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Resource Sharing in Energy Communities: A Cooperative Game Approach

Ahmed S. Alahmed, Lang Tong

TL;DR

This paper formulates energy communities as cooperative games where distributed energy resources are shared behind a DSO meter under net energy metering. It analyzes two DER scheduling regimes—centralized control and decentralized local scheduling—and proves that both yield superadditive value functions and balanced games, ensuring a nonempty core and a stable grand coalition. The authors develop five ex-post payoff allocation mechanisms and compare them to an ex-ante Dynamic-NEM scheme, showing that ex-post rules may fail individual rationality under centralized scheduling while D-NEM achieves welfare-maximizing outcomes with reduced coordination. Numerical results with real data demonstrate that welfare gains grow with coalition size, favor centralized scheduling for total welfare, and highlight the trade-offs between stability, fairness, and computational complexity. The findings provide a rigorous game-theoretic basis for designing stable, fair, and scalable resource-sharing policies in energy communities.

Abstract

We analyze the overall benefits of an energy community cooperative game under which distributed energy resources (DER) are shared behind a regulated distribution utility meter under a general net energy metering (NEM) tariff. Two community DER scheduling algorithms are examined. The first is a community with centrally controlled DER, whereas the second is decentralized letting its members schedule their own DER locally. For both communities, we prove that the cooperative game's value function is superadditive, hence the grand coalition achieves the highest welfare. We also prove the balancedness of the cooperative game under the two DER scheduling algorithms, which means that there is a welfare re-distribution scheme that de-incentivizes players from leaving the grand coalition to form smaller ones. Lastly, we present five ex-post and an ex-ante welfare re-distribution mechanisms and evaluate them in simulation, in addition to investigating the performance of various community sizes under the two DER scheduling algorithms.

Resource Sharing in Energy Communities: A Cooperative Game Approach

TL;DR

This paper formulates energy communities as cooperative games where distributed energy resources are shared behind a DSO meter under net energy metering. It analyzes two DER scheduling regimes—centralized control and decentralized local scheduling—and proves that both yield superadditive value functions and balanced games, ensuring a nonempty core and a stable grand coalition. The authors develop five ex-post payoff allocation mechanisms and compare them to an ex-ante Dynamic-NEM scheme, showing that ex-post rules may fail individual rationality under centralized scheduling while D-NEM achieves welfare-maximizing outcomes with reduced coordination. Numerical results with real data demonstrate that welfare gains grow with coalition size, favor centralized scheduling for total welfare, and highlight the trade-offs between stability, fairness, and computational complexity. The findings provide a rigorous game-theoretic basis for designing stable, fair, and scalable resource-sharing policies in energy communities.

Abstract

We analyze the overall benefits of an energy community cooperative game under which distributed energy resources (DER) are shared behind a regulated distribution utility meter under a general net energy metering (NEM) tariff. Two community DER scheduling algorithms are examined. The first is a community with centrally controlled DER, whereas the second is decentralized letting its members schedule their own DER locally. For both communities, we prove that the cooperative game's value function is superadditive, hence the grand coalition achieves the highest welfare. We also prove the balancedness of the cooperative game under the two DER scheduling algorithms, which means that there is a welfare re-distribution scheme that de-incentivizes players from leaving the grand coalition to form smaller ones. Lastly, we present five ex-post and an ex-ante welfare re-distribution mechanisms and evaluate them in simulation, in addition to investigating the performance of various community sizes under the two DER scheduling algorithms.
Paper Structure (28 sections, 5 theorems, 37 equations, 3 figures, 1 table)

This paper contains 28 sections, 5 theorems, 37 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Member Resources, Payment, and Surplus
  4. Flexible Consumption, Renewable DG, and Net Consumption
  5. Customer Payment and Surplus
  6. Community Energy Management Models
  7. Community with Centralized Scheduling
  8. Community with Decentralized Scheduling
  9. Energy Community Cooperative Game
  10. Coalitions and Value Functions
  11. Community with Centralized Scheduling
  12. Community with Decentralized Scheduling
  13. Payoff Allocation, Imputation, and Core
  14. Balanced Games
  15. Payoff Allocation Mechanisms
  16. ...and 13 more sections

Key Result

Lemma 1

The cooperative game under centralized DER control $({\cal H},\nu^\ast)$ is superadditive, i.e., $\nu^\ast({\cal N})+\nu^\ast({\cal T}) \leq \nu^\ast({\cal N} \cup {\cal T}),~~ \forall {\cal N},{\cal T}\subseteq {\cal H}, {\cal N} \cap {\cal T}=\emptyset$.

Figures (3)

  • Figure 1: Energy community coalition framework. Player's flexible consumption and renewables are $d_i, r_i \in \mathbb{R}_+$, respectively, and their net consumption is $z_i\in \mathbb{R}$. The arrows point to the positive direction of energy flow.
  • Figure 2: Average daily welfare normalized difference and gain (%).
  • Figure 3: Daily welfare gain (%) of players ($|{\cal N}| = 6$) under decentralized$^\dagger$ and centralized$^\ast$ DER controls. Top panels (left to right): equal division, egalitarian, proportional. Bottom panels (left to right): ChakrabortyPoollaVaraiya:19TSG, Shapley, D-NEM.

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Definition 1: Payoff allocation and imputation
  • Definition 2: Core and coalition stability
  • Definition 3: Balanced game
  • Theorem 1: Balancedness under central DER scheduling
  • Theorem 2: Balancedness under decentral DER scheduling
  • Lemma 3