# Optimal Allocation of Agents among Collective Self-Consumption Communities

Youen Froger, Anthony Roy, Jean-Christophe Olivier, Salvy Bourguet, François Auger

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Youen Froger, Anthony Roy, Jean-Christophe Olivier, Salvy Bourguet, François Auger. Optimal Allocation of Agents among Collective Self-Consumption Communities. IEEE PowerTech 2025, Jun 2025, Kiel, Germany. hal-05158478

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Submitted on 11 Jul 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# Optimal Allocation of Agents among Collective Self-Consumption Communities

FROGER Youen¹, AUGER François¹, ROY Anthony¹, OLIVIER Jean-Christophe¹, BOURGUET Salvy¹

¹ Nantes Université, Institut de Recherche en Énergie Électrique de Nantes Atlantique, IREENA, UR 4642, F-44600 Saint-Nazaire, France

## 1. Context

* Decarbonation of electricity generation in the electrical network

* Growing need for flexibility and a better match between production and consumption of electrical energy

* Development of collective self-consumption communities (CSC)
  * Allocate energetic actors in multiple CSC communities.

* Need for fairness among actors

* Complementarity of actors.

* Developing an algorithm to allocate actors in multiple CSC communities

* Comparison of two objective functions

<figure><img src="image_2.png" /><figcaption>Fig. 1: Geographic distribution of actors</figcaption></figure>

* A geographic criterion, based on French regulation for CSC is used to choose the potential communities.

* Studied case (artificial) : 5 producers, 5 professional consumers (pro.) and 16 residential consumers (res.), over a day of hourly data.

* Production = consumption (total)

* Two different objective functions:

1. Minimization of total cost

2. Maximisation of the least-savings actor's savings

## 2. Formulated problem (MILP)

### Input data:

* Each actor's geographical position

* Energy exchanges requirements for each actor

* Potential communities

* Buying/selling rates between actors and communities

* Buying/selling rates between each actor and his provider (P) / surplus buyer (SB)

### Decision variables (output):

* Each actor's participation rate to each potential community he could join

* Energy exchanged between each actor and the each potential community he could join

* Energy exchanged between each actor and his SB/P

### Constraints :

* Each actor only participates to one community

* Each actor reaches his energy exchanges requirements, provided by his community and his SB/P

* An actor can either be a seller or a buyer at each time step.

* Communities don't produce nor consume energy. They can't store it either. So they must buy all the energy the sell and sell all they buy.

### Objective functions

1. Minimization of total costs (consumer's costs - producer's profits)

2. Maximization of least savings actor (compared to the situation without communities)

<figure><img src="image_3.png" /><figcaption>Fig. 2: production/consumption curves for each actor</figcaption></figure>

## 3. Results

### Optimized communities

<figure><img src="image_4.png" /><figcaption>Fig. 3a: Geographic répartition of optimized communities (objective 1)</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Fig. 3b: Geographic répartition of optimized communities (objective 2)</figcaption></figure>

### Exchanged energy

<figure><img src="image_6.png" /><figcaption>Fig. 4a: Exchanged energy (objective 1)</figcaption></figure>

* Makes the biggest possible communities

* Prioritizes biggest consumers because of their bigger consumption

* Doesn't include all actors

Gini coefficient:

* Tool to characterize economic inequalities

* The bigger it is, the bigger the inequalities are

* for *n* persons having *y*<sub>*i*</sub> income,

$$G = \frac{2 \sum_{i=1}^{n} iy_i}{n \sum_{i=1}^{n} y_i} - \frac{n+1}{n}$$

* Includes all actors

* Greatly reduces total savings.

* Reduce inequalities

<table><thead><tr><th rowspan="2">Objective</th><th>Objectif 1 value</th><th>Objectif 2 value</th><th>Total savings</th><th rowspan="2">Gini coefficient ↓</th><th rowspan="2">Computation time (ms) ↓</th></tr><tr><th>(€) ↓</th><th>(€) ↑</th><th>(€) ↑</th></tr></thead><tbody><tr><td>Objective 1</td><td>453</td><td>0</td><td>462</td><td>0,23</td><td>974</td></tr><tr><td>Objective 2</td><td>573</td><td>0,12</td><td>343</td><td>0,15</td><td>452</td></tr></tbody></table>

### Maximal computable problem size

<figure><img src="image_7.png" /><figcaption>Fig. 5: Maximal actor count for which the problem could be solved, for each reference day count</figcaption></figure>

* Each actor is the center of a potential community

* Memory complexity: O((actor count)<sup>4</sup> * (time step count)<sup>2</sup>)

* This approach, while interesting at a small scale don't scale up well

## 4. Conclusions - Perspectives

* **Flexibility:** To further improve self-consumption, it will be important to consider each actor's flexibility possibilities.

* **New computation algorithm:** Two possibilities are investigated: aggregation of actors, and approached resolution on a bilevel optimization problem.

## 5. Fundings and acknowledgements

This work benefited from state aid managed by the Agence Nationale de la Recherche (ANR) under the "France 2030" programme, bearing the reference ANR-22-PETA-0009 (FlexTASE project, in the framework of PEPR TASE).

This work also benefited from data collected and shared by the Laboratoire de Génie Électrique de Grenoble and the Laboratoire d'Économie Appliquée de Grenoble, in the framework of FLEXTASE -ANR-22-PETA-0009- with OTE's support.

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