# Multiple-scale distributed PV potential penetration in a densely populated city: A case study of Grand Paris metropolis

Qiqi Tao, Alexis Tantet, Jordi Badosa, Sylvain Cros, Philippe Drobinski

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Qiqi Tao, Alexis Tantet, Jordi Badosa, Sylvain Cros, Philippe Drobinski. Multiple-scale distributed PV potential penetration in a densely populated city: A case study of Grand Paris metropolis. Sustainable Cities and Society, 2025, 122, pp.106232. 10.1016/j.scs.2025.106232. hal-05345170

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# Multiple-scale distributed PV potential penetration in a densely populated city: A case study of Grand Paris metropolis

Qiqi Tao<sup>D*</sup>, Alexis Tantet, Jordi Badosa, Sylvain Cros, Philippe Drobinski<sup>*</sup>

LMD/IPSL, École Polytechnique, Institut Polytechnique de Paris, ENS, Université PSL, Sorbonne Université, CNRS, Palaiseau, France

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## ARTICLE INFO

### Keywords:

- Energy transition

- Rooftop photovoltaic (PV)

- Energy balance

- Renewable energy

- Self-consumption

- Self-sufficiency

## ABSTRACT

Urban sustainability is a critical challenge for climate action, and increased photovoltaic (PV) production is expected to help meet this challenge. However, due to the variable nature of PV, its integration adds complexity to grid management, requiring careful consideration of the energy balance. This study addresses the challenges of energy transition and urban sustainability in densely populated cities through a case study of rooftop photovoltaic (PV) integration in the Grand Paris metropolis. Focusing on energy balance metrics such as self-consumption rate (SCR) and self-sufficiency rate (SSR), the research explores the benefits of distributed PV installations across residential and commercial sectors. Using hourly electricity consumption profiles and PV generation data, the analysis evaluates the impact of energy-sharing schemes within and across urban subregions (city center and semi-urban periphery) and between sectors. The results show that, over an extended scope, cross-sector energy sharing can improve SCR and SSR by up to 6.5% across sectors and 10% across geographical subregions. 3.19 TWh of regional residential consumption and 0.44 TWh of commercial consumption could be covered by PV, accounting for 22.4% of the total for both sectors. The periphery benefits significantly from increased SSR, linked to lower building density and higher PV capacity. Economically, rooftop PV reduces energy costs most in peripheral regions, with expanded energy-sharing perimeters enabling additional savings for central areas. These findings suggest that broader energy-sharing frameworks in metropolitan areas can optimize PV utilization, enhance grid stability, and contribute to resilient, sustainable urban energy systems.

## 1. Introduction

Cities are geographic units that significantly impact climate change and have a substantial potential for implementing climate mitigation measures (Davi et al., 2022). Urban sustainability will be one of the primary challenges of this century (Cuesta-Fernández et al., 2023; Droege, 2018; Mi et al., 2019; Pincel, 2017). Emerging concepts like Positive Energy Districts (PEDs) showcase the potential of urban districts to go beyond net-zero energy goals by actively generating surplus renewable energy through integrated strategies, including photovoltaic (PV) systems and energy-efficient urban designs (Castillo-Calzadilla et al., 2023). The ongoing urbanization process will generate resource availability and sustainability issues at local and global levels, which must be addressed effectively. Led by several initiatives, such as the Covenant of Mayors and the Global Urban Platform C40, hundreds of cities worldwide have committed to decarbonizing or becoming carbon neutral as soon as possible (Hoffmann, 2011; Van Der Heijden, 2016). However, achieving these targets requires addressing critical energy challenges within the dense fabric of urban areas. Given the

spatial density of population and energy consumption, decarbonizing large metropolitan areas is critical for contributing to the EU's net-zero carbon target (Cramer et al., 2018; Cuesta-Fernández et al., 2023).

In this context, the Grand Paris metropolis, as one of the largest and most energy-intensive cities in Europe, provides a compelling case study. Paris and its suburbs cover only 0.15% of France's metropolitan territory, with an area of 814 square kilometers, but are home to more than 7 million people, or 10% of the country's population. The region consumes 67% of its energy from fossil fuels, with only 10% of its energy supply produced locally (7.4% from renewable energy and energy recovery) (Drobinski et al., 2022). Responsible for 10% of the country's greenhouse gas emissions, the Grand Paris metropolis must address various energy-related challenges, such as high population density, energy dependency, and vulnerability to climate change.

The French government has set ambitious targets to increase the share of renewable energy in the national energy mix, aiming to achieve a 40% share of renewable energy by 2030. Rooftop photovoltaics (PV) presents a promising opportunity to contribute to this

<footnote>* Corresponding author.
E-mail addresses: qiqi.tao@hotmail.com (Q. Tao), philippe.drobinski@lmd.ipsl.fr (P. Drobinski).</footnote>
## Nomenclature with units

### Abbreviations

<table><tr><td>ENS</td><td>Energy not supplied</td></tr><tr><td>PV</td><td>Photovoltaic</td></tr><tr><td>SAIDI</td><td>System Average Interruption Duration Index (hours)</td></tr><tr><td>SDFC</td><td>Short duration failure cost (€/kWh)</td></tr><tr><td>PRO</td><td>The commercial sector</td></tr><tr><td>RES</td><td>The residential sector</td></tr></table>

### Economic variables

<table><tr><td>C<sub>y</sub><sup>inverter</sup></td><td>Annualized investment costs of on-grid PV inverter (€/kWp/year)</td></tr><tr><td>C<sub>y</sub><sup>LL</sup></td><td>Cost of lost load (€)</td></tr><tr><td>C<sub>y</sub><sup>PV</sup></td><td>Initial investment cost of on-grid PV panels (€/kWp)</td></tr><tr><td>C<sub>y</sub><sup>PV</sup></td><td>Annualized investment costs of on-grid PV panels (€/kWp/year)</td></tr><tr><td>π<sub>a</sub></td><td>Initial purchase price for each kilowatt-hour of electricity consumed (€/kWh)</td></tr><tr><td>π<sub>v</sub></td><td>The feed-in tariff (FIT) (€/kWh)</td></tr><tr><td>P<sup>Peak</sup></td><td>Peak demand (kW)</td></tr></table>

### Electricity variables

<table><tr><td>β</td><td>Temperature sensitivity coefficient (kWh/K)</td></tr><tr><td>E<sup>b</sup></td><td>Basic electricity consumption (kWh)</td></tr><tr><td>E<sup>C</sup></td><td>Electricity energy consumption (kWh)</td></tr><tr><td>E<sup>PV</sup></td><td>PV production (kWh)</td></tr><tr><td>E<sup>SC</sup></td><td>Electricity energy consumption covered by PV (kWh)</td></tr><tr><td>E<sup>th</sup></td><td>Temperature-sensitive electricity consumption (kWh)</td></tr><tr><td>P<sup>C</sup></td><td>Electricity consumption power (W)</td></tr><tr><td>P<sup>PV</sup></td><td>PV power (W)</td></tr><tr><td>CDD</td><td>Cooling degree-days (K)</td></tr><tr><td>HDD</td><td>Heating degree-days (K)</td></tr><tr><td>NC<sub>i</sub></td><td>Converted number of households or commercial users per IRIS</td></tr><tr><td>NC</td><td>Total regional number of households or commercial users</td></tr><tr><td>NCI</td><td>Number of households or commercial users per IRIS from annual data</td></tr><tr><td>SCR</td><td>Self-consumption rate (%)</td></tr><tr><td>SSR</td><td>Self-sufficiency rate (%)</td></tr></table>

For example, the French Electricity Transmission System Operator (known as RTE) has proposed several future energy scenarios, of which Scenario M1 emphasizes distributed PV (i.e., rooftop PV) and that 35 GW of residential rooftop PV is looking forward to being installed in France by 2050 (about half of all individual houses) (RTE, 2021) under this scenario. According to International Energy Agency (2023), solar power will dominate future electricity generation technologies, accounting for 30% of global electricity generation by 2050. Among the proposed technologies, distributed rooftop PV is strongly promoted through subsidies in many countries (Avril et al., 2012; Nousdilis et al., 2018; The European Commission, 2016).

The benefits of distributed PV generation are various. It helps diversify energy sources, improves grid efficiency by reducing transmission

losses (Begovic & Kim, 2011; Hoff & Shugar, 1995), and enables local consumption, reducing extraction from the grid (Ambabile et al., 2021; Nousdilis et al., 2018). Distributed PV is also instrumental in advancing electrification goals (Torres-Rivas et al., 2022), and promoting the environmental sustainability of urban areas, especially in the context of the European requirement for near-zero energy buildings (European Parliament and Council, 2021). This shift toward local consumption and decentralized generation, accelerated by economic factors such as lower electricity tariffs and reduced investment costs, signifies a transformative change in energy production and consumption patterns. Additionally, decentralized energy generation empowers citizens by increasing their control over energy resources (Vernay et al., 2023).

Under the beneficial context of distributed PV generation, a growing body of research in rooftop photovoltaic deployment focuses on assessing the potential for urban PV power generation (Fakhraian et al., 2021). Typically, these studies use high-resolution spatial tools, such as Geographic Information Systems (GIS) (An et al., 2023; Chen et al., 2022; Gassar & Cha, 2021; Groppi et al., 2018; Kodysh et al., 2013), or statistical models based on building typologies (Fakhraian et al., 2021; Saez et al., 2024; Shi et al., 2021) or stratified-sample vector GIS maps (Izquierdo et al., 2008), to quantify self-generation capacity within urban environments. For example, Torres-Rivas et al. (2022) found that rooftop PV systems could supply 8%-30% of residential electricity in Catalonia, while Montero et al. (2022) observed that dedicating 30%-50% of roof space to PV in 14 hospitals in southwestern Spain could cover up to 30% of their energy needs. In Osaka, Japan, Yuan et al. (2016) demonstrated that rooftop PV might cover 56% of commercial and 34% of industrial electricity demands. Guillén-Lambea et al. (2023) used the Energy Self-Sufficiency Urban Module (ESSUM) framework to evaluate urban districts' solar energy potential using GIS and LCA methodologies, revealing that prioritizing rooftop installations can achieve up to 20% electricity self-sufficiency and substantial reductions in CO2 emissions. These studies emphasize PV deployment's immense but location-dependent potential, especially in dense urban areas where maximizing self-generation faces unique challenges (Fina et al., 2019; Natanian et al., 2019; Vulkan et al., 2018).

However, due to the variable nature of distributed PV, their integration introduces complexity into grid management (Bacha et al., 2015; Mansouri et al., 2019; Wan et al., 2015). A generation that does not match demand will be injected into the grid, potentially leading to reverse power flows and voltage fluctuations, destabilizing grid operations (Olowu et al., 2018). These issues require careful energy balancing to maintain grid reliability and quality. Indeed, the increasing amount of distributed rooftop PV implies an increasingly complex energy balance. Severe imbalances imply (1) the need for additional generation capacity in other interconnected areas in the face of growing electricity consumption, (2) possible upward adjustments in the transmission capacity of distribution and transmission networks if congestion issues occur, and (3) additional line losses.

As cities increasingly shift toward decentralized energy models, ensuring grid resilience and efficiency will require innovative solutions (Hoff & Shugar, 1995; Torres-Rivas et al., 2022). Energy sharing among PV consumers has emerged as an effective solution to address PV surplus and reduce storage system investments (Diab et al., 2024). Different definitions such as energy communities, peer-to-peer, and transactive energy markets are given in previous studies (Capper et al., 2022; Gorbatcheva et al., 2024; Schwidtal et al., 2023) and the economic objectives are mostly the key focus to maximize the energy sharing profitability (Cosic et al., 2021; D'Adamo et al., 2024; Fina et al., 2022; Reis et al., 2022; Roy et al., 2023; Viti et al., 2020). On the other hand, technical aspects of energy sharing schemes such as the energy allocation rules have also been studied (Contreras-Ocana et al., 2021; Gjorgievski et al., 2022; Roy et al., 2023). The time scale is another key factor that will impact the accuracy of the energy balance analysis as indicated by Saez et al. (2024) and hourly data are more
<figure><img src="image_4.png" /><figcaption>**Fig. 1.** (a) Map of the ratios between residential electricity consumption $E^{RES}$ over the sum of residential and commercial electricity consumptions $E^{RES} + E^{PRO}$ for the Grand Paris metropolis with white lines representing more than 2700 IRIS cells (Ilots Regroupés pour l'Information Statistical). The thick black line outlines Paris, surrounded by its periphery. During the present study, the smaller center is named Paris center, and the periphery is named Paris surroundings. The inset map shows in blue an example of rooftop areas identified by APUR (2019). (b) Ratios between the favorable rooftop surfaces for PV installation (i.e. for which the radiation potential is greater than 1000 kWh/m² per year) and the inhabitable housing surfaces estimated using the APUR data. (Both maps and the subsequent ones are produced for a plate carrée projection.)</figcaption></figure>

suitable for actual self-consumption analysis. Beyond technical assessments, regulatory frameworks and economic incentives such as feed-in tariffs (FiT) and tax exemptions, play a pivotal role in shaping the adoption rates of rooftop PV across different regions (Agdas & Barooah, 2023; Campoccia et al., 2014; Castaneda et al., 2018; Dong et al., 2021; Escobar et al., 2020; Nguyen et al., 2023; Schick & Hufendiek, 2023). In the case of France, FiTs and tax exemptions reinforce the energy-sharing model, which are key drivers in promoting rooftop PV in both residential and commercial sectors. The legal framework currently supports electricity sharing within communities, allowing users within a maximum distance of 10 km (up to 20 km by ministerial dispensation) to share locally produced electricity (Escobar et al., 2020). Finally, the impact of large-scale deployment of rooftop PV in several European countries has been studied. Arcos-Vargas et al. (2019) suggests a combination of roof-mounted (72%) and ground-mounted (25%) photovoltaic (PV) panels could meet most of the city's energy needs. In Italy, Canova et al. (2022) proved that collective self-consumption schemes for residential buildings have shown promise, with potential cost savings of up to 32% and carbon emissions reductions of up to 60% when combining PV systems with heat pumps. And Cuesta-Fernández et al. (2023) studied the metropolitan areas of Valencia and found that rooftop PV in the whole metropolitan area could potentially cover 79.2% of residential electricity demand and thanks to including the metropolitan area, PV coverage rate improves by 30%.

Despite the growing recognition of the potential for rooftop photovoltaics (PV) to contribute to urban sustainability, significant research gaps persist in this field. Many existing studies predominantly focus on one single sector (mostly the residential sector), neglecting the potential benefits of energy exchange across various sectors – such as commercial and industrial – within metropolitan areas, which could enhance overall PV utilization rates. Meanwhile, the economic interests of consumers indirectly impact rooftop PV promotion and affect the difficulty of implementing new energy policies on a large scale.

Additionally, policy-oriented large-scale deployment analyses often rely on annual data, leading to an overestimation of profitability and self-consumption capabilities. While there is considerable detail in assessing PV potential, energy consumption data frequently lack the same level of accuracy, particularly regarding spatial and temporal resolutions. This discrepancy underscores the need for comprehensive assessments that not only quantify PV potential but also accurately reflect the complex dynamics of energy consumption in densely populated urban settings. Addressing these gaps is crucial for optimizing rooftop PV deployment and achieving ambitious renewable energy targets in metropolitan regions.

This study aims to address these gaps by systematically examining the interplay between rooftop PV deployment and electricity supply-demand dynamics across multiple scales within the Grand Paris metropolis, where the center of Paris and its surroundings show different characteristics (e.g., Fig. 1(a) shows the ratio of residential electricity consumption over both residential and commercial electricity consumption, whereas Fig. 1(b) shows the ratio of the useful roof area to the residential area). Specifically, we aim to:

* Quantify the extent to which rooftop PV installations contribute to electricity supply-demand balance at scales ranging from neighborhoods of approximately 2000 people to the entire metropolis, encompassing 12 million residents.

* Analyze the spatial and temporal variations in energy balance across central Paris and its peripheral areas, leveraging hourly real-time electricity consumption data downscaled for residential and small commercial sectors.

* Investigate the role of inter-sectoral energy exchanges in optimizing PV utilization and reducing grid instability.

* Evaluate the self-consumption rate (share of consumption covered by PV relative to total production) and self-sufficiency rate (share of consumption covered by PV relative to total consumption) as
indicators of PV deployment efficiency across urban and suburban settings.

To achieve these objectives, we employ a novel methodology that integrates a temperature-sensitive consumption model to estimate the hourly evolution of electricity consumption per consumer for the residential and commercial sectors, allowing to downscale hourly real-time electricity consumption geographically (Albert & Rajagopal, 2015; Gouveia et al., 2017). This allows for a robust assessment of rooftop PV's contribution to grid stability and energy cost reduction. The novelty of this study lies in its multi-scale geographic analysis, its inclusion of inter-sectoral energy exchange dynamics, and its use of an hourly real-time consumption dataset, enhanced with a downscaling methodology adaptable to large territorial coverage. To measure the contribution of rooftop PV to the electricity balance, we use two metrics: the self-consumption rate, defined as the share of consumption covered by PV relative to total production, and the self-sufficiency rate, defined as the share of consumption covered by PV relative to total consumption. These metrics are indeed key indicators for evaluating PV surplus performance (Gjorgievski et al., 2020; Luthander et al., 2015; Salom et al., 2011).

The paper is organized into four sections. Section 2 describes the methodology of energy balance evaluation, the consumption model, and the data used for the Grand Paris metropolis case study. Section 3 presents and discusses the results. Finally, Section 4 draws conclusions and the perspectives of future studies.

## 2. Methodology and materials

This section presents the indicators used to evaluate the energy balance with the integration of distributed rooftop PV, as well as the simplified economic metrics used. It explains how the residential and commercial sectors' hourly electricity consumption per consumer is estimated when only aggregated data are available to assess self-consumption and self-sufficiency rates. We also present the data for the application to the Grand Paris metropolis. This study's total period of historical data is less than 30 years, so the results and conclusions drawn apply only to the current climate.

### 2.1. Energy balance indicators

The degree of mismatch between PV generation and electricity consumption is measured using the following two indicators. First, we define quantities $P_i^{C,x}(t)$ and $P_i^{PV,x}(t)$ respectively as the electricity consumption power and the PV electricity generation power for the sector $x$ (RES for residential or PRO for commercial) in a given basic unit $i$ (in the present study the basic unit of an energy-sharing community is defined with the IRIS cells) at time step $t$ with a time step of one hour generally. The $E_i^{C,x}$ and $E_i^{PV,x}$ are thus defined as the energy transferred during the total time period $T$ with $E_i^{C,x} = \sum_{i=0}^{T} P_i^{C,x}(t)$ and $E_i^{PV,x} = \sum_{i=0}^{T} P_i^{PV,x}(t)$. Then, the Self-Sufficiency Rate (SSR) that measures the share of consumption $E_i^{SC,x}$ covered by PV relative to total consumption $E_i^{C,x}$ for the sector $x$ in the given cell $i$ is defined as:

$$ 
\begin{aligned}
\text{SSR}_i^x[\%] &= \frac{E_i^{SC,x}}{E_i^{C,x}} \times 100\% \\
&= \frac{\sum_{i=0}^{T} \min(P_i^{C,x}(t), P_i^{PV,x}(t))}{\sum_{i=0}^{T} P_i^{C,x}(t)} \times 100\%.
\end{aligned}
\quad (1) $$

And the Self-Consumption Rate (SCR) that measures the share of consumption $E_i^{SC,x}$ covered by PV relative to total production $E_i^{PV,x}$ for the sector $x$ in a given cell $i$ is defined as:

$$ 
\begin{aligned}
\text{SCR}_i^x[\%] &= \frac{E_i^{SC,x}}{E_i^{PV,x}} \times 100\% \\
&= \frac{\sum_{i=0}^{T} \min(P_i^{C,x}(t), P_i^{PV,x}(t))}{\sum_{i=0}^{T} P_i^{PV,x}(t)} \times 100\%.
\end{aligned}
\quad (2) $$

The indicator for the region (in our case, the entire Grand Paris metropolitan area) or for the subregions (urban or suburban areas), that the region and its subregions may contain a certain number of previously defined basic units, is defined in the same way when considering energy exchange between the cells inside, replacing the unit consumption and production with the cumulative consumption and production of the subregion or region. Let A be a set of basic units (i.e., A = P for all IRIS cells in the Paris center and A = S for all IRIS cells in the Paris surroundings, and A = GP for the entire Grand-Paris with GP = PUS), and the SSR and SCR are defined as:

$$ 
\begin{aligned}
[\text{SSR}]_A^x[\%] &= \frac{E_A^{SC,x}}{E_A^{C,x}} \times 100\% \\
&= \frac{\sum_{i=0}^{T} \min(\sum_{i \in A} P_i^{C,x}(t), \sum_{i \in A} P_i^{PV,x}(t))}{\sum_{i=0}^{T} \sum_{i \in A} P_i^{C,x}(t)} \times 100\%,
\end{aligned}
\quad (3) $$

and

$$ 
\begin{aligned}
[\text{SCR}]_A^x[\%] &= \frac{E_A^{SC,x}}{E_A^{PV,x}} \times 100\% \\
&= \frac{\sum_{i=0}^{T} \min(\sum_{i \in A} P_i^{C,x}(t), \sum_{i \in A} P_i^{PV,x}(t))}{\sum_{i=0}^{T} \sum_{i \in A} P_i^{PV,x}(t)} \times 100\%.
\end{aligned}
\quad (4) $$

Then, we define the average SSR and SCR at the IRIS level by:

$$ \langle \text{SSR} \rangle_A^x[\%] = \frac{\sum_{i \in A} E_i^{SC,x}}{\sum_{i \in A} E_i^{C,x}} \times 100\% = \frac{\sum_{i \in A} \text{SSR}_i E_i^{C,x}}{\sum_{i \in A} E_i^{C,x}} \times 100\%, \quad (5) $$

and

$$ \langle \text{SCR} \rangle_A^x[\%] = \frac{\sum_{i \in A} E_i^{SC,x}}{\sum_{i \in A} E_i^{PV,x}} \times 100\% = \frac{\sum_{i \in A} \text{SCR}_i E_i^{PV,x}}{\sum_{i \in A} E_i^{PV,x}} \times 100\%. \quad (6) $$

A weighted average is needed to evaluate the average performance of SSR and SCR without considering the energy sharing between the cells. This is because the cells inside a domain or a subdomain do not have the same PV generation or electricity consumption. With the above definitions, for all the domains or subdomains, we have $[\text{SSR}]_A^x \ge \langle \text{SSR} \rangle_A^x$. However, if C = AuB where A and B are two disjoint sets of cells, it may be that $[\text{SSR}]_C^x < \langle \text{SSR} \rangle_A^x$. To reach an SSR of 100%, we need both for the total production to be larger or equal to the total consumption and for the production to occur at the time to satisfy the consumption at each time step. When the first condition is satisfied, the SSR cannot be larger than $\frac{E_i^{PV}}{E_i^{C,x}}$.

The same weighting procedure can also be applied to compute the weighted average of SCR and SSR from different sectors with:

$$ 
\begin{aligned}
\langle \text{SSR} \rangle_A^{x_1, x_2}[\%] &= \frac{E_A^{SC, x_1} + E_A^{SC, x_2}}{E_A^{C, x_1} + E_A^{C, x_2}} \times 100\% \\
&= \frac{\text{SSR}_A^{x_1} E_{A}^{C, x_1} + \text{SSR}_A^{x_2} E_{A}^{C, x_2}}{E_A^{C, x_1} + E_A^{C, x_2}} \times 100\%,
\end{aligned}
\quad (7) $$

and

$$ 
\begin{aligned}
\langle \text{SCR} \rangle_A^{x_1, x_2}[\%] &= \frac{E_A^{SC, x_1} + E_A^{SC, x_2}}{E_A^{PV, x_1} + E_A^{PV, x_2}} \times 100\% \\
&= \frac{\text{SSR}_A^{x_1} E_{A}^{PV, x_1} + \text{SCR}_A^{x_2} E_{A}^{PV, x_2}}{E_A^{PV, x_1} + E_A^{PV, x_2}} \times 100\%.
\end{aligned}
\quad (8) $$

These weighted averages of different sectors will be different compared to the aggregated SCR and SSR computed based on Eqs. (3) and (4) that compares the mismatch of total consumption and PV generation powers. If both sectors have heterogeneous consumption profiles, the SCR and SSR may be improved thanks to the complementary. Thus for
the aggregated values we have:

$$ 
\begin{aligned}
[\text{SSR}]_{A}^{x_1,x_2} [\%] &= \frac{E_{A}^{\text{SC},x_1,x_2}}{E_{A}^{\text{C},x_1} + E_{A}^{\text{C},x_2}} \times 100\% \\
&= \frac{\sum_{t=0}^{T} \min(P_{A}^{\text{C},x_1} + P_{A}^{\text{C},x_2}(t), P_{A}^{\text{PV},x_1} + P_{A}^{\text{PV},x_2}(t))}{\sum_{t=0}^{T} P_{A}^{\text{C},x_1} + P_{A}^{\text{C},x_2}(t)} \times 100\%,
\end{aligned}
\quad (9) $$

and

$$ 
\begin{aligned}
[\text{SCR}]_{A}^{x_1,x_2} [\%] &= \frac{E_{A}^{\text{SC},x_1,x_2}}{E_{A}^{\text{PV},x_1} + E_{A}^{\text{PV},x_2}} \times 100\% \\
&= \frac{\sum_{t=0}^{T} \min(P_{A}^{\text{C},x_1} + P_{A}^{\text{C},x_2}(t), P_{A}^{\text{PV},x_1} + P_{A}^{\text{PV},x_2}(t))}{\sum_{t=0}^{T} P_{A}^{\text{PV},x_1} + P_{A}^{\text{PV},x_2}(t)} \times 100\%.
\end{aligned}
\quad (10) $$

## 2.2. Economic evaluation

Extending the contracted perimeter for rooftop PV systems introduces significant economic and operational challenges, primarily due to the requirement for an expanded internal network within the microgrid. Indeed, the broader literature highlights the economic implications of rooftop PV deployment. For example, Galvin (2022) points out that low feed-in tariffs discourage households from installing larger rooftop systems, limiting their economic viability and increasing reliance on grid electricity. Similarly, Hirth (2015) observes that as solar penetration rises, its market value declines, creating difficulties in achieving large-scale deployment without subsidies. Gorman et al. (2020) further note that shifting electricity rate designs toward fixed charges may incentivize households to disconnect from the grid, complicating the economics of rooftop solar. Moreover, Astier et al. (2022) indicate that small, distributed rooftop solar systems can lead to higher grid costs compared to centralized solar parks. Collectively, these studies suggest that while rooftop solar offers potential benefits, its integration into the grid entails significant costs that warrant careful evaluation.

In addition, Alcarruz et al. (2022) examines the additional costs associated with transforming passive networks into energy communities, finding that larger communities can achieve lower annual investment and operational costs. However, these larger communities require more extensive internal networks, which increases the likelihood of lost load scenarios, reinforcing the economic challenges discussed.

In the specific context of France, the electricity system is designed to limit potential power supply shortages to a maximum of three hours per year on average, consistent with European standards to meet peak demand under extreme conditions IEA (2022). In dense regions such as the Paris metropolis, the reinforcement of the grid to allow widespread rooftop photovoltaic deployment would be complex to quantify but is less relevant due to the existing system's robustness. The French grid is sized to meet regulatory loss-of-load thresholds, ensuring sufficient reliability and mitigating the need to account for additional internal connection losses. As such, the methodology proposed by Alcarruz et al. (2022) is not directly applicable in this case.

Given this context, the study simplifies the analysis by treating rooftop PV investment as a constant, assuming that all suitable rooftops are equipped with panels, and focuses on electricity prices as the main cost driver. More results are shown in Appendix B and confirm the robustness of this assumption, as electricity prices are shown to be the primary determinant of total costs. During the current study, the normalized cost per kilowatt-hour purchased is focused which can be expressed as follows:

$$ \text{Price} = \frac{\text{Cost}}{E^C} = \frac{E^C \pi_a - E^{\text{SC}} \pi_v}{E^C} = \pi_a - \text{SSR} \pi_v \quad (11) $$

where $\pi_a$ is the initial purchase price for each kilowatt-hour of electricity consumed and $\pi_v$ is the FIT (feed-in tariff). With this definition, we have that:

$$ \text{Price}_A > \text{Price}_B \equiv \text{SSR}_A < \text{SSR}_B \quad (12) $$

## 2.3. Hourly electricity consumption model

In energy balance studies, the evolution of the electricity consumption of buildings over time (especially hours, also known as building demand curves) is important because demand curves have a strong impact on the grid (Linssen et al., 2017; Montero et al., 2022; Roberts et al., 2019). One of our study's objectives is to examine the complementary impacts of different sectors and urban areas on the energy balance. Therefore, we must obtain hourly electricity consumption profiles for both Residential (RES) and Small Businesses (PRO) sectors at smaller geographic scales. As needed, we can aggregate these data to any larger area.

Fig. 2(a) shows the daily consumption of households (RES), while Fig. 2(b) shows the daily consumption of all small businesses (PRO) in the region. We can see that both data have similar seasonality due to temperature sensitivity. Indeed, the outdoor temperature affects electricity consumption, especially outside a certain comfort range. Total consumption can generally be divided into different components: a regular part not influenced by temperature plus a weather-sensitive part. Thus for each given area i, hourly consumption profile $E_i^{\text{C},x}(d, h)$ can be split into a temperature-sensitive part $E_i^{\text{th},x}(d, h)$ and a base part $E_i^{\text{b},x}(d, h)$ as:

$$ E_i^{\text{C},x}(d, h) = E_i^{\text{th},x}(d, h) + E_i^{\text{b},x}(d, h). \quad (13) $$

The relationship between surface air temperature and energy consumption in a given area is known as the temperature sensitivity of consumption and shows different seasonal patterns in summer and winter. Various methods have been used to study the non-linear relationship between electricity consumption and temperature, e.g. Tao et al. (2024). These methods can be classified according to whether the temperature is used directly as an input or transformed first. A commonly used approach is the degree-day method, which involves segmenting temperature variations into derived variables such as heating degree-days (HDD) and cooling degree-days (CDD) (Moral-Carcedo & Vicéns-Otero, 2005) where

$$ \text{HDD}_i := \sum_{d=1}^{N} \max(0; T_i^h - T_i(y, d)) \quad (14) $$

$$ \text{CDD}_i := \sum_{d=1}^{N} \max(0; T_i(y, d) - T_i^c), $$

with $T_i(y, d)$ the daily-mean surface air temperature for a day $d$ of year $y$ averaged over cell $i$, $T_i^h$ and $T_i^c$ with $T_i^c \ge T_i^h$ the heating and cooling setpoints for cell $i$, and $N$ is the number of days during which the degree days are calculated. Thus, the daily temperature-sensitive consumption $E_i^{\text{th},x}(d)$ for each sector $x$ for each area $i$ can be estimated using the degree-days (HDD$_i$ and CDD$_i$) and temperature sensitivity coefficients $\rho_i^{\text{h},x}$ and $\rho_i^{\text{c},x}$ for each sector following Tao et al. (2024):

$$ E_i^{\text{th},x}(d) = (\text{HDD}_i(d) \rho_i^{\text{h},x} + \text{CDD}_i(d) \rho_i^{\text{c},x}) \text{NC}_i. \quad (15) $$

In addition, since temperature-sensitive electricity use is related to daily variations in outdoor temperatures, the hourly variations in the electricity use curves are mainly due to basic, non-temperature-dependent electricity use such as lighting and cooking. However, the number of occupants per hour in residential buildings and small commercial businesses' equipment and lighting habits are difficult to control, and detailed and accurate data are difficult to obtain. These variables may vary simultaneously between weekdays and holidays. Therefore, our estimated hourly electricity consumption is the average
<figure><img src="image_5.png" /><figcaption>Fig. 2. Daily consumption evolution summed over the Grand Paris metropolis with $P \le 36$ kVA during the 2020/04/02–2022/01/01 period. The blue line represents daily running averages. (a) Residential electricity consumption (RES) and the blue dots represent daily consumption on weekends and public holidays. (b) Small businesses' electricity consumption (PRO) and the blue dots represent daily consumption on Sundays and public holidays.</figcaption></figure>

electricity consumption per household or per business and will vary on weekdays and holidays. With two main assumptions, we can finally downscale the regional electricity consumption into sub-regional areas:

* The daily temperature-sensitive consumption $E_i^{th,x}(d)$ is assumed to be evenly distributed during the 24 h.

* The hourly consumption profile $E_i^{b,x}(d, h)$ is assumed to be the same for all households or all business sites in the same region but has different profiles depending on the month and type of day, as consumer habits may change.

So that Eq. (13) can be replaced by the following equation based on the assumptions:

$$E_i^{C,x}(d, h) = \frac{1}{24} E_i^{th,x}(d) + NCI_i E_i^{b,x}(d, h), \quad (16)$$

where $NC_i$ is the number of households or commercial sites inside the area $i$, and $NC$ is the regional number of households or commercial sites with $NC = \sum_{i \in A} NCI_i$. The regional hourly electricity consumption $E_i^{C}(d, h)$ is the sum of all sub-regional hourly consumptions $E_i^{C,x}(d, h)$, hence at the regional level, we have:

$$\begin{aligned} E_i^{C}(d, h) &= \sum_{i \in A} E_i^{C,x}(d, h) \\ &= \frac{1}{24} \sum_{i \in A} E_i^{th,x}(d) + \sum_{i \in A} NCI_i E_i^{b,x}(d, h) \\ &= \frac{1}{24} \sum_{i \in A} E_i^{th,x}(d) + NCI_i E_i^{b,x}(d, h). \end{aligned} \quad (17)$$

We can finally determine the consumption profiles for each sector $E_i^{b,x}(d, h)$ using the inputs $NC$, $E_i^{C}(d, h)$ and the previously determined temperature-sensitive consumptions $E_i^{th,x}(d)$. After that, the hourly electricity consumption of each area $E_i^{C,x}(d, h)$, whether residential or commercial, is estimated using Eq. (16). To include as much data as possible, hourly consumption is estimated for the whole period when HDD and CDD are available, from 2011 to 2020. When examining the energy balance performance, all ten years of data are used for the average to eliminate the multi-year effect.

## 2.4. Grand Paris metropolis case study data

### 2.4.1. Electricity consumption data

The study used data from Enedis, the French public company managing France's electricity distribution network. We analyzed data on all contracts for electricity consumption up to 36 kVA by households and small commercial users in the Grand Paris metropolis from April 2020 to December 2021. Two main datasets are available: the first provides electricity consumption data recorded half-hourly, 24 h a day, 365 days a year, at the administrative regional level for several different groups of consumption profiles (Enedis, 2020); the other dataset provides aggregated annual electricity consumption data for different sectors at the IRIS level from 2011 to 2018 (included). The IRIS is the basic (and smallest) administrative unit for which official statistical data is published in France. It consists of a division of the territory into “districts” with a population of about 2000 inhabitants (IGN, 2009).

Although both sets of data (annual consumption and hourly profile consumption) come from the same source, Enedis, the total number of sites for the Grand Paris metropolis region is inconsistent. The first step is to convert the number of sites per IRIS corresponding to the hourly consumption dataset using population weighting for the two sectors studied (residential and commercial):

$$NC_i = \frac{\overline{NCI_i(y)}}{\sum_{i \in A} NCI_i(y)} NC \quad (18)$$

where $NC_i(y)$ is the annual dataset's number of households or commercial users per IRIS.

After correction, the total consumption per sector is given as:

For the economic evaluation, the initial electricity price $\pi_a$ was considered to be the same for both the residential and commercial sectors and was given as 20 euro cents per kilowatt-hour, while $\pi_v$ was also set the same for both sectors and was given as 13.39 euro cents per kilowatt-hour as the value of the year 2020 (Eurostat, 2023).

### 2.4.2. Photovoltaic data

The Atelier Parisien d'Urbanisme (APUR) makes available to the public a dataset containing information on the solar potential (in
<caption>**Table 1**</caption>

Annual electricity consumption and PV production for the Grand Paris metropolis and its two subdomains (center and surroundings) for different sectors.

<table><thead><tr><th rowspan="2">Perimeter</th><th colspan="2">Residential (RES)</th><th colspan="2">Small Businesses (PRO)</th><th colspan="2">RES+PRO</th></tr><tr><th>E<sup>C</sup> (TWh)</th><th>E<sup>PV</sup> (TWh)</th><th>E<sup>C</sup> (TWh)</th><th>E<sup>PV</sup> (TWh)</th><th>E<sup>C</sup> (TWh)</th><th>E<sup>PV</sup> (TWh)</th></tr></thead><tbody><tr><td>Paris center</td><td>5.0</td><td>0.7</td><td>2.1</td><td>0.1</td><td>7.1</td><td>0.8</td></tr><tr><td>Paris surroundings</td><td>7.9</td><td>2.9</td><td>2.2</td><td>0.3</td><td>10.1</td><td>3.2</td></tr><tr><td>Grand Paris</td><td>12.9</td><td>3.6</td><td>4.3</td><td>0.4</td><td>17.2</td><td>4.0</td></tr></tbody></table>

KWh/m²/year) of each building in the Grand Paris metropolis, indicating its average annual solar radiation, calculated by simulating the average annual solar radiation and taking into account the shading effects of buildings (APUR, 2019). APUR also provides a combination of the building layers corresponding to the footprint with the assignment of typological and morphological information (APUR, 2020). This data layer contains more than 1 million buildings in vector form. Information such as floor area, construction period, and height are available. With this data, we no longer need hypothetical PV simulation data for potential PV studies. In addition, since this paper focuses on maximizing the available solar energy to investigate the impact of distributed PV integration on the energy balance, we used all potential rooftop PV areas that meet certain criteria rather than optimizing the size of the PV system. Indeed, the optimal PV sizing for rooftop PV may have been overly optimistic and overestimated actual PV availability (Narjabadifam et al., 2022; Yeligeti et al., 2023). Fig. 1(b) shows the ratio between the favorable rooftop areas (i.e., areas where the annual potential is ≥1000 kWh/m²) and the residential areas at the IRIS level.

On the other hand, Photovoltaic Geographical Information System (PVGIS, 2022) provides a GIS-based estimate of the hourly PV production for a given site with the chosen PV installation technology and PV panel size and orientation. Roof areas were extracted from the APUR dataset and combined with PVGIS to obtain the PV potential production for each IRIS. Several hypotheses were made when extracting the hourly PV potential at the IRIS level:

* Residential rooftop surface is considered “favorable” for PV installation if the solar irradiance potential is greater than 1000 kWh/m² per year, and only this part of the rooftop surface is taken into account. This means that rooftops with shading problems are not considered.

* The solar irradiance is the same inside a given IRIS (no difference between buildings inside an IRIS), but the variation in different areas is considered by PVGIS.

* The inclination and azimuth are set to be automatically optimal values provided by PVGIS.

* The panel technology chosen for now is crystalline silicon.

However, we cannot distinguish the rooftop of the RES sector from that of the PRO sector with APUR data. To do so, we consider that the roof area is equally distributed according to the number of users, which means that the PV generation of different sectors should be proportional to the number of users by sector. Therefore, for each IRIS we have:

$$ \frac{E_i^{\text{PV,PRO}}}{E_i^{\text{PV,RES}}} = \frac{NC_i^{\text{PRO}}}{NC_i^{\text{RES}}} \qquad (19) $$

Finally, the hourly PV production at different geographical scales is matched to the hourly electricity consumption for the SCR/SSR calculation for different sectors.

### 2.4.3. Calibrated base demand profiles

Using the methodology described in Section 2.3, we have calculated the average residential and commercial electricity consumption curves for the Grand Paris metropolis for holidays and weekdays in different months. Using these demand curves, we can then estimate each cell's total electricity consumption with a known number of consumers per sector. Based on the total electricity consumption curves, the mismatch

between supply and demand can be analyzed by comparing demand with PV generation. Figs. 3(a) and 3(b) show the average daily electricity consumption pattern of the typical four seasons for residential consumers, and Figs. 3(c) and 3(d) for the commercial sector. Profiles of 12 months are used for further energy balance analysis but are not shown here. The seasonal features are typical enough to represent the monthly differences. We also recall that these electricity consumption curves do not include temperature-related electricity consumption.

During working days, the RES profiles show that the highest daily consumption is mostly in the evening, around 19:00, except in summer. Meanwhile, local maximums also occur on workdays before people leave home for work around 7:00 - 8:00 and at lunchtime around 12:00. The difference between the evening peak and the midday peak is particularly large in winter but not evident for other seasons. During weekends, opposite to working days, the highest RES daily consumption is mostly at midday except in winter. Meanwhile, the local maximum in the morning disappears since people no longer prepare to leave for work. No matter the season or the type of day, the local minimum always arrives during nighttime when people sleep and during the afternoon around 14:00 and 16:00 when people are at work. The differences between seasons may be related to seasonal changes in people's behavior. For example, in the summer, many people go on longer vacations and engage in more outdoor activities, while in the winter, they spend more time indoors.

For the PRO profiles, electricity consumption is generally higher on weekdays than on holidays. During the weekdays, the local maximums of PRO consumption occur around 10:00–11:00 and around 17:00–18:00. During the daytime on working days, the PRO consumption remains at a relatively high level, and the period of large PRO consumption from 7:00 to 19:00 correlated to a large extent with the period of PV generation. On public holidays, however, the PRO daily consumption curve remains relatively flat except for the small local maxima in the morning and evening for the winter and autumn months. Our consumption profile results align with other European studies regarding the average demand curve for households (Aberilla et al., 2020; Mavroyeoryos et al., 2017; Møller Andersen et al., 2013). Therefore, we verify that our model can reproduce the qualitative features we expect from the demand.

All statistical analyses and modeling were conducted using Python, a versatile open-source programming language renowned for its extensive libraries and applications in data analysis and urban planning research. All the Python code and the non-proprietary data used for the current study are available via the Energy4Climate Interdisciplinary Center (E4C) datahub (E4C, 2019) that ensures the replicability and transparency of our methodologies, aligning with best practices in computational research.

## 3. Results and discussions

### 3.1. Supply-demand balance analysis

Maps of self-consumption rate (SCR) and self-sufficiency rate (SSR) for the residential (RES) and commercial (PRO) sectors, along with the case of complementary sectors, are shown in Fig. 4. Without exchange between different sectors or IRIS, the average SCR for all IRIS in Grand Paris is approximately 74.4% for RES and 96.4% for PRO. The corresponding SSR values are 20.5% for RES and 9.9% for PRO. These
<figure><img src="image_6.png" /><figcaption>Fig. 3. Average of the base electricity consumption for each hour of the day and for each season over the period between April 2020 and January 2022. (a) Weekday electricity consumption for RES. (b) Weekday electricity consumption for PRO. (c) Weekend and holiday electricity consumption for RES. (d) Weekend and holiday electricity consumption for PRO. The Central European Time (CET) standard is used.</figcaption></figure>

results are also summarized in the third row and first four columns of Table 2, which also present all the average and aggregated SSR and SCR for the different perimeters in the table form to facilitate the readability and comparison.

### 3.1.1. Geographic variation in SSR and SCR

The SSR is consistently higher in the peripheral areas of Paris compared to the city center, regardless of sector. It suggests that local PV production in the peripheral areas can offset a greater proportion of consumption. This is possibly due to the lower density of buildings and potentially greater PV installations in the peripheral areas compared to the dense city center. This difference in building density can also be seen on the map in Fig. 1(b). The solarizable rooftop relative to the inhabitable housing surface ratio is lower in cities with higher building densities than in the suburbs, which correlates with the SSR maps.

Conversely, in the city center, the SCR reaches 100%, indicating full local utilization of PV. However, peripheral areas exhibit surplus PV production, particularly from the RES sector, resulting in lower SCR values. As shown in Table 1, this surplus can be redirected to the city center to reduce losses and enhance PV coverage in both zones.

### 3.1.2. Impact of perimeter extension

The analysis of energy sharing between distinct IRIS within a sub-domain, presented in the fourth and fifth rows of Table 2, reveals significant improvements in SCR and SSR. These results are computed following Eqs. (3) and (4) for the aggregated perimeter extension, while Eqs. (5) and (6) are used for the IRIS-weighted average where no energy exchange occurs. Compared to the IRIS-weighted average presented in the first two rows, all SCR and SSR values increase, regardless of the sector.

* RES: SCR and SSR improve by 0.8% in the Paris center and 13% in the periphery.

* PRO: SCR and SSR improve by 5% in the periphery, with no change in the center.

* RES+PRO: SCR and SSR improve by 0.8% in the center and 19% in the periphery. For Grand Paris, SCR and SSR increase by 26% compared to IRIS-weighted averages.

These gains result from inter-IRIS complementarity, reducing grid injection and maximizing consumption coverage. When viewed from an energy balance perspective, this improvement is more pronounced in the Paris surroundings than in the Paris center, irrespective of the sector in question. The improvement thanks to the perimeter extension can also be seen directly in the increase of PV-covered electricity consumption as shown in Table 3. These values are related to the total PV production shown in Table 1 for each sector and subdomains, that the total PV production is the expectation of PV-covered consumption when consumption is perfectly matched to the PV production. Similar to the results of SSR, the Paris center does not observe significant change while the Paris surroundings profit more from using the surplus with a relative improvement of 13%. And such improvement is more important for the residential sector.

When combining the two subdomains (Paris center and surroundings) and comparing them to Grand Paris as a whole, notable improvements are observed:

* Paris Center: SSR increases by 102% (from 11.1% to 22.4%).

* Paris surroundings: SCR increases by 13% (from 85% to 96.4%).

However, improvements in SSR and SCR are heterogeneous across the two subdomains (e.g. SSR for Paris surroundings and SCR for Paris center are larger than the Grand Paris aggregated value). The global performance is analyzed by comparing the aggregated values to the weighted averages of the subdomains (Grand Paris weighted-average). The results prove that the loss of energy balance performance in some cells due to the peripheral expansion of the users involved is insignificant compared to the potential gains. Both SSR and SCR improve by 10% (20.4% to 22.4% and 88% to 96.4%). These results validate the benefits of treating Grand Paris as a single renewable energy community where electricity is shared across geographic boundaries.
<figure><img src="image_7.png" /><figcaption>Fig. 4. Map of self-consumption rate (SCR) and self-sufficiency rate (SSR) at the IRIS level. (a) Self-consumption rate (SCR) for RES. (b) SCR for PRO. (c) SCR for RES+PRO. (d) Self-sufficiency rate (SSR) for RES. (e) SSR for PRO. (f) SSR for RES+PRO.</figcaption></figure>

<caption>**Table 2**</caption>

Annual self-sufficiency rate (SSR) and self-consumption rate (SCR) for the Grand Paris metropolis and its two subdomains (center and surroundings) compared to the weighted average of IRIS values for different sectors.

<table><thead><tr><th rowspan="2">Perimeter</th><th colspan="2">Residential (RES)</th><th colspan="2">Commercial (PRO)</th><th colspan="2">RES + PRO<br>weighted-average</th><th colspan="3">RES+PRO</th></tr><tr><th>SSR (%)</th><th>SCR (%)</th><th>SSR (%)</th><th>SCR (%)</th><th>SSR (%)</th><th>SCR (%)</th><th>SSR (%)</th><th>SCR (%)</th><th>E<sup>PV</sup>/E<sup>FC</sup> (%)</th></tr></thead><tbody><tr><td>Paris center</td><td>13.1</td><td>99.2</td><td>6.0</td><td>100.0</td><td>-</td><td>-</td><td>11.0</td><td>99.3</td><td>-</td></tr><tr><td>IRIS weighted-average</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Paris surroundings</td><td>25.1</td><td>68.7</td><td>13.7</td><td>94.9</td><td>-</td><td>-</td><td>22.6</td><td>71.3</td><td>-</td></tr><tr><td>IRIS weighted-average</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Grand Paris</td><td>20.5</td><td>74.4</td><td>9.9</td><td>96.4</td><td>-</td><td>-</td><td>17.8</td><td>76.8</td><td>-</td></tr><tr><td>IRIS weighted-average</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Paris center</td><td>13.2</td><td>100.0</td><td>6.0</td><td>100.0</td><td>11.1</td><td>100</td><td>11.1</td><td>100</td><td>11.1</td></tr><tr><td>Paris surroundings</td><td>28.4</td><td>77.8</td><td>14.4</td><td>100.0</td><td>25.4</td><td>80.0</td><td>27.0</td><td>85.0</td><td>31.7</td></tr><tr><td>Grand Paris</td><td>22.5</td><td>81.9</td><td>10.3</td><td>100.0</td><td>-</td><td>-</td><td>20.4</td><td>88.0</td><td>-</td></tr><tr><td>weighted-average</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Grand Paris</td><td>24.6</td><td>89.5</td><td>10.3</td><td>100.0</td><td>21.0</td><td>90.7</td><td>22.4</td><td>96.4</td><td>23.2</td></tr></tbody></table>

This approach demonstrates that power sharing between the city and its periphery is mutually beneficial, leading to better energy balance outcomes. Additionally, the results highlight that improvements are more significant for rural areas with higher PV production potential. These findings align with prior studies, such as those by Cuesta-Fernandez, who observed a 30% improvement in PV coverage when energy exchanges were allowed between the city of Valencia and its metropolitan ring for the residential sector. Our study extends this understanding by analyzing SCR and SSR indicators, which are based on hourly data rather than annual totals, providing a more precise measure of energy balance. This methodological choice avoids the

overestimation of PV-covered consumption inherent in annual data, as noted by Saez et al. (2024).

### 3.1.3. Impact of sectoral interactions

The integration of RES and PRO sectors further amplifies improvements, as detailed in the last four rows and last three columns of Table 2. These results are computed following Eqs. (9) and (10) for the aggregated sectors RES+PRO, while Eqs. (7) and (8) are used for the RES+PRO weighted average where no energy exchange occurs inter-sectorally.
<caption>**Table 3**</caption>

Comparison of the electricity consumption covered by PV between the case of aggregating individual IRIS ($\sum_A E_A^{SC}$) and the case of perimeter extension ($E_A^{SC}$) for the Grand Paris metropolis and its two subdomains (center and surroundings) for different sectors.

<table><thead><tr><th rowspan="2">Perimeter</th><th colspan="2">Residential (RES)</th><th colspan="2">Small Businesses (PRO)</th></tr><tr><th>Σ<sub>A</sub> E<sup>SC</sup> (TWh)</th><th>E<sup>SC</sup><sub>A</sub> (TWh)</th><th>Σ<sub>A</sub> E<sup>SC</sup> (TWh)</th><th>E<sup>SC</sup><sub>A</sub> (TWh)</th></tr></thead><tbody><tr><td>Paris center</td><td>0.66</td><td>0.66</td><td>0.13</td><td>0.13</td></tr><tr><td>Paris surroundings</td><td>1.99</td><td>2.25</td><td>0.30</td><td>0.32</td></tr><tr><td>Grand Paris</td><td>2.65</td><td>3.19</td><td>0.43</td><td>0.44</td></tr></tbody></table>

* RES: SCR remains 100% in the center and improves by 9% (77.8% to 85%) in the periphery.

* PRO: SSR improves by 85% in the center (6% to 11.1%) and 87.5% in the periphery (14.4% to 27%).

* Grand Paris: SCR improves by 8% (89.5% to 96.4%), while SSR improves by 117% (10.3% to 22.4%).

However, the simultaneous improvement of the SSR and SCR is not observed. In contrast to the improvements, the total SCR decreases compared to PRO alone, while the SSR decreases compared to RES alone. Although the SSR and SCR losses for each sector appear significant, it is necessary to analyze global performance to determine whether complementary effects improve the overall energy balance. To do this, the results must be compared with the weighted average values of the sectors presented in the columns named 'RES + PRO weighted average' calculated with Eqs. (7) and (8). For the Paris center, it can be demonstrated that all PV production will be consumed in place when both sectors are consuming the energy, regardless of whether or not sharing the surplus between them. This leads to the SSR's maximal value of 11.1%, as described in Section 2.1. Nevertheless, the improvement resulting from the energy sharing between sectors is significant for the Paris surroundings. In this case, both SSR and SCR improve by 6% (25.4% to 27% and 80% to 85%, respectively). Similarly, in the case of Grand Paris, both SSR and SCR improve by 6.5% (21% to 22.4% and 90.7% to 96.4%, respectively).

Consequently, the enhancement in PV offset and the diminution in PV loss exemplify the advantages of complementarity between sectors with respect to the PV energy balance. This improvement is once more evident in the Paris surroundings. This highlights the potential for collaboration between sectors to optimize the energy system and achieve greater efficiency in resource utilization.

### 3.1.4. Seasonal variation

Table 4 shows SCRs and SSRs with different energy balance perimeters for different seasons. Seasonal variations in the energy balance are evident. France is a heating-dominated country (Martinopoulos et al., 2018), and demand is more concentrated in the winter months when solar radiation is lower and less PV power is generated. Consequently, less PV generation is available in winter than in summer, and less consumption can be covered, resulting in a lower SSR. On the other hand, the SCR describes the remaining PV electricity supply. This ratio is more important in winter than in summer for the same reasons of seasonal variation of electricity consumption and, therefore, puts more pressure on the grid in winter. Due to the complementarity between the different sectors and the number of users, the perimeter improvement also applies to all seasons, but with seasonal variations: for both SSR and SCR, the progress is more significant in summer.

### 3.2. Economic impacts

Fig. 5 shows the map of simplified normalized costs calculated based on Eq. (11). The average savings per kilowatt-hour are 6 cents for the Paris surroundings and 2 cents for the Paris center compared to the initial electricity price of 20 cents in 2020 (Eurostat, 2023). From an

<figure><img src="image_8.png" /><figcaption>**Fig. 5.** IRIS map of average electricity cost (Euro cents per kWh c€/kWh) at the IRIS level after energy sharing between the residential and the commercial sectors with each IRIS as a microgrid.</figcaption></figure>

economic point of view, it is clear that rooftop PV installation is more profitable for residents and businesses in the surrounding areas. This difference between the two subdomains can be explained with Eq. (12).

Fig. 6 shows the distributions of normalized costs for all IRIS in the Paris center and the Paris surroundings separately, as well as the value of the initial purchase price and the price after regional energy sharing, which is considered as the optimal case from the energy balance perspective. Regarding regional energy sharing, the average electricity cost is 0.154 euros per kWh. Comparing the final price with the IRIS distributions, we can see that all the consumers in the Paris center would benefit more thanks to the perimeter extension compared to the initial case of only local consumption. In contrast, 57% of consumers in the peripheral areas of Paris would benefit less compared to the case of microgrids at the IRIS level. However, as mentioned in the previous section, the overall electricity surplus would be significantly reduced, as would the potential cost of feeding the surplus into the grid. Power sharing between the city and the periphery is a win-win project, both from the technical point of view of energy balancing and from the point of view of consumers.

It is worth noting that, this study focuses more on the grid balance perspective while from the economic perspective, other important factors are excluded. Actually, the variability of the cost per kWh due to the different distribution of consumption and production is analyzed as another indicator of regional variability, like the SSR and SCR in the previous section. SSR and SCR are the critical variables that influence the profitability of a PV system in a mature market (Cucchiella et al., 2017; D'Adamo, 2018; Sarasa-Maestro et al., 2016). Indeed, these previous researches indicate that an important economic evaluation indicator such as the payback time (PBT), which is commonly used in previous studies, is inversely proportional to self-consumption ratios. Hence, instead of making more assumptions about the economic evaluation, the current study focuses only on the savings in electricity costs.
<caption>**Table 4**</caption>

Self-sufficiency rate (SSR) and self-consumption rate (SCR) for the region Grand Paris and its two subdomains (center and surroundings) compared to the weighted average of IRIS values under different seasons for the sum of RES and PRO sectors.

<table><thead><tr><th rowspan="2">Perimeter</th><th colspan="4">SSR (%)</th><th colspan="4">SCR (%)</th></tr><tr><th>Spring</th><th>Summer</th><th>Autumn</th><th>Winter</th><th>Spring</th><th>Summer</th><th>Autumn</th><th>Winter</th></tr></thead><tbody><tr><td>IRIS weighted-average Paris center</td><td>14.1</td><td>21.0</td><td>10.0</td><td>4.5</td><td>99.7</td><td>99.6</td><td>99.8</td><td>100.0</td></tr><tr><td>IRIS weighted-average Paris surroundings</td><td>30.1</td><td>39.1</td><td>22.3</td><td>11.8</td><td>74.1</td><td>62.5</td><td>76.6</td><td>96.5</td></tr><tr><td>IRIS weighted-average Grand Paris</td><td>23.5</td><td>31.5</td><td>17.2</td><td>8.8</td><td>79.1</td><td>69.8</td><td>81.2</td><td>97.2</td></tr><tr><td>Paris center</td><td>14.2</td><td>21.1</td><td>10.0</td><td>4.5</td><td>100.0</td><td>100.0</td><td>100.0</td><td>100.0</td></tr><tr><td>Paris surroundings</td><td>35.8</td><td>46.4</td><td>25.8</td><td>12.2</td><td>88.2</td><td>74.1</td><td>88.6</td><td>100.0</td></tr><tr><td>Grand Paris</td><td>29.2</td><td>41.8</td><td>20.6</td><td>9.0</td><td>98.3</td><td>92.5</td><td>97.3</td><td>100.0</td></tr></tbody></table>

<figure><img src="image_9.png" /><figcaption>**Fig. 6.** Distribution of IRIS normalized cost compared to the regional value of 15.4 €/kWh with energy sharing in the Grand Paris metropolis between all residential and commercial users (dashed red line) and the initial electricity buying price of 20 €/kWh (dashed black line). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)</figcaption></figure>

The overarching conclusion from these results is that increasing the perimeter of energy sharing in urban environments improves the performance of SSR and SCR indicators. This suggests the potential for regional energy strategies to optimize the use of PV production, thereby contributing to more sustainable and resilient urban energy systems.

## 4. Conclusion

This paper explores the integration of distributed photovoltaic (PV) generation in the Grand Paris metropolis, using the energy supply-demand balance with a focus on the self-consumption rate (SCR) and self-sufficiency rate (SSR). Our analysis reveals that the complementary nature of different residential and commercial sectors enables a significant improvement in the total offset energy and reduces the loss of PV surplus across all locations. This complementarity is crucial in the Paris surroundings, markedly enhancing energy efficiency.

From the supply-demand perspective, lower building density and larger roof areas in the Paris outskirts allow a higher SSR (27%). In contrast, central Paris, characterized by high building density, predominates local PV consumption with minimal surplus, resulting in only an 11% coverage of energy consumption and leaving a surplus due to imperfect simultaneity between residential consumption and PV production. Introducing energy sharing between different sectors and different subdomains can mitigate these losses and reduce grid pressure, a benefit that amplifies with geographical expansion. While the perimeter extension is particularly more beneficial for the Paris surroundings from the energy balance perspective, it is important to notice that it is also more advantageous for the more urban area of the Paris center from a simplified economic perspective, considering only electricity prices. Moreover, considering the entire Grand Paris metropolis as a unified renewable energy community that permits electricity sharing among all inhabitants and businesses emerges as the most optimal scenario. This arrangement covers 22.4% of consumption with rooftop PV, achieving 96.4% of the potential in perfect production-consumption simultaneity.

While this study provides valuable insights, its limitations, namely the simplification of economic considerations, must be acknowledged.

Economic aspects, such as conflicts between user and grid interests and potential deterioration of power-sharing, should be quantitatively considered before policy recommendations are made. Therefore, it is recommended for future work to delve deeper into the economic impacts, particularly to quantitatively assess both the benefits and potential deteriorations of power-sharing with consideration of the investment and distribution costs that are crucial for large-scale distributed PV integration. Although the results show that a larger perimeter is always better from the energy balance perspective, the effect on the grid within the perimeter is unclear. The costs of improving the distribution and cable operation could offset the potential benefits. On the other hand, as discussed in previous studies, the overall profitability of energy communities is highly dependent on government policies. However, in reality, this feed-in tariff could vary with the type of consumer and depends on the price, which also depends on the contracted power. This emphasis on economic factors is essential for a comprehensive understanding of the challenges and opportunities in this field.

Finally, the electricity consumption in the current study is based on historical data and is assumed not to change. However, citizens' adoption of distributed PV systems marks a shift in how energy is produced and consumed. By producing electricity at the point of use, individuals can reduce their dependence on the grid and have the opportunity to tailor energy consumption and production to their interests and needs, potentially accelerating electrification efforts. This decentralization of energy production increases the flexibility of the electricity system, as consumers can adjust their energy use according to availability and potentially participate in demand response programs. This evolution of consumption patterns should be considered, especially in projections of future energy balances.

### CRediT authorship contribution statement

**Qiqi Tao:** Writing – review & editing, Writing – original draft, Visualization, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. **Alexis Tantet:** Writing – review & editing, Validation, Supervision, Formal analysis, Data curation, Conceptualization. **Jordi Badosa:** Writing – review & editing, Validation, Formal
<figure><img src="image_10.png" /><figcaption>Fig. 7. Hourly residential electricity consumption evolution of the Grand Paris metropolis with $P \le 36$ kVA during the 2020/04/02–2022/01/01 period. The blue lines represent real values and the orange dashed lines represent predicted values with the model. (a) Residential electricity consumption (RES) and the blue dots represent daily consumption on weekends and public holidays. (b) Example for the summertime (Juin to August) (c) Example for the wintertime (December to February).</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 8. Total annual cost of upgrading into urban community microgrids for Grand Paris metropolis and its two subdomains. Estimation method based on Alcarruz et al. (2022).</figcaption></figure>
<table><caption>**Table B.5**
Economic assumptions used for calculating the total costs (Canova et al., 2022; Commission de Régularisation de l'Energie, 2021; Gabdushev & Vanin, 2023; IEA, 2022; Vartiainen et al., 2023).</caption><thead><tr><th>C<sup>PV</sup><br>(€/kWp)</th><th>C<sup>PV</sup><sub>y</sub><br>(€/kWp/year)</th><th>C<sup>inverter</sup><sub>y</sub><br>(€/kWp/year)</th><th>SAIDI<br>(hours)</th><th>Peak demand<br>(kW)</th><th>Short duration<br>failure cost (SDFC)<br>(€/kWh)</th></tr></thead><tbody><tr><td>1450</td><td>137</td><td>25</td><td>2</td><td>1.4</td><td>33</td></tr></tbody></table>

analysis, Data curation, Conceptualization. **Sylvain Cros:** Writing – review & editing, Validation, Formal analysis, Data curation, Conceptualization. **Philippe Drobinski:** Writing – review & editing, Validation, Supervision, Formal analysis, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

This work has been carried out at the Energy4Climate Interdisciplinary Center (E4C) of IP Paris and Ecole des Ponts ParisTech, which is in part supported by 3rd Programme d'Investissements d'Avenir [ANR-18-EUR-0006-02]. It was funded by namR company through a collaboration grant. We acknowledge the E-OBS dataset from the EU-FP6 project UERRA (http://www.uerra.eu) and the data providers in the ECA&D project (https://www.ecad.eu) as well as APUR for their data (https://www.apur.org).

## Appendix A. Validation of the hourly electricity consumption model

During the present study, we have electricity consumption data from April 2020 to December 2021 recorded half-hourly, 24 h a day, 365 days a year, at the administrative regional level for several different groups of consumption profiles. The temperature-sensitive parts are extracted following Tao et al. (2024) with the data as inputs and the basic hourly consumption profiles are trained with the model described in Eq. (17). After that, the model predicted values are compared to their initial values for validation, which gives us an R² score as shown in the first subfigure in Fig. 7. Such validation is done for both the residential sector and the commercial sector with an R² of 0.94 and 0.81 respectively.

## Appendix B. Cost evaluation of urban PV upgrading

To estimate the cost of urban PV upgrading, we follow the methodology proposed by Alcarruz et al. (2022) who considered the costs of PV upgrade as three parts: investment cost which includes the investment of PV panels and inverters, operation cost which is the energy purchased minus energy sales, and the cost due to the lost load. So the total annual cost $C_{y}^{total}$ is expressed as:

$$C_{y}^{total} = (C_{y}^{PV} + C_{y}^{inverter}) \cdot \frac{E^{PV}}{8760} + (\pi_{a} \cdot (E^{C} - E^{SC}) - \pi_{v} \cdot (E^{PV} - E^{SC})) + C^{LL} \quad (20)$$

where $C_{y}^{PV}$ and $C_{y}^{inverter}$ are the investment costs of on-grid PV panels and inverter chargers and $C_{y}^{LL}$ is the cost due to lost load of internal connections. As explained in Section 2.2, the French grid is already sized to meet regulatory loss-of-load thresholds, ensuring sufficient reliability and mitigating the need to account for additional internal connection losses. As such, the methodology proposed by Alcarruz et al. (2022) is not directly applicable but should be transformed to

be adapted. Hence, the cost due to lost load is computed from the microgrid perspective indicator the System Average Interruption Duration Index (SAIDI). SAIDI is the average cumulative outage duration for each customer served and the value in France is obliged to be maximally 2 h per consumer (IEA, 2022). Then, energy not supplied (ENS) is calculated as a worst-case scenario by multiplying SAIDI with the peak demand $P^{Peak}$, being 1.4 kW in our case per user (average of RES and PRO):

$$ENS = P^{Peak} \cdot SAIDI \cdot NC. \quad (21)$$

Finally, the cost of lost load is obtained with:

$$C^{LL} = ENS \cdot SDFC. \quad (22)$$

All values for the economic parameters are presented in Table B.5. The annuity of any investment cost is computed following the 7% discount rate and the same lifespan as considered in the references.

Fig. 8 shows the annual total cost per kilowatt-hour of PV production (all values are normalized by $E^{PV}$) of both subdomains of Grand Paris as well as the case that considers the whole region as one single community. During the current study, we estimated that the ENS for Grand Paris is around 11.5 GWh, which is overestimated compared to other studies (ENTSO-E, 2023). Also, we internalize the cost of the lost load in the geographical perimeter considered, but this is overestimated because there is no isolated operation and the lost load is not necessarily attributable to this geographical perimeter. The overestimated cost due to the loss of load still gives an insight into its order of magnitude compared to other factors. The results prove that the main cost is related to the electricity price hence the assumption could be considered robust.

## Data availability

Data will be made available on request.

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