Derrick Kwadwo Danso
email: derrickkdanso@gmail.com

Baptiste François

Benoit Hingray

Arona Diedhiou

Assessing hydropower flexibility for integrating solar and wind energy in West Africa using dynamic programming and sensitivity analysis. Illustration with the Akosombo reservoir, Ghana

Keywords: renewable energy integration, optimal mix, solar and wind energy, hydropower operations, residual demand variability, West Africa

For the first time, acceptable S&W integration levels in Ghana is shown.

• Dynamic programming is used for flexible hydropower operations to integrate S&W.

• A 20% penetration of S&W can be fully integrated by flexible hydropower operations.

• A S&W ratio of 1:3 minimizes residual demand variability for higher penetrations.

• The extra storage strongly influences residual demand in solar-dominated mixes.

Ta

Air Temperature TC,STC

PV cell temperature at standard test conditions

Introduction

Planning for future electricity systems to satisfy the growing electricity demand while complying with the Paris Agreement urges further development of Variable Renewable Energy (VRE) such as solar and wind (S&W) energy. VREs have great potential worldwide [START_REF] Ellabban | Renewable energy resources: Current status, future prospects and their enabling technology[END_REF][START_REF] Moriarty | Can renewable energy power the future?[END_REF]. However, the multi-scale variability stemming from VRE driving variables such as wind, solar radiation and cloud cover [START_REF] Danso | Spatio-temporal variability of cloud cover types in West Africa with satellite-based and reanalysis data[END_REF][START_REF] Engeland | Space-time variability of climate variables and intermittent renewable electricity production -A review[END_REF] could jeopardize the stability of these future electricity systems [START_REF] Anvari | Short term fluctuations of wind and solar power systems[END_REF]. The difficulty to reliably forecast the VRE sources also complicates the integration into the power grid [START_REF] Widén | Variability assessment and forecasting of renewables: A review for solar, wind, wave and tidal resources[END_REF].

To cope with temporal and spatial mismatches between VRE generation and the demand, which also presents its own patterns of variability due to a combination of various socio-economic factors, future electricity systems will need to be highly flexible [START_REF] Cochran | Integrating Variable Renewable Energy in Electric Power Markets: Best Practices from International Experience, Summary for Policymakers[END_REF]. Flexibility-permitting measures include storage, energy transport and demand side management [START_REF] François | Integrating hydropower and intermittent climate-related renewable energies : a call for hydrology[END_REF][START_REF] Kies | The Demand Side Management Potential to Balance a Highly Renewable European Power System[END_REF][START_REF] Weitemeyer | Integration of Renewable Energy Sources in future power systems: The role of storage[END_REF]. The present study focuses on using diversity and energy storage from large hydropower (HP) reservoirs, whose storage and release operations provide significant flexibility potential (e.g., [START_REF] Huertas-Hernando | Hydro power flexibility for power systems with variable renewable energy sources: an IEA Task 25 collaboration[END_REF][START_REF] Ming | Hydropower reservoir reoperation to adapt to largescale photovoltaic power generation[END_REF].

In the developed regions of the world, studies have shown that HP plants can provide flexibility to cope with intermittent S&W generation (e.g., in Europe and North America [START_REF] Huertas-Hernando | Hydro power flexibility for power systems with variable renewable energy sources: an IEA Task 25 collaboration[END_REF], South America (de Oliveira Costa Souza [START_REF] De Oliveira | Assessing complementarity and optimising the combination of intermittent renewable energy sources using ground measurements[END_REF][START_REF] Sawe | An optimal mix of solar PV, wind and hydro power for a low-carbon electricity supply in Brazil[END_REF] and Asia [START_REF] Ming | Hydropower reservoir reoperation to adapt to largescale photovoltaic power generation[END_REF][START_REF] Ming | Robust hydroelectric unit commitment considering integration of large-scale photovoltaic power: A case study in China[END_REF]). Some of these studies focused on national electricity systems that currently dominated by HP generation like in Switzerland [START_REF] Dujardin | Interplay between photovoltaic, wind energy and storage hydropower in a fully renewable Switzerland[END_REF] and Norway [START_REF] François | Effects of Increased Wind Power Generation on Mid-Norway's Energy Balance under Climate Change: A Market Based Approach[END_REF]. Other studies focused on the scale of the power plant and aimed at defining optimal designs or rule curves to reduce VRE generation curtailment [START_REF] Jurasz | Large scale complementary solar and wind energy sources coupled with pumped-storage hydroelectricity for Lower Silesia (Poland)[END_REF][START_REF] Kougias | A methodology for optimization of the complementarity between small-hydropower plants and solar PV systems[END_REF]. It is important to note that most of these studies considered scenarios for which the electricity demand remains at the historical level while existing conventional production means are replaced by VRE generation (e.g., [START_REF] Dujardin | Interplay between photovoltaic, wind energy and storage hydropower in a fully renewable Switzerland[END_REF]. Sometimes, new VRE power plants are simply added with no modification of the other components of the electricity system (e.g., [START_REF] François | Effects of Increased Wind Power Generation on Mid-Norway's Energy Balance under Climate Change: A Market Based Approach[END_REF]. Additionally, most of these studies considered scenarios in which the total generation from S&W is also always significantly lower than HP plant capacity.

An important region that is currently undergoing a massive energy transition towards a more zero-carbon economy dominated mostly by renewables like S&W is West Africa (WA). This region is also experiencing enormous increase in electricity demand due to population and economic growth, therefore, the development of large shares of renewables will go a long way to meet the electricity demands in a way that will not jeopardize the goals of the Paris Agreement. This expected massive development of S&W power has been proposed to be complemented by HP plants in the region whose flexibility will be utilized to balance the intermittent nature the S&W-dominated production [START_REF] Falchetta | Hydropower dependency and climate change in sub-Saharan Africa: A nexus framework and evidence-based review[END_REF][START_REF] Sterl | A new approach for assessing synergies of solar and wind power: implications for West Africa[END_REF]. However, there is currently no data-driven evidence that HP reservoirs in the region can successfully complement the intermittent S&W generation. Results of similar works in other parts of the world are likely to differ from this region which present significantly different climatic, socioeconomic and infrastructural characteristics. For instance, the West African Monsoon, which exhibits a high interannual variability [START_REF] Gbobaniyi | Climatology, annual cycle and interannual variability of precipitation and temperature in CORDEX simulations over West Africa: CORDEX SIMULATIONS OVER WEST AFRICA[END_REF], is the main trigger for precipitation. Thus, it strongly influences both the seasonality and interannual variability of water inflows to HP reservoirs [START_REF] Boadi | Impact of climate change and variability on hydropower in Ghana[END_REF] and of the solar resource across the region [START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF]. As a result, many open questions remain when dealing with the potential of using HP plants to foster the integration of utility-scale shares of S&W power generation in WA. These include but not limited to:

• Will large reservoirs be able to cope with the expected large S&W power generation when the latter dominates the energy mix? • Does the relative contribution between S&W sources matter to ease the integration? • How would S&W integration modify the hydropower dam operations, and would they result in a significant alteration of water availability for other uses? • To what extent would the use of an additional short-term electricity storage facility (e.g., a battery to store excess S&W generation) facilitate this integration? Would this reduce or increase the alteration of water availability for other uses? • Does the optimal share of S&W generation depend on the portfolio of electricity storage facilities and/or the S&W penetration level?

To address these questions, we have developed an analysis framework that combines the use of in-situ and global hydrometeorological databases, energy models that simulate wind and solar photovoltaic (PV) generation, and a dynamic programming algorithm for optimization of the HP reservoir operations [START_REF] Bellman | Dynamic Programming[END_REF]. Through a sensitivity analysis, we explore several scenarios of increase in electricity demand and the subsequent development in S&W power capacity to meet the demand increase.

We illustrate the application of the proposed analysis framework using Ghana as a case study. Ghana is representative of many West African countries where several large HP plants contribute significantly to the total electricity generation [START_REF] Gyamfi | Improving electricity supply security in Ghana-The potential of renewable energy[END_REF], although the full potential has not yet been developed [START_REF] Irena | Africa 2030: Roadmap for a Renewable Energy Future[END_REF]. The region is also characterized by abundant renewable energy sources (IEA, 2014;[START_REF] Yushchenko | GIS-based assessment of photovoltaic (PV) and concentrated solar power (CSP) generation potential in West Africa[END_REF], even though their exploitation is currently very low. However, as the population and economy grow, the demand for electricity is also rising quickly (e.g., demand is projected to double by 2040; [START_REF] Ouedraogo | Energy consumption and economic growth: Evidence from the economic community of West African States (ECOWAS)[END_REF]. As a result, a massive development of S&W energy is expected in the region to supply future demand (World Bank, 2019). While the present study does not provide definitive answers to the above questions, the research has been articulated to find out the possibility of integrating large shares of S&W energy in Africa at a scale of a case study. This is achieved by a unique integration of several known models in the proposed analysis framework. The novelty and contributions of the present study are thus mostly specific to West Africa but also, the unique integration of different models in a unified framework to determine: i) the extent to which S&W energy development remains acceptable for a successful integration in West Africa, and more especially in Ghana where the Akosombo reservoir is a key infrastructure for the region, ii)

the optimal shares of S&W in the energy mix to ensure the success of integration, and iii)

the impact of S&W integration on reservoir outflows and potential water uses downstream.

The article is organized as follows: Section 2 presents the analysis framework and Section 3 presents the considered case study. The results are illustrated in Section 4. A discussion of the results is presented in Section 5, which also concludes and provides insights for future research.

Analysis framework and models

Analysis framework

This research assumes the following narrative: the demographic and economic growth in West Africa lead to an increase in demand for electricity; which is in line with the historical trend in the region [START_REF] Adom | Modelling aggregate domestic electricity demand in Ghana: An autoregressive distributed lag bounds cointegration approach[END_REF]. Investments in electricity systems would result in a massive development in S&W energy sources. Several scenarios of increase in electricity demand are considered. For each scenario, different shares of S&W power generation are investigated. Storage and release operations of the HP reservoir are optimized to minimize the residual demand that would eventually be supplied by a backup generation, potentially at high monetary and carbon costs.

For the reference scenario (i.e., current demand and no S&W generation), the electricity demand is primarily supplied by HP generation and other backup production means (e.g., thermal power generation units, small HP plants) (Figure 1). Hereafter, the electricity demand time series is normalized for the sake of simplicity (i.e., daily average demand = 1). Power generation time series are further normalized with respect to the average daily demand for the reference scenario. For the future scenarios, the following assumptions and simplifications are considered:

• No change in hydro-meteorological conditions. For instance, the impacts of warmer temperatures on the electricity demand are disregarded; the effect that climate change may have on the availability of solar, wind, and hydro energy sources (e.g., [START_REF] Bichet | Potential impact of climate change on solar resource in Africa for photovoltaic energy: analyses from CORDEX-AFRICA climate experiments[END_REF][START_REF] Oyerinde | Quantifying Uncertainties in Modeling Climate Change Impacts on Hydropower Production[END_REF] is not considered either. • Six scenarios of increase in electricity demand (∆𝐷) are considered. They range from 25% to 150% increase (step of 25%) with respect to the historic average. This range fairly ensures that the uncertainty associated with the expected increase in electricity consumption within the region [START_REF] Pappis | Energy Projections for African Countries[END_REF] is catered for. Given the above-described normalization, a 100% increase in demand (i.e., ∆𝐷 = 100%) leads to an average demand equal to 2. • Additional S&W power capacity is built so that generation from the newly deployed S&W plants matches the ∆𝐷 on average. Table 1 provides the relative contribution of S&W to total electricity generation for each ∆𝐷 scenario. For each future demand scenario, five combinations of S&W generation are explored (Figure 1). • When the S&W generation exceeds demand, the electricity in excess is lost (Figure 1). To limit S&W losses, we investigate the use of an additional short-term electricity storage that could be provided from batteries and/or pumped hydro storage. When short-term electricity storage is included in the modeling framework, the excess S&W generation at any given time is stored up to the storage capacity of this facility and released as soon as the S&W generation becomes less than the electricity demand. Storage capacities ranging from 1 to 24 hours of average daily electricity demand are investigated. • The residual electricity demand that cannot be supplied by S&W and HP generation is assumed to be supplied by a backup production means. Although the operations of the backup sources used to supply the residual demand are not explicitly modeled, it is assumed, however, that minimizing the variability of the residual demand minimizes the variability of the backup generation as well. This will ultimately minimize the associated operation and maintenance costs of the backup plant. As such, the operations of the HP reservoir are optimized to minimize the variability of the residual demand. The analysis framework described above is summarized in Figure 1. Hereafter, the term raw residual demand will refer to the leftover demand once supply from S&W energy sources has been deducted from the demand. The time series of raw residual demand is input to the short-term electricity storage model, which outputs a time series of demand for HP. The term residual demand is used to refer to the final leftover demand to be supplied by the backup generation means. Figure 1: Flow chart of the analysis framework

To assess the potential of the HP reservoir to cope with the high variability of electricity generation due to S&W generation, sub-daily simulations of the reservoir operations are considered. The sub-daily resolution allows to account for the daily cycle of electricity demand and solar radiation. Time series of water inflow to the reservoir, S&W power generation, and electricity demand are required for the simulations. These time series could be obtained from observations or simulation models as described further in this section.

VRE electricity generation modeling

The HP generation 𝑃 𝐻𝑃 is estimated using the equation below:

𝑃 𝐻𝑃 (𝑡) = 𝑅(𝑡) • 𝐻 • 𝜉 • 𝜌 • 𝑔, ( 1
)
where 𝑅 is the water release from the reservoir to the HP station, and 𝐻 is the reservoir elevation (assumed constant); 𝜉, 𝜌 and 𝑔 are constants namely: the overall system efficiency (turbines, generators, transformers etc.), water density and acceleration due to gravity.

The S&W power generation time series are calculated from weather variables and for generic solar PV panels (Equation 2) and wind turbines (Equation 3). The locations and sizes of the different S&W farms that will eventually be built will be defined from strategic development scenarios available for the region of interest. To our knowledge, there is no well-defined plan to site future S&W farms across the considered region at present. Such a plan could for instance be obtained following a multi-criteria analysis as in [START_REF] Enevoldsen | How much wind power potential does europe have? Examining european wind power potential with an enhanced socio-technical atlas[END_REF]. Without such information, the spatial distribution of PV farms is assumed to be uniform over the region. Wind farms are assumed to be uniformly distributed along the Atlantic coast.

Solar power generation across the considered region is given by Equation 2 (François et al. 2016;Perpiñan et al. 2007):

𝑃 𝑃𝑉 (𝑡) = ∑ 𝐵 𝑖 𝐼 𝑒𝑓𝑓 (𝑡, 𝑖) (1 -𝜇(𝑇 𝑎 (𝑡, 𝑖) -𝑇 𝑐,𝑆𝑇𝐶 ) -𝜇 𝐶 𝐼 𝑒𝑓𝑓 (𝑡, 𝑖)), (2)
where 𝐼 𝑒𝑓𝑓 (W/m 2 ) is the effective solar irradiance received by the solar farm i with an optimal tilt, which is estimated following the method described in [START_REF] Mcpherson | An Open-Access Web-Based Tool to Access Global, Hourly Wind and Solar PV Generation Time-Series Derived from the MERRA Reanalysis Dataset[END_REF]. The air temperature 𝑇 𝑎 (˚C) alters the efficiency of the solar panels. B is a constant generation parameter that is defined as the product of the surface area of the PV array (m 2 ) by the generator and invertor efficiencies (%), and with 𝜇 and C respectively the temperature and the radiation dependent efficiency reduction factors (%). 𝑇 𝑐,𝑆𝑇𝐶 (˚C) is the PV cell temperature corresponding to standard test conditions.

The wind power generation at a given hour t and from a particular wind turbine is estimated as a function of the wind speed. We adapted the power curve of a generic wind turbine with a rated power of 1000 kW (1 MW), cut-in wind speed of 2.5 m/s, and cut-off wind speed of 25 m/s to estimate the power generation from the average hourly wind speed. If the wind speed at t (𝑣) is the same as any of the predefined wind speed values on the power curve, the corresponding power generation value is assigned. However, when 𝑣 lies within any two predefined wind speed values (𝑣 1 and 𝑣 2 ) on the power curve, the wind power generation is then determined by a simple interpolation technique [START_REF] Davis | Interpolation and Approximation[END_REF] based on the power values (𝑝 1 and 𝑝 2 ) associated with the two predefined wind speed values (Equation 3):

𝑃 𝑊 (𝑣, 𝑡) = 𝑝 1 + 𝑣 -𝑣 1 𝑣 2 -𝑣 1 (𝑝 2 -𝑝 1 ), (3)
with 𝑃 𝑊 the hourly wind power generation (Wh).

Electricity generation mix scenario

Hydro, wind and solar power generation are normalized following equation 4:

𝑃 * (𝑡) = 𝑃(𝑡) 𝑃 ̅ (4)
where, P* is the normalized power at time t, P is the electricity generation value at t estimated from the relevant model (i.e., Equations 1 through 3) and hydro-meteorological forcing; 𝑃 ̅ is the average electricity generation from the considered energy source. Note that average of P* equals 1 for all three energy sources.

For a specific demand scenario ∆𝐷, the total electricity generation from the system is defined as:

𝑃 𝑡𝑜𝑡 * = 𝐶 𝐻𝑃 𝑃 𝐻𝑃 * + 𝐶 𝑃𝑉 𝑃 𝑃𝑉 * + 𝐶 𝑊 𝑃 𝑊 * + 𝐶 𝐵𝑎𝑐𝑘𝑢𝑝 𝑃 𝐵𝑎𝑐𝑘𝑢𝑝 * , (5)
where 𝑃 𝐵𝑎𝑐𝑘𝑢𝑝 , 𝑃 𝐻𝑃 , 𝑃 𝑃𝑉 and 𝑃 𝑊 are power generation from backup, hydro, solar and wind energy sources, respectively. 𝐶 𝐵𝑎𝑐𝑘𝑢𝑝 , 𝐶 𝐻𝑃 , 𝐶 𝑃𝑉 and 𝐶 𝑊 are weights that scale the contribution from each energy source.

Note that by definition of the analysis framework (Section 2.1), the equations below stand whatever the considered scenario:

𝐶 𝐻𝑃 + 𝐶 𝐵𝑎𝑐𝑘𝑢𝑝 = 1, (6)
𝐶 𝑃𝑉 + 𝐶 𝑊 = ∆𝐷. (7)
Hereafter, the combined generation from S&W will be noted 𝑃 𝑃𝑉+𝑊 * and will be defined for a specific demand scenario ∆𝐷 as:

𝑃 𝑃𝑉+𝑊 * = [𝑆 𝑃𝑉 𝑃 𝑃𝑉 * + 𝑆 𝑊 𝑃 𝑊 * ]. ∆𝐷, (8)
with

𝑆 𝑊 = 1 -𝑆 𝑃𝑉 , (9)
where 𝑆 𝑃𝑉 and 𝑆 𝑊 are the relative shares from solar and wind energy sources.

Reservoir operations optimization

A Dynamic Programming (DP) algorithm [START_REF] Bellman | Dynamic Programming[END_REF] is used to find the optimal operations of the water reservoir and its associated HP plant. DP is a well-known optimization method that has been intensively used for water resource planning [START_REF] Tilmant | Restoring a flow regime through the coordinated operation of a multireservoir system: The case of the Zambezi River basin: RESTORING A FLOW REGIME IN A MULTIRESERVOIR SYSTEM[END_REF][START_REF] Tilmant | Agricultural-to-hydropower water transfers: sharing water and benefits in hydropower-irrigation systems[END_REF], real-time operations (e.g., [START_REF] Feng | Optimization of large-scale hydropower system peak operation with hybrid dynamic programming and domain knowledge[END_REF] and climate change impact analysis (e.g., [START_REF] François | Estimating Water System Performance Under Climate Change: Influence of the Management Strategy Modeling[END_REF][START_REF] Minville | Adaptation to Climate Change in the Management of a Canadian Water-Resources System Exploited for Hydropower[END_REF]. The use of other methods such as linear programming, genetic algorithms and particle swarm optimization to find the optimal release sequence is not investigated in this study. However, the choice of another optimization algorithm should not alter the results and conclusion of the study. There reader is referred to the review by [START_REF] Dobson | An argument-driven classification and comparison of reservoir operation optimization methods[END_REF] for a comprehensive comparison among reservoir operation optimization methods.

Here, we consider that the HP reservoir is only operated to generate hydroelectricity, except for the satisfaction of a minimum release to preserve the ecological continuity downstream of the dam. Although operations of many real HP reservoirs have to cope with water uses such as irrigation, transport, and domestic water extractions, they are disregarded in this study. This is because of their minor, if not none, influence on the management of most reservoirs built for hydroelectric power in the region [START_REF] Rodgers | The GLOWA Volta Project: A framework for water resources decision-making and scientific capacity building in a transnational West African Basin[END_REF]. However, they could be easily integrated either as a constraint or within the objective function of the optimization problem (e.g., [START_REF] François | Estimating Water System Performance Under Climate Change: Influence of the Management Strategy Modeling[END_REF].

Optimization models typically maximize or minimize a chosen objective function over a given period. The considered objective function aims at minimizing the variability of the residual demand:

𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒 𝑓 = ∑ 𝑅𝐷(t) 2 𝑡=𝑇 𝑡=1 , (10)
subject to:

𝑆 𝑚𝑖𝑛 ≤ 𝑅 ≤ 𝑆 𝑚𝑎𝑥 ( 11
)
𝑅 𝑚𝑖𝑛 ≤ 𝑆 ≤ 𝑅 𝑚𝑎𝑥 (12) 𝑆(𝑡 + 1) = 𝑆(𝑡) + 𝑄(𝑡) -𝑅(𝑡) (13)
where the residual demand 𝑅𝐷 at a given time step 𝑡 equals the positive value of the difference between VRE generation and the electricity demand D (Equation 14); 𝑆 and 𝑄 are the storage in the HP reservoir and additional storage facility respectively.

𝑅𝐷(𝑡) = | min({(𝑃 𝐻𝑃 (𝑡) + 𝑃 𝑃𝑉+𝑊 (𝑡) + 𝑃 𝑆 (𝑡)) -𝐷(𝑡)}, 0) | (14)
where 𝑃 𝐻𝑃 , 𝑃 𝑃𝑉+𝑊 and 𝑃 𝑆 are electricity generations from the HP plant and solar PV and/or wind energy sources, and from the short-term electricity storage, respectively. The use of a quadratic exponent in Equation 10 is common practice to favour the reduction of large deviations between the electricity demand and what is actually supplied, at the expense of the frequency of days for which the demand is not totally satisfied. The optimization of reservoir operations is subject to different constraints, namely the minimum/maximum possible operating levels of the reservoir (Equation 11), and water release has to be larger than the minimum downstream discharge requirement and lower than the maximum turbine release capacity (Equation 12). The mass balance constraint is given in Equation 14. Note that precipitation and evaporation from to/from the reservoir are not included in the mass balance equation.

Equation 10 is solved using Sample Stochastic Dynamic Programming. Defined as a Short-Sighted Management by [START_REF] François | Estimating Water System Performance Under Climate Change: Influence of the Management Strategy Modeling[END_REF], this version of DP allows to account for the uncertain nature of future electricity demand and inputs to the system (e.g., inflows to the reservoirs, S&W generation, and electricity demand) while keeping the associated computation cost low. The main idea is to solve the Bellman equation by averaging over a calendar year the N year-long Bellman matrix obtained via a deterministic dynamic programming algorithm. More details on this algorithm alongside its comparison with other implementations of DP are available in [START_REF] François | Estimating Water System Performance Under Climate Change: Influence of the Management Strategy Modeling[END_REF].

To account for the strong diurnal cycles of both the S&W power generation and of the electricity demand, simulations are carried out at a 3-hour time step. This additionally makes the optimization doable on a common desktop computer. The main outputs of the management model are the optimized water release from the reservoir (HP in units of average daily demand) and the reservoir water storage levels (in MWh units).

3 Case study and database

Ghana and the Akosombo reservoir

Ghana is a West African country located along the Atlantic Ocean and the Gulf of Guinea (Figure 2). The country-scale demand for electricity has more than doubled since 2006 [START_REF] Eshun | A review of the trends in Ghana's power sector[END_REF]. The total electricity generation in Ghana during 2010 was about 10,200 GWh comprising of a mix of HP and thermal sources in proportions of 68% and 31% respectively [START_REF] Gyamfi | Improving electricity supply security in Ghana-The potential of renewable energy[END_REF]. To cope with this rapid increase in electricity demand, the government has recently invested in fossil-based generation sources [START_REF] Kumi | The Electricity Situation in Ghana: Challenges and Opportunities[END_REF]. Besides, several investments are planned to develop both solar (mainly PV) and wind energy (REMP, 2019) to supply part of the increasing electricity demand. The Volta Basin (Figure 2) is shared among six West African countries; 46.4% of its surface area is in Burkina Faso while 38.6% in Ghana, 6.7% in Togo, 4.1% in Benin, 2.4% in Mali, and 1.8% in Ivory Coast (FAO, 1997). In 1965, the Volta river was dammed for the construction of the Akosombo reservoir, also known as the Volta lake. Akosombo is the largest man-made reservoir based on surface area [START_REF] Nilsson | Reservoirs[END_REF] and the third-largest in the world based on storage volume [START_REF] Sawe | An optimal mix of solar PV, wind and hydro power for a low-carbon electricity supply in Brazil[END_REF]. With a surface area of 8,502 km 2 and a storage volume of 148 km 3 (McCartney et al., 2012), it is a key part of Ghana's electricity system. Fed by water inflows from three main upstream sub-basins: Oti, Black Volta, and White Volta and other minor secondary tributaries [START_REF] Amisigo | Impacts of Climate Change on Stream Inflows into the Volta Lake[END_REF]. The HP plant located right downstream of the Akosombo reservoir is the largest of three HP stations in Ghana with an installed capacity of 1,020 MW [START_REF] Kotir | Drivers of Change and Sustainability in Linked Social-Ecological Systems: An Analysis in the Volta River Basin of Ghana, West Africa[END_REF]. Six Francis turbines with a unit output of 173 MW are used to convert falling water from the reservoir into electricity with an annual net generation of around 6,500 GWh. Electricity generated from the Akosombo reservoir each year is strongly dependent on annual precipitation amounts. For instance, historical records show that extremely dry conditions in the past decades led to very low reservoir levels and disruptions in HP generation [START_REF] Kabo-Bah | Multiyear Rainfall and Temperature Trends in the Volta River Basin and their Potential Impact on Hydropower Generation in Ghana[END_REF].

Database

The main inputs to the reservoir optimization model used in this study are the time series of water inflows into the reservoir from the three main sub-basins, the time series for S&W generation, and the electricity demand (i.e., for future scenarios). Records of water inflows at hydrological stations located in each subbasin (Figure 2) were obtained from the Volta Basin Authority. Figure 3 shows the average annual cycles of observed mean specific discharge (black curve) into the reservoir computed with the inflows from the three main upstream sub-basins and the observed storage level evolution in the Akosombo reservoir (pink curve). The temporal pattern of inflows into the reservoir is very consistent from one year to the other and shows a peak during September and October months. However, the volume of water flowing into Akosombo reservoir during this period may vary significantly from one year to another, as indicated by the deviation between the 25 th and 75 th percentiles, which mainly follows from the inter-annual variability in the intensity of the wet season in the region [START_REF] Boadi | Impact of climate change and variability on hydropower in Ghana[END_REF][START_REF] Kabo-Bah | Multiyear Rainfall and Temperature Trends in the Volta River Basin and their Potential Impact on Hydropower Generation in Ghana[END_REF]. As a result, the Akosombo reservoir starts filling up from August following the onset of a significant amount of inflows in July from the upstream rivers. The maximum storage levels are reached during October and November after which the level steadily decreases owing to low inflows (as a result of low rainfall in the Volta basin during this period [START_REF] Kunstmann | Impact of regional climate change on water availability in the Volta basin of West Africa[END_REF]) and release of water for electricity generation. Weather variables required for computing S&W power generations are obtained from high-resolution satellite products and weather reanalyses. Solar PV power generation is computed with SARAH2 (Surface Radiation Data Set -Heliosat) hourly solar irradiance time series at 0.05° resolution [START_REF] Pfeifroth | Surface Radiation Data Set -Heliosat (SARAH) -Edition[END_REF] extracted from EUMETSAT Satellite Application Facility on Climate Monitoring (CM-SAF) over the whole Ghanaian mainland territory (Figure 2). Wind speed data at 50m altitude from the Modern-Era Retrospective Reanalysis for Research and Applications (MERRA-2) [START_REF] Rienecker | MERRA: NASA's Modern-Era Retrospective Analysis for Research and Applications[END_REF]) is used to compute the time series of wind power generation. MERRA-2 has been used several times for assessing wind power generation across several regions in the world (e.g., [START_REF] Staffell | Using bias-corrected reanalysis to simulate current and future wind power output[END_REF][START_REF] Zhang | Quantitative synergy assessment of regional wind-solar energy resources based on MERRA reanalysis data[END_REF]. For this study, wind speed data was extracted from only the coastal areas of Ghana (Figure 2), which are considered to be suitable for wind power generation due to relatively higher wind speeds (WWEA Technical Committee, 2014).

The temporal profile of hourly electricity demand was provided for the year 2014 by the Ghana Grid Company via [START_REF] Waite | Global trends in urban electricity demands for cooling and heating[END_REF]. The demand for electricity varies through the year with maximum values occurring between January and April and the lowest values around August, following the seasonal variations of the temperature and humidity in the area [START_REF] Kondi | Sensibilité météorologique de la demande en électricité dans les villes d'Afrique de l'Ouest[END_REF]. The sub-daily variability is small (Figure 4a) with a peak during the evening (around 21h) and a valley early in the morning (3h to 6h), although the overall fluctuation within a day is not as significant as for countries located in higher latitudes where the population use more domestic appliances, especially during evening hours. Due to the lack of a more comprehensive database for the electricity demand in Ghana, the demand profile available for 2014 is replicated for all other years in the simulation period. Given the availability of all databases considered in this research, the analysis framework presented above was carried out for 20 years from 1992 to 2011. Within this period, the long-term average contribution of power generation from the Akosombo HP is estimated to be about 57% based on various reports of the Energy Commission of Ghana. The remaining 43% is then allocated as the mean generation contribution from backup sources to supply the residual demand. As such, the coefficients 𝐶 𝐻𝑃 and 𝐶 𝐵𝑎𝑐𝑘𝑢𝑝 in Equations 5 and 6 are defined equal to 0.57 and 0.43, respectively.

Results and Discussion

Validation of the reservoir management model

Figure 5 illustrates the performance of the DP algorithm at reproducing the observed Akosombo reservoir levels obtained for the reference scenario (i.e., electricity demand as in 2014 and no S&W power generation). The reservoir management model performs pretty well at reproducing both the interannual variability (Figure 5a) and annual evolution (Figure 5b) of the observed storage levels. The comparison of the simulated storage levels with the observations yielded a correlation coefficient, Nash-Sutcliffe efficiency and percent bias of 0.94, 0.82, and -14.8 respectively. Also, one can note the good performance of the model for simulating the low-frequency variability of the storage levels. These low storage periods (e.g., in 1998 and 2006/7) have resulted from severe droughts that started during the preceding year (1997 and 2006) [START_REF] Bekoe | The Impact of Droughts and Climate Change on Electricity Generation in Ghana[END_REF]. Figure 6a illustrates the HP generation obtained through the reference scenario, which highlights seasonal fluctuation of the HP generation so that the variability of the residual demand to be supplied by the backup production means is minimized.

Figure 5: Normalized storage levels in Akosombo for the 1992-2011 period: observations and simulations with the reservoir management model. Some deviations between simulated and observed storage curves are nevertheless noted in Figure 5. They could be explained by several factors. First, the contribution of the Akosombo reservoir to the nation-wide electricity generation is set to its long-term average (i.e., 𝐶 𝐻𝑃 = 0.57), which does not completely represent the effect of climate variability on the yield of the reservoir, neither the integration over time of the new installed power capacity (e.g., the several fossil fuel-powered power plants which have been installed since 2000 (Energy Commission of Ghana, 2020)). Additionally, the electricity demand was assumed to be constant from one year to the other, but it likely increased continuously over the period as suggested by the observed electricity consumption in the neighboring countries [START_REF] Kondi | Sensibilité météorologique de la demande en électricité dans les villes d'Afrique de l'Ouest[END_REF]. Second, the day-to-day management of the reservoir was simulated using the reservoir management model presented in Section 2.4, which, being an optimization model, is not meant to reproduce verbatim the historical operations of the reservoir [START_REF] Khadem | What do economic water storage valuations reveal about optimal vs. historical water management?[END_REF]. However, the overall performance of the model is satisfying for the considered analysis framework and objectives of this study.

Temporal variability of wind and solar energy generation in Ghana

Figure 4 illustrates the average daily and seasonal patterns for wind and solar PV power generation. Wind power generation is slightly higher in the evening through the night than during the day (Figure 4a). The sub-daily variability of wind power is rather low when compared to solar power; coefficients of variation (CV) equal 0.14 and 1.24 respectively. The seasonality of wind power generation is conversely much larger than that of solar power (daily CVs are 0.41 and 0.13 respectively). Solar power generation remains roughly constant through the year with, however, minimum values during the rainy season as a result of the increased nebulosity due to the monsoon arrival and the high convective activity in this region [START_REF] Danso | Cloudiness Information Services for Solar Energy Management in West Africa[END_REF][START_REF] Plain | Accounting for low solar resource days to size 100% solar microgrids power systems in Africa[END_REF]. Wind power presents a bimodal seasonality with a first peak in March and a second peak during the monsoon period (in July and August). With regards to the inter-annual variability, the wind energy highlights a significantly larger variability than the one stemming from solar PV, as indicated by the deviation between the interquartiles in Figure 4. Interestingly, the daily pattern of the wind energy is quite close to the daily pattern of demand (Figure 4a), while at the seasonal scale, the solar PV generation pattern is much closer to the demand pattern (Figure 4b).

Effects of relative contribution from solar and wind on the losses

Figure 6b-d illustrates the influence of the relative contribution from S&W power generation on the electricity balance for the scenario ΔD = 100%. When only solar PV generation is used in addition to HP generation from the Akosombo reservoir, the demand for HP generation gets to null values almost every day during daylight hours (Figure 6b). Losses occur almost every day from the late morning through to the late afternoon. Although losses occur only during a few hours during the day, the total losses can be significant. On the other hand, when only wind power is used, losses do not occur every day (Figure 6d). However, the variability of the wind generation leads to longer periods during which demand for HP is null and losses are large. These periods may last several days, which is in agreement with the dynamic of wind energy at the considered spatial scale as reported in the review by [START_REF] Engeland | Space-time variability of climate variables and intermittent renewable electricity production -A review[END_REF]. Figure 7a scales up the results discussed in Figure 6b-d to all electricity demand scenarios and S&W generation mixes. For up to 50% increase in demand, which corresponds to a contribution from S&W to total generation close to 33% (Table 1), losses are small and almost independent on the relative share between S&W (as indicated by the SPV variable on the x-axis). In parts of the US and Europe, [START_REF] Ueckerdt | Analyzing major challenges of wind and solar variability in power systems[END_REF] found that significant losses arising from overproduction of S&W occurs for penetrations above 20%, much lower than the 33% penetration found for our study region. For demand increase larger than 50%, losses surge sharply; especially if the generation from solar energy dominates the mix with the wind (i.e., SPV > 0.5). For instance, for demand scenario ΔD = 150%, more than 30% losses are incurred if only solar PV is used to match the demand increase (i.e., SPV = 1). In such a case, an optimal mix of solar PV and wind power (in a ratio of about 1:3) will be needed to minimize the losses from S&W production. Figure 7: Influence of the demand increase (y-axis) and the relative solar PV share (SPV, x-axis) on the loss (%, heat map); a) no short-term electric storage is used; b) a 24-hours capacity storage is considered.

S&W losses can be reduced if an additional short-term storage is available (Figure 7b). This is illustrated in Figure 6e-h with storage (i.e., orange) and release (i.e., green) operations from the short-term storage. We note that with 24 hours of short-term storage capacity, most of the excess generation can be stored for later use. This is especially true when solar PV dominates the mix since losses, although occurring almost every day, are low in magnitude and, as such, are easily handled with 24 hours of short-term storage capacity (Figure 6e); as opposed to energy mix with high wind power share (Figure 6h).

Figure 8 illustrates, for the demand scenario ΔD = 150%, the trade-off between the short-term storage capacity and the incurred losses. Three main results can be drawn out from this figure. Firstly, the addition of the short-term storage facility has a limited effect on wind power losses (dark blue curve). In fact, the availability of 24 hours of storage capacity only reduces the losses by less than 5% when compared with the simulations with no short-term storage. In this case, and given the price of electricity storage options, a cost-effective solution might be to accept the occurrence of losses as suggested by (Klinge [START_REF] Jacobsen | Curtailment of renewable generation: Economic optimality and incentives[END_REF]. Secondly, as indicated in Figure 7b, no loss occurs for energy mixes with solar share SPV larger than 0.5 if 24-hours of short-term storage is available. It is also worth noting that, for these energy mixes, 12 hours of storage capacity is enough to limit losses below 3% of total S&W generation. Finally, following from the two points above, the S&W combination that minimizes the losses depend on the installed short-term storage capacity influence. For instance, with 12 hours of storage capacity, the energy mix SPV = 0.75 shows almost no loss while losses were high when smaller storage capacity is available. Figure 8: Influence on the storage capacity available from the short-term electricity storage on the losses incurred by solar and/or wind energy. Results are shown for the largest demand increase scenario (i.e., ΔD = 150%).

Effects of S&W generation on the residual demand

The integration of S&W into the energy mix results in a sharp increase in the variability of the residual demand, especially for scenarios of large increases in demand (Figure 9). [START_REF] Ueckerdt | Analyzing major challenges of wind and solar variability in power systems[END_REF] found that challenges of adding S&W to the power mix increases with penetration, and is independent of the S&W mix. Our results however, show that the challenges (in this case the raw residual demand variability) of adding more S&W shares, are greater when solar PV dominates the mix (i.e., SPV > 0.5). This is also true for the S&W losses as already discussed (Figure 7a). The combination of 25% solar and 75% wind (i.e., SPV = 0.25) minimizes the variability of the raw residual demand. It is important to note that VRE generation from two different energy mixes, for instance, the mixes SPV = 0 and SPV = 0.5, can lead to raw residual demand with significantly different temporal structures, although they may have similar standard deviation indicators (see the green and dark blue curves in Figure 10d). Broadly speaking, the seasonal (Figure 10a) and daily (Figure 11a) structures of the variability of the raw residual demand depends on the S&W combinations and their overall contribution to the system supply (Table 1). Energy mix entailing large losses have consequently a larger raw residual demand (red curve Figure 10d for mix SPV = 1). Figure 9: Influence of the demand increase (y-axis) and the relative solar PV share (SPV, x-axis) on the standard deviation of the hourly a) raw residual demand, b) residual without no short-term storage and c) residual demand with short-term storage. The ability of the Akosombo reservoir to smooth out the raw residual demand is shown when comparing the left and middle columns in Figures 9, 10 and 11. For the demand increase scenario ΔD = 25% (i.e., S&W penetration of 20%), the raw residual demand is successfully smoothed down to the level obtained for the reference scenario, whatever the chosen mix between S&W. In southwestern China, a slightly higher S&W penetration of 27% was found to be optimal irrespective of the mix combination, when integrated into the power system with the help of current HP installations in the region [START_REF] Zhang | Coordinated optimal operation of hydrowind-solar integrated systems[END_REF]. For a larger increase in demand (ΔD > 25%) and thus higher penetration, the residual demand presents some variability for all S&W mixes (Figure 9b, 10e and 11e). It is higher for mixes with larger PV shares due to high losses. Studies have shown that the plant site of plays a crucial role in the optimization of the size and mix of S&W generation [START_REF] Tang | Optimizing the sizes of wind and photovoltaic power plants integrated into a hydropower station based on power output complementarity[END_REF]. In this study, the optimal combination that minimizes the residual demand variability for larger S&W generation is found to be a mix with 25% solar PV and 75% wind. This optimal combination is different from those found for other regions (e.g., in Brazil (de Oliveira Costa Souza [START_REF] De Oliveira | Assessing complementarity and optimising the combination of intermittent renewable energy sources using ground measurements[END_REF][START_REF] Sawe | An optimal mix of solar PV, wind and hydro power for a low-carbon electricity supply in Brazil[END_REF], in China [START_REF] Zhang | Optimal sizing of the grid-connected hybrid system integrating hydropower, photovoltaic, and wind considering cascade reservoir connection and photovoltaic-wind complementarity[END_REF] and in Europe [START_REF] Heide | Seasonal optimal mix of wind and solar power in a future, highly renewable Europe[END_REF]. From an economic standpoint, the feasibility of this mix would need further assessment as the investments for a massive wind power development in the region are often deemed questionable because of the relatively low wind potential in the region (WWEA Technical Committee, 2014).

Considering economic constraints and the historical record of S&W development in WA, one can argue that some of the S&W scenarios considered in the present work cannot realistically be achieved in the shortto mid-term future. In Ghana for example, a 20% penetration of S&W is the most realistic scenario (out of all the investigated scenarios) in the next 20 to 30 years. Thus, our results give ample confidence that in the near to mid-term future, the Akosombo reservoir will be able to provide the flexibility required to cope with this extra S&W generation. The flexibility provided by the Akosombo HP plant would be independent of the S&W mix in this case. Additionally, no additional storage facilities would be needed in such realistic scenarios (Figure 9).

Interestingly, the use of a short-term storage does not significantly modify the residual demand for energy mixes with larger wind shares (i.e., low SPV values) but largely alters it for mixes with larger PV shares (i.e., high SPV values). For the latter, the use of a short-term storage reduces total residual demand (red curves from Figure 10e to 10f and Figure 11e to 11f) and its variability (Figure 9b to 9c). The reason is similar to the one discussed regarding the losses; a long continuous period of excess wind cannot be handled efficiently by means of a short term-storage (Figure 6h), which somewhat leads eventually to a similar demand for HP. On the other hand, the daily variability stemming from solar PV fits well with the usage of a short-term storage.

Based on a least-cost analysis, [START_REF] Barasa | A cost optimal resolution for Sub-Saharan Africa powered by 100% renewables in 2030[END_REF] suggested that solar PV and wind energy with some complement from HP could dominate the electricity supply in Sub-Saharan Africa countries. Our results however show that even with the incredible flexibility provided by the largest HP reservoir in the region, a massive development of S&W (e.g., up to a 60% share of the total generation) would require huge investments in PV electricity storage in addition to the already existing water reservoir. This would be especially critical when solar PV dominates unless large S&W generation losses are accepted. The acceptance of losses would be an option with however, the need to oversize PV and wind farms to avoid unsatisfied demand.

Effects of solar and wind power integration on reservoir operations

Effects on sub-daily variability of hydropower generation

The reference daily average profile of HP generation is consistent with the demand profile with maximum values between 18h and 21h and minimum values between 03h and 06h (Figure 12). The changes in the operation of the Akosombo reservoir result from the integration of S&W. The magnitude and temporal structure of the change depend on the respective shares of solar PV and wind in the mix. They are more significant for large increases in electricity demand (a larger contribution of S&W to total generation).

When solar PV dominates the S&W mix, HP generation will be low during the day (9h to 15h) and high at night (Figure 12) because of sunlight availability and absence during the day and night respectively. The inclusion of a short-term storage extends the period during daytime when HP generation is reduced (Figure 12d) as stored PV generation during the first part of the day is released during the late afternoon (Figure 6e). Larger water releases for HP generation will be required at night than during the day, which may be beneficial for nocturnal activities such as fishing [START_REF] Tsikata | Living in the shadow of the large dams: long term responses of downstream and lakeside communities of Ghana's Volta River Project, African social studies series[END_REF]. In contrast, reduced water releases during the daytime may negatively impact downstream water uses such irrigation and recreational activities. When only wind power is used to match up the increase in demand, HP generation from 9h to 15h is slightly larger than for reference scenario. This is due to the relatively lower wind power generation during the daytime (Figure 4). At night, the S&W generation configurations with high wind shares (𝑆 𝑃𝑉 = 0.25 and 𝑆 𝑃𝑉 = 0) require less HP generation than those with high solar PV shares. The flexibility provided by the Akosombo reservoir to balance generation from S&W means that water release from the dam inherits at least part of the S&W variability. Broadly speaking, the higher the increase in electricity demand, the larger the variability of HP generation (Figure 13a). The variability of HP generation is also larger for configurations with high solar PV shares, which directly results from the large sub-daily variability of the solar resource. The larger water release variability is often deemed more challenging to cope with for the agricultural sector and could lead to a lower performance for the irrigation canals [START_REF] Clemmens | Improving irrigated agriculture performance through an understanding of the water delivery process[END_REF]. A re-regulation reservoir right downstream [START_REF] Anindito | A new solution to mitigate hydropeaking? Batteries versus re-regulation reservoirs[END_REF] or runoff regulation [START_REF] Zhang | Optimal sizing of the grid-connected hybrid system integrating hydropower, photovoltaic, and wind considering cascade reservoir connection and photovoltaic-wind complementarity[END_REF] would then be required possible solutions to smooth out the variability of water releases from the reservoir. Figure 13: Standard deviations of the HP generation without a short-term storage (left) and with a '24hours' capacity short-term storage facility (right), for all increased demand scenarios and for all configurations of S&W generations.

A less expected result is that the variability of HP generation would be increased further by the inclusion of a short-term storage facility in the system (Figure 13b). The reason is that the short-term storage can actually increase the variability of the residual demand to be smoothed out by the HP dam. This increase in variability can come from long periods when the demand for HP is null. This would be a critical issue especially when solar PV dominates a high S&W generation. However, this result directly follows the rather rough rules used to simulate the storage/release operations of this storage facility. Adapted management of this storage would likely help to solve part of this issue. For instance, the smooth release of stored energy (during the whole nighttime for instance each day) would likely be an efficient option for this. It could even allow reducing the importance of the re-regulation reservoir mentioned above.

Effects on reservoir storage

The average annual cycle of relative change (to the reference scenario) of water storage in the Akosombo reservoir is illustrated in Figure 14 for demand scenarios ΔD = 25% and ΔD = 150%. For an increase in demand up to ΔD = 25%, the mix with 100% wind share (Spv = 0) leads the water storage level to increase by 7% in September (Figure 14a) and decrease by 4% in June. The mix with 100% solar PV generally leads to slightly higher water levels (up to 5%) throughout the year. The presence of a short-term storage does not affect these changes in the reservoir storage fluctuation for all S&W mixes (Figure 14b). Additionally, the modification to the seasonality of the reservoir storage is not significant whatever the mix of S&W power generation (Figure 15 a, b, andc). This is because a short-term storage is often not needed when the contribution of S&W to total generation is low. As already discussed, out of all the investigated scenarios for the study region, a 20% S&W penetration remains the most realistic in the near to mid future. This means that, whatever the decision made today regarding the shares solar PV and wind power in the S&W power generation mix, the impacts on the annual cycle of the reservoir water storage will not be clearly seen in the near future but significantly later. For larger increases in electricity demand, the alteration of the reservoir level can be more significant. For instance, for the demand scenario ΔD = 150%, the storage level would increase by more than 15% in September for the mixes with large wind share (Figure 14c). This likely follows from the high wind power generation during the Akosombo filling season from July to November (Figure 4). In June, just before the filing season, the reservoir level decreases by about 13%, relative to the reference storage, for the mixes with large wind share. As discussed in Section 4.3, solar dominated mixes lead to large losses of solar production during the day when the contribution of S&W is high. Consequently, the demand for HP is increased to compensate for the lost solar power. The mean reservoir storage level thus progressively decreases over the simulation duration. When the demand increases by 150% and only solar PV is used, the interannual mean level of storage is thus, lower than the reference storage on average (Figure 14c). This result is in contrast to [START_REF] Fang | Optimal sizing of utility-scale photovoltaic power generation complementarily operating with hydropower: A case study of the world's largest hydro-photovoltaic plant[END_REF] who found that, PV integration exerts little influence on the Longyangxia reservoir storage variations, for one of the world's largest hydropower-PV complementary operations. They attributed the little influence of PV integration to the large storage volume of the Longyangxia reservoir (24.7 km 3 ) which is significantly lower than the Akosombo reservoir (148 km 3 ). Thus, the contrasting results could be linked to the differences in objective function, operational rules and constraints, the contribution of S&W to total electricity generation, as well as the underlying variability of the demand and solar resource.

Despite its small capacity, the importance of the short-term storage in the solar PV dominant configurations is clear. The short-term storage induces a shift up of the Akosombo storage of about 18% in June and at least 4% in all other months relative to the reference storage (Figure 14d) with almost no change in seasonality (Figure 15d). This translates to an increase of at least 15 MWh in all months (Figure 15f). This increase in storage level is due to the reduction in solar PV losses, as illustrated in Figure 7. When only wind power is used (𝑆 𝑃𝑉 = 0), the effect of the short-term storage on the Akosombo storage is significantly smaller, likely due to the limited reduction in losses from wind power generation (Figure 7). The slight change in seasonality, however, likely follows from the strong seasonal signal of the wind power generation, and thus of the associated generation losses.

Conclusion

This study investigated the potential of large HP reservoirs to provide flexibility to ease the integration of large shares of S&W generation in WA. A case study of Ghana and the Akosombo HP plant showed that when S&W contribution to total generation is small (penetration up to 20%), the residual demand variability can be totally smoothed out, whatever the share of solar PV and wind power in the energy mix. Considering economic constraints and the historical record of S&W development in WA, a 20% penetration remains the most realistically achievable (out of the investigated development scenarios) in the next 20 to 30 years. This result from our analysis help to inform policymakers and provide an answer to an often-debated topic in WA: the extent up to which S&W can be developed and successfully integrated into the region without added significant financial implications.

For an extremely high S&W development scenario (penetration more than 20%), the Akosombo HP plant can still reduce a large part of the residual demand variability, but a significant part remains, especially when solar PV dominates the S&W mix. A short-term storage can help to further lower the residual demand variability for solar PV dominating configurations but its role is insignificant when wind dominates. In all cases, a mix of 25% solar PV and 75% wind power was found to produce a residual demand with the least variability. From an economic standpoint, the feasibility of this mix would need further assessment as the investments for a massive wind power development in this region are often deemed questionable due to the relatively low wind potential in the region.

An important extension of our work would the inclusion of other uses of the reservoir such as irrigation and domestic water extractions as well as other system constraints (e.g., backup sources capacity) in our modelling framework. It will also be necessary to consider the influence of climate change on the availability and variability of renewable energy resources as well as changes in the temporal structure of electricity demand. Nevertheless, this study allows for an important assessment of the potential of the Akosombo reservoir to ensure the successful integration of S&W power in Ghana. The approach used here could be applied to assess reservoirs in other WA countries considering the similarities in climatic and socioeconomic characteristics.

Figure 2 :

 2 Figure 2: Map of Ghana (black borders) and the Volta basin showing the river network in the region and the location of the Akosombo dam. Hypothetical solar PV farms and wind farms are sited respectively at 29 locations uniformly distributed across region and 8 coastal offshore areas.

Figure 3 :

 3 Figure 3: Average annual cycle of observations of mean specific discharge (MSD, black curve) to the reservoir from the three upstream catchments and Akosombo reservoir storage (pink curve). Shaded areas indicate the deviation between the 25th (lower bound) and 75th (upper bound) percentiles.

Figure 4 :

 4 Figure 4: Normalized mean (a) daily and (b) annual, cycles of potential solar and wind power generation in Ghana. Daily cycle has been computed from hourly generation values whiles annual cycle has been computed from daily generation values. Shaded areas indicate the deviation between the 25th (lower bound) and 75th (upper bound) percentiles.

Figure 6 :

 6 Figure 6: Illustration of the electricity balance for a 3-weeks period in 2010. a) Reference scenario; demand as in 2014 and no generation from solar PV and wind. b-d) demand scenario ∆D = 100% with a relative share of solar SPV equal to 1 (b), 0.5 (c) and 0 (d). e-g) show similar configuration to b-d) but a short-term storage is considered to reduce solar and wind losses.

  Figure 10: Average annual cycle of the raw residual demand (a and d), the residual demand without shortterm storage (b and e) and the residual demand with short-term storage (c and f). The bold curves in color represent the average cycle of the residual while the shaded area illustrate the deviation between the 25 th and 75 th percentiles of the residual.

Figure 11 :

 11 Figure 11: Average daily cycle of the raw residual demand (a and d), the residual demand without shortterm storage (b and e) and the residual demand with short-term storage (c and f). The bold curves in color represent the average cycle of the residual while the shaded area illustrate the deviation between the 25 th and 75 th percentiles of the residual.

Figure 12 :

 12 Figure12: Average daily cycle of HP generation for increased demand scenarios ΔD = 25% and ΔD = 150% simulated without a short-term storage (a and c) and with a short-term storage (b and d). The bold curves in color represent the average cycle and shaded area illustrate the deviation between the 25 th and 75 th percentiles of the residual.

Figure 14 :

 14 Figure 14: Average annual cycle of relative change (to the reference [%]) in storage of the Akosombo reservoir for increased demand scenarios ΔD = 25% (top) and ΔD = 150% (bottom), simulated without a short-term storage (a, c), and with a short-term storage (b, d).

Figure 15 :

 15 Figure 15: Average annual cycle of storage in the Akosombo reservoir for increased demand scenarios ΔD = 50% (top) and ΔD = 150% (bottom), simulated (a, d) without storage, (b, e) with a short-term storage and (c, f) difference between configurations with storage and without storage. The bold curves in color represent the average storage cycle and the shaded area illustrate the deviation between the 25 th and 75 th percentiles.

Table 1 :

 1 Contribution from S&W to totals generation for the considered electricity demand scenarios. Contributions from solar and wind energy sources (𝐶 𝑃𝑉 and 𝐶 𝑊 ) are defined in Equation7.

	ΔD Total electricity demand	Contribution from S&W	Relative contribution
		(1+∆𝐷)	(𝐶 𝑃𝑉 + 𝐶 𝑊 )	from S&W (%)
	0	1 (Reference)	0	0
	0.25	1.25	0.25	20
	0.50	1.5	0.50	33.3
	0.75	1.75	0.75	42.9
	1.0	2.0	1.0	50
	1.25	2.25	1.25	55.6
	1.50	2.5	1.50	60

Acknowledgment

The authors will like to thank the German Federal Ministry of Education and Research (BMBF) and West African Science Centre on Climate Change and Adapted Land Use (WASCAL) for funding the thesis of the first author. The first author wishes to express his profound gratitude to Prof. Adamou Rabani of WASCAl-GRP-CCE for his support during the period of the thesis. We thank the Volta Basin Authority and Ghana Meteorological Agency for providing the observed hydrometeorological data used in this study.

Variable Renewable Energy WA West Africa Wh Watt hour WWEA World Wind Energy Authority Variables


Géraud Delport

Fabien Vialla

Cyrielle Roquelet

Stéphane Campidelli

Christophe Voisin

Jean-Sébastien Lauret
email: jean-sebastien.lauret@lac.u-psud.fr

Aimé Cotton

Davydov splitting and self-organization in a porphyrin layer noncovalently attached to Single wall carbon nanotubes

Keywords: Self-assembly, Energy transfer, Hybrid nanomaterials, Functionalization, Davydov Splitting, Nanotube, Porphyrin

Over the years, the development of selfassembled nanomaterials has lead to major breakthroughs in various domains such as catalysis, [START_REF] Daniel | Chemical reviews[END_REF] electronics, [START_REF] Yu | [END_REF] or photonics. 3 For instance, thin lms made of self-assembled organic or hybrid materials are promising building blocks for optoelectronic devices, such as heterojunctions solar cells 4 or organic LEDs. 5 Self-assembled nanomaterials have remarkable light harvesting and charge transport properties, that are often connected to their degree of organization. 6 Therefore, one key challenge in nanoscience is to understand and control the organization of nanomaterials at the supramolecular scale.

In this context, many groups have developed self-assembled nanocompounds based on carbon materials (nanotube, fullerene ...). 917 In particular, our groups have evidenced an ultraecient (∼ 100%) energy transfer in compounds made of tetraphenylporphyrins (TPP) molecules (donor) and carbon nanotubes (acceptor). 1822 This eect is even more remarkable in the context of non-covalent functionalization. In addition, despite the weak πstacking interaction these compounds show outstanding chemical stability in water. 21,23 In a previous thermodynamics study, we demonstrated that the reaction is cooperative in the context of a Hill model. One possible origin of the cooperativity of the reaction lies in molecule-molecule interaction. 24 Therefore, these observations raise two questions: the origin of the possible TPP-TPP interaction and the degree of organization of the molecules at the nanotube surface.

In this article, we show that porphyrin molecules self-assemble to form an organized shell around the nanotube. In particular, we show that the interaction between the phenyl substituents is central for the self-assembly. This eect has been investigated by modifying chemically the molecule. The degree of organization has been probed by using a polarized photoluminescence (PL) spectroscopy approach. Beside chemical stability, a spectroscopic signature of the interaction between TPP is a strong Davydov splitting resulting from a dipole-dipole interaction.

Concomitantly with our experimental investigations, some theoretical predictions on the organization of TPP around nanotubes have been reported. First, a recent DFT study from W. Orellana 7 has predicted a cooperative behavior during the adsorption of TPP on nanotubes. He has calculated several TPP patterns at the surface of a (6, 5) nanotube (NT). The most stable one turns to be a eight TPP building block, due to the phenyl-phenyl stabilizing interaction. A binding energy per molecule in the organized structure of 1.95 eV (188 kJ.mol -1 ) was extracted, which is signicantly larger than the 1.31 eV (126 kJ.mol -1 ) value obtained for the adsorption of a single TPP. Thus, the cooperation of the porphyrins leads to a stabilization of the global TPP/NT system. The author attributed this eect to the stabilizing π-stacking interaction between the phenyl groups of adjacent porphyrins. 25 Likewise, Bassiouk et al. have performed molecular mechanics simulations and have also predicted an organized structure of the TPP molecules around the nanotube. 26 In our experiments, the functionalization is performed in an aqueous suspension with sodium cholate micelles. In this process, the porphyrins have to overcome the cholate/NT binding energy barrier to reach the NT surface. The binding energy of cholate on nanotubes have been calculated by Carvhalo et al. 8 The value is of the order of 160 kJ.mol -1 . It places the binding energy of cholate in between the one of a single TPP and the one of the eight TPP conguration reported by W. Orellana (see gure 1(a)). Therefore, it suggests that the TPP-TPP interaction is a key parameter to surpass the cholate/NT binding in order to enable the stacking of the TPP onto the NT surface.

To experimentally test this theory, we have functionalized (6, 5) NTs with two kinds of porphyrins using the micelle swelling method. 21,27 The photoluminescence excitation (PLE) map of TPP/NT compounds is displayed in gure 1(c). In addition to the intrinsic S 22 →S 11 transition of the (6,5) NTs, an additional resonance is observed for an excitation energy at 2.82 eV. This transition is a direct signature of the energy transfer from the TPPs to the nanotube. 19 It corresponds to a photon absorption on the Soret band (B) of the porphyrins stacked on the NT, and an emission on the S 11 excitonic transition of the NT. 24 In a second sample, we have used modied porphyrins 5,10,15,20-(tetra-4-tert-butylphenyl)-porphyrin (TtbPP). These molecules have tertbutyl substituents on the phenyl groups, that increase their steric hindrance (see gure 1(b)) and may prevent the phenyl-phenyl interaction. The PLE map of the nal TtbPP/NT sample (gure 1 (d)) does not display any evidence of functionalization: no TtbPP→NT energy transfer and no shift of the optical transitions. In principle, the blocking substituents should not hinder the interaction of the TPP macrocycle with the nanotube surface. Therefore, the absence of functionalization seems to be specically related to the suppression of the phenyl-phenyl interaction induced by the steric hindrance of the tertbutyl, conrming the importance of such interaction to achieve chemically stable compounds. This strongly supports that the stacking reaction arises from small clusters of few TPP interacting together through the phenyl-phenyl interaction, as predicted by Orellana et al. 7 This phenyl-phenyl interaction implies some ordering (at least local) of the TPP molecules at the surface of the nanotube. In the following, we look for spectroscopic evidences of such order, using polarized PLE (see gure S4 in the S.I. for details). For dierent excitation frequencies ω, we have measured the PL anisotropy r(ω) (gure S5 in S.I.):

r(ω) = I V V (ω) -G(ω)I V H (ω) I T (ω) (1)
where I V V (resp. I HH ) is the PL intensity using two vertical (resp. horizontal) polarizers. G(ω) = I HV /I HH is a correction factor 28 and

I T (ω) = I V V (ω) + 2GI V H (ω)
is the total PL intensity. The anisotropy diagram (gure S5 in S.I.) allows us to determine the maximum of the anisotropy coecient r max . This coecient lies between 0.4 and -0.2 for any solution of randomly oriented luminescent objects, 28 while the upper limit (resp. the lower) is obtained when these objects have fully parallel (resp. orthogonal) absorption and emission dipoles. For the TPP/NT suspension, r max is here evaluated to 0.25, in good agreement with the literature. 29 From r(ω), it is possible to extract I and I ⊥ . These PL intensities represent two dierent PL processes in which the excitation and emission dipoles are either aligned (I ) or orthogonal (I ⊥ ): 28

I (ω) = r(ω) + 0.5 × r max 1.5 × r max I T (2)
I ⊥ (ω) = r max -r(ω) 1.5 × r max I T (3)
Figure 2(a) displays the I and I ⊥ PLE contributions for the TPP/NT sample and for a detection energy xed at 1.24 eV (S 11 of the (6,5) chirality). In the S 22 spectral region (at 2.1 eV), the signal is concentrated in the I intensity, in agreement with the literature for pristine nanotubes samples in surfactants. 29 It corresponds to the resonant absorption and emission of light polarized along the NT axis, in connection with the optical selection rules of nanotubes. [START_REF] Lefebvre | Physical review letters[END_REF] In the Soret (B) region, through the energy transfer, the behavior is more complex, with two subbands located at dierent energies. A similar splitting has been evidenced in isolated TPP, [START_REF] Weigl | [END_REF] and corresponds to the orthogonal Soret transitions B x and B y (see gure 2 (a) inset). The low energy one (B x ) is here located at 2.82 eV. We see that it is concentrated in the I signal, proving that the TPP absorption dipole is aligned with the emission dipole of the NT. As this emission dipole is aligned with the NT axis, we can deduce that the B x dipoles of the TPP are also along this direction. Therefore, this experiment shows that, on average, all the TPP molecules share the same orientation with their O x direction along the nanotube axis. This is the rst optical evidence of an organization of the adsorbed TPPs on NTs. In addition, this polarization diagram reveals the presence of the high energy subband B y at 2.98 eV in the I ⊥ intensity. This is consistent with an orientation of the TPP molecules with their O y direction perpendicular to the NT axis. Similar results were found for other chiralities in experiments on HiPCO NT samples (see gure S6). Interestingly, confocal PL experiments revealed that such eect is also present at the single TPP/NT nanocompound level (see gure S7). This proves that the alignment of TPP along the NT axis occurs in dierent experimental conditions, and that the compound is stable enough to keep its supramolecular structure upon deposition on a substrate.

The value of the B x /B y energy splitting is of the order of 160 meV in TPP/NT compounds (see gure 2 (a)). To compare this splitting to the one of isolated TPP, we have performed a similar polarized PLE experiment on isolated TPP in a DCM/castor oil organic phase. The castor oil is a viscous solvent that is employed to slow down the rotational dynamics of TPPs below their PL lifetime, so that the rotational depolarization eect becomes negligible. [START_REF] Lakowicz | Principles of uorescence spectroscopy[END_REF] A 10-90% DCM-castor oil volume ratio was chosen to achieve such eect. Figure 2 (b) displays the polarized PLE signal of this TPP sample detected on the PL of the Q bands. The two orthogonal Soret components (see gure S9 in S.I. for the Q bands) of the porphyrins can be observed. The B x resonance is observed at 2.94 eV and the B y one at 2.99 eV. Therefore, the B x /B y splitting is of 50±10 meV that is signicantly smaller than the one found on the hybrid nanocompounds (160±10 meV). Thus, the adsorption process on the NT clearly leads to an enhancement of the splitting between the B x and B y bands.

To determine the origin of these results, we have considered two main physical eects. The rst one is the attening of the molecule upon adsorption on a subtrate. [START_REF] Xu | [END_REF] Under such hypothesis, Chernia et al 34 have predicted that the B x and B y bands would both undergo a similar redshift without an increase of the split-ting. In a calculation detailed in S.I., we have quantied that both bands undergo a redshift of ∼ -40 meV. As a conclusion, this attening cannot explain the observed enhancement of the B x /B y splitting. The other possible origin is an electronic coupling between organized TPP at the nanotube surface. Davydov splitting eects have been observed in aggregates of porphyrins under many dierent congurations, 3537 including adsorption on graphene. 38,39 In this context, the respective red and blue shift could be the signature of an inequivalent dipole coupling for the B x and B y transitions. To model this eect, we have calculated the spectral shifts of the Soret band components within a linear aggregate of porphyrins as it could exist along the nanotube template (see gure 2 (c)). This conguration has been chosen for its simplicity. The case of a more realistic helical structure 26 is treated in the SI. We have used Kasha's theory on coherent molecular aggregates . 40 In the following, the two components of the Soret band will be treated as orthogonal transition dipoles -→ µ x and -→ µ y (of amplitude µ 0 = 8.3 D, extracted from the TPP extinction coecients, see gure S10 in S.I. for the details of the evaluation). This allows to evaluate the coupling term h∆ω between two parallel dipoles:

h∆ω = µ 2 0 4πε 1 -3 cos 2 (θ) r 3 (4)
where r is the distance between the dipoles and θ is the angle between the dipoles and the axis connecting the two dipoles. Starting from the initial transition energy ω 0 of the two coupled dipoles, it leads to a nal transition energy of hω dimer = hω 0 + h∆ω. Based on the results from gure 2 (a), we will consider that every TPP has its x direction aligned with the nanotube axis. We will also assume a distance of r = 1.4 nm between neighbour molecules (the TPP diameter is 1.25 nm), as it was measured by STM for similar TPP aggregates on graphene. 41 The numerical value of the coupling term h∆ω is then evaluated for the -→ µ x (θ = 0) and -→ µ y (θ = π/2) set of dipoles. This yields respectively h∆ω x = -32 meV (redshift) and h∆ω y = +16 meV (blueshift).

Then, we evaluate the energy position of the two optical transitions ω x and ω y , as a function of the number of coupled porphyrins (gure 2 (d)). Starting from the intrinsic 50±10 meV found in castor oil, the energy splitting varies from 98 ± 10 meV for the dimer case up to 150±10 meV for aggregates of 8 monomers or more. This nal value has the same order of magnitude as the experimental splitting reported in gure 2(a) on TPP/NT complexes (160±10 meV). Therefore, this dipole-dipole coupling model for a linear chain of TPP is able to explain the observed increase of the Soret energy splitting for TPP/NT samples. Note here that the Davydov splitting saturates for ∼8 coupled monomers. This corresponds also to the number of TPP molecules in a cluster for which the best stability of the hybrid compound has been predicted. 7 In this framework, no variation of the Davydov splitting is expected as a function of the concentration, and even the rst small cluster stacked on the nanotube should show similar B x /B y splitting to the one of the fully covered compound. Moreover, as shown in S.I., this model also provides similar energy splittings for helical aggregates that were also predicted recently. 26 Finally, we investigate the reason why the B y resonance is four times weaker than the B x one in the TPP/NT samples. Indeed, this is in contrast with the situation in isolated TPP, where the B x and the B y transitions have similar amplitudes (see gure 2 (a) and (b)). This result can be interpreted as a consequence of a local eld eect at the surface of the NT. As explained in a previous report (see also in the SI), an incoming electric eld with a polarization perpendicular to the NT axis will have a locally screened amplitude, while no screening occurs for a parallel electric eld. 42 Consequently, using the data reported earlier, 42 we evaluate a reduction by a factor four of the number of photons absorbed on the B y transition (orthogonal to the NT axis) as compared to the B x one (parallel to the NT axis).

We end up with a full model able to reproduce quantitatively the polarized spectra obtained on the NT/TPP samples. The inputs of the model consist in the data obtained on isolated TPP in castor oil (see gure 2(b)). Tak- ing into account the eects described above, we obtain the simulated spectra described on gure 3 (see gure S15 for the detail of each step). It reproduces both the energy position of the lines and their relative amplitude, validating our analysis. Nevertheless, the measured resonances have larger width than the simulated ones. This can be due to some disorder in the porphyrin layer (dierent angles, distances, ...) leading to a weak dispersion in the energy splitting. Changes in width can also be explained by vibronic coupling eects within the aggregates 43 that have been neglected in the present model. Finally, we end up with a scheme where the stacking unit is composed of at least eight TPP molecules that are interacting together through the phenyl-phenyl interaction. In all clusters, each TPP molecule orientates its O x direction along the nanotube axis. In these aggregates, the molecule-molecule distance is small leading to a dipole-dipole coupling which signature is the observed Davydov splitting.

Conclusion

We carried out a comprehensive optical study of the cooperative stacking of porphyrin molecules onto carbon nanotubes. First of all, the role played by the phenyl groups in the organization process has been demonstrated experimentally by modifying their chemical structure. Moreover, we have shown through polarization sensitive experiments that the TPP molecules selforganize in a specic way with their O x direction along the nanotube axis. This supramolecular organization leads to an electronic coupling between the molecules stacked onto the nanotube. A dipole-dipole model applied to this structure predicts an enhancement of the natural B x /B y splitting of the molecule. This prediction has been conrmed experimentally by means of polarization resolved PLE experiments. Finally, our model, taking account all the physical eects (screening, attening of the molecule, Davydov splitting) allows to reproduce the experimental data. It represents a signicant advance in the understanding of the supramolecular organization of TPP molecules around nanotubes.

Bek

Figure 1 :

 1 Figure 1: (a) Binding energies for TPP/ NT systems (one and eight molecules) and cholate/NT systems as calculated in 7 and; 8 (b) Chemical representation of the 5,10,15,20-(tetraphenyl)-porphyrin (TPP) and the 5,10,15,20-(tetra-4-tert-butylphenyl)-porphyrin (TtbPP); PLE map of the TPP/NT sample (c) and the TtbPP/NT sample (d). (e) Scheme of the energy transfer process.

Figure 2 :

 2 Figure 2: (a) I and I ⊥ PLE components from a TPP/NT suspension, for an emission energy of 1.24 eV (corresponding to the (6,5) functionalized nanotubes). The maximum of the Soret absorption band at 2.952 eV of the non interacting TPPs in cholate is marked with a vertical line. Inset: sketch of the molecule and denition of the axes. (b) I and I ⊥ PLE components within the Soret band of isolated TPP molecules (PL detected on the Q x (0,0) band at 1.91 eV) in a DCM/castor oil mix. The maximum of the absorption Soret band of the TPPs at 2.967 eV is shown with a vertical dashed line. (c) Schematic of an array of porphyrins at the surface of a carbon nanotube, with their µ x dipoles aligned to the nanotube axis; (d) Evolution of the low energy hω x and the high energy hω y bands as a function of the number of porphyrin monomers in the aggregate.

Figure 3 :

 3 Figure 3: Comparison between the measured I and I ⊥ PLE intensities for NT/TPP and the full model. The inputs of the model are the data obtained on isolated TPPs in castor oil.

Acknowledgement J.S.L. is partially funded by "Institut Universitaire de France".

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