# Designing policies to reduce the carbon footprint of mini-grids in Africa

Théo Chamarande, Sandrine Mathy, Benoit Hingray

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Théo Chamarande, Sandrine Mathy, Benoit Hingray. Designing policies to reduce the carbon footprint of mini-grids in Africa. Applied Energy, 2025, 396, pp.126296. 10.1016/j.apenergy.2025.126296. hal-05125326

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# Designing policies to reduce the carbon footprint of mini-grids in Africa

Théo Chamarande*<sup>a</sup>, Sandrine Mathy<sup>b</sup>, Benoit Hingray<sup>c</sup>

<sup>a</sup> ESPACE-DEV, Univ Montpellier, IRD, Univ Antilles, Univ Guyane, Univ Réunion, Univ Perpignan (UPVD), Montpellier, France

<sup>b</sup> Univ. Grenoble Alpes, CNRS, INRAE, Grenoble INP, GAEL, 38000 Grenoble, France

<sup>c</sup> Univ. Grenoble Alpes, CNRS, INRAE, IRD, Grenoble INP, IGE, 38000 Grenoble, France

* Corresponding author: theo.chamarande@ird.fr, UMR Espace-DEV, 500 Rue Jean-François Breton, 34 090 Montpellier, France

## Abstract:

Mini-grids with a low carbon footprint are a promising solution for providing electricity in rural areas, while being compatible with the objectives of the Paris Agreement. Public policies are needed to encourage their development and their design should consider the different point of view from each stakeholder involved in mini-grid projects (State, developer, users). We propose a multi-criteria approach to evaluate a set of policies to limit the carbon footprint of mini-grids. Our method is based on the simulation of fictitious mini-grids and on the calculation of four indicators: the mitigation cost, the policy cost, the average levelized cost of energy (LCOE) at the national level, and the disparity of individual mini-grid LCOE within the country. We applied the methodology to Senegal, Madagascar, Kenya and Nigeria chosen for the diversity in solar resource and fuel price. Our results advocate for the combination of fuel tax and subsidy on solar panels and batteries to further reduce the carbon footprint of mini-grids. Using fuel tax revenues to equalize the LCOE of mini-grids within a country allows a cost-efficient reduction of the carbon footprint while reducing the cost disparities between mini-grid projects.

## Keywords:

Mini-grids, Sub-Saharan Africa, Public policies, Carbon footprint, Rural electrification

Word count: 6771
List of abbreviations:

* BAU: Business As Usual

* CFP: Carbon footprint [gCO2,eq/kWh]

* CFP*: Lowest carbon footprint

* GHG: Greenhouse Gases Emissions

* GHI: Global Horizontal Irradiance [W/m²]

* LCOE: Levelized Cost of Energy [$/kWh]

* LCOE*: Lowest LCOE

* MG(s): Mini-grid(s)

* PV: Photovoltaic

* SDG: Sustainable Development Goal
# 1 Introduction

The seventh sustainable development goal (SDG) of the United Nations requires reconciling a sharp increase in affordable energy production to ensure universal access by 2030 with a lower environmental impact of the energy systems (United Nations, 2021). On the one hand, around 730 million people are indeed lacking access to electricity in the world (United Nations, 2021). On the other hand, among environmental impacts, global pathways likely limiting global warming to 1.5°C require achieving net zero greenhouse gases (GHG) emissions by 2050, with full decarbonization of power systems as a priority (Intergovernmental Panel On Climate Change (Ipcc), 2023).

According to the International Energy Agency, mini-grids (MGs) will play a key role in accelerating electrification in rural areas and in reconciling the affordability and sustainability criteria of SDG 7 (International Energy Agency, 2022). A large literature already shows that MGs can supply energy at a lower cost than national grids in many regions (Huld et al., 2017; Mentis, 2016; Moner-Girona et al., 2019), and the abundance of renewable energy, especially solar energy, in these regions allows to significantly reduce GHG emissions of these MGs (Antonanzas-Torres et al., 2021; Baldi et al., 2022). However, if more and more solar MGs are installed, a large part of the currently operating MGs still rely on a significant fraction of diesel based electricity production (Africa Minigrid Developers Association, 2020).

A first method of reducing the use of fossil fuels, which are responsible for GHG emissions, is to tax these fuels or their emissions. A tax on CO2 emissions exists in many countries (World Bank Group, 2025), mainly in Europe, but also for recent years in some emerging countries such as South Africa ("Carbon Tax | South African Revenue Service," 2021). Taxes on fossil fuels are more common in Africa (e.g., in Uganda, Kenya, South Africa ("Carbon Tax | South African Revenue Service," 2021; Kenyan Government, 2012; Kerckhoven et al., 2015)), even if they are not introduced for environmental reasons. However, given the strong growth in energy demand in Sub-Saharan Africa, the specific context of rural electrification and recent discoveries of gas and petrol in certain countries, subsidies on energy technologies may be preferred to fuel taxes.

Several countries, as well as various international programs ((Green Climate Fund, 2025), Green Mini-grid project (Green Mini-Grids, 2025.), etc.) implemented subsidies to boost the development of renewable energies to meet electricity demand, particularly in rural areas. These international or national programs encourage the development of solar-powered mini-grids by financing part of the investment costs. Several African countries have also introduced tax exemptions for solar equipment to reduce their cost (George et al., 2019; Juma and Chitedze, 2019; Odoom and Awuah, 2023). Nevertheless, these subsidies in their various forms remain very limited when compared with those for national grids and with the funds required to achieve universal electricity access (Maqelepo et al., 2022; Sustainable Energy for all, 2021).

In this context, optimizing the impact of funds and of public policies is key. This includes optimizing the impacts on MG electricity costs and on MG GHG emissions. The majority of articles studying the links between electrification MGs and public policies cover several aspects, such as the need for clear regulations on planning, the types of governance and business model to be promoted, or electricity pricing rules (Bhattacharyya and Palit, 2016; Gollwitzer et al., 2018; Muchunku, 2024; Nyarko et al., 2025; Sesan et al., 2024; Soares et al., 2023). Apart from a few specific case studies dealing with the effect of subsidies on the financial viability of MGs (e.g., Ethiopia (Wassie and Ahlgren, 2024), Tanzania (Maqelepo et al., 2025), Kenya (Wamalwa et al. 2025)), the majority of studies remain
qualitative. Moreover, the design of public policies to reduce GHG emissions from MGs has not yet been addressed to our knowledge.

Reducing the GHG emissions of MGs has a cost that can be different depending on the policy implemented. Quantifying the GHG emissions that can be avoided per dollar invested for different policies allows to optimize the costs of reducing GHG emissions. A few studies have attempted to quantify these costs on the scale of the national electricity grid, focusing on the imposition of different carbon prices (Assoumou and McIsaac, 2022; Buskirk, 2006; Dioha and Kumar, 2020). However, these studies do not cover MGs. Moreover, they focus on direct GHG emissions linked to the combustion of fossil fuels, and do not include indirect emissions linked to the life cycle of renewable technologies. Looking at the carbon footprint (CFP) of a MG, i.e. including indirect emissions linked to the extraction of materials, their transformation, the installation of equipment and end-of-life management, their GHG emissions are far from negligible (>200gCO2/kWh (Chamarande et al., 2024b)).

Finally, the design of public policies requires consideration of the interests of different stakeholders, particularly in the context of rural electrification with off-grid MGs in Sub-Saharan Africa (Chamarande et al., 2024a). For instance, while MGs are less costly than extending the national grid in many areas, they may not be profitable for private developers (Malhotra et al., 2017; Ryota Keeley et al., 2019). A policy to reduce the CFP of MGs could increase the already high investment costs for developers, and make the cost of electricity prohibitive for low-income populations (Bandi et al., 2022; Wen et al., 2023). Minimizing the CFP instead of the LCOE when sizing MGs usually leads to a LCOE increase by 20% to 40% (Chamarande et al., 2024b). Relying only on massive subsidies of renewables from the state or international institutions to reduce the CFP reduces the scope of these institutions for financing other sectors, and limits the development of renewable-based MGs to the availability of public funds. The geographical distribution of the impacts of a public policy on mini-grids should also be considered in the design of this policy to anticipate the possible increase in certain inequalities across the territory (disparities of electricity price or reliability).

To the best of our knowledge, these aspects are not addressed in current studies. This article proposes a multi-criteria methodology for designing public policies to reduce the CFP of MGs while taking into account each of the stakeholders involved in deploying these policies. Our criteria allows us to assess not only the efficiency of a policy, but also its impact on the state's public finances, on the LCOE that drives developers profitability and the electricity affordability for users, and on cost disparities between different locations. The methodology is illustrated for four African countries, with different configurations in terms of solar resource and fuel price: Senegal, Madagascar, Kenya and Nigeria.

The originality of the approach is three-fold. First, we consider the total CFP of MGs when usually only CO2 direct emissions are considered. Second, for each country, we consider an ensemble of locations to account for the diversity of climate within the country. Three, for each location, we simulate a large set of fictitious hybrid MG combining solar PV, batteries and diesel generators for rural electrification, when usually only specific case studies are investigated. The methodology and study cases are presented in section 2. The costs of CFP reduction are estimated in section 3.1 and the implementation of a "CFP price" policy in section 3.2. Sections 3.3 and 3.4 present respectively the results for single policies (subsidies on PV or batteries, tax on fuel) and combined policies (tax + redistribution, bonus/malus). These different policies are compared in section 3.5, and recommendations for policymakers are given in conclusion, section 4.
## 2 Methodology

Our aim is to represent and analyze the impact on the sizing of MGs of support policies to reduce MG CFP. To do this, we consider fictitious MGs composed of solar PV, batteries and a diesel genset. We assume that MG developers size the components to ensure that the electric demand is fully supplied and by selecting the lowest LCOE (the lowest LCOE is called LCOE* in the following) configuration. This LCOE* configuration is determined for each location by simulating a large range of configurations (250 PV production capacities and 40 storage capacities, more details in Appendix A) and by computing the LCOE to find the lowest one. In addition to the LCOE, the CFP of each configuration is computed, especially the one of the LCOE* configuration. Taxes or subsidies on the components impact the LCOE* configuration and its CFP. It is thus possible to define the minimum level of taxes and/or subsidies to reach a given CFP reduction objective. This methodology is illustrated in four study cases in Africa.

### 2.1 MG modelling and calculation of the CFP and the LCOE

The functioning of MG is simulated using timeseries of solar production and electric demand accounting for the multi-scale variability of the resource (infra-day, day-to-day, seasonal). As policies are usually applied at a national/regional scale, such timeseries should be available on multiple locations in the region of interest to account for the diversity of solar resource and electricity demand patterns within this region. Solar production timeseries with an hourly resolution over multiple years and on different locations can be computed from irradiance and temperature data that are available from satellite estimation and/or meteorological reanalysis (e.g., Heliosat SARAH2 (Pfeifroth et al., 2017) and ERA5 (Hersbach et al., 2020) in this paper). Regarding demand data, it is hard to find real consumption data, but typical load profiles accounting for infra-day and seasonal variations can be used (Huld et al., 2017; Li et al., 2018; Louie, 2018; Mandelli et al., 2017).

The installed capacity of the genset is chosen equal to the maximum power of the electric demand to ensure that this demand can always be supplied. The batteries and the genset follow simple rules so that the production meets the demand at each timestep and the genset runs the closest possible to its nominal power (this allows maximizing its energy production efficiency). Once the PV and storage capacities have been set, the diesel consumption and the number of operating hours of the genset can be calculated, as well as the corresponding LCOE and CFP. More details on the simulation and LCOE and CFP calculations can be found in Appendix A.

By simulating a large number of MG fictitious configurations, we can identify among all configurations that have the same CFP, the one with the lowest LCOE value. The least LCOE configurations obtained for different CFP values respectively define an *envelope curve* in a (CFP, LCOE) bi-dimensional space. This is illustrated in Figure 1 with data available for a given location in Kenya (-4°N; 38.5°E). The envelope curve includes the configuration with the lowest possible CFP value (CFP*), the configuration with the lowest possible LCOE (LCOE*) and the configuration with the largest CFP value (the diesel only configuration).
<figure><img src="image_2.png" /><figcaption>Figure 1: Envelope curve for a location in Kenya (-4°N; 38.5°E) and a "hybrid" load profile that mixes domestic and productive uses. Each dot of the envelope curve corresponds to the hybrid MG configuration which gives the lowest possible LCOE value (LCOE*) for the CFP value considered. The renewable fraction corresponds to the part of the energy demand covered by solar energy and storage.</figcaption></figure>

## 2.2 Marginal cost curves of CFP reduction

As illustrated in Figure 1, a large panel of configurations typically exists between the LCOE* configuration and the CFP* configuration. In this example, the CFP of the LCOE* configuration can be reduced by around 50% with a 10% increase of the LCOE and a 3% increase of the LCOE is enough to decrease the CFP by 25% (as shown in (Chamarande et al., 2024b), such CFP reduction costs are found almost all over the African continent).

It is then possible to calculate the LCOE increase to reduce the CFP (including direct and indirect emissions) compared with the LCOE* configuration. We consider a theoretical framework with $LCOE_{CFPprice}$, the LCOE that includes a price on the MG CFP ($Price_{CFP}$):

$$LCOE_{CFPprice} = LCOE + CFP \cdot Price_{CFP} \quad (1)$$

A non-zero $Price_{CFP}$ value modifies the envelope curve and the corresponding LCOE* configuration. The higher the $Price_{CFP}$ value, the higher the reduction of the CFP of the lowest LCOE configuration (cf. Figure 2).

<figure><img src="image_3.png" /><figcaption>Figure 2: Envelope curves for different level of $Price_{CFP}$. Red dots show the LCOE* configurations for five $Price_{CFP}$: 0, 40, 80, 120 and 160 $/tCO$_2$. These graphs refer to a location in Kenya (-4°N; 38.5°E) and a hybrid load profile.</figcaption></figure>
Note that a certain level of CFP reduction can be achieved provided an adequate *Price*<sub>CFP</sub> value is fixed. In the following, the *Price*<sub>CFP</sub> required to achieve a given objective of CFP reduction is called the marginal cost of carbon emission reduction. The marginal cost curve, i.e., the curve of the price *Price*<sub>CFP</sub> as a function of the CFP reduction objective is illustrated in Figure 3 for the previous location.

<figure><img src="image_4.png" /><figcaption>Figure 3: Marginal cost of carbon emission reduction for a location in Kenya (-4°N; 38.5°E) and a hybrid load profile. The five red dots refer to the values for the LCOE* configurations with the five *Price*<sub>CFP</sub> values taken in Figure 2: 0, 40, 80, 120 and 160 US$/tCO<sub>2</sub></figcaption></figure>

The marginal cost curve can be estimated for all locations of a given area (e.g., a country) and can help design public policies (tax, subsidies, norms) by using the individual curves or by taking an average of the different curves obtained for that area.

## 2.3 Public policies to support the deployment of low CFP MGs

Our goal is to evaluate different public policies to reduce the CFP of MGs. The first policy we consider is a CFP price (cf. section 3.2). In addition, we consider three “single” policies (cf. section 3.3):

- Solar PV panels subsidy

- Battery subsidy

- Fuel tax

Note that these three policies are typically implemented in many countries outside the MG context. In a second step, we consider combinations of such policies (section 3.4). We illustrate three possible combined policies:

- “PV + bat sub”: both PV panels and batteries are subsidized, with potentially different levels of subsidy.

- “Bonus/Malus” is a combination between a fuel tax and subsidies for solar PV and batteries. It is designed in order that the public cost of the subsidies is almost equal to the revenues from the fuel tax (<1% difference) and that the level of the fuel tax is minimized.

- “Tax + red.” is a fuel tax alone (without PV panel or battery subsidies) considering the revenues from the tax are redistributed between the different MG to equalize the LCOE of the different projects.

The LCOE and CFP resulting from these seven different policies are compared to the business as usual (“BAU”) case, i.e. without any policy.

We carry out a multidimensional evaluation of these different policies through four indicators: the “LCOE variation”, the “policy cost” to public finances, the “mitigation cost” of CFP reduction and the “LCOE disparity” between individual MGs within a country.
<figure><img src="image_5.png" /><figcaption>Figure 4: Mean annual Global Horizontal Irradiance (GHI) for Kenya, Senegal, Nigeria, and Madagascar</figcaption></figure>

To account for the variability of the solar resource within each country, we consider fifteen or so hypothetical MGs for different locations evenly distributed in the country (cf. Appendix Figure B.1). The solar PV production for each location is computed using the global horizontal irradiance (GHI) from Heliosat SARAH 2 and the air temperature from ERA5 reanalysis at 15 min resolution over a two-year period.

<table><caption>Table 1: Characteristics of the countries studied. The mean capacity factors and their standard deviations are computed only on the locations selected. Surface area values are taken from the World Bank ("World Bank Open Data," 2025) and fuel costs from the German cooperation (GIZ) report (GIZ, 2020).</caption><thead><tr><th></th><th>Kenya</th><th>Senegal</th><th>Nigeria</th><th>Madagascar</th></tr></thead><tbody><tr><td>Surface Area (km²)</td><td>580 370</td><td>196 710</td><td>923 770</td><td>587 295</td></tr><tr><td>Mean Capacity factor CF<sub>mean</sub> [-]</td><td>0.181</td><td>0.183</td><td>0.175</td><td>0.169</td></tr><tr><td>Coefficient of variation of CF [%]</td><td>4.4</td><td>1.8</td><td>6.1</td><td>9.2</td></tr><tr><td>Number of locations studied in the country</td><td>15</td><td>14</td><td>16</td><td>15</td></tr><tr><td>Fuel cost assumption [$/L]</td><td>1</td><td>1</td><td>0.6</td><td>1</td></tr></tbody></table>

The electric demand for all the MGs are typical load profiles derived from the literature as in (Chamarande et al., 2024b). The domestic load profile (cf. Figure 5) has the higher peak power demand and nighttime consumption, whereas the productive load profile has a much higher daily consumption. In the following, results will be presented for a hybrid load profile (i.e., combining domestic and productive uses). This daily profile is repeated each day of the year. In the following, the mean power demand is referred as *D*.
# 3 Results and discussion

## 3.1 Diversity of the costs to reduce the CFP

The marginal cost curve of CFP reduction differs from one location to the other due to differences in the solar resource and variability, or in the cost of fuel. Three characteristics of these curves can be compared (cf. Figure 6 and SM Table B.1):

- The CFP values of the LCOE* configurations,

- The slope of the marginal cost curves,

- The maximal CFP reduction that can be achieved.

<figure><img src="image_6.png" /><figcaption>Figure 6: Marginal cost curves of CFP for 60 MGs (15 in Kenya, 14 in Senegal, 16 in Nigeria and 15 in Madagascar) and a hybrid load profile. The red dashed curves correspond to the mean curve for the country and are obtained by taking the mean CFP on all MGs within the country for each marginal cost of CFP reduction. The graph is zoomed below 250$/tCO2 but the curves can go further in terms of marginal costs and CFP reductions. The parameters used to construct these curves are described in Appendix A.</figcaption></figure>

Within a country, the differences between locations are mainly driven by the differences in the solar resource. They tend logically to be larger for larger countries. For instance, the curves are very close to each other in Senegal, they are rather different in Nigeria or in Kenya. They can also be boosted by specific geographic features. The diversity of climates in Madagascar, due to its island nature is for
instance much higher than that in Kenya whereas the surface of both countries is similar. This variability is expected to influence the way CFP reduction costs are shared among MG projects as shown in sections 3.3 and 3.4.

A mean marginal cost curve (red dashed curves in Figure 6) for each country can be computed to design a policy at the national scale (average on the 14 to 16 locations). Each point of these curves is obtained by setting a value of *Price*<sub>CFP</sub> that applies to all MGs within the country and by taking the average CFP of all these MGs. Then, exploring a range of *Price*<sub>CFP</sub> values allows to build the entire curve. These curves differ from one country to the other because of the local solar resource specificities. They also differ because of the socio-economic specificities such as the fuel cost. The fuel cost actually explains the slope break in the curve of Nigeria. The low fuel cost there leads to LCOE* configurations without PV production and where the introduction of a CFP price would lead to a large integration of solar PV in the systems, hence the large CFP reduction.

## 3.2 Implementing a CFP price

In this section, we consider that a tax on the CFP is implemented at a national level to reach a given CFP reduction objective. Figure 7 shows the three costs related to this policy, calculated as presented in section 2.3 and averaged at national scale (as the red dashed curves from Figure 6).

<figure><img src="image_7.png" /><figcaption>Figure 7: Cost indicators related to the implementation of a CFP price for the four countries and a hybrid load profile. Curves are obtained with a CFP price between 0 and 1500$/tCO2.</figcaption></figure>

Apart from the fact that the curves for Nigeria go further in CFP reduction than for the three other countries, the curves have similar shapes. The relationship between the CFP reduction and ΔLCOE or the policy costs is almost linear for CFP reduction lower than 40% (from 0 to -40%, -65% for Nigeria). Focusing on the linear part, ΔLCOE and policy costs tend to be lower when the solar resource is better (e.g., values for Senegal and Kenya are lower than for Madagascar between 0 and -40% of CFP reduction). The mitigation cost, which represents the costs linked to a change in the MG configuration, has a lower effect on the LCOE increase (<33% of the LCOE) compared to the policy cost (up to 70% of LCOE), which represents here the revenues from the CFP price for the State. The
high ΔLCOE values are thus mostly due to the costs specifically related to the CFP price (high level of price) than to a change in the MG configuration.

The mitigation cost curves are parabolic, showing that the more the CFP is reduced, the more expensive it is to reduce it further. This is also shown by the high CFP price required to get high CFP reduction levels. To reach a 45% CFP reduction, the CFP price has to vary from 217 to 531 $ according to the country (cf. Table 2). These CFP prices levels are high compared to the carbon prices proposed by some international institutions: for instance, the World Bank will use in 2030 an additional cost related to carbon between 50-100$/tCO2 in their cost-benefit analyses to arbitrate between projects to fund (not only energy projects) (World Bank,2024).

<table><caption>Table 2: CFP price level [$/tCO2] to reach a given CFP reduction for the four countries. The values to reach a 50% CFP reduction for Kenya and Madagascar are much higher as it is very close to the maximum CFP reduction. "Close to maximum" corresponds to CFP values that have less than a 1% relative difference with the lowest CFP values. The corresponding CFP reduction is indicated in brackets and CFP price values are rounded to the ten for this line.</caption><thead><tr><th>CFP reduction</th><th>Kenya</th><th>Senegal</th><th>Nigeria</th><th>Madagascar</th></tr></thead><tbody><tr><td>-10%</td><td>54</td><td>52</td><td>20</td><td>57</td></tr><tr><td>-20%</td><td>135</td><td>144</td><td>32</td><td>149</td></tr><tr><td>-30%</td><td>211</td><td>189</td><td>78</td><td>242</td></tr><tr><td>-40%</td><td>274</td><td>270</td><td>163</td><td>344</td></tr><tr><td>-45%</td><td>339</td><td>531</td><td>217</td><td>508</td></tr><tr><td>-50%</td><td>5700</td><td>Unreachable</td><td>276</td><td>1695</td></tr><tr><td>-60%</td><td>Unreachable</td><td>Unreachable</td><td>438</td><td>Unreachable</td></tr><tr><td>-70%</td><td>Unreachable</td><td>Unreachable</td><td>841</td><td>Unreachable</td></tr><tr><td>Close to maximum</td><td>7050 (-50,6%)</td><td>6670 (-48,6%)</td><td>8450 (-71,7%)</td><td>8120 (-51,8%)</td></tr></tbody></table>

Note that in this case, the CFP price is related to the total CFP and not only to the direct emissions as it is usually the case. In practice, this CFP price would be difficult to implement due to the variability and uncertainties of CFP values for solar PV and batteries (Besseau, 2019). But a CFP price can serve as a theoretical reference policy to which other policies can be compared (cf. sections 3.3 to 3.5).

## 3.3 Implementing CFP reduction policies through fuel tax or solar product subsidies

In the following sections (3.3 to 3.5), we only show the results obtained for Senegal and Madagascar as they present the most contrasted results among the four countries studied, but very similar results are found for Kenya and Nigeria (cf. Appendix B, Figures B.2 to B.6). First, we compare the costs of single policies (subsidies on solar PV, subsidies on batteries and fuel tax) in Figure 8.
<figure><img src="image_8.png" /><figcaption>Figure 8: Cost indicators variations related to the implementation of a fuel tax, PV subsidy and battery subsidy for Senegal and Madagascar, and a hybrid load profile. Curves are obtained with a subsidy level between 0 and 100% and a fuel tax level between 0 and 1200%. The CFP price curves are the same as in Figure 7. The green stars in the curves refer to different levels of subsidies or fuel tax. From the right of the graph to its left, they represent subsidy levels of 0%, 25%, 50% and 75% and fuel tax of 0%, 150%, 300%, 450%, 600%, 750%, 900% and 1050%.</figcaption></figure>

The curves for the three single policies in Figure 8 are similar to the curves related to CFP price in Figure 7 with a linear part that becomes rounder when approaching the maximum CFP reduction reachable by the policy. However, especially in the case of subsidies, high levels of incentives can be counterproductive and lead to stop or even reverse CFP reduction. The CFP* configuration consists in a trade-off between solar PV and battery capacities and their CFP per unit installed (Chamarande et al., 2024b); it can thus not be reached with a too large support to battery (or to PV panels). On the contrary, the diesel tax allows to reduce further the CFP compared to subsidies, and even close to the lowest CFP achievable, but this can require high taxation levels (e.g., here an increase of more
than 250% of the fuel cost to reduce by 50% the average CFP in Madagascar, cf. Appendix B Table B.2) ...

Note that, as direct emissions are only produced by the combustion of fuel, the fuel tax can also be interpreted as a tax on direct emissions. A conversion can be made using the emissions of one liter of diesel: 2.6kg CO2/L. For Kenya, Senegal and Madagascar, a fuel tax of 50% corresponds to an increase of 0.5$ per liter of diesel, which is equivalent to a tax on direct emissions of approximately 0.192$/kg CO2, being 192$/tCO2. As we considered a lower fuel cost for Nigeria (0.7$/L), a 50% fuel tax would be equivalent to a direct emissions tax of 135$/tCO2.

One major difference between subsidies and fuel tax is the way costs are shared among actors. A fuel tax benefits the public finances (positive policy cost) whereas the subsidies require funds from public finances and reduce costs for developers, operators or users of MG (if the cost reduction is transferred to the electricity tariffs).

Without considering which stakeholders are affected by the policy cost (absolute values), subsidies have higher policy costs than taxes, and the subsidy on solar PV is more expensive than the subsidy on batteries. The CFP of MG is a non-linear function of the PV and battery capacities. Each additional percent of CFP reduction requires a larger increase of PV and/or battery capacities and is thus more expensive. This leads to the fast increase of subsidy costs compared to the fuel tax.

The fuel tax has a lower effect on the LCOE than the CFP price as it taxes only the fuel, and not solar PV or batteries through their indirect GHG emissions. Regarding subsidies, the LCOE decreases more with the PV subsidies than with battery subsidies because PV panels represent a larger share of the total MG costs.

By construction, the “CFP price” policy is the policy with the lowest mitigation costs. For small CFP reductions, mitigation costs between the different policies are not very different. For high CFP reductions, the PV subsidy leads quickly to higher mitigation costs compared to other policies.

Looking at the national scale (cf. Figure 8), the three performance indicators are relatively similar for Madagascar and Senegal. However, the impact of these policies on the disparity of LCOE within these two countries is not the same. Figure 9 shows the LCOE variations obtained for the different locations of each country when an average 30% CFP reduction compared to the BAU is achieved. Table 3 gives the level of tax/subsidy to reach this 30% CFP reduction.
<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /><figcaption>Figure 9: LCOE distribution (tax/sub included) related to the implementation of a CFP price, a fuel tax, a PV subsidy and a battery subsidy for each MG of Senegal and Madagascar. BAU refers to the business as usual case, i.e., without any policy. In the other cases, a 30% CFP reduction is achieved at the national level.</figcaption></figure>

<table><caption>Table 3: Subsidy and tax levels on each component or fuel to reach a 30% CFP reduction at the national scale for the four different countries.</caption><thead><tr><td>Policy</td><td>CFP price [$/tCO2]</td><td>PV sub [%]</td><td>Bat sub [%]</td><td>Fuel tax [%]</td></tr></thead><tbody><tr><td>Kenya</td><td>211</td><td>72</td><td>42</td><td>41</td></tr><tr><td>Senegal</td><td>189</td><td>75</td><td>41</td><td>39</td></tr><tr><td>Nigeria</td><td>78</td><td>39</td><td>44</td><td>31</td></tr><tr><td>Madagascar</td><td>242</td><td>68</td><td>49</td><td>45</td></tr></tbody></table>

As explained in section 3.1, the LCOE* configurations depend on location. In the same way, the impact of different public policies depend on location. Whatever the policy, the spatial disparity of the LCOE is small in Senegal, where the solar resource is homogeneous. The spatial disparity is conversely large in Madagascar where taxes (on CFP or on fuel) even tend to exacerbate the disparities. Taxes actually “penalize” MGs with low local solar resource that use more diesel and conversely favor those with better solar resource (cf. Figure 9). To a lesser extent, subsidizing batteries has a similar effect, but subsidizing PV does not. It conversely reduces disparities. When PV panels are largely subsidized, large PV capacities can be installed to increase solar production.
Increasing the PV production capacity is especially profitable for MGs where the solar resource is low. It is much less for MGs with a good solar resource except if additional storage is also considered. In absence of additional storage, part of the additional production would actually be lost in those cases.

## 3.4 Combining different instruments

None of the policies evaluated on its own produces a positive balance on all the evaluation criteria: either the impact on LCOE is really strong (taxes), or the cost to public finances is really high (subsidies), or the mitigation cost is really far from the optimum in terms of economic efficiency of the mitigation represented by the CFP price. In this section we study combinations of these single policies (fuel tax, solar PV subsidy and battery subsidy) in order to consider whether a more positive outcome is achievable:

- A combination of PV and battery subsidies without tax ("PV + bat sub")

- A fuel tax whose revenues are used to subsidize solar PV and batteries (Bonus/Malus, "B/M")

- A fuel tax whose revenues are redistributed to each MG in order to equalize the LCOE ("Tax+red.")

The costs for these three combined policies are given in Figure 10 and in Appendix B Figure B.4.
<figure><img src="image_11.png" /><figcaption>Figure 10: Costs variations related to the implementation of PV and battery subsidies, a bonus/malus and a fuel tax with redistribution for Senegal and Madagascar, and a hybrid load profile. The four gray curves are the same as in Figure 7 and Figure 8.</figcaption></figure>

The mitigation costs for the three combined policies are very close to the minimum mitigation costs achievable (the mitigation costs of the CFP price). Once again, the main differences are mainly due to the distribution of policy costs between stakeholders.

Combining subsidies on PV and on batteries allows to reduce further the CFP of MGs compared to subsidizing only one of these components. The maximum CFP reduction can be obtained with such a combination but it represents a large policy cost for public finances as around 80% of the total costs of MGs would be subsidized.

On the contrary, the two other policies (fuel tax + redistribution of revenues and Bonus/Malus) are neutral for public finances. These two policies are very similar in terms of average mitigation cost,
policy cost and average variation of LCOE, but they differ in terms of tax/subsidy levels and in terms of LCOE distribution between MGs within a country.

The Bonus/Malus policy makes it possible to reduce the level of the tax and subsidies compared to the policy focusing on only one component. The level of the fuel tax in the Bonus/Malus is much lower than the one in the "Tax + redistribution" policy (cf. Table 4), making the implementation of this policy easier. However, taxing only the fuel used for electricity generation without affecting the transport sector may be difficult as MG operations and vehicles use the same type of fuel (cf. below in section 3.5).

<table><caption>Table 4: Subsidy and tax levels to reach a 40% CFP reduction with the three combined policies at the national scale for the four different countries. The level of CFP reduction selected here (40%) differs from the one of Table 3 as the combined policies allow to further reduce the CFP of MGs. "PV sub" only or "Bat sub" only were not able to reach a 40% CFP reduction.</caption><thead><tr><th rowspan="2">Policy</th><th>Tax + red.</th><th colspan="2">PV + Bat subsidies</th><th colspan="3">Bonus/Malus</th></tr><tr><th>Fuel tax [%]</th><th>PV sub [%]</th><th>Bat sub [%]</th><th>PV sub [%]</th><th>Bat sub [%]</th><th>Fuel tax [%]</th></tr></thead><tbody><tr><td>Kenya</td><td>53</td><td>20</td><td>41</td><td>0</td><td>11</td><td>41</td></tr><tr><td>Senegal</td><td>58</td><td>36</td><td>31</td><td>10</td><td>0</td><td>48</td></tr><tr><td>Nigeria</td><td>62</td><td>0</td><td>53</td><td>0</td><td>32</td><td>24</td></tr><tr><td>Madagascar</td><td>72</td><td>29</td><td>47</td><td>2</td><td>17</td><td>52</td></tr></tbody></table>

The fuel tax combined with an equalization of the LCOE avoids the disparities between MGs within the country (cf. Figure 11). Given the large CFP reduction target aimed in this example, the revenues are enough to completely compensate for the disparities linked to the solar resource and supply the electricity to users at the same cost, no matter their location in the country. Such a mechanism is similar to tariff equalization often used on national grids, but instead of a tax applying to user consumption, it would be a tax applying on the operators' fuel consumption. On the contrary, the Bonus/Malus and the PV + battery subsidies tend to increase the disparities between MGs.
<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /><figcaption>Figure 11: LCOE disparities (tax/sub included) related to the implementation of a CFP price, a fuel tax, a PV subsidy and a battery subsidy for each MG of Senegal and Madagascar. BAU refers to the business as usual case, where no policy is implemented. In the other cases, a 40% CFP reduction is achieved at the national level. Using a subsidy only on PV ("PV sub") or on batteries ("Bat sub") does not allow to reach the 40% reduction level, hence the absence of boxplot.</figcaption></figure>

## 3.5 Comparison of public policies

Figure 12 and Figure B.6 summarize the comparison of the four performance indicators between the seven policies for each country. Results are very similar from one country to the other: as expected, the lowest mitigation costs are obtained with the CFP price. The lowest LCOE disparities are obtained with the fuel tax + redistribution to MGs. PV subsidies give the lowest LCOE for users and the fuel tax gives the highest revenues for the public finances. The “best” policy may thus differ depending on the country's situation and the policy preferences. However, considered in a multi-criteria approach with our four performance indicators, the fuel tax with redistribution performs best on three out of four indicators.
<figure><img src="image_14.png" /></figure>

Figure 12: Comparison of policy indicators for Senegal (left) and Madagascar (right) considering a 30% CFP reduction objective. Each graph gathers the CFP price, fuel tax, PV subsidies and battery subsidies and the combined policies (both PV and battery subsidies, Bonus/Malus and Fuel + redistribution of tax revenues). The LCOE disparity indicator is calculated as the coefficient of variations of the LCOE for all locations in the country. For all indicators, performance increases when moving away from the graph centre, e.g. in both countries, "Tax+red" has the best performance for "LCOE disparities" indicator.

The fuel tax with redistribution may be hard to implement as it would impact other sectors using the same type of fuel like industries and transports. It would then be difficult to estimate the amount of tax revenues that should be redistributed to MG users. This highlights one limit of our work: these policies should be evaluated at the level of the whole energy system. These other sectors also need to decrease their greenhouse gas emissions, and such fuel tax could foster energy efficiency. Moreover, the tariff equalization objective proposed here for MGs could be extended to all electricity users, including the national grid. As the national grid tariff is lower than MG tariffs in many African countries such as Kenya (Wamalwa et. al 2025), such a policy would reduce MG tariffs. It would thus improve the performance of the policies concerning the ΔLCOE indicator and allow a fairer electrification policy by harmonizing tariffs between rural and urban populations.

In this article, we designed policies considering a reliability of 100%, i.e., the energy demand is entirely supplied. In practice, a lower reliability may be accepted when sizing mini-grids for rural electrification to reduce the costs of the system. The costs and level of interventions to reduce the CFP of mini-grids with a reliability lower than 100% would differ from what we presented (cf. Appendix B, Figures B.7 and B.8 for examples with a reliability of 90%). Not only are LCOE lower, but the CFP is also smaller. Relaxing the reliability constraint can therefore be seen as an alternative strategy to the policies described in this article for reducing the CFP of mini-grids. As an example, the mean CFP of Kenyan mini-grids without any policy (BAU case) in our study is around 400gCO2/kWh. A CFP value of 300gCO2/kWh could be reached by applying a CFP price around 130$/tCO2, but it could also be obtained by reducing the reliability to 90% (cf. Appendix B, Figure B.8). As this reduction is obtained at the detriment of user satisfaction, the additional cost from the CFP price should be compared to the willingness of users to pay for a given reliability criteria. Exploring the trade-offs between reliability, CFP and LCOE, and how these trade-offs may be used to lower the CFP of mini-grids should be the subject of further research.

Even if our results focus on four indicators, the choice of the policy should consider other aspects such as social acceptability, the political context, the potential windfall effects for operators of solar product manufacturers, etc. Another indicator should consider the robustness of the policy to a
misestimation of the socio-economic context. In our methodology, the design of the policy relies on a good knowledge of the demand load profiles and of the techno-economic parameters related to the components and to the MG project. Due to the large variability of these characteristics, it may be hard for the designer of the public policy to estimate the values of the different parameters required to calculate the LCOE and the CFP. As examples, the CFP values of solar PV and batteries are highly dependent on the manufacturing processes and difficult to estimate (Besseau, 2019); installation and maintenance costs can differ a lot from one location to another depending on local constraints and climate, location accessibility, etc. Load profiles are also very variable due to the diversity of communities and their electricity uses. The CFP reduction, the policy costs and/or the LCOE variations estimated when designing the policy may likewise differ greatly from what expected, potentially leading to much higher LCOE increases for MG users or costs for public finances. Estimating these uncertainties related to policy design could help policymakers to select the best possible policy to effectively reduce the CFP of MGs.

## 4 Conclusion and policy implications

This article compares the performance of various public policies to lower the CFP of MGs in the context of rural electrification in Sub-Saharan Africa. Multiple criteria are used to evaluate these policies: the maximum CFP reduction achievable, the CFP mitigation cost, the policy cost for the public finances, the impact on the average LCOE at national scale, and the impact on the LCOE disparities within the country. These policies consist in single policies (fuel tax, subsidy on PV panel or on batteries) or combined policies (subsidies on both PV panels and batteries, fuel tax to finance subsidies on PV panels and batteries, and a fuel tax to finance LCOE equalization between MGs) to drive MG developers towards low CFP configurations. Their performances are compared to a CFP price that would be applied on both direct and indirect CO2 emissions and which minimizes the mitigation cost of CFP reduction.

To do this, we simulate 60 fictitious MGs scattered over four countries (Kenya, Senegal, Nigeria, and Madagascar). We first built the marginal cost curves of CFP reduction that gives the CFP price that would be required to reach a given CFP reduction objective. These curves first depend on the solar PV resource and variability. In countries with contrasted climate zones like Madagascar, the curves vary greatly from one location to another. On the contrary, in countries with a homogenous solar resource, as in Senegal, the marginal costs of CFP reduction is very stable in space. The fuel price in each country is a second driver of these curves. For example, in Nigeria where fuel price is low, significant CFP reduction can then be implemented with a low CFP price. Maximum CFP reductions are around 50% for Senegal, Kenya and Madagascar, and 70% in Nigeria.

The marginal cost curves show that an ambitious average CFP reduction objective, e.g., 40% for Senegal, Kenya and Madagascar, would imply a more than 20% increase of the LCOE and corresponds to a large CFP price level (>270$/tCO2). In Nigeria, the LCOE increase would be approximately the same, but with a CFP price around 160$/tCO2.

Single policies that could be easier to implement were compared to this CFP price policy. A subsidy on PV panels or on batteries leads to limited CFP reductions, and it can even lead to overinvestment in PV or battery capacity for high levels of subsidies. Subsidies lead to significant LCOE decreases, but at the detriment of public finances. A fuel tax makes it possible to reach more significant CFP reductions, which are close to the maximum, but the consequence is a high impact on LCOE increase. Each of these policies has its limitations.
We assess the potential of combined policies to overcome some of these limitations. A subsidy on both batteries and PV enables the maximum reduction of the CFP to be achieved, but the burden on public finances remains high. A subsidy financed by a fuel tax means that public finances are not impacted, and allows significant CFP reductions with a lower level of fuel tax. Revenues from a fuel tax can also be used for LCOE equalization between MGs within a country.

Indeed, all policies have an impact on LCOE disparities between MG projects. A fuel tax or battery subsidies exacerbate these disparities by favoring the locations with a good solar resource and penalizing the ones with lower solar potential. As our results show that the economic efficiency of the policies are very close to each other (apart from subsidizing only PV panels or batteries), this question of sharing the costs related to the policy between MG stakeholders and MG projects should be at the heart of the policy design.

Fuel taxes are more advantageous for public funds, but at the detriment of MG operators who can report these additional costs to the MG users. A fuel tax combined with a redistribution to equalize LCOE allows a more equitable sharing of costs for decentralized renewable electricity production. Subsidies on both solar PV panels and batteries could result in a lower cost of electricity for users and a more favorable environment for MG developers who usually have difficulties to access capital for MG projects.

Going towards MG configurations with lower CFP compared to the LCOE* configuration requires indeed to increase the initial investment, which is hard to fund in the current MG financial context. In addition to the design of incentives on PV, battery and fuel costs, it may be possible to reduce the CFP of MG by decreasing the risks associated to MG projects (possible future competition with future grid extensions, ability to pay of low-income populations, possible instability of political context and lack of clear policies, etc.) (Agutu, 2022; Falchetta, 2022; Williams, 2015). Such policies of lowering the cost of capital can be implemented by the States, but it is important to notice that international development finance institutions could also play a major role by catalyzing private investment towards renewable-based systems (Briera and Lefèvre, 2024).

The methodology proposed in this article can be easily reproduced to different contexts for public policy design. We give some illustrations of the results in various climatic and economic contexts in Africa alone, but other regions on other continents with specific climatic and economic contrasts (e.g. Latin America, South Asia) could be studied. However, the design of the policy and the potential CFP reduction achievable are highly dependent on a good identification of the initial context (cost and CFP for each component and load profiles, reliability level). Thus, it would be interesting to add in the policy design an analysis of the policy robustness to a misestimate of the initial context and to explore strategies related to demand-side management (e.g., reducing the reliability of mini-grids).

This paper only touches upon the importance of the context in which MGs are developed, and other articles already show the complexity surrounding the development of MGs for rural electrification in Africa (Falchetta, 2021; Gregory and Sovacool, 2019; Njoh et al., 2019). The design of suitable policies needs to integrate this complexity by considering aspects such as the low affordability of newly electrified populations, the difficulties to finance projects both at the beginning and on its whole life cycle, the current regulations, and institutional practices. For instance, assuming that MG developers always select the LCOE* configuration can be considered as a very simple hypothesis and improvements have to be done in understanding what are MG developers practices when sizing MGs (Chamarande et al., 2024a).

Finally, the work presented here with fictitious MGs is a first step to illustrate how to quantify and optimize economic incentives to reduce MG CFP considering economic efficiency (cost minimization)
and distributive impacts among stakeholders. This approach must be followed by transposition to real conditions in the field: locations selected on the basis of the areas that really need electrification and the amount of electricity potentially consumed in these regions according to the types of consumers. Results for each country are obviously dependent on the solar resource of the selected locations and the average of the MG CFP should be weighted by the estimated energy consumption of each MG.

Author Contributions: conceptualization and methodology: T.C., B.H. and S.M.; software, formal analysis, writing - original draft preparation: T.C.; writing - review and editing T.C., B.H. and S.M.

Conflict of Interest: The authors declare no conflict of interest.

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

# Appendix A - Methods

## Method for MG simulation

We consider fictitious hybrid MG using solar PV, diesel genset and batteries to supply typical load profiles. We simulate the functioning of these MGs over two years using meteorological data to estimate the solar PV production and simple dispatch rules for the batteries and the genset to ensure that the electrical consumption is fully supplied. These simulations are performed for a large range of configurations (PV panels and storage capacities) to compute the LCOE and the CFP and determine the ones that minimize the LCOE. The following presents the different steps of these simulations and calculations, it was adapted from (Chamarande et al., 2024b) as the same methodology was applied for MG modeling.

### PV production

The solar PV production is estimated at 15 min resolution using the global horizontal irradiance (GHI) from Heliosat SARAH 2 (Pfeifroth et al., 2017) and the air temperature from ERA5 reanalysis (Hersbach et al., 2020). These data are taken over two years for each location.

First, the decomposition model of the Sandia National Laboratory (Maxwell, 1987) is used to compute the direct (DNI) and the diffuse (DHI) irradiances from the global horizontal irradiance (GHI) and solar angles. Then, the global tilted irradiance (GTI) is calculated using equation (A.1).

$$GTI = DNI \cdot \cos(\theta) + DHI \qquad (A.1)$$

Where $\theta$ is the “effectiveness” angle, a function of solar angles and panel inclinations and orientation. For this study, we assume that PV panels have a tilt angle equal to the latitude (Bahrami, 2016) and are oriented towards the south (resp. north) in northern (resp. southern) hemisphere. Then, the estimated solar PV production is estimated using equation (A.2) as in [42]:

$$P = \eta_{PV} \cdot (1 + \alpha(T_m - 25^{\circ}C)) \cdot C_{PV} \cdot \frac{GTI}{1000 \frac{W^2}{m}} \qquad (A.2)$$
Where $C_{PV}$ [$W_p$] is the peak power of installed PV panels, $1000 \frac{W}{m^2}$ corresponds to the irradiance at standard conditions, $\bar{\bar{\bar{\bar{\Gamma}}}}$ is the sensitivity of panel efficiency to the module temperature $T_m$ which is computed using equation (A.3) and $\bar{\bar{\bar{\bar{\Gamma}}}}_{PV}$, the panel efficiency that accounts for inverter efficiency and losses of the PV production system.

$$T_m = T_{amb} + \gamma \cdot GTI \qquad (A.3)$$

Where $T_{amb}$ is the ambient temperature and $\gamma$ is a parameter related to the mounted type of the system (roof integrated, free standing...). We consider a mean value: $\bar{\bar{\bar{\bar{\Gamma}}}} = 0.04 \cdot C \cdot \frac{m^2}{W}$ and for the sensitivity of the panel efficiency to temperature, we take the value for crystalline silicon cells: $\bar{\bar{\bar{\bar{\Gamma}}}} = -0.0035/^{\circ}C \cdot [42]$.

## Demand

Figure A.1 shows three different daily load profiles which are estimated from the literature for a fictitious community (Huld et al., 2017; Li et al., 2018; Louie, 2018; Mandelli et al., 2017). The mean power demand $\bar{D}$ is the same for the three profiles to allow comparisons of the results. The hybrid load profile is a mix between a load profile for productive uses and one for domestic uses of electricity. The productive uses consume mostly during the day whereas a domestic load profile is characterized by a high peak demand in the evening and electricity consumption at night.

<caption>Figure A.1: Three daily load profiles used in the study</caption>

We consider that the energy demand is the same for each day throughout the year.

## Battery modelling and energy dispatch

A simple modelling is used for battery storage with the same efficiency for charge and discharge: $\bar{\bar{\bar{\bar{\Gamma}}}}_{sto} = 0.95$. We assume that the storage can only be charged by a solar PV production higher than the demand, so the genset cannot be used to charge the batteries. If PV production is higher than the demand and storage is full, the production is curtailed. If the PV power is below the demand, both the genset and the batteries can supply the demand. To reduce genset consumption, the energy dispatch rule is to maximize the genset efficiency, i.e., it is used as close as possible to its nominal power. The battery is therefore mainly used during the lowest consumption hours.
<figure><img src="image_15.png" /><figcaption>Figure A.2: Simulation of solar, genset and batteries dispatching for a few days in March. The y-axis corresponds to a normalized power: 1 corresponds to the mean power demand.</figcaption></figure>

The hours of the sequence that cannot be supplied with the storage are supplied by the genset (Figure A.2). The power to be produced by the genset for each time of the simulation period gives the total fuel consumption for the period, and in turn the direct emissions of the genset. The fuel consumption $f_{conso}(t)[L]$ at time t is estimated as:

$$f_{conso}(t) = \frac{E_{gen}(t)}{HV_f * \eta_{gen} \left(\frac{P_{gen}(t)}{K_{gen}}\right)} \quad (A.4)$$

Where $E_{gen}(t)[kWh]$ is the electrical energy to be supplied by the genset at time t, where $P_{gen}(t)[kW]$ and $\eta_{gen}$ [-] are the genset power and efficiency, and $K_{gen}$ its nominal power, and where $HV_f = 10 \frac{kWh}{L}$ is the heating value of diesel. Following (Getnet Tadesse Ayele, 2014; Stiel and Skyllas-Kazacos, 2012), the genset efficiency is considered as a function of its load factor $\frac{P_{gen}(t)}{K_{gen}}$ (cf. Figure A.3). To make sure that the electric demand is always supplied, the genset nominal power is set to the maximum value of the electric load profiles, e.g. $K_{gen} \approx 3D$ for the domestic load profile (cf. Figure A.1).

<figure><img src="image_16.png" /><figcaption>Figure A.3: Genset efficiency $\eta_{gen}$ as a function of its load factor $\frac{P_{gen}}{K_{gen}}$. This efficiency is the ratio of the electricity output of the genset on the thermal energy from the fuel.</figcaption></figure>
## CFP calculation

The CFP is calculated per kWh of supplied energy. It encompasses the emissions related to the whole lifecycle of the components, from the mining of the material needed and the manufacturing to the end-of-life of the components. The total CFP<sub>tot</sub> [tCO2] of the MG is estimated from the CFP values of the different MG components:

$$CFP_{tot} = K_{bat}CFP_{bat}\left(1 + \frac{L}{L_{bat}}\right) + K_{PV}CFP_{PV} + K_{gen}CFP_{gen}\left(1 + \frac{L}{L_{gen}}\right) + CFP_{fuel}F_{conso} \quad (A.5)$$

Where $K_{bat}$[kWh], $K_{PV}$[p], $K_{gen}$[kW] are respectively the capacity installed for the batteries, the PV panels and the genset; $CFP_{bat}$[tCO<sub>2</sub>/kWh], $CFP_{PV}$[tCO<sub>2</sub>/kW<sub>p</sub>], $CFP_{gen}$[tCO<sub>2</sub>/kW], $CFP_{fuel}$[tCO<sub>2</sub>/L] are respectively the carbon footprint associated to 1kWh of installed batteries, 1kW<sub>p</sub> of installed PV, 1kW of genset power capacity and 1L of fuel; $F_{conso}$[L] is the fuel consumption over the lifetime of the project L[yrs] and $L_{bat}$[yrs], $L_{gen}$[yrs] are respectively the lifetime of batteries and genset. We consider a project lifetime of 15 years, so we assume that it is not needed to replace the PV panel. The genset lifetime in years $L_{gen}$ is derived from a lifetime expressed in functioning hours $L_{gen,hrs}$[hrs] using equation (A.6) with $F_{use}$[hrs] the number of the genset use hours over the whole project lifetime:

$$L_{gen} = \frac{L_{gen,hrs}}{\frac{F_{use}}{L}} \qquad (A.6)$$

Finally, the carbon footprint by kWh of energy supplied CFP is given by equation (A.7):

$$CFP = \frac{CFP_{tot}}{E_{supply}} \qquad (A.7)$$

Where $E_{supply}$[kWh] is the energy supplied over the project lifetime.

Values taken for the different parameters used in this calculation are given in Table A.1 and correspond to mean values estimated by Besseau in (Besseau, 2019).

<table><thead><tr><th>CFP<sub>bat</sub> [tCO<sub>2</sub>/kWh]</th><th>CFP<sub>PV</sub> [tCO<sub>2</sub>/kW<sub>p</sub>]</th><th>CFP<sub>gen</sub> [tCO<sub>2</sub>/kW]</th><th>CFP<sub>fuel</sub> [tCO<sub>2</sub>/L]</th></tr></thead><tbody><tr><td>0.3</td><td>1</td><td>0.02</td><td>2.6x10<sup>-3</sup></td></tr></tbody></table>

<table><caption>Table A.1: Parameter values used for the CFP calculation. CFP<sub>PV</sub> and CFP<sub>Bat</sub> also include the carbon footprint for inverters.</caption><thead><tr><th>L[yrs]</th><th>L<sub>bat</sub>[yrs]</th><th>L<sub>gen,hrs</sub>[hrs]</th></tr></thead><tbody><tr><td>15</td><td>7</td><td>25000</td></tr></tbody></table>

### 4.1.1 LCOE calculation

We do not include the cost related to the distribution system in the LCOE calculation. As for the CFP, total system costs are estimated using costs by unit of installed component and by litre of diesel fuel consumption (cf. equation (A.8)).
$$C_{tot} = K_{bat}\alpha_{bat} + K_{PV}\alpha_{PV} + K_{gen}\alpha_{gen} + C_{fuel}\sum_{yr=1}^{L}\frac{F_{conso,yr}}{(1+d)^{yr}} \quad (A.8)$$

Where $C_{fuel}$ [$\$L$] is the cost of 1L of fuel, $F_{conso,yr}$ [L] is the fuel consumption for one year; d is the discount rate and $\alpha_{bat}$ [-], $\alpha_{PV}$ [-] and $\alpha_{gen}$ [-] are the costs related to installation, replacement and maintenance of the components over their lifetime as shown by equations (A.9), (A.10) and (A.11).

$$\alpha_{bat} = C_{bat} \cdot \left( \frac{1 - (1 + d)^{(L+L_{bat})}}{(1 + d)^L - (1 + d)^{(L+L_{bat})}} + \sum_{k=1}^{L} \frac{P_{O\wedge M,bat}}{(1 + d)^k} \right) \quad (A.10)$$

$$\alpha_{PV} = C_{PV} \cdot \left( 1 + \sum_{k=1}^{L} \frac{P_{O\wedge M,PV}}{(1+d)^k} \right) \quad (A.11)$$

$$\alpha_{gen} = C_{gen} \cdot \left( \frac{1 - (1 + d)^{(L+L_{gen})}}{(1 + d)^L - (1 + d)^{(L+L_{gen})}} + \sum_{k=1}^{L} \frac{P_{O\wedge M,gen}}{(1 + d)^k} \right) \quad (A.12)$$

Where $C_{bat}$ [$\$kWh$], $C_{PV}$ [p], $C_{gen}$ [$\$kW$] are respectively the installation costs associated to 1kWh of installed batteries, $1kW_p$ of installed PV and $1kW$ of genset; and $P_{O\wedge M,bat}$ [-], $P_{O\wedge M,PV}$ [-] and $P_{O\wedge M,gen}$ [-] are proportionality coefficients between investment and maintenance costs related to each component (maintenance and operation costs are assumed to be time invariant and proportional to the investment cost of each component). The mean values considered for the different parameters are given in Table A.2 (IRENA, 2017, 2016a, 2016b).

<table><thead><tr><th>C<sub>bat</sub> [$\$kWh$]</th><th>C<sub>PV</sub> [p]</th><th>C<sub>gen</sub> [$\$kW$]</th><th>C<sub>fuel</sub> [$\$L$]</th></tr></thead><tbody><tr><td>350</td><td>1900</td><td>500</td><td>1 (0.6 for Nigeria)</td></tr></tbody></table>

<table><caption>Table A.2: Parameters values for the LCOE calculation, lifetimes of components are given in Table A.1, $C_{PV}$ and $C_{Bat}$ also include the costs for inverters.</caption><thead><tr><th>P<sub>O∧M,bat</sub> [%]</th><th>P<sub>O∧M,PV</sub> [%]</th><th>P<sub>O∧M,gen</sub> [%]</th><th>d [%]</th></tr></thead><tbody><tr><td>3</td><td>2</td><td>10</td><td>10</td></tr></tbody></table>

Finally, the LCOE is computed using equation (A.13):

$$LCOE = \frac{C_{tot}}{\sum_{k=1}^{L} \frac{E_{supply}}{(1+d)^k}} \quad (A.13)$$
4.1.2 Estimation of the envelope curve

By setting a configuration (K<sub>bat</sub>, K<sub>PV</sub>), we can simulate the functioning of the MG and compute the diesel consumption required over the project lifetime such that 100% of the electricity demand is supplied. Then, using this diesel consumption and this (K<sub>bat</sub>, K<sub>PV</sub>) values, we calculate the LCOE and the CFP associated to this configuration. We do so for a large range of configurations i.e. a range of couples (K<sub>bat</sub>, K<sub>PV</sub>) that could have a storage capacity in the range 1 to 20 hours of mean demand equivalent [hrs<sub>eq</sub>] with a step of 0.5hrs<sub>eq</sub>, and a PV capacity in the range of 0 to 2.5 K<sup>0</sup><sub>PV</sub> with a step of 0.01. One hrs<sub>eq</sub> of storage corresponds to D × 1hr = DkWh and it has been found that, in a 100% PV MG configuration, a storage capacity equivalent to 15 to 20hrs<sub>eq</sub> allow to satisfy more than 95% of the demand, whatever the location in Africa (e.g. (Chamarande et al., 2021)). To ease the comparison between sites, we use a normalized PV capacity in the following corresponding to the ratio K<sub>PV</sub>/K<sup>0</sup><sub>PV</sub>.

The lowest LCOE (LCOE*) configuration can be estimated by selecting the couple (K<sub>bat</sub>, K<sub>PV</sub>) with the
minimum LCOE from the simulated configurations.

Figure A.4: Lowest LCOE (LCOE*) and lowest CFP (CFP*) configurations in a LCOE vs. GHG graph. The black line is the envelope curve. The colour gives the normalized PV capacity installed (dark dots refer to configuration with low penetration of solar, and light dots to high penetration of solar) and the size of the dots gives the normalized storage capacity installed. Each U-shape line corresponds to a given storage capacity (only one out of three storage capacities simulated is represented). Each point of each line to a given PV capacity. To each point corresponds finally a given genset production, i.e. the production required to satisfy the demand all along the period. This graph is obtained for a location in Angola (-12.5°N; 17.5°E) with a hybrid load profile

The LCOE and CFP values obtained for all simulated PV capacity/storage configurations can be
presented in a (CFP, LCOE) graph. As illustrated in Figure A.4 for a given location, not all (LCOE, CFP)
MG combinations are possible. As an example, it is not possible here to have a LCOE below 0.37 and
a CFP below 200$\frac{g\text{CO}_2}{\text{kWh}}$. Thus, by selecting the lowest LCOE value obtained for each value of CFP, it is
possible to draw a curve that defines the limit between the (LCOE, CFP) values that are possible and
the ones that are not. This curve is used in sections 2.1 and 2.2 to illustrate the effect of adding a
price to the carbon footprint.
We can notice that this curve consists in two parts: a first part from the diesel only configuration to the LCOE* configuration where an increase of the PV capacity allows to reduce both the LCOE and the CFP, and a second part from the LCOE* configuration to the CFP* one, which corresponds to the pareto front between the LCOE and the CFP. Keeping these two parts, and not only the second one, allows to see how the progressive integration of solar energy modifies the LCOE and the CFP values.

Note also that we decided to impose a 100% reliability level for the sizing of mini-grids but lower reliability levels can be considered. For instance, a reliability level of 90% would modify the envelope curve (cf. Appendix B, Figure B.7) presented above (Figure A.4), and thus, the results presented in this article. However, preliminary analyses on the marginal cost of carbon indicate that the results would not be largely modified.

## Appendix B - Supplementary Figures

<table><caption>Table B.1: Mean values and variations of the CFP for the LCOE* and CFP* configurations for the four countries</caption><thead><tr><th></th><th>Kenya</th><th>Senegal</th><th>Nigeria</th><th>Madagascar</th></tr></thead><tbody><tr><td>Mean CFP of LCOE* configuration [gCO2/kWh]</td><td>403</td><td>386</td><td>724</td><td>464</td></tr><tr><td>Coefficient of variation of the CFP of LCOE* configuration [%]</td><td>8.4</td><td>2.0</td><td>27</td><td>14</td></tr><tr><td>Mean CFP of CFP* configuration [gCO2/kWh]</td><td>197</td><td>196</td><td>203</td><td>221</td></tr></tbody></table>

<figure><img src="image_17.png" /><figcaption>Figure B.1: CFP of the LCOE* configuration for each location in the four countries with a hybrid load profile in the BAU case. From left to right: Kenya, Senegal, Nigeria, Madagascar</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>Figure B.2: Cost indicators variations related to the implementation of a fuel tax, PV subsidy and battery subsidy for Kenya and Nigeria, and a hybrid load profile. Curves are obtained with a subsidy level between 0 and 100% and a fuel tax level between 0 and 1200%. The CFP price curves are the same as in Figure 7. The green stars in the curves refer to different levels of subsidies or fuel tax. From the right of the graph to its left, they represent subsidy levels of 0%, 25%, 50% and 75% and fuel tax of 0%, 150%, 300%, 450%, 600%, 750%, 900% and 1050%.</figcaption></figure>

<table><caption>Table B.2: Fuel tax levels [%] to reach a given CFP reduction objective.</caption><thead><tr><th>CFP reduction [%]</th><th>Kenya</th><th>Senegal</th><th>Nigeria</th><th>Madagascar</th></tr></thead><tbody><tr><td>-10</td><td>14</td><td>15</td><td>7</td><td>15</td></tr></tbody></table>
<table><tr><td>-20</td><td>28</td><td>29</td><td>16</td><td>31</td></tr><tr><td>-30</td><td>41</td><td>39</td><td>31</td><td>45</td></tr><tr><td>-40</td><td>53</td><td>58</td><td>62</td><td>72</td></tr><tr><td>-45</td><td>98</td><td>146</td><td>75</td><td>112</td></tr><tr><td>-50</td><td>570</td><td>Unreachable</td><td>97</td><td>255</td></tr><tr><td>-60</td><td>Unreachable</td><td>Unreachable</td><td>134</td><td>Unreachable</td></tr><tr><td>-70</td><td>Unreachable</td><td>Unreachable</td><td>387</td><td>Unreachable</td></tr></table>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /><figcaption>Figure B.3: LCOE disparities (tax/sub included) related to the implementation of a CFP price, a fuel tax, a PV subsidy and a battery subsidy for each MG of Kenya and Nigeria. BAU refers to the business as usual case, where no policy is implemented. In the other cases, a 30% CFP reduction is achieved at the national level.</figcaption></figure>
<figure><img src="image_21.png" /><figcaption>Figure B.4: Cost indicators variations related to the implementation of PV and battery subsidies, a bonus/malus and a fuel tax with redistribution for Kenya and Nigeria, and a hybrid load profile. The four gray curves are the same as in Figure 7 and Figure B.2.</figcaption></figure>
<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

Figure B.5: LCOE disparities (tax/sub included) related to the implementation of a CFP price, a fuel tax, a PV subsidy and a battery subsidy for each MG of Kenya and Nigeria. BAU refers to the business as usual case, where no policy is implemented. In the other cases, a 40% CFP reduction is achieved at the national level. Using a subsidy only on PV ("PV sub") or on batteries ("Bat sub") does not allow to reach the 40% reduction level, hence the absence of boxplot.

<table><caption>Table B.3: Optimal subsidies and taxations levels for each policy to reach the maximum CFP reduction possible with a 5% tolerance. These values are obtained for the four countries and a hybrid load profile.</caption><thead><tr><th rowspan="2">Policy</th><th>Tax</th><th colspan="2">Sub</th><th colspan="3">Bonus/Malus</th></tr><tr><th>Fuel tax [%]</th><th>PV sub [%]</th><th>Bat sub [%]</th><th>PV sub [%]</th><th>Bat sub [%]</th><th>Fuel tax [%]</th></tr></thead><tbody><tr><td>Kenya</td><td>246</td><td>75</td><td>28</td><td>14</td><td>1</td><td>189</td></tr><tr><td>Senegal</td><td>220</td><td>72</td><td>50</td><td>14</td><td>1</td><td>176</td></tr><tr><td>Nigeria</td><td>508</td><td>83</td><td>61</td><td>18</td><td>1</td><td>382</td></tr><tr><td>Madagascar</td><td>248</td><td>75</td><td>52</td><td>17</td><td>1</td><td>199</td></tr></tbody></table>
<figure><img src="image_24.png" /><figcaption>Figure B.6: Comparison of policy indicators for Kenya (left) and Nigeria (right) considering a 30% CFP reduction objective. Each graph gathers the CFP price, fuel tax, PV subsidies and battery subsidies and the combined instruments (both PV and battery subsidies, Bonus/Malus and Fuel + redistribution of tax revenues). The LCOE disparities indicator is calculated as the coefficient of variations of the LCOE for all locations in the country. The axes are built such that a good performance for an indicator is far from the graph centre, e.g. "Tax+red" has the best performance for "LCOE disparities".</figcaption></figure>

<figure><img src="image_25.png" /></figure>
Figure B.7: Comparison of the “envelope curves” (LCOE=f(CFP)) for one location in each country obtained with a reliability level of 100% (use in all the article) and a reliability of 90%, meaning that 10% of the energy demand is not supplied.

<figure><img src="image_26.png" /></figure>

Figure B.8: Comparison of the mean national marginal cost of carbon in each country obtained with a reliability level of 100% (use in all the article) and a reliability of 90%, meaning that 10% of the energy demand is not supplied. The red dashed lines presented here are the same as the ones presented in Figure 6. The same methodology to estimate these curves was applied for the blue curves.

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