Rostyslav Bilyy
email: r.bilyy@gmail.com

Solomiya Paryzhak

Kostiantyn Turcheniuk

Tetiana Dumych

Alexandre Barras

Rabah Boukherroub

Fujia Wang

Gleb Yushin
email: gleb.yushin@mse.gatech.edu

Sabine Szunerits
email: sabine.szunerits@univ-lille1.fr

Aluminum oxide nanowires

come

Introduction

Vaccination has made an enormous contribution to global health and is considered one of the greatest medical accomplishments for achieving global safety against dangerous diseases.

Since the efficiency of a particular vaccine correlates directly with the percentage of a given population that has been vaccinated, the vaccine market requires cost-effective and efficient solutions to attain broad vaccination coverage [1]. The technologies involved in manufacturing different types of vaccines influence 42 strongly vaccine costs. The high price of antigen expression 43 makes many vaccines less affordable to (and thus less used by) 44 low-income population [2]. Adding effective adjuvants to vac-vants to enhance the body's immune response to an antigen would allow the development of next generation of safer, more effective, and more affordable vaccines. Aluminum (Al) salt-based adjuvants (most commonly in the form of aluminum oxyhydroxide (AlOOH), aluminum hydroxide (Al(OH) 3 ) are used in human vaccines since 1930s and are commonly referred to as "alum" [4][5][6]. The presence of oxygencontaining groups on their surface [7][8][9] provides fast antigen adsorption and yield a vigorous response from the immune system compared to alternatives [10]. While aluminum oxide (Al 2 O 3 ) is more robust, it is significantly less effective than other Al-based adjuvants and is commonly much less used. Furthermore, Al salt-based adjuvants exhibit relatively low cytotoxicity as compared to pathogen stimulants or virusomes and have proven to cause a fewer number of local severities [11,12].

Recent studies showed that the shape and dimensions of the adjuvant particles may affect the immune response against protein and peptide antigens [13,14]. For example, enhanced adjuvant activity of small, elongated particles (nanorods or nanosticks) of AlOOH and Al(OH) 3 with diameters of 4-20 nm and aspect ratio of 8-10 was recently reported [14][15][16], although the origin of the improved performance remained largely unclear.

Earlier, some of us demonstrated that different size nanoparticles thrust the activity of neutrophils, which boosts the immune system response toward co-injected antigens [17,[START_REF] Muñoz | Proc. Natl. Acad. Sci[END_REF]. This mechanism of neutrophils activation is highly dependent on the size of the particles, e.g. bacteria, fungi, nano-and microparticles [START_REF] Muñoz | Proc. Natl. Acad. Sci[END_REF][START_REF] Desai | [END_REF]. It results in the formation of neutrophil extracellular traps (NETs), which effectively isolate foreign bodies and suppress local self-limiting inflammation [20]. The mechanism of NETs' action is realized by the entrapping of foreign particles by unbound DNA and histones, both decorated by toxic proteinous content of neutrophils' granules [21]. Formation of NETs was recently demonstrated as an important player responsible for adjuvant action of injected alum, reported to recruit neutrophils, and their activation leading to stimulation of DNA sensors and provoking local inflammatory response [22].

Since the NETs' formation is particles' size-dependent, we hypothesized that the utilization of high-aspect ratio Al-based vaccine adjuvants can greatly contribute to establishing more potent immune responses through neutrophils' activation.

Unfortunately, relatively expensive synthesis of nanorods (due to the use of harsh chemicals, elevated reaction temperatures, and low reaction yields), which was demonstrated earlier [14], as well as their potential damages to the smallest blood vessels may become barriers for their use in low-cost vaccination.

In this article, we have chosen to investigate if Al 2 O 3 nanowires (NWs) can activate neutrophil cells upon injection to the body and possibly enhance adjuvant properties over other Albased adjuvants. We choose to compare our findings to aluminum-based adjuvants, commonly used in commercially available vaccine formulations. Our interest was partially triggered by our recent discovery of an innovative approach for ultra-low-cost synthesis of c-alumina NWs (c-Al 2 O 3 NWs) of variable dimensions and controllable aspect ratio [23,24]. These nanomaterials are produced by exposing bulk Al alloys to alcohols at near room temperature and atmospheric pressure, fol- S1). This is only slightly (Fig. 2b), as indicated by the significantly higher amount of anti- Some of us have recently shown that nanoscaffolds may be able to induce activation of polymorphonuclear neutrophils to form neutrophil extracellular traps [START_REF] Muñoz | Proc. Natl. Acad. Sci[END_REF], networks of extracellular fibers produced as an immune response to neutralize infection [START_REF] Brinkmann | [END_REF]. Localization of neutrophils leads to localized self-limiting inflammation, which results in isolation of inflammatory stimuli with NETs [31] and, as discovered recently, is an important trigger of alum action [22]. This phenomenon is mainly responsible for the strong self-limiting (fast resolved) inflammation caused by some nanoparticles [START_REF] Muñoz | Proc. Natl. Acad. Sci[END_REF] (best illustrated by gout attack, caused by monosodium urate needle-like crystals, to be as spontaneously resolved as it appears).

Since c-Al 2 O 3 NWs provoked increased humoral immune response, we were interested to follow up the fate of the c-Al 2 O 3 NWs upon injection in the body. We used a lately described mouse air pouch model [32], where sterile air is injected under the skin at the back of the mouse to form a cavity, which is being infiltrated with immune cells followed by c-Al 2 O 3

Cell viability and internalization

The HeLa cell line derived from cervical carcinoma [ATCC Ò CCL-

110 3 159

 3 lowed by heat treatment in air. No catalysts, toxic metals, 111 external stimuli, or costly synthesis systems are required. We 112 expect the future industrialization will allow formation of these 113 c-Al 2 O 3 NWs at a cost of a few dollars per pound, which is almost 114 negligible for vaccination applications. The tests conducted for 115 the first time on 20-to 60-micron-long, 20-40 nm diameter, 116 $1000 aspect ratio NWs substantially exceeded our expectations 117 and demonstrated c-Al 2 O 3 NWs to be extremely effective vaccine 118 adjuvant, inducing excellent humoral immune response. Quite 119 remarkably, c-Al 2 O 3 NWs did not damage the microvasculature 120 of the tissues and were found to be easily entrapped by NETs 121 and passivated. When compared with state of the art commercial 122 Al-based adjuvant, the proposed low-cost c-Al 2 O 3 NWs were 123 found to be both more efficient and safer. Our findings highlight 124 great promises of NWs for substantial breakthroughs in the 125 development of safer, more effective, and more affordable 126 vaccines. 127 Results and discussion 128 c-Al 2 O 3 NWs have been synthesized by the protocol described by 129 some of us previously [23]. It relies on the de-alloying of bulk Al-130 Li alloy in ethanol at 60 °C for 24 h, which yields Al ethoxide 131 NWs. Subsequent heat-treatment at 800 °C for 1 h results in 132 the formation of c-Al 2 O 3 NWs, as shown in the scanning elec-133 tron microscopy (SEM) micrograph (Fig. 1a). The microstructure 134 of the NWs is uniform. The average NWs' thickness is $20 nm, 135 average length 20-60 mm, and aspect ratio exceeding $1000. 136 We believe that the dimensions of the NWs are sufficient to acti-137 vate neutrophils (typically 12-17 mm in diameter). In particular, 138 of a typical length of 35 lm [25], the crystals of monosodium 139 urate, which are formed in the condition of the gout, can be 140 effectively ingested by the neutrophils [26,27]. The crystallinity 141 of the c-Al 2 O 3 NWs was revealed by the transmission electron 142 microscopy micrograph (TEM, Fig. 1b). The c-Al 2 O 3 NWs are 143 polycrystalline with an average crystal diameter of 15-20 nm. 144 The rough surface and sharp ends of the c-Al 2 O 3 NWs can pro-145 mote the membrane damage in neutrophils, resulting in the pro-146 motion of the NET formation [18]. The characteristic selected 147 area electron diffraction (SAED) pattern in Fig. 1b area exhibits 148 strong and prominent diffraction rings indexed as 311, 222, 149 400, and 440 reflections of c-Al 2 O 3 (Fig. 1c). Thermogravimetric 150 analysis (TGA) shows clearly the conversion of Al(OEt) 3 NWs to 151 Al 2 O 3 NWs (Fig. 1c). Organic carbon-and hydrogen-containing 152 groups, which constitute almost $40 wt.% of the mass, burn in 153 air until 400 °C. In the range of 500-1000 °C, the mass of the Al 2 O 3 NWs is stabilized. The high-angle XRD pattern (Fig. 1d) 155 of the Al 2 O 3 NWs displays diffraction peaks at 2h of 14.66°, 156 37.18°, 39.03°, 45.36°, 60.15°, and 66.70°, indexed as (2 crystal planes of c-158 Al 2 O 3 NWs, respectively. The chemical composition of c-Al 2 ONWs was further validated by FTIR (Fig.1e) and XPS analysis 160 (Fig.1f). The FTIR spectrum exhibits a broad band centered at 161 3495 cm À1 due to OH (stretching) band and/or adsorbed water. 162 There is a general lack of peaks related to oxygen-containing 163 groups besides the presence of bands related to AlOOH, such as 164 the bands at 3298, 3091, 1070, and 1165, assigned to v as (Al)-165 OH, v s (Al)-OH, stretching vibrations, and d as Al-O-H modes for RESEARCH: Original Research AlOOH. The bands below 1000 cm À1 at 864, 749, and 583 cm À1 167 are caused by the formation of the c-Al 2 O 3 phase. Furthermore, 168 the XPS survey spectrum, together with the high-resolution 169 core-level spectrum of Al 2p (74.6 eV), is shown in Fig. 1f,g (inset). 170 The atomic ratio between Al 2p /O 1s is 0.65 close to that of the the-171 oretical value of 0.66 for c-Al 2 O 3 . 172 A commercial Al-based adjuvant (alum) (Fig. S1a) and com-173 mercial aluminum oxide microparticles (Al 2 O 3 MPs) (Fig. S1b) 174 were used as control materials throughout this study. Fig. S1c 175 shows X-ray diffraction (XRD) patterns of alum. The XRD pat-176 terns indicate that alum has an aluminum oxide hydroxide (c-177 AlO(OH)) (boehmite) structure with the average crystallite size 178 2.2 nm (Fig. S1). Zeta-potential measurements in water at 25 °C 179 (Fig. S1d) indicate that alum adjuvant formulation has a positive 180 surface charge of +6.6 ± 0.3 mV (Table

181 3 186 1

 31 Fig.S3, FigS4a-b). The humoral immune response after a second vaccination caused by the "c-Al 2 O 3 NWs + OVA" was significantly stronger compared to that effect of "alum + OVA"

219OVA

  IgG antibodies formed 35 days after immunization at the 220 dilution factor of 1/2000. Further analysis of antibody titers 221 (dilution factor at which antibody is still effective) revealed 222 (Fig. S3) that titers of antibodies obtained after c-Al 2 O 3 NWs 223 + OVA immunization were 1/64000; after the use of alum -224 1/16000, for Al 2 O 3 MPs and OVA alone, they were as low as 225 1/2000 and 1/1000, correspondingly; the cut-off was set to 0.5 226 OD value (Fig. S3). Both adjuvants were not inducing acute-227 phase antibodies of IgM type (Fig S4b), which signifies that there 228 is no inflammation left. 229 The cellular immune response was assessed using an estab-230 lished model of delayed type hypersensitivity (DTH) reaction 231 [29], modified by us to be less invasive animal treatment protocol 232 [18]. The DTH is a part of the cell-mediated immune response 233 associated with Th1 reactivity in response to insoluble foreign 234 antigens. It is a localized inflammatory reaction prototypical 235 in vivo assay to study cell-mediated host immune response medi-236 ated by CD4+ T lymphocytes (small leukocytes, white blood 237 cells). These cells promote T-helper cell type 1 (Th1) production 238 of interferon-c (a soluble cytokine). This immune response is 239 characterized by an influx of innate immune cells, with macro-240 phages and the dendritic cells predominating. Therefore, after 241 the formation of antibodies (day 28), mice were challenged with 242 OVA injected between the fingers of the footpad (right foot), 243 while PBS served as control and injected to the left foot 244 (Fig. 2a). Footpad swelling, being proportional to the strengths 245 of cellular immune response, was measured in dynamics for few days, until swelling disappeared. The DTH reaction (usually evaluated at 6-24 h after antigen exposure) was comparable for both groups of animals, immunized with OVA in the presence of either alum or c-Al 2 O 3 NWs (Fig. 2c), while it was significantly lower for Al 2 O 3 MPs or OVA alone. The swelling of the footpad faded after 72 h of the DTH challenge, which correlates with the normal responsiveness to the antigen. Absence of exaggerated cellular response with much stronger humoral response for c-Al 2 O 3 NWs makes them immunologically favorable agents for the use in vaccines.

FIG. 2 3 300

 23 FIG. 2 Humoral and cellular immune responses in Balb/c mice provoked by OVA using alum, cc-Al 2 O 3 NWs, Al 2 O 3 MPs, or OVA alone acting as adjuvants: (a) experimental design and (b) humoral immune response. Anti-OVA IgG-specific levels in serum (humoral immune response), each dot represent the response of specific animal; sera dilution was 1:2000; (c) cellular immune response; DTH reaction measured as a foot swelling. Data are M ± sem for all studied animals in the group; n = 12, 13, 4, 5, correspondingly.

FIG. 3

 3 FIG. 3 Formation of neutrophil extracellular traps (NETs): sequestering of c-Al 2 O 3 NWs and alum by aggregated NETs after 24 h of incubation in mouse air pouch. Dotted red circles show capillary damage and edema. No significant damage to capillaries is observed after c-Al 2 O 3 NWs' treatment.

FIG. 4 FIG. 5

 45 FIG. 4 Activation of peripheral blood-derived neutrophils upon the contact of Al-based adjuvants. Data of three different healthy donors (a-c) are presented. Intensity of NETs' formation is presented as a mean fluorescent intensity of Sytox green dye upon the contact with extracellular DNA: c-Al 2 O 3 NWs and alum but not Al 2 O 3 MPs cause rapid activation of human peripheral blood neutrophils (d-f), which is noticeable during the first minutes of incubation. Strong (PMA) and weak (48 mM bicarbonate) inducers of NETs' formation show their response after 120 min.

469andFor correct comparison, Al 2 O 3 ,

 23 Refinement). Totally, 34 mice were analyzed: 12 mice immu-470 nized with alum + OVA, 13 mice immunized with c-Al 2 O 3 NWs 471 + OVA, 4 mice immunized in Al 2 O 3 MPs + OVA, 5 mice immu-472 nized with OVA alone; immunization was done in 3 indepen-Al 2 O 3 NW, and Al(OH) 3 were 476 used as pure compounds and prepared as dispersions just before 477 immunization after pre-heating to 150 °C for 2 h to eliminate 478 LPS. The dispersions of 'alum + OVA', 'Al 2 O 3 MPs + OVA', and The 50 mL of 'adjuvant (20 mg mL-1) + 50 mL OVA (1 mg mL-1)' RESEARCH: Original Research in PBS were injected intraperitoneally (PI) in mice at day 1 and 486 day 15 of the experiment. The DTH test was performed 28 days layer on top of RBCs was taken and subjected to hypotonic lysis of RBCs. Isolated granulocytes were cultured in 96-well culture plates at 5 Â 10 6 cells per milliliter with special inducers of NETosis and with the fluorescent nucleic acid dye Sytox green (Life Technologies). The fluorescence was measured in kinetics for 3 h using BioAssay Reader HTS7000 (Perkin Elmer), excitation 480/15 nm, emission 535/20 nm.

  Sigma) and seeded at a density of 1.5 Â 10 4 -449 cells/well in a 96-well plate. The culture medium was replaced 450 with a fresh medium without b-mercaptoethanol that contains 451 the compounds from 0 to 400 mg mL À1 . After 24 h, the cell viabil-452 ity was evaluated using Calcein-AM and PI co-staining. The cells

	2 TM , ECACC, Sigma-Aldrich, Saint-Quentin Fallavier, France] and the U-87 MG cell line derived from human brain (glioblastoma astrocytoma) [ATCC Ò HTB-14 TM , Sigma-Aldrich, Saint-Quentin Fallavier, France] were cultured and maintained in Dulbecco's Modified Eagle's medium (DMEM, Gibco Ò ) supplemented with 10% fetal bovine serum (FBS, Gibco Ò ) and 1% penicillin-strepto-mycin (Gibco 436 590 nm) was measured using a microplate reader (PHERAstar 437 FS, BMG LABTECH GmbH, Germany). Each condition was repli-438 cated five times and the mean absorbance value of non-exposed 439 cells was taken as 100% cellular viability. 440 Cytotoxicity studies on macrophages 441 The human monocytic THP-1 cells were cultured and main-442 tained in culture in Roswell Park Memorial Institute medium 443 (RPMI 1640, Invitrogen) supplemented with 10% fetal bovine 444 serum (FBS, Gibco Ò ), 1% penicillin-streptomycin (Gibco Ò ) and 445 50 mM b-mercaptoethanol in a humidified incubator at 37 °C 446 and 5% CO 2 . THP-1 monocytes were differentiated into macro-447 phages by a 5-day incubation with 20 nM phorbol 12-myristate 448 13-acetate (PMA,

Ò ) in a humidified incubator at 37 °C and 5% CO 2 .

Cells were seeded at a density of 10 4 cells/well in a 96-well plate and grown for 24 h before assay. The culture medium was replaced with a fresh medium that contains c-Al 2 O 3 NWs and alum hydroxide 2% at different concentrations. After 24 h, the old medium was aspirated, washed with PBS and replaced with 431 a fresh medium. The cell viability was evaluated using Uptiblue 432 (Interchim) method. Briefly, 10 lL of the Uptiblue solution was 433 added to each well containing 100 mL of DMEM with 10% FBS 434 and the plate was incubated for 4 h in the humidified incubator. 435 The fluorescence of each well (excitation 540 nm/emission 453 were stained without any washing by addition of 10 mL of 454 Calcein-AM/PI mix solution (45 mM/30 mM) in each well and 455 incubated at 37 °C for 30 min. Subsequently, the stained cells 456 were observed with 4Â objective (GFP and Texas Red filter cubes) 457 using a Cytation TM 5 Cell Imaging Multi-Mode Reader (BioTek 458 Instruments SAS, France). 459 Animals 460 Six-week-old male Balb/c mice were used. The mice were housed 461 in cages covered with air filters in a temperature-controlled room 462 with a 12-h light and 12-h dark schedule and kept on a standard 463 diet with drinking water available ad libitum. Studies involving 464 animals, including housing and care, method of euthanasia, 465 and experimental protocols, were approved by the Ethics com-466 mittee of Danylo Halytsky Lviv National Medical University, pro-467 tocol 20180226/2 & 20130624/6; all experiments were designed 468 to comply with principles of the 3Rs (Replacement, Reduction

Please cite this article in press as: R. Bilyy et al., Materials Today (2018), https://doi.org/10.1016/j.mattod.2018.10.034

Acknowledgments

Sila Nanotechnologies, Inc; the Centre National de la Recherche Scientifique (CNRS), the University Lille 1, the Hauts-de-France region, the CPER "Photonics for Society", the Marie Sklodowska-Curie action (H2020-MSCA-RISE-2015, PANG-690836), Volkswagen-Stiftung grant #90361, and Ministry of Healthcare of Ukraine are acknowledged for financial support.

Servier Medical Art is acknowledged as a source of some illustrative materials. We thank S. Peshkova for technical assistance.

Data availability

The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.mattod.2018.10.034.


Alexis Vessat
email: alexis.vessat@umontpellier.fr

The role of unmet demand in the dynamics of energy supply forms: The case of electricity market structures in sub-Saharan Africa

Keywords: Centralized electricity production, electricity market reform, sub-Saharan Africa, decentralized mini-and off-grid production systems, demand fragmentation, supply dynamics and changes, rural electricity demand, access to electricity JEL Classification: Q40, Q42, Q49

The energy sector in sub-Saharan Africa is in a state of flux. Based on an approach borrowed from industrial economics, using historical examples that point to three successive transformations of electricity market structure, our analysis differs from previous studies by looking at demand as a consequence of supply. Our results show, an extremely fragmented demand for energy in sub-Saharan African countries, within which a very dynamic unmet demand drives change in how supply is offered.

New forms of energy provisioning introduced on the electricity market put into question the initial ongrid network model. The appearance of decentralized electricity production shows that there is a potential for going beyond current limitations and moving away from a supply structure focused on the maintenance and improvement of on-grid networks without consideration of the needs of rural populations on one hand, and on the other hand, the establishment of expensive mini-grids that provide inferior energy services to rural populations. New territorial linkages focus on mechanisms seen in energy demand.

Section 1. Introduction

Since the beginning of the 2000s, sub-Saharan Africa has experienced sustained economic growth at a faster rate than the rest of the world economy, despite growing demographic pressure. Nevertheless, this growth rate is not homogeneous (UNCTAD, 2014;World Bank, 2017). These fluctuations in growth can have external causes such as variations in the price of petroleum, but also internal causes such as inadequacies in the energy infrastructure (African Energy Outlook, 2014;[START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: lessons from Five Key Countries[END_REF].

Sub-Saharan Africa (SSA) can thus be characterized by both its wealth in energy resources and its poverty in the production and consumption of electricity. Even though the African continent contains a little more than 14% of the world's population, it consumes less than 4.5% of primary energy (World Energy Outlook, 2017).

The inadequacy of the electricity sector in SSA represents a cost of about 2 points of GDP in economic growth (World Bank, 2017). Currently the combined electrical production capacity of the 48 countries of Sub-Saharan Africa adds up to 80 GW, half of which is for South Africa. The per-capita production capacity is only 0.08 GW (versus 1.94 GW for France). Over the past 20 years, capital growth, or the electric power installed in the principal on-grid network, has only increased about 1.7% per year (Eberhard & al, 2011). In a simulation, the International Energy Agency has determined that to reach the objective of universal access to electricity, $630 billion would need to be invested over a period stretching from 2014 to 2040 (source??). A similar study carried out by the World Bank's Infrastructure and Local Development Project finds a need for $400 billion invested through 2030 (World Bank, 2014). All of these simulations have been developed in a context where over 25% of energy production facilities (outside of South Africa) are not considered operational.

In sub-Saharan Africa, electricity is provided through centralized networks that primarily supply urban areas. The power infrastructure, a remnant of post-colonial decisions on organizing the electricity market, is mostly based on market demand and passes through the main on-grid network. There are many deficiencies in how the development of power infrastructure has been structured.

The introduction of private energy supply as part of a trend towards deregulation in the electricity sector in the 1990s has improved the centralized supply, but there remains a substantial gap between supply and demand. The demand for energy increased by 45% between 2000and 2012(African Energy Outlook, 2014), while production capacity only increased by 19% over the same period [START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: lessons from Five Key Countries[END_REF]. Current supply therefore only covers part of overall demand.

Demand in sub-Saharan Africa is fragmented into at least three components:

 Market-based demand, served by the on-grid network. While this demand is met by current offerings, it is coming up against the limits of the networks;

 Unmet non-grid market demand, power customers outside the on-grid centralized network. These households buy extremely expensive energy resources (kerosene or diesel) for decentralized energy production that is both inefficient and expensive. This demand mechanism leads to the search for new models and thus an increase in decentralized solutions like minigrids, made possible by the overall drop in the production costs of renewable energy systems.

The new organizational modes for decentralized supply (mini-grid and, since the 2000s, offgrid) transfer households' willingness to pay a monthly fee to decentralized networks, which allows new consumers to have access to electricity without going on-grid. This transfer puts into question the electricity production model initially adopted by African governments. The perspectives for developing the mini-grid are encouraging; for example, the IEA envisages the installation of 100 to 200,000 mini-grids in SSA by 2040 (source ???);  Out-of-market demand includes all the households that use primary biomass as their main source of energy. Biomass remains the biggest energy source, especially for household needs like cooking, for most rural households in Sub-Saharan Africa (African Energy Outlook, 2014): more than half of total primary energy demand. These households have no access to electricity. This out-of-market demand represents 580 million people and 310 terrawatt hours of potential electricity consumption [START_REF] Bazilian | Access scenarios to 2030 for the power sector in sub-Saharan Africa[END_REF]. This demand fragmentation coincides with the many upheavals seen throughout the power system: the on-grid supply is seeing competition from decentralized production solutions like mini-grid and off-grid systems. Even though these technologies are a considerable step forward compared to conventional electricity production methods, they remain inaccessible for a large number of households, especially those in rural areas, where the power services offered are limited. This article thus focuses on the demand mechanisms in a situation where the rise of renewable energy sources (solar, small hydropower, wind, bioenergy) in electricity production enables decentralized solutions that were previously inaccessible and stimulates demand with a retroactive effect on the organization of supply. This article uses an industrial economics approach with historical examples throughout Sub-Saharan African countries. It is organized as follows. Part 2 presents the contributions and limits of the vertically integrated centralized supply system that dominated the electricity sector in Sub-Saharan African countries from . Part 3 presents two very important and completely independent changes in supply beginning in the 1990s. The first change is related to new entrants (independent private producers or IPPs) whose goal was to create competition in the market. The second change was the introduction of the mini-grid, which, due to its greatly reduced price, created an alternative to conventional means of electricity production. The emergence of decentralized solutions stimulated non-grid demand, which encouraged their further development. Part 4 contextualizes the emergence of new forms of off-grid energy supply since the 2000s, in combination with the distancing of certain rural populations, which led to a second stimulation of energy demand. Finally, Part 5 looks at a set of theoretical propositions that illustrate the dynamics of unmet demand and the changes in forms of supply that these dynamics bring about, aligning demand functions with the capacity limitations of the different networks.

Part 2. From 1950 to 1990, establishment of a vertically integrated monopoly with the objective of on-grid electricity access for urban areas

Due to their inherent characteristics, network industries are natural monopolies [START_REF] Chevalier | Les réseaux de gaz et d'électricité : multiplication des marchés contestables et nouvelle dynamique concurrentielle[END_REF]. In Sub-Saharan Africa, electricity has primarily been distributed through centralized grid systems. The electricity companies set up vertically integrated systems, integrating production, transportation, distribution, and sales of electricity within the same entity [START_REF] Girod | Reforms in sub-Saharan Africa's power industries[END_REF][START_REF] Hansen | Energie, Economie et politiques. Préface de Marcel Boiteux[END_REF]. This electricity market structure model remains extremely common: it is still used in half of SSA countries [START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: lessons from Five Key Countries[END_REF].  Gains realized from economies of scale (due to activities with a growing scale of production), transactions costs, or range [START_REF] Eberhard | Demise of standard model for power sector reform and the emergence of hybrid power markets[END_REF].

Economic characteristics of vertical organizations in SSA

Vertical integration has three major assets:

 Growth in electrical production capacity

With high demographic pressure in urban areas, growth in electrical production capacity was made possible by using energy resources (petroleum, coal, diesel) and imported power plants [START_REF] Coquery-Vidrovitch | La politique de réseaux d'électrification en Afrique. Comparaison Afrique de l'Ouest[END_REF]Varashin, 2002), as well as through an emphasis on the region's hydroelectricity potential [START_REF] Coquery-Vidrovitch | La politique de réseaux d'électrification en Afrique. Comparaison Afrique de l'Ouest[END_REF]. 3 In the 1960s, four major dams were built in SSA: Akosombo in Ghana (1962)(1963)(1964), Kainji in Nigeria (begun in 1969), Mount Coffee in Liberia, and Kossou in Côte d' Ivoire (1969Ivoire ( -1971)). This increase in nominal output is illustrated in Table 1 below The priority given to providing electricity to urban areas completely excluded rural areas from access to electricity; moreover, most of the urban households on the grid were wealthier. 7  Development of a grid system providing a low-cost link from the energy resources to be extracted to the areas where they are consumed [START_REF] Saupique | L´ électrification de la ville de Dakar après 1945[END_REF][START_REF] Segreto | Electrifier un rêve : l´ industrie électrique dans les colonies[END_REF].

In certain territories, the extension of railroad lines coincided with the development of electricity [START_REF] Coquery-Vidrovitch | La politique de réseaux d'électrification en Afrique. Comparaison Afrique de l'Ouest[END_REF]. The industrial needs of certain colonies (mining regions) involved access to electricity. 8 Certain plans, especially those developed in France, depended on modernizing production equipment of the grid system to (i) promote mining and energy operations and (ii) economically integrate the colonies.

The development of the grid system in fact allowed for the extraction of fossil fuels (coal and petroleum in Nigeria and South Africa) and mined resources (aluminum from bauxite in Ghana, copper in Zambia, uranium deposits in Niger).

Limitations of vertical integration

A broad consensus has now arisen as to the productive and allocative inefficiencies of vertical integration in SSA. The arguments that have been made (World Bank, 1993;[START_REF] Joskow | Markets for Power: An Analysis of Electric Utility Deregulation[END_REF][START_REF] Bacon | A scorecard for energy reform in developing countries[END_REF][START_REF] Bacon | Global Electric Power Reform, Privatization and Liberalization of the Electric Power Industry in Developing Countries[END_REF] are as follows:

1. The lack of appropriate scale and lack of investment in maintenance and the development of new production units

The first event was the drying up of domestic funds, leading to low domestic savings as well as financial difficulties in the power companies themselves, which was exacerbated by bad payment behavior by several actors, especially the states themselves [START_REF] Wamukonya | Power sector reform in developing countries: mismatched agendas[END_REF]. These difficulties were combined with an outsized power infrastructure, often referred to as white elephants (Lappara, 2002).9

This phenomenon was followed by a lack of external financing [START_REF] Naudé | Investing geography and institutions as determinants of foreign direct investment in Africa using panel data[END_REF][START_REF] Wernick | The impact of governing institutions on foreign direct investment flows: evidence from African nations[END_REF], due to both the lack of transparency in many SSA countries, as indicated by the Mo Ibrahim Foundation [START_REF] Mauro | Corruption and Growth[END_REF], Tanzi & Davoodi, 2002a) and multiple deficiencies seen at the governance level (institutional and regulatory frameworks, operation patterns, and fee structures).

These two weaknesses forced the power companies to look for other sources of financing10 [START_REF] Wamukonya | Power sector reform in developing countries: mismatched agendas[END_REF].

Unfamiliarity with the technology, as symbolized by the spread of thermal energy, often to the detriment of local resources

This can be seen in large power main losses (representing 20-30% of total electricity production), insufficient load factors, substantial waste of resources, and productivity slowdowns (up to 40%), leading to numerous cuts in electricity production and the use of back-up generators, which can make up 50% of total electricity production and cost $0.20-0.30 per kWh produced [START_REF] Karekezi | Energy Policies Issues in Africa[END_REF][START_REF] Chevalier | Les réseaux de gaz et d'électricité : multiplication des marchés contestables et nouvelle dynamique concurrentielle[END_REF][START_REF] Plane | La privatisation de l'électricité en Côte-d'Ivoire : évaluation et interprétation des premiers résultats[END_REF][START_REF] Sambo | Renewable Energy for Rural Development. The Nigerian Perspective[END_REF]. This unfamiliarity resulted in the limiting of production plants, which in most SSA countries do not exceed an output of 500 MW.

3.

The financial state of the public monopoly, subject to numerous deficits, put into doubt the ability to ensure power service

The pace of growth in the urbanization rate did not allow the development of a critical mass of paying end users for the power companies. Consequently, the power companies' debt skyrocketed within a context of successive economic crises that could be seen in a rise in interest rates and in the price of petroleum, which were not accounted for in the companies' fee structures.

In 1990, when the Ivorian electricity company was almost $300 million in debt (World Bank, 1995), this was due to multiple errors in revenue collection (70-85%) (World Bank, 1995;ANARE, 2005). For the same reason, the Kenyan KPLC built up $300 million in debt between 1945and 1990[START_REF] Wamukonya | Power sector reform in developing countries: mismatched agendas[END_REF][START_REF] Wamukonya | Power Sector Reforms in Sub-Saharan Africa: Some Lessons[END_REF].

4.

The impossibility of meeting emerging rural demand while improving the quality of electricity furnished to urban and peri-urban households Electricity supply was focused on developing access to electricity in urban areas. Between 1970 and1990, the rate of urban access in SSA increased from 28% to 38% [START_REF] Turkson | Power sector reform and distributed generation in Sub-Saharan Africa[END_REF].

However, this notable progress looks weak in comparison to other developing countries in Latin America and South and East Asia, where much higher access rates have been achieved 11 .

It is due to these limitations that private solutions began emerging in the 1990s. Two innovations appeared: one organizational (private producers) and the other technological (mini-grids), which engendered new demand dynamics.

Part 3. From 1990 to mid 2000s, deregulation and demand segmentation

In the 1990s, two major changes considerably weakened the traditional forms of power supply.

A uniform deregulation process opposing several demand segments: Monopsony as applied to the electricity sector

The introduction of private producers who would establish real competition on the electricity market took place in a context of deregulation of infrastructure industries.

 The introduction of new producers able to compete on the market

Organizational forms copied from developed countries (unbundling, third-party access to the grid, vertical and horizontal separation of the grid) were confronted with the intrinsic characteristics of the electricity sector in SSA: immature grid systems and rapid growth in demand [START_REF] Plane | La privatisation dans les pays en développement : déterminants et conséquences macroéconomiques[END_REF][START_REF] Bacon | A scorecard for energy reform in developing countries[END_REF]Turkson, 2000). 12 11 Over the same period, urban access grew from 67% to 82% in Latin America, from 39% to 53% in South Asia, and from 51% to 82% in East Asia [START_REF] Turkson | Power sector reform and distributed generation in Sub-Saharan Africa[END_REF].

12 Only a few SSA countries (Kenya, Uganda, Nigeria, Ghana) have dealt with questions related to third-party access or vertical or horizontal separation of networks [START_REF] Bacon | Global Electric Power Reform, Privatization and Liberalization of the Electric Power Industry in Developing Countries[END_REF].

Deregulation was thus limited to the entry of independent private producers (IPP), whose goal was to establish competition on the market. These IPP were mostly funded by multilateral lending agencies13 ; investment in these projects has grown considerably over the last few years [START_REF] Izaguirre | Private Participation in Energy[END_REF][START_REF] Castellano | Brighter Africa[END_REF][START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: Investment trends and policy lessons[END_REF].

The electricity market thus hinges on a hybrid structure combining the former operator, now buyer, with the new entrants. The structure functions with competitive calls for tender. Any accords between the two parties are regulated by electricity buying agreements entered into over long periods (World Bank, 1993;USAID, 1994). Several specific clauses (amount of energy allocated; amount of fees to be invoiced for fuel and insurance; force majeure; transfer, cancellation, and modification of legal, refinancing, and revenue stream provisions) are set in advance to guarantee financial viability for the state-owned utilities while securing revenue streams for the new entrants.

Over 20 IPPs were established between 1990 and 2011, producing a total of 4 GW (Eberhard, 2011).

The IPPs have made several contributions:

 Growth in existing production facilities

In some cases, IPPs exceeded the production capacities of the state-owned utilities (Karekezi & Kimani, 2002;[START_REF] Eberhard | Demise of standard model for power sector reform and the emergence of hybrid power markets[END_REF]. In Togo, the IPP in Lomé (CTL) increased the country's total installed capacity from 149 to 249 MW, supplying the equivalent of 67% of the country's total nominal capacity. in Uganda, Bujagali, an IPP established in the 1990s, increased total production capacities by almost 30% (or 250 additional MW), going so far as to make up 45% of total production in 2013. In Kenya, IberAfrica built a plant that produced 109 MW between 1996 and 2008 [START_REF] Eberhard | Demise of standard model for power sector reform and the emergence of hybrid power markets[END_REF]. Some IPPs also use renewable energy: hydroelectricity in the Bugajali plant in Uganda with a nominal capacity of 250 MW; geothermal in the Kenyan IPP Or Power; wind power in two IPP plants in Lake Turkana in Kenya that produce 300 MW, and another in Kinangop province that was in the 60 MW category; biomass using bagasse in Mauritius that powers a 110-MW IPP plant. On the other hand, the state-owned utilities have not chosen to utilize renewable energy.

A complete list of IPPs can be found in a table in Appendix 1.

 Improved urban access

Electricity supplied by IPPs has considerably improved access to the grid (Eberhard & al, 2011). This access increased from 23% in 1990-1995 to 27% in 1996-2000 to 30% in 2000-2005.  Improved financial situation for the state-owned utilities IPPs considerably improved the techno-economic performance of the state-owned utilities in terms of revenue collection, better customer billing, and decreased system losses. In Côte d'Ivoire, for example, the revenue collection rate of the EECI approached 98%. Similarly, in Eritrea, power outages dropped to nine hours per year after the market was privatized (United Nations Economic Commission for Africa, 2006). NamPower, the Namibian public power company, considerably reduced its system losses in electricity transportation and distribution, from 14% in 1998 to 8% in 2004 (United Nations Economic Commission for Africa, 2006). And in Senegal, SENELEC increased sales by 5.7% (United Nations Economic Commission for Africa, 2006).

 Renewable-energy IPPs are competitive with state-owned thermal plants

This can be seen in several examples. The Bugajali hydroelectric station in Uganda (250 MW) produced power at $0.10/kWh, much less than the thermal power produced by the state-owned utilities ($0.24-0.27/kWh). Similarly, the OrPower geothermal station in Kenya produced power assessed at $0.09/kWh, much less than the thermal plants ($0.20-0.33/kWh) However, IPPs have several disadvantages:

 Over-concentration in certain SSA countries

This is especially true in South Africa, which over four years saw 6327 MW of independently produced power [START_REF] Eberhard | Renewable energy auctions in South Africa outshine feed-in tariffs[END_REF][START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: lessons from Five Key Countries[END_REF][START_REF] Eberhard | Renewable energy auctions in South Africa outshine feed-in tariffs[END_REF]. Due to competitive tenders for renewable energy, the cost of this energy has decreased by 46% for wind power and 71% for solar [START_REF] Eberhard | Renewable energy auctions in South Africa outshine feed-in tariffs[END_REF]REN21, 2016).

In the rest of Sub-Saharan Africa, only 21 power projects were funded, with a total investment of less than $2 billion [START_REF] Izaguirre | Private Participation in the Electricity Sector[END_REF]. The guaranteed electricity buy-back programs in Kenya and Uganda were not attractive enough (BNEF & &l, 2014).

 IPP plants generally continue to use thermal energy, ignoring the whole range of renewable energy

In 2014, 82 % of IPPs used thermal energy: heavy fuel oil (HFO) and natural gas [START_REF] Karekezi | Have power sector reforms increased access to electricity among the poor in East Africa[END_REF]. 14 Very few IPP plants use renewable energy exclusively. For example, in 1998, less than 5% of these plants used hydropower. The thermal IPPs widely reinforced the lack of technological proficiency: only 41% of them were still operational in 2001 (Financial Times Energy, 2011a-c).

IPPs are also vulnerable to fluctuations in the price of HFO: from the 1990s to the mid 2000s, its price was over $40 per tonne, which greatly reduced these plants' competitiveness (Ormat, 2009).

Finally, from an organizational point of view, the overdependence on thermal energy led to long and costly transactions among the various stakeholders (Agence Française de Développement, 2012).

 The buyer structure faces multiple organizational problems

This is especially due to delays in certain IPP projects (GTI Dakar, Bui Hydro's Kounoune plant in Ghana, Bugajali in Uganda, and the Lomé Thermal Plant in Togo) leading to substantial changes in the clauses in IPP fixed contracts (e.g., AES Barge's Okpai plant in Nigeria and Independent Power Tanzania Limited's (IPTL) Songas plant in Tanzania).

Organizational problems linked to overly generous contract clauses should be emphasized.

Many IPPs have been accused of artificially inflating their costs (e.g., IberAfrica, an IPP in Kenya). Many state-owned utilities therefore needed to renegotiate their contracts, especially in terms of end-use fees (in the case of the Power 4 and Songas IPPs in Kenya and the AES in Nigeria).

The creation of IPPs was limited, in the end, by the lack of transparency throughout the countries of Sub-Saharan Africa. It should be noted that quite often IPP contracts were hastily negotiated in crisis situations, beginning in the 1990s, when many competitive calls for tender were cancelled [START_REF] Eberhard | Demise of standard model for power sector reform and the emergence of hybrid power markets[END_REF].

 IPPs target the urban consumption niche, mostly ignoring rural demand

In Africa, IPP plants were mostly established close to the grid system to reach a critical mass of urban users while mostly ignoring rural demand.

The introduction of private producers was accompanied by a second change that affected electricity supply throughout Sub-Saharan Africa. Mini-grids created a new demand dynamic at a time when HFO prices were rising and the cost of renewable energy was trending downward.

A novel demand mechanism: mini-grids in Sub-Saharan Africa.

 A technological innovation, based on the new and more decentralized mini-grid system offering an alternative to conventionally produced on-grid power.

Mini-grids can be connected to either local thermal production or hybrid production including renewable energy, if available and depending on local demand, which varies widely. Mini-grids have certain advantages:

 Because of the sparseness of supply, mini-grids have spread throughout SSA, using mostly renewable energy sources

In comparison with grid systems, renewable mini-grids seem to be an unbeatable option given the decentralization of rural electrification. The technological developments attributed to mini-grids led to upheavals in the organizational and contractual frameworks of upcoming projects (Agence Française de Développement, 2012). We should also consider industrial auto-production, with excess power sold at a fixed rate. Power production through small independent producers requires setting a rate structure for electricity (Agence Française de Développement, 2012).

 The development of mini-grids was spurred by the reduction in renewable energy costs and the increase in petroleum prices

The cost of solar panel production has dropped significantly in terms of its primary components like the module, converter, and wiring, making it more competitive (Agence Française de Développement, 2012), especially given the parallel rise in the price of imported petroleum.

Moreover, this technology can be used in hybrid configurations combining diesel with renewable energy. Diesel is now no longer used as the main production fuel but as a back-up (IRENA,

2016).

Many such mini-grids have thus been created, substituting for diesel plants connected to the main grid system in, for example, South Africa, Sudan, Kenya, Nigeria, and Senegal. In sub-Saharan Africa, there is no less than 19.7 MW of installed capacity in the form of hybrid mini-grids combining diesel and renewable energy (IRENA, 2016).

Mini-grids are becoming more competitive. At the beginning of the 2000s, each kWh they produced is estimated to have cost $1.90-5.90 (for a baseline 200 KW system), while the cost of a hybrid system was estimated at $2.50-10.90 per watt (IRENA, 2017).

 The rapid growth in renewable mini-grids can be explained by financial support to the entire industry

The boom in mini-grids can be attributed to numerous aid programs established through many countries in sub-Saharan Africa providing subsidies to encourage the emergence of these systems. For example, AMADER (the Malian agency for the development of domestic energy and rural electrification) set up 150 mini-grids in Mali; the Senegalese agency for rural electrification had a similar initiative. Similarly, over 200 renewable mini-grids are owned and operated by village electricity consumer societies. This subsidy policy is still necessary. It can also be accompanied by cross-subsidization, when the mini-grids set up include small urban clusters or large villages with a concentration of economic activity, as in the Sava Valley in Madagascar.

 Mini-grids a new form of supply, help stimulate demand, especially in rural households

Due to their decentralized nature, these technological options meet the needs of rural power demand. Demand for electricity is low in SSA, characterized by power needs mostly related to lighting (Agence Française de Développement, 2012). Consumption generally peaks sharply in the evening (3-4 times the rate in the morning) and is otherwise very low throughout the day. This demand needs to be developed in order to ensure that decentralized production systems can be profitable, and to create return on investment by avoiding low usage rates when rural demand is saturated due to a low connection rate (Agence Française de Développement, 2012). The combined demand of rural households can only grow with the help of appropriate household appliances, which requires income growth. The dynamics around demand involve a progressive increase in productive and commercial use of electricity in combination with increase in rural incomes, thus ensuring the profitability of rural electrification programs.

Their development is still hindered by certain limits, however.

 Mini-grids are still subject to the costs of compensating for intermittency in renewable energy

Intermittency brings up the question of calibrating production to meet demand in order to avoid under-utilization of equipment and the ensuing rise in cost per kWh. One of the main problems with solar mini-grids is that production needs to be during the day, while demand in most rural communities tends to be nocturnal. These technologies thus need to store their electricity in expensive batteries.

With renewable mini-grids, the cost of compensating for intermittency are so high that some customers, especially those in rural or peri-urban areas, decide to go on-grid to have guaranteed access to electricity. Such is the example of Sri Lanka, where electricity from renewable mini-grids built and managed by VECS (village electricity consumer societies) was extremely expensive as compared to that from the state-owned CEB (Ceylan Electricity Board), which provided better-quality and more reliable electricity (Tenenbaum & al, 2015). Rural and peri-urban households, moreover, tend to compare the basic-needs electricity rate offered by the state-owned utility, about $0.025-$0.03/kWh, to mini-grid prices at $0.25/kWh.

 Mini-grid power is prohibitively expensive for rural populations, given the inferior power services they offer

The costs for a solar mini-grid, mostly related to batteries and photovoltaic modules, make them financially inaccessible for most rural communities. 15It should be noted that existing mini-grids are often linked to small distribution networks of less than 11 kilovolts (KV) that only produce a low installed capacity of about 8 to 10 MW [START_REF] Tenenbaum | Quand la lumière vient d'en bas : Comment les petits producteurs d'électricité et les mini-réseaux peuvent promouvoir l'électrification rurale et les énergies renouvelables en Afrique[END_REF]. Despite examples that point to the possibility of developing larger mini-grids, such as the solar systems connected to industrial activities in the South Deep mine in South Africa, the power that these systems provide is still extremely limited due to intermittent energy production [START_REF] Tenenbaum | Quand la lumière vient d'en bas : Comment les petits producteurs d'électricité et les mini-réseaux peuvent promouvoir l'électrification rurale et les énergies renouvelables en Afrique[END_REF].

 Mini-grids are in competition with thermal plants on the grid

In many cases, renewable mini-grids rare extremely expensive. For example, in Uganda, one kWh of power from a renewable mini-grid costs about $16.40. The rates offered to residential customers are currently $0.50/kWh, two to three times higher than the preferential rates offered to low-income customers by the state-owned companies. Renewable mini-grids create strong tariff differentiation, to the point at which they end up being connected to the national power network to eliminate this large disparity between state power customers and mini-grid customers [START_REF] Tenenbaum | Quand la lumière vient d'en bas : Comment les petits producteurs d'électricité et les mini-réseaux peuvent promouvoir l'électrification rurale et les énergies renouvelables en Afrique[END_REF].

The appearance of off-grid power in the 2000s led to a new demand dynamic as these solutions targeted rural populations who had been excluded from both the main power grid and mini-grids. Off-grid power made its appearance in the 2000s, forcing public services to reconsider other institutional agency models [START_REF] Ackermann | Distributed generation: a definition[END_REF]. According to the IEA, 60% of future access to electricity will pass through off-grid systems (IEA, 2010;[START_REF] Mandelli | Off-grid systems for rural electrification in developing countries: Definitions, classification and a comprehensive literature review[END_REF].

The main advantage of off-grid power is that it aims to satisfy rural demand, which has been unmet up to now. More specifically, it makes it possible to monetize a latent willingness to pay that has not been satisfied by on-grid solutions. Many studies have highlighted that this population pays much more than do on-grid customers, or $10.00 per resident per month (IEA, 2012;African Energy Outlook, 2014).

Off-grid power has come to rural areas through solar home systems 16 . These innovative systems are based in local businesses that want to invest in rural electrification. In terms of supply, the technology appears to be flexible, using small home solar power systems that generate 20-100 watts.

In terms of demand, off-grid power aims to satisfy the power needs of rural households by providing them with lighting and a way to charge their phones. [START_REF] Baurzhan | Off-grid solar PV: Is it an affordable or appropriate solution for rural electrification in Sub-Saharan African countries?[END_REF] show that under certain conditions, home solar systems would allow a 5-person household to save the equivalent of $31.20 per year if they own one mobile phone, $62.40 for two, and $93.60 for three [START_REF] Baurzhan | Off-grid solar PV: Is it an affordable or appropriate solution for rural electrification in Sub-Saharan African countries?[END_REF].

 Solar off-grid power is becoming competitive due to the sharp fall in the cost of solar power components

In 2016, off-grid solar installations produced electricity that cost $0.83/kWh, using the 10% discount rate in 2016 [START_REF] Baurzhan | Off-grid solar PV: Is it an affordable or appropriate solution for rural electrification in Sub-Saharan African countries?[END_REF][START_REF] Quansah | Solar Photovoltaics in Sub-Saharan Africa -Addressing Barriers, Unlocking Potential[END_REF]. 16 Kenya, South Africa, Zimbabwe, and Tanzania are the countries on the cutting edge of off-grid solar power: they have developed 320 000, 150 000, 113 000, and 65 000 home solar systems respectively (IRENA, 2015b).

There are two categories of cost reduction depending on installed capacity. For systems with an installed capacity of 1 kW or more, cost reductions are mainly related to the photovoltaic array (14.5 to 17.5 %), batteries (11 to 21 %), converters (11 to 22 %), and other materials (29 to 36 %).

For systems under 1kW, total installation costs vary from $20.00 for a 20W system to $1270 for a 100 W system. Because of the small size of the off-grid solar system, the main cost is replacing the battery, which varies between $56 and $214 per year. This cost, however, is falling sharply. Current home solar systems are based on deep-cycle lead-acid batteries, but a new generation of lithium-ion batteries are about to come onto the market (IRENA, 2016), making these systems even more affordable.17  Off-grid power is competitive with kerosene lamps, driving the demand function for rural households The competitiveness of off-grid solar installations should be examined in terms of the power services provided to households. Currently, households with no access to the grid pay between $84 and $270 per year for lighting and phone charging needs (BNEF, Lighting Global, World Bank & Gogla, 2016& IRENA, 2016). Very small home solar systems are still very affordable in comparison to traditional lighting solutions such as candles, kerosene lamps, and battery-operated flashlights. The cost of an offgrid solar installation was estimated to be $51 in 2016, which is 2.3% of average household income. In comparison, rural households can spend $56 on kerosene lamps, or 2.6% of average household income.

Off-grid solar power remains competitive with kerosene lamps because it offers a better quality of light. For example, a 2W LED bulb produces about 380-400 lumens of light as opposed to 8-40 lumens emitted by a kerosene lamp.

The limits of off-grid power

 It is expensive for most of the rural population

Three-quarters of those living below the poverty line live in rural areas [START_REF] Eberhard | Independent Power Projects in Sub-Saharan Africa: lessons from Five Key Countries[END_REF]. The monthly energy expenses of these households rarely exceed $2. Therefore, an off-grid solar installation remains extremely expensive for these households [START_REF] Karekezi | Renewable energy strategies for rural Africa: is a PV led renewable energy strategy the right approach for providing modern energy to the rural poor of Sub-Saharan Africa?[END_REF], representing 100-200% of their average annual income [START_REF] Karekezi | Have power sector reforms increased access to electricity among the poor in East Africa[END_REF]African Energy Outlook, 2014). Despite a general tendency towards lower costs for solar installations, they would currently make up a large portion of household budget (estimates vary from 22 to 61%). The reduction in cost for off-grid solar technology is thus insufficient. [START_REF] Baurzhan | Off-grid solar PV: Is it an affordable or appropriate solution for rural electrification in Sub-Saharan African countries?[END_REF] confirm this hypothesis in their analysis of solar energy in sub-Saharan Africa. Using their calculations of the levelized cost of energy (LCOE) of off-grid solar technology ($0.83/kWh) and considering an annual rate of cost reduction in solar arrays of 4% and 7.67% respectively, the authors find that it would take between nine and seventeen years for solar home system to be competitive with conventional diesel plants.

 Off-grid power must still compete with thermal plants

In forecasted scenarios, off-grid access to electricity is a dominant solution (African Energy Outlook, 2014;World Energy Outlook, 2017). By the year 2030, the cost of these technologies will have continued to fall sharply (African Energy Outlook, 2014;World Energy Outlook, 2017).

Nevertheless, due to their high initial costs, off-grid solutions must still compete with on-grid thermal systems, often backed up with diesel generators. Diesel and petrol are subsidized in some SSA countries that produce and export them (Nigeria, Angola, Gabon). These low fuel prices are attractive to consumers, who are more likely to choose low-cost fossil fuel solutions over renewable off-grid options (African Energy Outlook, 2014;World Energy Outlook, 2017).

 Off-grid power still provides inferior power service to customers, who take on the problem of intermittency

Off-grid solar solutions (Pico solar lanterns, solar home systems) have low installed capacities (between less than 3 watts and 2 kW). While they are ideal in the sense that they provide access to electricity to people far from the main grid, these solutions are still limited in terms of the power service they can provide to end consumers (African Energy Outlook, 2014). This is particularly true for solar kits (Agence Française de Développement, 2012), which, despite the 50% drop in price over the last 15 years, still produce only 50 watts and only produce energy for light, phone charging, and audiovisual use for only 3-6 hours for even the most powerful systems. Consequently, these off-grid systems cannot offer sufficient energy services to rural and peri-urban populations (Agence Française de Développement, 2012), making grid access remain relevant.

In sub-Saharan Africa, the power system is still characterized by major changes in electricity supply. Starting with an inadequate grid system, production solutions focused on more decentralized solutions (mini-grid and off-grid), which are, however, limited and expensive (for example, some developers lock their off-grid supply). These various changes are the results of shifts in electricity demand. In fact, there are many levels of demand across sub-Saharan Africa, with all electricity systems hinging on the baseline price of on-grid electricity. All of these changes can be illustrated through theoretical propositions showing the dynamics of unmet demand and their impact on the forms of electricity supply production.

Part 5. The dynamics of unmet demand and their consequences on the major changes in supply types observed in electricity production.

The appearances of new forms of electricity supply following the development of the mini-grid in the 1990s and off-grid power in the 2000s led to different dynamics at the demand function level. We will analyze them through several theoretical propositions:

Proposition 1. Two limitations to natural monopoly are free-riding and back-up costs, the first of which is internalized and the second not;

Proposition 2: Supply-level dynamics: decentralized solutions emerge as a response to inadequacies in the centralized on-grid supply and become competitive (decentralized technology based on renewable energy) with conventional means of production under certain conditions;

Proposition 3. Demand dynamics depend on the type of power (on-grid, mini-grid, off-grid), Proposition 4. All these dynamics throughout the electrical network move in a cobweb curve, spinning demand around a new equilibrium price.

Proposition 1. Illustration of the inadequacy inherent in natural monopolies

Natural monopolies use conventional means of production to meet the demand that they encounter. The point of natural monopolies is to be able to increase the number of beneficiaries without rationing by spreading costs among the growing number of consumers.

In the case of SSA, this principle finds its first limit in consumers who do not pay for power, or free-riders. This limit can be internalized by a natural monopoly.

On the other hand, natural monopolies in SSA are faced with another limit that is not internalized: technical weaknesses that cause a discontinuous distribution of electricity. To deal with this, the natural monopoly needs to offer a back-up supply.

The increase of on-grid demand shifts the supply curve, making the cost of back-up power visible. Within the equilibrium of supply and demand, the two limiting principles of natural monopolies can be summarized by free-riding and unmet demand that cannot be covered by the main grid system. The equilibrium point for the grid system is at (P *on-grid ; Q *on-grid

). The cost of back-up power is prohibitive (Cross-hatched section with high P back-up ). This shows the inability of the natural monopoly to resolve inadequacies observed in the grid system. As a result of demand pressure, new decentralized systems, mini-grid and off-grid, arise in the attempt to compete with conventional means of grid production.

Proposition 2. Decentralized supply forms and how they fit with on-grid, mini-grid, and offgrid systems

New decentralized supply types appeared in SSA as a result of the inadequacies of the grid system and the large unmet demand in rural areas. The emergence of these supply types was encouraged by technical progress in renewable energy.

However, these two technologies are not mature; mini-grid power faces competition from on-grid power at short distances and from off-grid at long distances.

Figure 4.

Cost comparison between on-grid, mini-grid, and off-grid power

We assume that price elasticity of demand for the quantity demanded is identical for each network. For off-grid power, since the cost of a solar kit is equivalent to the cost of electricity, it is seen as a vertical line.

Mini-grids are more profitable in dense communities sufficiently far from the grid network, where the consumer price of grid electricity is high, and in areas with reliable supplies of renewable energy (crosshatched area). Mini-grids are most cost-effective for applications requiring average quantities of electricity.

On the other hand, in very densely populated areas or very remote areas, on-grid and off-grid power are more competitive.

Proposition 3. Demand characteristics for on-grid, mini-grid, and off-grid power

On-grid supply P on-grid Q on-grid Quantities Quantities Quantities

Prices Prices Prices

Global demand

Marginal demand P mini-grid

Mini-grid supply Q on-grid Q mini-grid Off-grid supply

P off-grid Q off-grid

Global demand

Global demand Supply rations demand. Demand is constrained by the capacity the mini-grid can supply; the curve thus becomes vertical. Quantities consumed (Qmini-grid) are distinctly lower than those on the grid (only a few kilowatt hours consumed). The price of mini-grid power (Pmini-grid) is higher than that on the grid (Pongrid). where D1 is on-grid demand and D2 is aggregate demand (on-grid + mini-grid + off-grid). The supply function is also aggregate, represented by a bent curve. Two movements can be seen. Movement 1 takes place when Q * D1 = Q * D2. Variations in demand lead to an increase in price, from p * to p1. In response to Movement 1, Movement 2 translates a variation in demanded quantity, moving from Q * to Q1 (1'' on the graph). The price then falls (1''). The ensemble of networks tends to converge at an equilibrium set at P2 (1'''). These decentralized solutions converge towards this equilibrium without ever attaining it because of characteristics inherent in these immature networks.

Q mini-grid Q on-grid

Conclusion

In sub-Saharan Africa, centralized on-grid power supply has not been able to respond to the challenges of access to electricity for a large portion of the population. Privatization, which took place in the 1990s, was supposed to expand access by extending the networks that the older public companies were incapable of financing. This privatization was accompanied by two movements: one was competition in the electricity segment with IPPs and the second was the appearance of mini-grids based on renewable energy (solar, small hydroelectric, and wind). These mini-grids, the result in a change in supply coming from demand mechanisms, was an undeniable economic opportunity for rural households that had been excluded from access to electricity from conventional centralized means of production. The fairly rapid emergence of mini-grid power can also be explained by the considerable drop in installation costs and electricity pricing that remained competitive compared to the thermal production sources that had been the norm. Beginning in the 2000s, a second change took place with the appearance of off-grid power. All of these decentralized systems, however, share the problem of the inferior power services they deliver and their cost. Due to reasons inherent to these decentralized solutions, access to electricity through the grid has become relevant again, since the grid remains more economically sustainable.

In sub-Saharan African countries, electrification depends on innovative plans for developing electricity supply, leading to a co-existence, at a growing cost, of centralized and decentralized networks. It would be useful to examine the state of the current networks as well as the potential of joining decentralized networks to each other or to the central grid, leading to rural electrification. This new meshing of supply stemming from demand dynamics makes it possible to imagine new designs in energy policy that go beyond the current limitations: supply oriented towards the maintenance and improvement of the grid system without responding to the needs of rural populations and mini-grids supplying small amounts of expensive power to those rural populations.

%); IPS-AKFED ( 23

  These choices were dictated by former colonial capitals during the 1950s to imitate the structures established in developed countries. Vertical integration was justified by several technoeconomical efficiency arguments:  The development of new production capacity (Percebois & Girod, 1998),  State or external support 2 necessary to develop a sector requiring high capital intensity (Varashin, 2002) and participating in the development and extraction of a range of energy resources in order to enhance certain productive activities (like hydroelectricity, which encouraged agricultural development),

Part 4 .

 4 Supply forms in the early 2000s: The emergence of off-grid power 4.1. Market fit of new off-grid forms of electricity production  Due to its versatility, off-grid power meets a segment of rural demand by exploiting the potential of renewable energy

Figure 1 .

 1 Figure 1.Comparison between annual expenses of an African household and the cost of a home solar system (less than 1 kW) in 2015

Figure 2 .

 2 Figure 2.Cost of solar home systems in sub-SaharanAfrica (2009Africa ( -2016) )

Figure 3 .

 3 Figure 3.The cost of back-up power

Figure 5 .

 5 Figure 5. On-grid demand

Figure 6 .

 6 Figure 6. Mini-grid demand

Figure 7 .

 7 Figure 7. Off-grid demand

Figure 8 .

 8 Figure 8. Cobweb model of the network ensemble

Table 1 :

 1 : Growth in nominal output and energy produced by several SSA

power plants Country Côte d'Ivoire Cameroon Gabon Ghana Kenya Madagas car Senegal State monopoly

	Sources: Kansara & Walkade (1983); Percebois & Girod (1998); Saupique (2002); Varashin (2002)
	
		Côte	Cameroon	Gabon	Volta	Kenya	Jiro sy	Senegal
		d'Ivoire	Electrical	Power and	River	Electricity	rano	National
		Electri-	Energy	Water	Authority	Generating	Malagasy	Electri-
		cal Energy (EECI)	(ENELCAM) , later Cameroon National Electrical Company	Company (SEEG)	(VRA)	Company (KPLC)	(JIRAMA)	city Com-pany (SENELE C)
			(SONEL)
	Additional	67 -	911 million	20 million	476-5276 102-466 MW 98 million	110

Supply of electricity to main urban centers

	MW  It provided better quality electricity, 6 1750 additional additional	GWh	in 1978	additional	million
	output or  It encouraged growth in industrial textile production GWh kWh kWh produced		kWh	addition
	GWh of	produce	produced	produced	from		produced	al kWh
	energy	d	from 1946	from 1946 to	1978 to		from	produce
	produced	betwee	to 1960	1960	1980.		1946 to	d from
		n 1960			Mostly		1960	1946 to
		and			hydroelec			1960
		1980			tric
					power
					plants
	Sales of	Abidjan:	-	-	-	-	-	In the
	electrical	13 millio						Dakar-
	power	n kWh						Rufisqu
	from these	(1955)						e-
	companies	57, 064						Thiès re
		533						gion:
		million kWh						37 million
		(1960)						kWh
		(Varashi n, 2002)						(1952)
	Urban households were first provided electricity through the grid network (Saupique, 2002) 4 . Sev-
	eral lines were thus maintained:
	 This would respond to the rapid growth in urban household demand stemming from colonial
	populations residing in the territory (Lappara, 2002; Mehyong & Ndong, 2011).
	Many European households used appliances imported from Europe (fans, telephones,
	refrigerators, lamps). These households drove intensified electrification efforts (especially in Côte
	d'Ivoire). 5 Similarly, in 1972, in N'Ndjamena (Chad) two major arteries in the colonial districts were
	provided electrical power.

Public funds: FIDES (Investment fund for economic and social development) and FAC (Funds for aid and cooperation); External funds (European Development Fund, USAID, or CRID).

A notable difference can be seen between the centralized planning preferred by the French High Commission for West Africa (AOF) and the self-government methods used by the British[START_REF] Mazrui | Comité scientifique internationale pour la rédaction d'une Histoire générale de l'Afrique[END_REF].

See the comment by Verteuil, former administrator of the EECI (Côte d'Ivoire Electrical Energy).

Enhancing the hydroelectric potential of Douala (Cameroun) resulted in the production of

MWh of electricity in 1952. 7 The Akosombo dam (Ghana) was launched in 1960, giving preferred access to urban households, while rural households had to wait until 1987 to gain very reduced access to electricity.8 Especially in South Africa for the power needs of (gold and diamond) mines[START_REF] Coquery-Vidrovitch | La politique de réseaux d'électrification en Afrique. Comparaison Afrique de l'Ouest[END_REF].

This was the case, for example, of the hydroelectric plant on the Turkwel river in Kenya during the 1980s; from 1945 to 1990, Nigeria built up a production capacity of 5 GW when its domestic demand was only at 2 GW.

This is the case of the Volta River Authority (VRA) in Ghana[START_REF] Edjekumhene | Power sector reform in Ghana: The untold story[END_REF][START_REF] Turkson | Power sector reform and distributed generation in Sub-Saharan Africa[END_REF].

The International Finance Corporation (IFC), a member of the World Bank, financed about one-third of private energy projects in Sub-Saharan Africa[START_REF] Hoskote | Independent Power Projects (IPPs): An Overview. Energy Note 2[END_REF][START_REF] Eberhard | Demise of standard model for power sector reform and the emergence of hybrid power markets[END_REF].

This trend is likely to continue due to the development of Combined Cycle Gas Turbine plants (CCGT).

A breakdown of the average costs of a solar mini-grid: 27% battery, 20% for the photovoltaics, 7% for the converter, 5% for the wiring and 4% for installation and transmission of electricity[START_REF] Irena | Renewable Power Generation Costs in[END_REF].

The average cost of a 1 kW home solar system with a storage capacity of 20-220 ampere hours (Ah) is about $2 per Ah. There is a wide variance in the cost of batteries, on a scale from $2.10 to $6.8 per watt produced(IRENA, 2016).