𝑝 ]. 𝐶 𝑃𝑉 0 correspond à la capacité PV nécessaire pour produire sur l'ensemble de la période simulée la même quantité d'énergie que celle demandée par une consommation constante D0. Cette valeur est inversement proportionnelle au facteur de charge 𝐶𝐹 [-] de la production PV. Nous nommons surdimensionnement le rapport 𝑥 = 𝐶 𝑃𝑉 /𝐶 𝑃𝑉 0 .

  Nous avons montré que les configurations optimales de MR 100% solaire sont relativement robustes aux hypothèses de coûts associées aux panneaux PV et aux batteries. En revanche, elles sont beaucoup plus sensibles à la co-variabilité entre la ressource solaire et la demande électrique. Nous avons ainsi pu établir des règles de prédimensionnement qui permettent d'éviter de passer par la simulation de nombreuses configurations de MR. Ces règles peuvent aider les développeurs de MR et les planificateurs de l'électrification rurale à évaluer le potentiel de ces MR sur de grandes zones, ainsi qu'à tester la sensibilité de leurs résultats aux hypothèses économiques en calculant rapidement le CAE pour plusieurs scénarios de coûts. 9.3 Les MR hybrides : un compromis entre la minimisation de la CAE et de l'EC ?Cette section résume les résultats du chapitre 3 du manuscrit et reprend les résultats de l'article : T. Chamarande, B. Hingray, S. Mathy, Reducing the carbon footprint of mini-grids in Africa : the value of solar PV (soumis à Applied Energy en mai 2023). même que pour les MR 100% solaire, le dimensionnement des MR hybrides est souvent optimisé pour minimiser le coût de l'électricité[START_REF] Gabra | Techno-economic analysis of stand-alone wind micro-grids, compared with PV and diesel in Africa[END_REF],[START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF],[START_REF] Boadzo | A study on dairy farm-based hybrid renewable energy systems in South Africa[END_REF]. Plusieurs études ont comparé les configurations obtenues par ces optimisations avec une configuration qui n'utiliserait que du diesel. Il est alors possible d'évaluer l'impact sur le coût de l'électricité et la réduction des émissions de GES lorsque des panneaux solaires remplacent des générateurs diesel.Ces analyses considèrent le plus souvent la réduction des émissions de GES comme un co-bénéfice de l'optimisation économique du système[START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF],[START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF],[START_REF] Cader | Global cost advantages of autonomous solar-battery-diesel systems compared to diesel-only systems[END_REF], mais peu d'entre elles s'intéressent à ces réductions comme à un critère d'optimisation, i.e. minimiser les émissions de GES. Parmi celles qui le font, leur mesure des émissions de GES n'englobent que les émissions directes, c'est-à-dire celles associées à la combustion du diesel. Pour autant, les émissions associées aux panneaux PV et aux batteries sur l'ensemble de leur cycle de vie ne sont pas négligeables[START_REF] Antonanzas-Torres | Environmental life cycle impact of off-grid rural electrification with mini grids in West Africa[END_REF],[START_REF] Elkadeem | Sustainable siting and design optimization of hybrid renewable energy system: A geospatial multi-criteria analysis[END_REF]. L'extraction des matériaux (Lithium, Nickel, Cobalt, Cuivre…) et la forte intensité énergétique des procédés de fabrication de ces composants émettent des GES. Ces émissions ont été quantifiées pour des installations PV et des batteries, et sont fortement dépendantes du lieu d'installation et du mix énergétique du territoire dans lequel les composants ont été produits[START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF],[START_REF] Frischknecht | Life Cycle Inventories and Life Cycle Assessments of Photovoltaic Systems[END_REF],[START_REF] Varlet | Comparative life cycle assessment of lithium-ion battery chemistries for residential storage[END_REF]. Comment sont modifiés ces résultats lorsque l'on fait varier les paramètres techniques, De même que dans la section précédente, nous simulons le fonctionnement d'un MR fictif mais cette fois, en ajoutant une production diesel. Ces simulations sont réalisées pour 93 localisations et 15 profils de demande (3 profils infra-journaliers et 5 saisonnalités différentes). Seuls les résultats obtenus avec le profil de demande hybride (50% domestique, 50% productif) sans saisonnalité sont présentés dans cette section. Les modèles de production PV et de stockage restent les mêmes que dans la section précédente (cf. section 9.2.1) mais la gestion du stockage est différente pour s'adapter aux contraintes du diesel. Lorsque le PV ne produit plus, par exemple en fin de journée, et que les batteries ne permettront pas de couvrir toute la demande nocturne, le genset fournit l'énergie manquante et assure une qualité de service de 100%35 (cf. Figure

	De économiques et environnementaux ?
	9.3.1 Méthode

Dès lors, cet article tente de répondre à plusieurs questions :

• Quelle est l'empreinte carbone (EC) des MR diesel, hybrides et 100% solaire en Afrique • Quel est l'impact de la prise en compte des émissions indirectes dans l'EC des MR hybrides ? • Quelles configurations permettent de minimiser cette EC sur le continent Africain ? • Quelles différences de CAE (Cout Actualisé de l'Electricité) et d'EC observe t'on entre la configuration qui minimise l'EC et celle qui minimise le CAE ? •

  Pour mieux comprendre l'influence de la co-variabilité entre la production PV et la demande électrique sur ces valeurs, on peut s'appuyer sur les indicateurs utilisés pour les règles de prédimensionnement dans la section précédente (cf. section 9.2.2). Globalement, on observe d'une part que plus la ressource moyenne est élevée, plus le CAE* et l'EC* sont faibles, et d'autre part, plus la co-variabilité saisonnière et inter-journalière 𝜎 𝐷𝑖𝑓𝑓 est élevée, plus les valeurs de CAE* et EC* sont élevées. Ces paramètres influencent aussi les différences relatives de CAE et d'EC entre les configurations associées aux CAE* et aux EC* (cf. Figure126).

  Nous avons montré que les émissions indirectes associées à la production PV et au stockage ne sont pas négligeables (autour de 200 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ). Les configurations associées à ces valeurs minimums d'EC sont très proches des MR 100% solaires précédemment étudiés (>95% de la demande électrique fournie par du solaire). Les configurations qui minimisent le CAE permettent de réduire le CAE d'environ 15% et l'EC d'environ 50% par rapport à des générateurs diesel. Réduire l'EC des MR au-delà de ces 50% n'est possible qu'au prix d'une augmentation du CAE pouvant aller jusqu'à 50% pour certaines localisations. Cependant, il reste possible d'obtenir des réductions significatives de l'EC des MR en acceptant une augmentation modérée du CAE.Pour mieux estimer l'efficacité de ces possibles réduction d'EC, on peut leur associer une valeur monétaire en traduisant nos résultats en termes de tonne de CO2 évitée par dollar additionnel dans les coûts de production de l'électricité. En considérant une valeur tutélaire du carbone à 120 𝑈𝑆$/𝑡 𝐶𝑂 2 ,𝑒𝑞 40 , on pourrait réduire de 15 à 20% l'EC des MR, ce qui constitue à l'échelle de l'Afrique un potentiel d'investissements intéressant pour des institutions comme le Fond Vert pour le Climat.

  Chamarande, E. Etienne, S. Mathy, Designing rural isolated mini-grids in Kenya: beyond technical and economic calculations, how does sizing crystallize regulatory, financial and institutional uncertain constraints? (soumis à Renewable and Sustainable Energy Transitions en mars 2023) qui est le fruit d'une collaboration avec Emilie Etienne, doctorante en sociologie à l'Université de Grenoble.L'enjeu de la réduction d'EC se place principalement au niveau du dimensionnement du MR, mais celuici est intégré dans un cadre plus large qui englobe des aspects tels que l'obtention des licences et du financement, ou la gestion du système une fois qu'il est installé. Pour mieux anticiper les limites à l'application des politiques publiques évoquées précédemment (cf. section 9.4), il est nécessaire de comprendre les pratiques des développeurs de MR et leurs contraintes lors du dimensionnement.Nous avons jusque-là considéré le dimensionnement comme la recherche d'un optimum économique. Cette vision est partagée par un grand nombre d'études, aussi bien dans la littérature scientifique que dans la littérature grise. Un grand nombre de méthodes, de logiciels et de guides ont été développés en se basant sur ce principe pour aider les développeurs dans leurs projets de MR[START_REF]Mini Grid Builder | Web based mini grid tool[END_REF]-[START_REF]Government of Canada[END_REF],[START_REF]HOMER Pro -Microgrid Software for Designing Optimized Hybrid Microgrids[END_REF],[START_REF] Cicilio | uGrid: Reliable Minigrid Design and Planning Toolset for Rural Electrification[END_REF]. Cependant, il semble que beaucoup de projets de MR échouent et que le dimensionnement est considéré comme un risque majeur et l'une des causes de ces échecs[START_REF] Semis | Livrable 2: Rapport d'état des lieux avec les données quantitatives et qualitatives sur l'état de fonctionnement de l'ensemble des ERILs et GDTs[END_REF],[START_REF] André-Bataille | Publication d'une étude de capitalisation de 16 projets d'électrification rurale à Madagascar[END_REF],[START_REF] Hazelton | A review of the potential benefits and risks of photovoltaic hybrid mini-grid systems[END_REF]. Comment comprendre cette différence entre l'apparente maîtrise des aspects techniques du dimensionnement et le taux relativement faible de succès des MR sur le terrain ? Pour répondre à cette question, cette section détaille l'environnement dans lequel sont développés les MR et illustre certaines limites de la vision purement technique du dimensionnement.9.5.1 MéthodePour traiter cette question, il nous semble nécessaire de changer d'approche. Contrairement aux approches quantitatives développées dans les sections précédentes et basées sur des simulations de MR fictifs, la méthode utilisée ici s'appuie sur l'analyse qualitative d'entretiens, de documents et d'observations faite sur le terrain. Pour le terrain, nous avons choisi de nous focaliser sur le Kenya qui a déjà une expérience assez longue sur les systèmes décentralisés solaires (MR et SHS44 ). Le travail présenté ici s'appuie sur 75 entretiens semi-directifs représentant environ 70 heures (cf. Table16) et sur la visite de 7 MR situés dans la partie sud-ouest du pays. La plupart des entretiens et des observations ont été réalisés au Kenya en avril-mai 2022, mais nous avons également mené des entretiens à distance quelques mois avant et après ce terrain. A ces sources d'informations s'ajoutent des études documentaires notamment de textes législatifs, de plan d'électrification, de conférence et de séminaires dédiés aux MR. La diversité des sources d'informations et des acteurs interrogés permet de croiser les points de vue et de faire ressortir les potentielles contradictions ou concordances dans les discours.

Table 16 :

 16 Caractéristiques des entretiens Les entretiens ont été enregistrés puis retranscrits pour pouvoir travailler sur les textes à l'aide du logiciel NVivo. Un premier codage

	Nb d'entretiens	Durée [h]

Même si ces MR 100% solaire n'utilisent pas d'énergies fossiles, leur empreinte carbone (EC) n'est pas nulle. Les émissions indirectes de CO2 liées aux équipements solaires et aux batteries ne sont pas négligeables et dans le deuxième chapitre, nous quantifions leur EC qui s'élève à environ 200𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ. De plus, les coûts associés à ces systèmes sont bien plus élevés que ceux obtenus avec des MR hybrides utilisant du diesel. Nos résultats montrent en effet qu'inclure un générateur diesel dans la production d'énergie permet de réduire d'environ 30% les coûts de production de l'électricité, en contrepartie d'un doublement de l'empreinte carbone. Ainsi, il n'est actuellement pas possible de minimiser à la fois les coûts et les émissions des MR, mais l'on peut identifier certaines configurations qui offrent des compromis intéressants entre ces deux objectifs.En pratique, la minimisation des coûts est priorisée par les développeurs de MR par rapport à la minimisation des émissions. Nous proposons, dans un troisième chapitre, d'évaluer différentes politiques publiques possibles (subventions, taxes) pour réduire l'EC de l'optimum économique. Nous évaluons en particulier leur efficacité en estimant la valeur économique d'une tonne de CO2 évitée. A travers les exemples du Kenya, du Sénégal, du Nigéria et de Madagascar, nous montrons qu'il est important de prendre en compte l'hétérogénéité de la ressource solaire et des contextes économiques dans la manière de définir les objectifs de réduction d'EC et les moyens d'y parvenir.Dans le dernier chapitre, nous menons une analyse qualitative pour mieux comprendre le cadre institutionnel dans lequel sont développés les MR en nous basant sur des documents, des entretiens et des observations collectées lors de la thèse, principalement au cours d'un terrain au Kenya. Cette étude permet d'observer comment les modes de financement et de régulation contraignent le dimensionnement des MR et d'identifier les potentiels obstacles à la mise en oeuvre de politiques publiques de réduction de leur EC.Finalement, nous concluons que les MR peuvent être une solution pour électrifier à un coût abordable avec de faibles émissions de GES, mais pour cela, de nombreux efforts restent encore à faire pour financer ces infrastructures, assurer leur pérennité et décarboner les chaines de production de leurs composants.

This target and the two following (for Senegal and for Kenya) correspond to GHG emissions reduction compared to a business-as-usual scenario by

SAIDI: System Average Interruption Duration Index; SAIFI: System Average Interruption Frequency Index

This study only includes 36 countries, excluding a large part of GHG emissions (Algeria, Egypt, Libya and South Africa are not included)

Solar Home Systems consist of one or a few PV panels and a battery, usually accompanied with light bulbs, mobile phone charger and sometimes a TV.

GIZ: Deutsche Gesellschaft für Internationale Zusammenarbeit, the german cooperation

IEEE: Institute of Electrical and Electronics Engineers

In this thesis, we define the system configuration as the installed capacities for production and storage systems. For solar MG, it corresponds to the installed solar PV power and the energy capacity of installed batteries.

By performance, we consider the different indicators (e.g., cost of electricity, level of service quality, GHG emissions, etc.) that could be optimized or constrained to select the best MG configuration.

ECREEE: ECOWAS Centre for Renewable Energy and Energy Efficiency

NGO: Non Gouvernemental Organisation

When the national grid extends to a village where a MG is already installed

In Nigeria, such importation taxes on solar products are up to 30%[START_REF] Nwadiaru | 6 -Enabling solar photovoltaics penetration in highly dependent African fossil fuel markets[END_REF]

E.g., UK since 2007, France with the "valeur tutélaire du carbone" introduced in 2001 and renamed the "valeur de l'action climat"

IBRD: International Bank for Reconstruction and Development

IDA: International Development Association

Including the indirect GHG emissions of the products that are imported increase the European GHG emissions by 20%.

Chapter 2: Energy for Sustainable Development, Chapter 3: Applied Energy, Chapter 4: Energy policy and Chapter 5: Renewable and Sustainable Energy Transition

In this section, we consider that the project lifetime is equal to PV panel lifetime, thus PV panels do not have any salvage value at the end of the project. Here, we also assume that the batteries do not have any value at the end of the project.

Note that, contrary to the previous chapter where the level of service quality was set to 95%, here we use a level of 100% as the diesel can be used for the few percent of the demand that are expensive when reached by solar energy alone.

In this chapter and in the following one, the CFP and LCOE calculations account for the potential value of the battery at the end of the project. For example, if a battery last 7 years and is installed one year before the end of the project, the CFP considered in the calculation will only be 1/7 of the 𝐶𝐹𝑃 𝑏𝑎𝑡 value.

Some authors distinguish nano, pico, micro and mini-grids depending on their size, relationship with the main power grid, AC/DC power, etc. As there is no consensus on this terminology[START_REF] Dunham | Cost-optimal evaluation of centralized and distributed microgrid topologies considering voltage constraints[END_REF],[START_REF] Irena | Off-grid renewable energy systems: Status and methodological issues[END_REF], in this article we use the term "mini-grid" for systems between 5kW to 1MW.

In Kenya, the regulator EPRA drafted a MG regulation, which was discussed with stakeholders in 2021. Official approval is still pending

GIZ stand for "Gesellschaft für Internationale Zusammenarbeit" ("Society for International Cooperation" in English).

This cross-subsidy might nevertheless be reduced in the future to lower electricity prices nation-wide: a white paper from the Ministry of Energy published in July 2022 suggests reducing the levy by 50%. See https://energy.go.ke/?p=11568 for more information.

For example, Powerhive's strategic advisors are one former UK Minister of State for Energy & Climate Change and the world-famous actor Leonardo Dicaprio.

Here as in the rest of the thesis, we include the imported GHG emissions into countries objectives, even if, in fact, only territorial GHG emissions are considered in the NDCs. We think that to effectively reduce global GHG emissions and to avoid climate justice issues, imported emissions should be included in those objectives.

Upper boundary of the IPCC estimates for 2030 to limit global warming to 1.5°C[START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. The lower boundary is estimated to 170 $/𝑡 𝐶𝑂 2 ,𝑒𝑞 .

Upper boundary of the IPCC estimates for 2030 to limit global warming to 2°C[START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]. The lower boundary is estimated to 60 $/𝑡 𝐶𝑂 2 ,𝑒𝑞 .

This electricity tariff reduction is not immediate, the solar components manufacturers could take advantage of these subsidies to increase their price, or the MG developers could keep the cost reductions to increase their margin.

If the replacement of batteries is also included in the subsidies.

Note that usually, only direct emissions are included in the calculation of the carbon intensity of the electricity mix. Indirect emissions should be included when planning energy systems to achieve net-zero emissions.

Ces institutions nationales et internationales contribuent aussi à la formation technique des développeurs de MR, notamment en publiant des guides pour dimensionner les MR et optimiser les coûts de ces systèmes. A ces contributions s'ajoutent celles du monde académique avec le développement de logiciels (HOMER[START_REF]HOMER Pro -Microgrid Software for Designing Optimized Hybrid Microgrids[END_REF], NREL REopt[START_REF]REopt Evaluates Centralized and Decentralized Microgrids in Sub-Saharan Africa | NREL[END_REF], RET Screen[START_REF]Government of Canada[END_REF]) qui se focalisent principalement sur l'analyse technico-économique des MR et l'optimisation des coûts de l'électricité. Certaines études ajoutent à cette analyse l'évaluation des émissions de GES des MR, le plus souvent en présentant les co-bénéfices associés à la réduction de l'utilisation du diesel[START_REF] Odou | Hybrid off-grid renewable power system for sustainable rural electrification in Benin[END_REF],[START_REF] Baldi | Planning sustainable electricity solutions for refugee settlements in sub-Saharan Africa[END_REF],[START_REF] Cader | Global cost advantages of autonomous solar-battery-diesel systems compared to diesel-only systems[END_REF]. La réduction des émissions de GES est alors le résultat de l'optimisation économique et elle ne contribue pas à définir le dimensionnement du système. D'autres études intègrent bien la réduction des émissions de GES dans une optimisation multicritère[START_REF] Das | Techno-economic and environmental assessment of a hybrid renewable energy system using multi-objective genetic algorithm: A case study for remote Island in Bangladesh[END_REF],[START_REF] Nsafon | Integrating multicriteria analysis with PDCA cycle for sustainable energy planning in Africa: Application to hybrid mini-grid system in Cameroon[END_REF],[START_REF] Ullah | Multi-criteria decision-making model for optimal planning of on/off grid hybrid solar, wind, hydro, biomass clean electricity supply[END_REF], mais il s'agit principalement de cas d'étude dont la généralisation des résultats à d'autres localisations et communautés n'est pas assurée. Enfin, la grande majorité de ces travaux ne prend pas en compte les émissions indirectes de GES associés à l'ensemble du cycle de vie des batteries et des panneaux PV, résumant l'empreinte carbone du système à la seule utilisation du diesel.[START_REF] Richmond | Electrification and appliance ownership over time: Evidence from rural India[END_REF] Il s'agit des coopérations internationales française (AFD), anglaise (DFID) et allemande(GIZ)

Il s'agit ici d'un résumé. Pour plus de détails, en particulier pour les équations du modèle, la localisation des MR, les profils de demande électrique et les valeurs des paramètres, vous pouvez vous référez à la partie méthode du chapitre 2 du manuscrit. Cette remarque est aussi valable pour les sections 9.3, 9.4 et 9.5.

Racine de l'erreur quadratique moyenne normalisée (cf. chapitre 2 pour plus de détails)

Contrairement à la simulation précédente des MR 100% solaires où on autorisait que 5% de la demande ne soit pas satisfaite, on considère ici que la demande doit être entièrement satisfaite.

Pour plus de détails, en particulier pour les équations du modèle, la localisation des MR, les profils de demande électrique et les valeurs des paramètres, vous pouvez vous référez à la partie méthode du chapitre 3

Cette partie n'est pas détaillée ici mais on peut se référer à la section 4.5.1 du manuscrit pour plus de détails.

Solar Home Systems : il s'agit de systèmes individuels composés d'un ou plusieurs panneaux avec une batterie permettant par exemple de couvrir la consommation d'un foyer.

Remerciements

Acknowledgements: We thank the Kenyan villages and the MG actors for their time and enthusiasm during sometimes lengthy interviews. Our gratitude likewise goes to the Nuvoni Centre for Innovation Research and Schneider Electric, with a special note to Sheilla Juma, for their invaluable knowledge and logistical support. Scientific exchanges with Pascale Trompette, Benoît Hingray and participants of the workshop "Governing Renewable Energy Rollouts in Financially Constrained Contexts" organized by the University of Stavanger also greatly enriched this work. This article is part of two PhD thesis funded by the French Ministry of High Education, Research and Innovation and by Schneider Electric.

This work is part of a PhD thesis funded by the French Ministry of High Education, Research and Innovation and by Schneider Electric.

than what is usually done in the literature, and finally, the estimation of the shadow price of carbon associated to CFP reduction.

All aspects of this study are detailed below in the form of an article: T. Chamarande, B. Hingray, S. Mathy, Reducing the carbon footprint of mini-grids in Africa: the value of solar PV (submitted in Applied Energy, April 2023) Reducing the carbon footprint of mini-grids in Africa: the value of solar PV.

Chamarande, T. 1,2,3,* , Hingray, B. 1 , Mathy, S. 2 1 Univ. Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP, IGE, 38000 Grenoble, France 2 Univ. Grenoble Alpes, CNRS, INRAE, Grenoble INP, GAEL, 38000 Grenoble, France 3 Schneider Electric, Grenoble * Corresponding author: theo.chamarande@univ-grenoble-alpes.fr

Abstract

Off-grid mini-grids (MGs) based on solar PV are a promising solution to ensure universal access to electricity in Sub-Saharan Africa without hampering the net-zero CO2 emissions objectives of the Paris agreement. In this paper, we investigate to what extent hybrid MGs (solar PV, storage and genset) can be a low-cost and low-carbon solution on the whole African continent. While in the general literature only the direct emissions of the genset are considered, we adopt a carbon footprint (CFP) approach that also includes the indirect GHG emissions of the PV and batteries. While MG sizing is generally based on the minimization of the levelized cost of electricity (LCOE), we study the nature of the tradeoffs between LCOE minimization and CFP minimization and their impacts on the configurations.

We first show that the least CFP (CFP*) values cannot go below a threshold between 180 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ and 250 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ depending on the climatic zone. When compared to a genset-only configuration, CFP* configurations lead to at least 75% CFP reduction and least LCOE (LCOE*) configurations lead to a 15% LCOE reduction and to a 50 to 65% CFP reduction. In all regions, the genset still supplies a few percentages of the energy in the CFP * configurations. In LCOE* configurations, the renewable fraction is from 50% to almost 80%.

Going from LCOE* to the CFP* lead to relatively high LCOE increase (often >20%), considering the low ability to pay of many rural communities in Africa. However, it is possible to reach significant CFP reduction at a lower cost by choosing a configuration between CFP* and LCOE*. In many cases, a 5% LCOE increase is enough to reduce the CFP of the least LCOE configuration by more than 25%, and a 10% by more than 40%.

These results obviously depend on a number of factors, such as the electric demand and the costs, CFP and lifetimes of each MG component. But in most cases, significant CFP reductions can be obtained with moderate additional costs, which could be covered by support mechanisms for the deployment of these low-carbon MGs. 4 Public policies to reduce the CFP of mini-grids

Context and objectives

In the previous chapter, we show that adding a virtual economic value to carbon emissions (shadow carbon pricing) allows to favor less emitting MG configurations. This shadow carbon price can be implemented through various public policies such as subsidies or taxes. In the present chapter, we try to answer the following questions:

• What are the public policies that would be required to incite MG developers to select lessemitting systems? • How efficient are these policies in terms of cost of carbon?

• How are the policy costs shared among the different MG projects within a country? And among the MG stakeholders (users, developers, governments, etc.)?

Our analysis is based a comparison of different examples of policies to reduce the CFP of MGs and illustrated for four contrasted African countries: Kenya, Senegal, Nigeria, and Madagascar. Innovation compared to previous works: Quantifying the cost of carbon required to decarbonize energy systems in Africa is a key issue. Most of previous studies aiming this quantification are looking at the whole electricity system and neglects off-grid systems. Our work fills this gap. Our focus on MG sizing allows to design specific policies for these off-grid systems and to evaluate their real potential of CFP reduction. By simulating the sizing of fictitious individual MGs with different climate resource and diesel costs, we are also able to see how national policies could differently impact these MG projects. Moreover, these simulations give the possibility to illustrate in practice how a carbon cost can be implemented by subsidies and taxes, and who will bear the costs of these policies. Finally, it also includes indirect GHG emissions in the calculation of the cost of carbon, whereas these indirect emissions are very often neglected in the literature.

All aspects of this study are detailed below in the form of an article: T.

Normalized daily mean power differences [-]

• Multiply the solar production profile 𝑃 𝐴𝐶 (𝑡) by 𝐶 𝑃𝑉 0 to obtain 𝑃 𝐴𝐶 1 (𝑡) [𝑊], the time series of the solar production with an oversizing factor 𝑥 = 1

• Compute for each day the mean of the differences between the normalized solar production and demand (𝑃 𝐴𝐶 1 (𝑡) -𝐷(𝑡))/𝐷 0 .

5.

Optimal oversizing PV capacity for cost ratio 𝒓 = 𝟏 using 𝒙 * 𝒆𝒔𝒕, 𝒓=𝟏 = 𝟎. 𝟖𝟑 + 𝟐. 𝟏𝟐𝝈 𝑫𝒊𝒇𝒇 • Compute the standard deviation of these daily mean differences, the value obtained is 𝜎 𝐷𝑖𝑓𝑓 [-] • Apply equation ( 15): 𝑥 * 𝑒𝑠𝑡, 𝑟=1 = 0.83 + 2.12𝜎 𝐷𝑖𝑓𝑓 to estimate the optimal oversizing factor for a cost ratio 𝑟 = 1

PV costs [$/𝒌𝑾 𝒑 ] and storage costs [$/𝒌𝑾𝒉]

• Compute the full unit costs of storage 𝛼 𝑆 [€/𝑊ℎ] using equation [START_REF]Climate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change[END_REF]:

)

SM related to chapter 4

Table 15 : Parameters values for the LCOE and CFP calculation [START_REF] Besseau | Analyse de cycle de vie de scénarios énergétiques intégrant la contrainte d'adéquation temporelle production-consommation[END_REF] [114], [START_REF] Irena | Electricity storage and renewables: Costs and markets to 2030[END_REF], [START_REF] Irena | Solar PV in Africa : costs and markets[END_REF] 9 Extended summary in French -Résumé étendu en français

Note for the readers:

This thesis was carried out at the Grenoble Alpes University, whose doctoral school requires that each thesis manuscript written in English be accompanied by an extended abstract in French. The following pages summarize the main results of the thesis using some of the figures extracted from the manuscript.

Note aux lecteurs et lectrices :

Cette thèse a été réalisée au sein de l'Université Grenoble Alpes dont l'école doctorale demande que chaque manuscrit de thèse rédigé en anglais soit accompagné d'un résumé étendu en français. Les pages qui suivent résument les principaux résultats de la thèse en s'appuyant sur certaines figures extraites du manuscrit.

Liste des abréviations :

• CAE : Coût Actualisé de l'Energie

Principaux résultats

Suivant la localisation, les efforts à fournir pour réduire les émissions sont très différents du fait de la ressource solaire disponible et du prix du diesel considéré (cf. Figure 129). L'optimum économique sans prix du carbone pour certains MR au Nigéria exclut complètement le solaire (𝐸𝐶 ≈ 1000 𝑔 𝐶𝑂 2 ,𝑒𝑞 /𝑘𝑊ℎ) et l 'EC moyenne sur le pays est d'ailleurs bien plus élevée que dans les autres pays. Les impacts de l'hétérogénéité spatiale de la ressource solaire se voient en particulier sur la dispersion des courbes. Au Sénégal, la ressource solaire est assez homogène d'où des courbes très resserrées autour de la moyenne alors qu'à Madagascar, les courbes sont plus espacées montrant que certaines zones du pays auront plus de mal à réduire leur empreinte carbone que les autres. Si l'on veut maintenant regarder d'un point de vue plus pratique la mise en place d'incitations économiques pour réduire l'EC des MR, on peut imaginer intervenir directement sur les coûts du diesel, des batteries ou des équipements solaires via des subventions ou des taxes. La Figure 130 permet de comparer ces différents outils en termes d'efficacité (coût moyen de la tonne de CO2 évitée) pour différents niveaux de réduction de l'EC moyenne.