# Energy communities typologies and performances: Impact of members configurations, system size and management

Maria Victoria Gasca, Rémy Rigo-Mariani, Vincent Debusschere, Yousra Sidqi

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Maria Victoria Gasca, Rémy Rigo-Mariani, Vincent Debusschere, Yousra Sidqi. Energy communities typologies and performances: Impact of members configurations, system size and management. Energy Reports, 2025, 14, pp.173 - 184. 10.1016/j.egyr.2025.05.049. hal-05122254

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Research paper

# Energy communities typologies and performances: Impact of members configurations, system size and management

Maria Victoria Gasca a,*, Remy Rigo-Mariani a,*, Vincent Debusschere a, Yousra Sidqi b,†

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## ARTICLE INFO

Keywords:

Energy communities

Prosumers

Collective self-consumption

Heterogeneity

## ABSTRACT

Energy communities have gained significant interest in recent years as they enable active citizen participation in the energy transition. Most research in energy communities delves into strategies for enhancing sustainability, economic viability, and fairness. However, these strategies' effectiveness largely depends on each energy community's specific characteristics, including members types and available assets. This study focuses on understanding the impact of input parameters across different energy community typologies. It examines community size, the percentage of prosumers, and the diversity of members' power profiles, analyzing 24,000 distinct configurations derived from an initial dataset of 92 load profiles. The study evaluates multiple setups for individual choices of solar photovoltaic systems and energy storage assets. The assessment applies a collective optimal management strategy to compare self-consumption and potential energy bill savings against a baseline where end-users operate individually. The same management strategy is applied consistently across various energy community typologies to demonstrate that the outcomes are primarily determined by the diversity of inputs (i.e., the energy community's specific characteristics) rather than the energy management approach itself. The results indicate that energy communities with more than 20 members do not experience significant performance enhancements, regardless of operational choices. Additionally, the findings highlight that diversifying member types is more beneficial than oversizing the generation and storage asset capacity. Ultimately, the results exhibit that energy communities with a percentage of only consumers yield favorable outcomes for all members. Optimal configurations are identified when the composition comprises 75% of prosumers with heterogeneous load profiles.

## 1. Introduction

In the context of the energy transition, consumers are increasingly incentivized to reduce/adapt their energy usage. These incentives aim to reduce their energy bills while fostering active participation in decentralized energy production with or without storage solutions. Within the collaborative frameworks promoted, energy communities (ECs) have emerged in recent years, where members can share and trade energy to further enhance the integration of distributed resources (Commission, 2019). The formation of ECs yields significant technical and economic advantages, such as more efficient use of local generation and lower energy bills thanks to reduced energy import from the upstream grid (Mustika et al., 2022).

ECs have been extensively studied in the literature from both the operational and long-term planning perspectives, taking into account economic and environmental criteria. Various business models have been proposed, ranging from centralized architectures to fully distributed frameworks. In the latter, asset management is conducted

individually, eliminating the need for community-level coordination. Instead of adhering to retail pricing structures, participants in decentralized approaches can engage in methods to trade internally with other members, such as in a local energy market structure. In contrast, in centralized approaches, an EC manager typically oversees community operations and facilitates interactions between members and external retailers (Lopez et al., 2024). Equitable/fair revenue distribution (Gasca et al., 2025; Fina, 2024), optimal sizing of ECs (Fioriti et al., 2021), and cost allocation mechanisms (Li et al., 2021b,a) are also conventionally investigated. In distributed frameworks, energy exchanges follow market mechanisms (e.g., pool or fully peer-to-peer transactions) dealing with intra-community trading complexities (Espadinha et al., 2023; Sarfarazi et al., 2024).

Most of the reviewed literature investigates management or ECs design strategies targeting technical and economic criteria (Marino et al., 2024). Results are oftentimes expressed in terms of savings

<footnote>a University of Grenoble Alpes, CNRS, Grenoble INP, G2Elab, 38000, Grenoble, France</footnote>

<footnote>b Lucerne University of Applied Sciences and Arts, Luzern, 62100, Switzerland</footnote>

<footnote>* Corresponding author.
E-mail address: remy.rigo-mariani@grenoble-inp.fr (R. Rigo-Mariani).</footnote>
<table><thead><tr><th colspan="2">Name abbreviation</th></tr></thead><tbody><tr><td>BS</td><td>Bill savings</td></tr><tr><td>CSC</td><td>Community self-consumption</td></tr><tr><td>ECs</td><td>Energy communities</td></tr><tr><td>EMS</td><td>Energy management system</td></tr><tr><td>PV</td><td>Photovoltaic</td></tr><tr><td>RE</td><td>Renewable energy</td></tr><tr><td colspan="2"><strong>Sets</strong></td></tr><tr><td>t ∈ T</td><td>Set of time steps (time step dt)</td></tr><tr><td>n ∈ N</td><td>Set of members within an EC of size N</td></tr><tr><td>x ∈ X</td><td>Set of tested ECs</td></tr><tr><td colspan="2"><strong>Variables</strong></td></tr><tr><td>P<sup>g</sup><sub>t,n</sub>, P<sup>g+</sup><sub>t,n</sub></td><td>Grid import/export of end-user n at time t</td></tr><tr><td>P<sup>cc</sup><sub>t,n</sub>, P<sup>cc+</sup><sub>t,n</sub></td><td>Grid import/export of the EC at time t</td></tr><tr><td>U<sup>g</sup><sub>t,n</sub></td><td>Grid power of the EC to export at time t ∈ {1,0}</td></tr><tr><td>U<sup>C</sup><sub>t,n</sub></td><td>Grid power of end-user n to export at time t ∈ {1,0}</td></tr><tr><td>U<sup>b</sup><sub>t,n</sub></td><td>Storage of end-user n charging mode at time t ∈ {1,0}</td></tr><tr><td>SOC<sub>t,n</sub></td><td>Storage state of charge of end-user n at time t</td></tr><tr><td>P<sup>b</sup><sub>t,n</sub>, P<sup>b+</sup><sub>t,n</sub></td><td>Storage charge/discharge of end-user n at time t</td></tr><tr><td>B<sup>l</sup><sub>n</sub></td><td>Bill of the end-user n</td></tr><tr><td>B<sup>C</sup></td><td>Total community costs</td></tr><tr><td>BS<sub>n</sub></td><td>Individual bill savings</td></tr><tr><td colspan="2"><strong>Parameters</strong></td></tr><tr><td>P&#773;<sup>pu</sup><sub>n</sub></td><td>Solar generation installed capacity of end-user n</td></tr><tr><td>P<sup>g</sup><sub>max</sub></td><td>Maximum power extracted from the grid of end-user n</td></tr><tr><td>P<sup>l</sup><sub>t,n</sub>, P<sup>pu</sup><sub>t,n</sub></td><td>Load and solar generation of end-user n at time t</td></tr><tr><td>P&#773;<sup>pb</sup><sub>n</sub></td><td>Solar generation installed capacity of end-user n</td></tr><tr><td>P<sup>C</sup><sub>max</sub></td><td>Maximum power extracted from the grid of the EC</td></tr><tr><td>P<sup>b</sup><sub>max</sub>, E<sup>b</sup><sub>n</sub></td><td>Battery rated power and capacity of the end-user n</td></tr><tr><td>SOC<sub>max</sub></td><td>Storage state of charge limits for all end-users</td></tr><tr><td>SOC<sub>t=0</sub></td><td>Initial storage state of charge of the end-user n</td></tr><tr><td>π<sup>-</sup>, π<sup>+</sup></td><td>Grid purchase price and feed-in tariff</td></tr><tr><td>η</td><td>Battery efficiency</td></tr><tr><td>P<sup>b</sup><sub>max</sub></td><td>Maximum battery installed capacity of end-user n</td></tr><tr><td>γ</td><td>Percentage of prosumers in an EC</td></tr><tr><td>H</td><td>Level of heterogeneity of end-users' power profiles</td></tr></tbody></table>

and/or technical improvement compared to a baseline scenario, in which there is no EC organization and every end-user is individually managed. However, it is worth noting that any observed results depend mainly on the EC setup rather than the proposed management/planning methods. Indeed, the main influencing factors include the consumers' power profiles and the installed capacities of solar and energy storage systems, i.e., the members' investment decisions. As highlighted in Asare-Bediako et al. (2011), the diversity of residential groups within a district contributes to the natural decrease of demand peaks due to heterogeneous electricity usages, i.e., higher chances to self-consume local generation. Likewise, as demonstrated in Eisner et al. (2023), an EC that includes both commercial and residential consumers tends to achieve higher cost savings, enhanced self-sufficiency, and improved efficiency in the utilization of locally generated electricity. Other factors that could impact the results include demand response, flexibility capacity provision, and the difference between internal and grid prices (Musilek and Hussain, 2024).

Among extrinsic factors, such as retail prices, the main factor influencing the performance of an EC is the people forming it, given their varying levels of acquisition power and economic capacities. Despite

governmental incentives to invest in renewable energy (RE) (Qadir et al., 2021), this remains sometimes not achievable for some communities. A sustainable society involves people of different economic backgrounds in collectively constructing a resilient and more renewable electrical grid. Overall, very few studies explore different configurations of ECs to generalize such intuitions. One noticeable example is detailed in Weckesser et al. (2021), where 180 different scenarios were studied, with different setups regarding storage sizes, operation strategy, and EC configuration to analyze the impacts of ECs on the distribution grid. Similarly, authors in Belloni et al. (2024) design the optimal size of photovoltaic (PV) panels and batteries across scenarios comprising diverse membership in ECs, involving different factors such as market signals and varying locations to reflect different weather conditions. Other studies focused on testing their proposed methods for scalability, such as (Faia et al., 2021), in which a novel method for peer-to-peer exchanges within ECs is proposed. This study evaluated execution times across different EC sizes (including configurations of 3, 5, 10, 15, or 20 members).

Table 1 offers a thorough review of existing research that investigates multiple factors and parameters influencing the outcomes of energy communities. Notably, none of these studies adopt a direct methodology for conducting sensitivity analyses on critical input parameters, such as community size, the ratio of prosumers within an EC, and the diversity of asset investments and load power profiles.

This research builds on previous studies by the same authors (Gasca et al., 2024), demonstrating that ECs with diverse member profiles perform better under the same energy management strategy. The main objective is now to identify the key factors that influence both economic and technical outcomes of EC, with a particular emphasis on the diversity of investment decisions within these communities. It seeks to address the question: “How does the typology of an EC, driven by end-users’ investment choices, influence major performance metrics?” Furthermore, it explores the parameters that exert the greatest impact on these metrics and whether it is advantageous to incentivize end-users to invest in larger RE assets for the formation of ECs. The proposed analysis encompasses 24,000 distinct EC configurations derived from an initial database of 92 end-user profiles taken from Quoilin et al. (2016) while systematically varying the capacities of installed PV systems and energy storage solutions. For each configuration, a management strategy and a cost allocation methodology are applied before evaluating the community’s performance.

Finally, the similarities and differences among end-user profiles are investigated to gain insights into the performance implications of forming ECs with members exhibiting either similar or diverse profiles. To the best of the authors’ knowledge, this work represents a novel contribution to the field, as there appears to be no direct examination of this issue in the existing literature to address ECs expansion planning.

The contributions of this paper are listed as follows:

* Quantitative assessment on various characteristics of ECs — including community size, the prosumer-to-consumer ratio, and the diversity of power profiles—impacting performance metrics.

* Simulations of the management and cost allocation for 24,000 ECs displaying various setups, considering end-users’ investment decisions.

* An analysis of variance and sensitivity assessments of ECs’ characteristics to identify their influence on major key performance indicators.

The remainder of the paper is organized as follows: Section 2 describes the system model and operational management of assets. The methodology proposed to generate the ECs configurations is explained in Section 3, where the classification of end-users and the parameters for the sensitivity analysis are described in more detail. Moreover, the assessment of the ECs’ performance is briefly explained in Section 4. Section 5 draws the results of the sensitivity analyses on the size, percentage of prosumers, and member power profiles before Section 6 discloses the conclusions.
<table><caption>**Table 1**

Literature review on composition and management strategies of energy communities.</caption><thead><tr><th>Ref</th><th>Performance metrics</th><th>Management method</th><th>Members</th><th>EC Tested</th></tr></thead><tbody><tr><td>Mustika et al. (2022)</td><td>CSC, Bill savings, CSS</td><td>Centralized and Decentralized</td><td>7</td><td>1</td></tr><tr><td>Gasca et al. (2025)</td><td>CSC, bill savings</td><td>Centralized and Decentralized</td><td>7</td><td>1</td></tr><tr><td>Fina (2024)</td><td>Bill cost allocation/savings</td><td>Centralized</td><td>12</td><td>1</td></tr><tr><td>Fioriti et al. (2021)</td><td>CSC, costs savings</td><td>Centralized</td><td>10</td><td>1</td></tr><tr><td>Espadinha et al. (2023)</td><td>CSS, Cost savings, CO2 Emissions</td><td>Centralized and Decentralized (P2P)</td><td>up to 27.000</td><td>278</td></tr><tr><td>Sarfarazi et al. (2024)</td><td>Community welfare, Market-driven curtailment, Operational system costs</td><td>Centralized</td><td>Not explicit</td><td>2</td></tr><tr><td>Marino et al. (2024)</td><td>CSC, economical benefits</td><td>Centralized and Decentralized</td><td>5</td><td>3</td></tr><tr><td>Eisner et al. (2023)</td><td>Self-sufficiency, self-consumption, yearly savings</td><td>Net metering, No EMS</td><td>8</td><td>1000</td></tr><tr><td>Musilek and Hussain (2024)</td><td>Green energy access, grid dependence, and cost reduction</td><td>Centralized and Decentralized</td><td>5</td><td>1</td></tr><tr><td>Weckesser et al. (2021)</td><td>Feeder voltage, line loading, Cost increase, LCOE transformer loading</td><td>Centralized</td><td>57–144–555</td><td>180</td></tr><tr><td>Faia et al. (2021)</td><td>Energy savings</td><td>Decentralized (P2P)</td><td>3–20</td><td>20</td></tr><tr><td>Belloni et al. (2024)</td><td>CSS, total costs, levelized costs of electricity (LCOE)</td><td>Decentralized, centralized, No assets scenario</td><td>10</td><td>1</td></tr><tr><td>Quoilin et al. (2016)</td><td>Social costs. Self-consumption, % of energy shared</td><td>Centralized and Decentralized with and without aggregator</td><td>10</td><td>1</td></tr><tr><td>Hafiz et al. (2019)</td><td>Electricity purchase savings</td><td>Centralized and Decentralized</td><td>5</td><td>1</td></tr><tr><td>Limmer (2023)</td><td>Stability and fairness Shapley value, Shapley-Core, Nucleous</td><td>Net metering, No EMS</td><td>3–15</td><td>1</td></tr><tr><td>Mussawar et al. (2023)</td><td>CSS, Net energy ratio, Energy surplus ratio, Peak import reduction, Energy cost savings</td><td>Centralized and Decentralized</td><td>6 building types</td><td>2 Scenarios</td></tr><tr><td>Minuto and Lanzini (2022)</td><td>CSS, total costs</td><td>Net metering, No EMS</td><td>100</td><td>3 Scenarios</td></tr><tr><td>Velkovski et al. (2024)</td><td>CSC, CSS energy sharing rate (ESR)</td><td>Centralized and Decentralized</td><td>14</td><td>1</td></tr><tr><td>Durillon et al. (2020)</td><td>PAR decrease, Euclidean Square Distance (ESD), environmental factor and flexibility</td><td>Decentralized</td><td>140</td><td>1</td></tr><tr><td>This work</td><td>CSC, Bill savings</td><td>Centralized and Decentralized</td><td>5–60</td><td>24 000</td></tr></tbody></table>

## 2. System model and management strategy

Let us consider an EC of *N* members who might invest individually in solar energy and storage assets. For each member *n* ∈ *N*, the power consumption and PV generation profiles are represented by ($P_{t,n}^l$) and ($P_{t,n}^{pv}$), respectively. The energy storage system may charge ($P_{t,n}^{b-n}$) and discharge ($P_{t,n}^{b+}$) according to the implemented management strategy, which ultimately influences the power exchanges with the main grid.

The members of the EC can decide to operate with an individualized or centralized energy management strategy (EMS) to control their assets. The individual EMS approach focuses on optimizing resources primarily for personal profit, which typically aims to reduce purchased power and increase power exported to the grid. Alternatively, end-users can join an EC, where a central entity manages the group to achieve collective benefits. This collaborative strategy ultimately targets individual end-users' benefits as well.

<footnote>*BESS: battery energy storage systems, CSC: Community self-consumption, CSS:community self-sufficiency, DR: Demand response, EMS:energy management system, RE: renewable energy.</footnote>
<figure><img src="image_3.png" /><figcaption>Fig. 1. Conventional power management for individuals.</figcaption></figure>

The models presented in this paper consider physical power flows, generation limit constraints, and operational characteristics of battery energy storage systems. These concepts are well-established in the literature and can be referenced in Gasca et al. (2025), Mustika et al. (2022).

## 2.1. Individual energy management strategy

The equations describing the energy management of individual assets are represented as constraints within an optimization model. These general constraints can be applied to various objectives within the same optimization problem. Fig. 1 illustrates the conventional power management for individuals, where each end-user trades electricity with the retailer solely, i.e., end-users are not organized in an EC.

It is assumed that individuals are mainly cost-driven, and thus individual battery is operated to minimize the individual bill ($B_n^I$) over a given horizon expressed as follows:

$$ \sum_n \min B_n^I = \sum_n \min \left( \sum_t (\pi^- \times P_{t,n}^{g-} - \pi^+ \times P_{t,n}^{g+}) \cdot dt \right) \quad (1) $$

$$ \text{s.t.} \quad P_{t,n}^{g-} + P_{t,n}^{PV} \times \overline{P_n^{PV}} + P_{t,n}^{b+} = P_{t,n}^{g+} + P_{t,n}^{b-} + P_{t,n}^{I} \quad \forall (n,t) \in \{T, N\} \quad (2) $$

$$ 0 \le P_{t,n}^{g+} \le u_{t,n}^{g} \cdot P_{max}^{g} \quad \forall (n,t) \in \{T, N\} \quad (3) $$

$$ 0 \le P_{t,n}^{g-} \le (1 - u_{t,n}^{g}) \cdot P_{max}^{g} \quad \forall (n,t) \in \{T, N\} \quad (4) $$

$$ 0 \le P_{t,n}^{b+} \le u_{t,n}^{b} \cdot P_{max}^{b} \quad \forall (n,t) \in \{T, N\} \quad (5) $$

$$ 0 \le P_{t,n}^{b-} \le (1 - u_{t,n}^{b}) \cdot P_{max}^{b} \quad \forall (n,t) \in \{T, N\} \quad (6) $$

$$ \text{SOC}_{t+1,n} = \text{SOC}_{t,n} + \left( \eta \cdot P_{t,n}^{b-} - \frac{P_{t,n}^{b+}}{\eta} \right) \cdot \frac{dt}{E_n^b} \quad \forall (n,t) \in \{T, N\} \quad (7) $$

$$ \text{SOC}_{min} \le \text{SOC}_{t,n} \le \text{SOC}_{max} \quad \forall (n,t) \in \{T, N\} \quad (8) $$

$$ \text{SOC}_{t=0,n} = \text{SOC}_{t=T,n} \quad \forall n \in N \quad (9) $$

Eq. (2) describes the power balance, where $\overline{P_n^{PV}}$ denotes the solar generation installed capacity. Additionally, $P_{t,n}^{g+}$ and $P_{t,n}^{g-}$ represent the power exchanges with the main grid, as shown in Fig. 1.

Moreover, a binary variable $u_{t,n}^g$ is introduced in (3) and (4) to prevent simultaneous production and consumption at the meter level - $u_{t,n}^g$ represents the activation of grid export and $P_{max}^g$ the maximum power imported/exported from/to the grid. Likewise, the behavior of the energy storage system is modeled through Eqs. (5) to (9) with a binary variable to avoid simultaneous charging/discharging. The battery is limited by the maximum capacity $P_{max}^b$ (depending on the member's type, as described later in Table 2). Furthermore, the state of charge ($SOC_{t,n}$) is updated with storage efficiency $\eta$ for a total energy capacity $E_n^b$. And, Eq. (8) expresses the min/max constraint on the battery's state of charge. Finally, (9) represents the principle of energy conservation within the energy storage system.

Furthermore, any energy import from the grid is charged at the retail price $\pi^-$, and the electricity generation can be sold at the price $\pi^+$. The retailer determines both prices by considering different factors, policies, and regulations (Li et al., 2021b). In this work, both purchase and selling prices are considered flat, i.e., constant over time.

<figure><img src="image_4.png" /><figcaption>Fig. 2. Energy community scheme.</figcaption></figure>

## 2.2. Centralized energy management strategy

In a centralized EMS, the EC operates as a unified entity interacting with its supplier, purchasing ($P_t^{c-}$) and selling ($P_t^{c+}$) excess energy. Fig. 2 illustrates the EC setup, with dashed lines representing the aggregated power. The main difference with the individual EMS is that in a centralized EMS, the community manager aims to minimize the exchanges with the power grid at the community level while excluding charges for internal energy exchanges.

In addition to the individual EMS constraints, at the community level, the overall optimization problem involves minimizing the net community bill, represented as $B^C$.

$$ \min B^C = \min \sum_t (\pi^- \times P_t^{c-} - \pi^+ \times P_t^{c+}) \cdot dt \quad (10) $$

$$ \text{s.t.} \quad P_{t,n}^{c+} - P_{t,n}^{c-} = \sum_n \left( P_{t,n}^{g-} - P_{t,n}^{g+} \right) \quad \forall (n,t) \in \{T, N\} \quad (11) $$

$$ 0 \le P_{t,n}^{c+} \le u_{t,n}^{c} \cdot P_{max}^{c} \quad \forall (n,t) \in \{T, N\} \quad (12) $$

$$ 0 \le P_{t,n}^{c-} \le (1 - u_{t,n}^{c}) \cdot P_{max}^{c} \quad \forall (n,t) \in \{T, N\} \quad (13) $$

Eq. (11) complements (2) by ensuring that the internal exchanges are balanced. Similar to (3) and (4), Eqs. (12) and (13) prevent the EC from exceeding its maximum capacity for production and consumption $P_{max}^c$. Additionally, the flows are calculated to avoid simultaneous energy import and export from or to the upstream grid by using the binary variable $u_{t,n}^c$.

## 3. Methodology

This work aims to evaluate the impact of different configurations of ECs on the technical and economic performances observed. Hence, a sensitivity analysis is conducted on several key parameters to achieve this assessment. These parameters encompass the size of the EC (N), the proportion of members investing in RE projects (i.e., percentage of prosumers $\gamma$), and the level of heterogeneity in energy consumption (H), which may reflect members' behavioral patterns.

Members are selected from a pool of J end-users to form different groups. This pool is characterized by specific power consumption profiles ($P_{t,n}^{PV}$) and solar power generation profiles ($P_{t,n}^{I}$), as if the same
<figure><img src="image_5.png" /><figcaption>Fig. 3. General methodology.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 4. Illustration of power profiles heterogeneity.</figcaption></figure>

members were to decide to invest in PV with a defined installed capacity ($P_n^{PV}$) and storage assets, e.g., a battery with a maximum capacity ($P_{max}^b$) equivalent to the PV installed capacity. The criteria for categorizing the members according to their investment decision on the assets are outlined in Table 2, which shows the three types of members considered for this study. Thus, four groups of members are formed considering these types. The procedure is illustrated in Fig. 3 in the section discussing about group formation.

For each parameter combination —such as forming ECs with ($N = 5$) members drawn from group 1, a probability ($\gamma = 100\%$), and a low level of heterogeneity ($H = Low$)— a defined quantity ($X$) of ECs is generated. It should be noted that multiple ECs can be produced using different member’s combinations from the same group. The selection of $X$ ECs is further detailed in Section 5.

Moreover, each formed EC adheres to an energy management strategy, which can be centralized or individual. The presented approach evaluates the differences between centralized EMS and the scenario where no EC is established and every individual trades with the grid independently (i.e., individual EMS). As a result, calculations are made regarding power imports and exports at both the community level and at the individual level. These values are then used to derive performance metrics for further evaluation, which is explained in Section 4.

### 3.1. Classification of members based on their investment decisions

Members were segmented into distinct groups to account for the variability of ECs across various initial investments and enhance the accuracy of the outcomes. This approach allows the generation of ECs tailored to specific members’ profiles. The first type of member consists of end-users who invest only in solar generation to meet their daily energy consumption without any storage, i.e., the maximum installed capacity of solar generation $P_n^{PV}$ is designed to cover the daily energy expenses. Members from the second type have the same installed capacity for PV as those from the first group, with additional investment

<table><caption>Table 2
Members installed capacity corresponding to pre-defined types.</caption><thead><tr><th>Type</th><th>PV installed capacity</th><th>Battery installed capacity</th></tr></thead><tbody><tr><td>1</td><td>P<sub>n</sub><sup>pv</sup></td><td>P<sub>max</sub><sup>b</sup> = 0</td></tr><tr><td>2</td><td>P<sub>n</sub><sup>pv</sup></td><td>P<sub>max</sub><sup>b</sup> ≈ P<sub>n</sub><sup>pv</sup></td></tr><tr><td>3</td><td>2 × P<sub>n</sub><sup>pv</sup></td><td>P<sub>max</sub><sup>b</sup> ≈ 2 × P<sub>n</sub><sup>pv</sup></td></tr></tbody></table>

in an energy storage device with a corresponding capacity. Members of the third type invest in PV systems sized to cover double their energy consumption, and a battery sized accordingly. Table 2 summarizes the different types of members.

Members are categorized into four distinct groups based on their characteristics. The first three groups are derived from a homogeneous type of members, whereas the fourth group is created with a linear combination of configurations from the other types, resulting in a diverse range of PV and energy storage capacities. The grouping approach is illustrated in Fig. 3.

### 3.2. Ecs' size and prosumer percentage

This research employs the technique of “drawing a sample with replacement” (Pathak, 1962) to select $N$ members from a pool of $J$ end-users (from a selected group $G$) and create ECs of several sizes. Moreover, when an EC configuration is created, only a certain percentage of members denoted as $\gamma$, display distributed assets, such as PV production and energy storage (i.e., corresponding to the three types introduced before). The remaining members are represented solely by their load profiles, i.e., purely consumers. For example, if $\gamma = 75\%$, the EC consists of 75% of prosumers (members who both produce and consume energy) and 25% of consumers (members who only consume energy).
### 3.3. Heterogeneity of members’ load power profiles

ECs can be established with members owning similar assets and specific capacities (i.e., from the same type). However, the variability in consumption patterns among these members may significantly influence energy-sharing efficiency. Therefore, this section introduces another parameter that corresponds to the disparity among members within the ECs, i.e., how different or “heterogeneous” the load power profiles are among the members forming the ECs. Initially, the heterogeneity among members of the EC is computed as the opposite of the Pearson correlation coefficient $ρ(P_n, P_m)$ (Kirch, 2008), as described in (14), which measures the similarity of load profiles between the members $n$ and $m$.

$$ρ(P_{i,n}, P_{i,m}) = \frac{\operatorname{cov}(P_{i,n}, P_{i,m})}{\sigma(P_{i,n}) \times \sigma(P_{i,m})} \qquad (14)$$

The covariance $\operatorname{cov}$ of the load power profiles among members within the pool is a similarity measure, while $\sigma$ represents the standard deviation of these individual load power profiles. Therefore, a low heterogeneity level indicates that the load power profiles of two or more members exhibit a similar consumption pattern, whereas a high heterogeneity level arises when the profiles are significantly different. This relationship is illustrated in Fig. 4. In panel (a), the members demonstrate closely aligned power consumption patterns, reflecting low heterogeneity. Conversely, panel (b) reveals distinct time schedules in the power consumption profiles, signifying a high level of heterogeneity.

To understand whether the power profiles of the members within the formed EC are sufficiently similar or heterogeneous, multiple ECs are systematically generated-exclusively for this parameter, by randomly aggregating members from the available pool $J$ of load profiles. This procedure generates $Y$ number of ECs characterized by their degree of heterogeneity $H$: High, Mean, and Low. The process of selecting these communities is outlined in Fig. 5. Where $Y$ was manually set to a sufficiently large value to guarantee that the resulting combinations of members span a wide variety of ECs.

When members consume and produce energy simultaneously, it may diminish their potential for internal sharing, ultimately leading to greater reliance on the grid. This study addresses this challenge by designing ECs that incorporate members with varying degrees of heterogeneity, optimizing the balance between production and consumption to enhance internal sharing capabilities.

## 4. Assessing ECs’ performance

To evaluate the performance of generated ECs, the centralized and decentralized energy management are compared based on two metrics. The first assesses the technical performance in the form of the community self-consumption ratio. The second evaluates the economic performance by calculating collective bill savings, which is determined by comparing the costs of individual versus centralized energy management.

### 4.1. Community self-consumption

The community self-consumption (CSC) quantifies the amount of community generation that is consumed locally by the community members. The CSC denotes locally all the energy produced that supplies the load and that is not exported to the upstream grid. The CSC of each formed EC following the implementation of the centralized energy management is described in (15).

$$CSC = 1 - \frac{\sum_{i} P_{i}^{C+}}{\sum_{n} P_{n}^{l}} \qquad (15)$$

### 4.2. Individual bill savings

The economic performance of the combinations of members forming ECs is assessed by comparing the bill increase/decrease between the decentralized and centralized frameworks. In decentralized frameworks, the collective bill is calculated as the sum of the individual EMS as in (1). Likewise, the collective bill in centralized frameworks is computed, as described in Section 2.2 and (10). Also, the bill savings (BS) per end-user can be calculated by the difference between the energy management frameworks, further divided by the number of members forming the EC, as in (16).

$$BS_n = \frac{\sum_n B_n^l - B^C}{N} \qquad (16)$$

## 5. Results and discussion

The results are based on the dataset from Quoilin et al. (2016) for the power consumption profiles spanning one year. The dataset is composed of $J = 92$ residential power profiles with ($P_n^{max} \le 8kW$). The operation is simulated while solving an optimal management problem over 24 days, representing one year. Especially, clustering techniques are employed to select two representative days per month for simplification (Rigo-Mariani, 2022). This approach ensures that the energy representation across the 24 days remains equivalent to the entire year. The PV power profiles are taken from Mustika et al. (2022) and reproduced proportionally for the types of members.

Since (X) communities of the same type can be created (composed of different $N$ members each time), it is crucial to ensure statistically representative results to balance representativeness and computational efficiency. Hence, it is essential to determine an optimal sample size of tested ECs (X). To this end, a series of tests are conducted with varying sample sizes, and the deviations of performance metrics from their mean values are analyzed.

Fig. 6 displays the deviation of the samples from the mean value of the community self-consumption for each tested number of ECs. For instance, for 20 tested ECs, the deviations from their mean are higher than 5% in both directions. The results show significant deviations from the mean performance metric (CSC) for smaller EC sample sizes. In contrast, samples exceeding 100 ECs demonstrate minimal deviations, consistently remaining below 2% from the mean value. These findings suggest that a sample size of $X = 100$ ECs achieves an optimal balance between the accuracy of performance assessments and computational efficiency.

### 5.1. Impact of the size of ECs

This section examines the implications of community size on the performance of ECs. Theoretically, as the size of an EC can increase indefinitely, a question arises: do larger ECs yield greater benefits compared to their smaller counterparts? Specifically, do they derive enhanced advantages from a more extensive members’ composition? To investigate this, a sensitivity analysis on ECs’ size $N$ is conducted, varying from 5 to 60 members. Distinct members’ groups were analyzed, as defined in Section 3, especially to consider different members’ investment decisions. To ensure clarity in analyzing results, all other parameters are kept constant, treating them as fixed (assumptions commonly adopted in the literature). Consequently, the prosumer percentage parameter is set to $\gamma = 100\%$ while randomly assigning levels of heterogeneity among members. Moreover, to ensure readability, the following figures illustrate the mean value and confidence interval from the assessed $X$ ECs ($X = 100$) using the bootstrap method (Bollen and Stinet, 1990). This statistical approach resamples the data to estimate the distribution of the mean values of the $X$ ECs formed in every iteration. The 2.5th percentile and the 97.5th percentile of the bootstrap distribution are considered to estimate the confidence interval, which captures the middle 95% of the bootstrap distribution.
<figure><img src="image_7.png" /><figcaption>Fig. 5. Algorithm to select *X* ECs with different levels of heterogeneity: H.</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. Representativeness of *X* tested ECs with respect to the metric: community self-consumption.</figcaption></figure>

The results of this analysis are illustrated in Fig. 7, which shows the impact of varying *N* across four distinct groups of members, analyzed through three key metrics: the annual community bill (a), bill savings per individual end-user (b), and community self-consumption rates (c). In particular, Fig. 7.(a) displays the annual community bill post-centralized energy management. As the figure shows, ECs formed with members from group 1 (i.e., moderate solar capacity with no storage) exhibit the highest annual energy bill, presumably due to the lack of storage in their asset mix. In contrast, the annual bill reduction compared to the baseline for ECs involving members from Group 2 is minimal for smaller communities (fewer than 10 members) relative to those ECs from Group 1; notably, the difference among those groups refers to the inclusion of storage devices in Group 2. It also suggests

that for ECs comprising less than 10 members, investing in additional storage devices does not lead to additional savings, confirming the results from previous works by the same authors in Gasca et al. (2024). Moreover, from Fig. 7.(a) ECs composed of members from Group 3 benefit from the lowest annual community bill, which aligns with their high installed capacities of PV systems and storage assets. Finally, ECs composed of members from Group 4, composed of a mix of members from the other groups, show a lower annual community bill than those ECs within the first and second groups and a higher bill than those in Group 3. This result implies that forming ECs with a mixed composition of members results in a competitive annual bill compared to homogeneous ECs.

Similar trends are visible in Fig. 7.(b), showing the bill savings per end-user, as expressed in (16). Being part of an EC is profitable
<figure><img src="image_9.png" /><figcaption>Fig. 7. Results of various ECs sizes when implementing centralized EMS, with $\gamma = 100\%$. (a) depicts the community bill, (b) shows the bill savings per end-user compared to the individual EMS, and (c) the community self-consumption.</figcaption></figure>

for all members (regardless of their investment decision), with positive bill savings when centrally managed. However, members of ECs composed of members from Groups 2 and 3 perceive smaller savings. Interestingly, members of ECs composed of members from Group 1 display higher bill savings when centrally managed because the surplus energy generated (if any) can be redistributed among members within the EC, which renders higher bill savings per member. In the case of members of ECs composed of members from Groups 2 and 3, the potential for enhancing self-consumption is limited due to over-sized solar capacities compared to the consumption levels in the community. Moreover, higher values are achieved by members of ECs composed of members from Group 4, given that a mixed composition of ECs centrally managing the resources yield the most collective benefits, compared to the individual EMS.

Furthermore, Fig. 7.(c) displays the community self-consumption in the case of ECs centrally managed. The highest CSC is achieved by ECs formed with members from Group 2, which indicates that the energy assets are properly sized to achieve the highest technical performance. All ECs with members investing in energy storage display higher CSC levels (over 78%). Consequently, since ECs composed of members from Group 1 do not invest in storage systems, a lower percentage of CSC is perceived. Given that ECs composed of members from Group 4 have a mixed composition with more diverse assets, the resulting ECs achieve greater CSC than those composed of members from Group 3. Those ECs evidently cannot self-consume all their PV production; hence, the surplus is sold back to the grid.

It is important to note that forming ECs with more than 20 members does not significantly change the economic and technical performance metrics. This behavior is consistent across all tested ECs, suggesting a potential threshold in size that affects performance based on the specified metrics.

## 5.2. Impact of the prosumers percentage

In the previous section, the formed ECs were composed entirely of prosumers (i.e., $\gamma = 100\%$). This section explores the question: “What if not all members of the EC invest in RE assets? How does this choice impact the collective benefits?”. To address these questions, different configurations of ECs are tested with varying percentages of prosumers. Moreover, since the earlier findings suggested that increasing the size of EC beyond 20 members does not substantially impact the analyzed performance metrics, a fixed size of $N = 20$ members for the studied ECs was set. In this context, $\gamma$ varies between 0% and 100%. For simplicity, four categories of $\gamma$ are tested: $\gamma = [0, 25, 50, 100]\%$.

Similarly to the previous analysis, Fig. 8 shows the impact of varying $\gamma$ across four distinct member groups, analyzed through three key metrics: the annual community bill (a), bill savings per individual end-user (b), and community self-consumption rates (c). The annual community bill, in Fig. 8.(a), exhibits an inverse relationship with the increase of $\gamma$. This phenomenon can be attributed to the increasing

number of prosumers contributing to enhanced local energy generation, which subsequently leads to reduced overall costs for the community members. The annual community bill is higher when ECs are composed of lower $\gamma$ due to greater power imports from the grid. For ECs composed of members from Group 3, the annual bill reduces considerably when $\gamma = 100\%$. The decrease compared to $\gamma = 75\%$ is, on average, around $5k\euro$.

Fig. 8.(b) presents an interesting outcome when there is a composition of 75% prosumers. When comparing the ECs composed of members from Groups 3 and 4, it shows that the bill savings per member are similar. In contrast, when the percentage of prosumers reaches 100%, the bill savings per member are significantly different. This may be due to the high PV and storage capacities, like those of members from Group 3, who find it less beneficial to transition from individual energy management to a centralized resource management system, given that the bill savings are determined by the difference between the individual and collective EMS. Moreover, for a $\gamma \le 70\%$, the difference in bill savings between ECs composed of members from Groups 3 and 4 becomes less significant. Therefore, a mixed composition of members can yield substantial bill savings, emphasizing the operational perspective of this analysis.

Regarding technical performances, an increase in prosumers corresponds to a decrease in CSC, as illustrated in Fig. 8.(c). The most significant effects of distinct prosumers percentages are observed in ECs with members without energy storage systems (from Group 1). Conversely, for ECs formed from groups that include energy storage, it is noticeable that CSC reaches 95% when at least 75% of the members are prosumers. Notably, ECs composed of members from Group 2 achieve the highest CSC, attributed to optimal asset sizing relative to the power profiles, which corresponds to the bill savings results.

Finally, ECs composed of members from Group 4 provide the best balance between the economic and technical performance metrics. This balance is demonstrated by significant bill savings comparable to those achieved by the ECs composed of members from Group 3, despite lower capital investments in assets. The operational outcomes with ECs composed of members from Group 4 are similar to those of ECs with the highest investment levels, highlighting the long-term advantages of having a diverse member composition to maximize returns on investment. Furthermore, CSC rates are high due to the variety of assets that enable effective resource sharing among members in the ECs.

## 5.3. Impact of members' power profiles heterogeneity

The previous section emphasizes the importance of heterogeneous member investments in RE assets to form ECs. This Section shifts focus to the heterogeneity in member consumption patterns, specifically, their power load profiles, rather than their capacity for RE generation. Consequently, a sensitivity analysis is conducted on the heterogeneity $H$ of member power load profiles by establishing ECs with high, mean, and low heterogeneity indices. This follows the methodology outlined
<figure><img src="image_10.png" /><figcaption>Fig. 8. Variations of prosumers percentages $\gamma$ when implementing centralized EMS, with $N = 20$. (a) depicts the community bill, (b) shows the bill savings per end-user compared to the individual EMS, and (c) the community self-consumption.</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Fig. 9. Heterogeneity among members forming ECs from groups 1, 2 and 3, with $N = 20$ and $\gamma = 75\%$, (a) depicts the community bill, (b) shows the bill savings per end-user compared to the individual EMS, and (c) the community self-consumption.</figcaption></figure>

in Section 3.3 and is conducted as described in Algorithm 5 for a fixed size EC of $N = 20$ members and a percentage of prosumers of $\gamma = 75\%$. ECs composed of members categorized in Group 4 have been omitted from the analysis due to their wide-ranging asset diversity, which could lead to ambiguous interpretations and potentially skew the insights regarding the influence of heterogeneous consumption behaviors.

The sensitivity analysis results for the parameter $H$ are displayed in Fig. 9. Notably, the data show that an increase in the heterogeneity of load power profiles leads to a reduction in the annual community bill, as illustrated in Fig. 9.(a), which suggests that a higher diversity yields a lower overall cost for all evaluated ECs. These findings indicate that including heterogeneous power consumption profiles can be advantageous. This effect is particularly significant for members exclusively investing in PV systems, such as those in Group 1, whose potential reduction in their annual bill can reach approximately 8.2%. In contrast, for members who, in addition to PV, include battery storage solutions, as seen in Group 2, the bill reduction is around 7.3%. Investing in storage does not guarantee higher bill savings.

The bill savings illustrated in Fig. 9.(b) show that ECs with high levels of heterogeneity $H$ experience a decrease in potential bill savings compared to those with lower levels of heterogeneity. The bill savings illustrated in Fig. 9.(b) show that ECs with high $H$, experience a decrease in potential bill savings compared to those with lower $H$. These results imply that implementing an individual management strategy may provide better financial outcomes in cases with significant diversity in load profiles. Specifically, the analysis indicates a potential reduction in annual bill savings of approximately 10%. This effect is particularly significant for ECs composed of members from Group 3, who experience a decrease in bill savings of around 8.6% when forming ECs with high $H$. In contrast, ECs composed of members from Group 1 see a smaller reduction in savings, averaging 7.4% per month. Compared to other groups, this decrease is somehow minor for members of ECs composed of Group 2, as the assets are designed for optimal self-consumption, and having a high $H$ does not significantly

impact the individual bill savings. Additionally, the difference in bill savings per member comprises only 0.58% of the annual community bill under low heterogeneity ECs, which may be considered negligible.

Furthermore, it is worth mentioning that while forming groups of $N = 20$ members may be challenging to find different levels of heterogeneous profiles (especially for the low level since it implies having 20 community members with very different consumption profiles), the same analysis was performed for groups of 10 community members, and the results were comparable.

Finally, the parameter $H$ does not significantly impact the performance metrics in comparison with the previous sensitivity analysis on other parameters. However, the results highlight that when members consume at similar times (or have similar power consumption profiles, in time and amplitude), the collective PV production is not self-consumed but sold to the grid at a high price, hence the higher annual costs. This is visible in the CSC metric displayed in Fig. 9.(c) where the Low $H$ level represents reduced CSC compared to a High $H$ level. However, the changes are not so significant for ECs composed of Groups 1 and 2. Notably, those ECs formed from Group 3 see an increase in CSC when having a High $H$ level due to their large investment in RE assets.

### 5.4. Sensitivity analysis

This section shifts focus to the statistical evaluation of the impact of the examined parameters on the performance of ECs. Specifically, a 3-way analysis of variance (ANOVA) (Herzog et al., 2019) is implemented to assess the extent to which the analyzed parameters represent a critical factor in bill savings and CSC. This approach allows us to quantify the impacting parameters’ critical role in determining the overall effectiveness of ECs.

The analysis of variance tests the null hypothesis, i.e., all results (classified by parameters) means are equal. Moreover, the “F-value” quantifies the variance ratio between group means and the variance within groups. It is used to determine whether statistically significant
<figure><img src="image_12.png" /><figcaption>Fig. 10. Graphical representation of the F-value from ANOVA test.</figcaption></figure>

differences exist between the means of multiple groups. For simplicity, Fig. 10 presents the F-values of the analyzed parameters. This represents a portion of the results of the ANOVA analysis. The complete ANOVA analysis is described in Appendix A.

The ANOVA analysis utilizes the “F-value” to indicate the extent of variability among considered parameters. Fig. 10 illustrates the “F-value” for the analyzed parameters for BS and CSC. The group-type and the percentage of prosumers are the most impacting parameters for both performance metrics (BS and CSC), given that a large “F-value” suggests that the group means are significantly different, indicating that the factor impacts the dependent variable. Interestingly, the size of the EC does not represent a significant variance for both metrics. This outcome confirms the conclusion of Section 5.1.

Furthermore, the impact of two simultaneous parameters is measured in the ANOVA test, as shown in the right-hand side of Fig. 10. The combination containing the groups (G) and the percentage of prosumers (γ) shows the highest contribution to the variance. Conversely, when combined with the size of the EC, these parameters do not present a high impact.

## 6. Conclusions

This paper analyzes various energy community typologies and their impact on major performance metrics, such as individual bill savings and collective self-consumption ratio. Rather than introducing a novel methodology aimed at maximizing specific advantages, this work provides an analytical framework for assessing the prevalent practice of deliberately choosing convenient input parameters when evaluating management strategies. This research thus focuses on member composition within the formed energy communities, as it is shown to be the most significant factor influencing performance outcomes. Presented assessments rely on constructing 24,000 energy community configurations, encompassing various energy community typologies. The results highlight the importance of mixing heterogeneous members with diverse energy usages and a wide range of installed generation and/or storage capacities.

The analysis focuses on three key parameters of the energy community: the size (i.e., the number of members), the proportion of prosumers (versus consumers), and the variability (heterogeneity) in power consumption profiles among its members. For every combination

of the input parameters, an energy community is created and evaluated by implementing collective optimal management for the energy community, to further perform a comparative assessment of bill savings and self-consumption metrics against a baseline scenario where all members operate independently.

The findings indicate that increasing the size of energy communities above 20 members does not significantly improve their performance metrics. Indeed, from the operational perspective, increasing the number of members in the energy communities does not necessarily translate into greater cost savings for members. Conversely, this suggests that individuals may join and leave large energy communities without significantly impacting the community managers overseeing. This scenario allows for more flexible contractual arrangements and reduces the likelihood of penalties associated with member disengagement.

Furthermore, this study explored the impact of the percentages of prosumers participating in energy communities, which significantly affects the overall results. For communities with the same type of member, a percentage of prosumers varying from 50% to 75% yields the best outcomes for energy communities, generating a self-consumption level between 70% and 98%. However, the inherently heterogeneous energy communities perceive a decrease in individual bill savings when the percentage of prosumers diminishes in their energy communities, which underscores the significance of composing energy communities with varied asset investments.

Moreover, energy communities can be composed of members who can choose to invest in different renewable energy assets. The results showed that for a mixed composition of assets, the bill savings corresponded closely to those observed in energy communities composed of members investing in large renewable assets, with a minimal impact on self-consumption levels. Nevertheless, large investments in renewable energy assets are not inherently correlated with a decrease in community energy bills. Furthermore, energy communities achieved optimal results with a prosumer ratio of 75% (characterized by diverse member load profiles and assets). This underscores the benefits of a heterogeneous energy community, demonstrating that over-investment in production and storage capacities is unnecessary to achieve higher efficiency.

Thus, the analysis emphasizes the importance of considering energy communities that capture nuanced social dynamics, with different investment capabilities. Further research will focus on a holistic approach that includes investment planning to evaluate the time of return on investment beyond the operational perspective. Additionally, the relative difference between retail and internal community prices may significantly influence performance metrics. An analysis of tariff designs could then provide deeper insights into the social and economic aspects of energy communities.

## CRediT authorship contribution statement

**Maria Victoria Gasca:** Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Methodology, Data curation, Conceptualization. **Remy Rigo-Mariani:** Writing – review & editing, Writing – original draft, Supervision, Funding acquisition, Conceptualization. **Vincent Debusschere:** Writing – review & editing, Supervision. **Yousra Sidqi:** Writing – review & editing, Supervision.

## 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 is supported by the French National Research Agency in the framework of the “Investissements d’avenir” program, France (ANR-15-IDEX-02), and the project LANTERN – Living labs interfaces for the energy transition funded by the Swiss Federal Office of Energy under the grant number SI/502544.
<table><caption>**Table A.3**
A three-way ANOVA with the following factors: Group, size, and percentage of prosumers.</caption><thead><tr><th>Group</th><th>N</th><th>γ</th><th>Test</th><th>BS</th><th>CSC</th></tr></thead><tbody><tr><td>1</td><td>5</td><td>25</td><td>1</td><td>278.62</td><td>...0.999</td></tr><tr><td>1</td><td>5</td><td>25</td><td>... 100</td><td>...211.38</td><td>...0.956</td></tr><tr><td>1</td><td>5</td><td>50</td><td>1...100</td><td>...311.08</td><td>...1</td></tr><tr><td>1</td><td>5</td><td>75</td><td>1...100</td><td>...206.18</td><td>...1</td></tr><tr><td>1</td><td>5</td><td>100</td><td>1...100</td><td>...187.89</td><td>...0.901</td></tr><tr><td>1</td><td>10</td><td>25...100</td><td>1...100</td><td>...253.18</td><td>...0.996</td></tr><tr><td>1</td><td>20</td><td>25...100</td><td>1...100</td><td>...230.64</td><td>...0.884</td></tr><tr><td>1</td><td>30</td><td>25...100</td><td>1...100</td><td>...220.55</td><td>...1</td></tr><tr><td>1</td><td>40</td><td>25...100</td><td>1...100</td><td>...225.61</td><td>...0.999</td></tr><tr><td>1</td><td>60</td><td>25...100</td><td>1...100</td><td>...233.53</td><td>...0.975</td></tr><tr><td>2</td><td>5</td><td>25...100</td><td>1...100</td><td>...187.89</td><td>...0.915</td></tr><tr><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td><td>...</td></tr><tr><td>4</td><td>60</td><td>25...100</td><td>1...100</td><td>...255.05</td><td>...0.995</td></tr></tbody></table>

<figure><img src="image_13.png" /><figcaption>**Fig. A.11.** Histogram of residuals of the fitted ordinary least squares model.</figcaption></figure>

## Appendix A. ANOVA analysis

ANOVA (Analysis of Variance) is a statistical technique used to assess differences among groups' metric means values when comparing three or more groups (Herzog et al., 2019). It facilitates evaluating whether at least one group's mean metric significantly deviates from that of the others. Moreover, it allows drawing inferences about the effects of one or more independent variables on a dependent variable. This method is used in experimental designs and empirical research, providing a framework to analyze the influence of categorical factors on quantitative outcomes while controlling for errors across multiple comparisons. Furthermore, several assumptions about the data must be fulfilled to ensure the validity of the results.

* The data within and between groups must be independent.

* The differences between observed and predicted values (residuals) should be normally distributed within each group.

* The variances of the groups should be similar.

* The independent variables in the analysis should have levels that are fixed rather than random.

The residuals from the ordinary least squares fitted model are analyzed to assess the normality assumption. These residuals should be normally distributed. Fig. A.11 shows the histogram of these residuals, allowing us to evaluate their conformity to a normal distribution.

The normality assumption is critical to defining the validity of employing this approach. Following the validation of the underlying assumptions, a three-way ANOVA is applied to the dataset, as illustrated in Table A.3.

A three-way ANOVA is intended to test the effects of three independent factors and their interactions on a dependent variable. The main hypothesis focuses on testing whether the independent variables affect the dependent variable. In this test, the independent variables are the group of members, the size of the EC, and the percentage of prosumers within the ECs, assessed through the bill savings and the community self-consumption (as the dependent variables).

To calculate the F-values, the ANOVA test requires the calculation of the sum of squares (SS) from every factor and their interactions, as in (A.1). Moreover, the degrees of freedom (df) of each factor is needed. For instance, since there are four groups, the df equals three for that factor. Hence, the F-value is calculated as in (A.2). The mean square is calculated by dividing the sum of squares by its respective degree of freedom. Details of these calculations can be found in Montgomery (2012).

$$SS = (x_x - Mean)^2 \qquad (A.1)$$

$$F\text{-value} = \frac{\text{Mean square effect}}{\text{Mean square error}} \qquad (A.2)$$

Table A.4 shows the results of the ANOVA test, including the SS, the degrees of freedom, the F-value, and the probability of the F-value ($\gamma(> F)$) for the CSC when forming an EC using a centralized EMS (on the left side of the table) and for the bill savings on the right.

In the ANOVA table, a zero value in $\gamma(> F)$ represents a high variance of the factor (i.e., the influence of the factor in the dependent variable). Nevertheless, given that the differences in the F-value are more noticeable than those of $\gamma(> F)$, only the most significant values were highlighted. The results show that the type of members (i.e., Group G) and the percentage of prosumers are the most impacting parameters in both performance metrics. The interactions between the parameters are also included in the analysis, as in Section 5, the interaction between the group types and the percentage of prosumers renders the highest value. A similar conclusion was already extracted from the graphical analysis since in ECs with more than 20 members, the variability of the performance metrics was low (refer to Fig. 7).

## Data availability

Data will be made available on request.
<caption>Table A.4</caption>

ANOVA table of the performance metrics. SS represents the sum of squares, (df) the degrees of freedom, (F) the F-value, and γ(> F) the probability of the null hypothesis. N refers to the size of the EC and γ the percentage of prosumers.

<table><thead><tr><th rowspan="2">Source</th><th colspan="4">Community self consumption</th><th colspan="4">Bill savings</th></tr><tr><th>SS</th><th>df</th><th>F</th><th>γ(>F)</th><th>SS</th><th>df</th><th>F</th><th>γ(>F)</th></tr></thead><tbody><tr><td>Group</td><td>35.64</td><td>3</td><td>10587.72</td><td>0</td><td>10305.32</td><td>3.0</td><td>6479.87</td><td>0.0</td></tr><tr><td>N</td><td>1.80</td><td>4</td><td>401.63</td><td>1.58e-315</td><td>1167.15</td><td>4.0</td><td>550.42</td><td>0.0</td></tr><tr><td>Per</td><td>29.65</td><td>3</td><td>8808.74</td><td>0</td><td>4909.07</td><td>3.0</td><td>3086.77</td><td>0.0</td></tr><tr><td>Group:N</td><td>0.52</td><td>12</td><td>38.49</td><td>1.40e-88</td><td>198.15</td><td>12.0</td><td>31.15</td><td>7.61e-71</td></tr><tr><td>Group:γ</td><td>20.48</td><td>9</td><td>2028.04</td><td>0</td><td>3744.18</td><td>9.0</td><td>784.76</td><td>0.0</td></tr><tr><td>N:γ</td><td>0.42</td><td>12</td><td>31.26</td><td>4.02E-71</td><td>71.617</td><td>12.0</td><td>11.25</td><td>9.51e-23</td></tr><tr><td>Group:N:γ</td><td>0.16</td><td>36</td><td>3.92</td><td>3.11E-14</td><td>74.32</td><td>36.0</td><td>3.89</td><td>4.51e-14</td></tr><tr><td>Residual</td><td>8.89</td><td>7920</td><td>NaN</td><td>NaN</td><td>4198.54</td><td>7920.0</td><td>NaN</td><td>NaN</td></tr></tbody></table>

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