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Decentralized Integration of Grid Edge Resources into Wholesale Electricity Markets via Mean-field Games

Chen Feng, Andrew L. Liu

TL;DR

The paper addresses the challenge of integrating distributed energy resources into wholesale electricity markets in a fully decentralized manner. It develops a discrete-time mean-field game framework where prosumers with solar and storage optimize bids and storage actions under real-time LMPs, proving the existence of a mean-field equilibrium for infinite populations and an $\epsilon$-Markov-Nash equilibrium for large finite populations. An online, single-loop learning algorithm enables prosumers to adapt their strategies using observed prices without centralized coordination, including mechanisms to handle demand and supply shocks. Numerical experiments on a IEEE 14-bus system with thousands of DERs show convergence of price beliefs, reduced price volatility, and lower energy costs, demonstrating the framework's potential to enhance grid efficiency while preserving prosumer autonomy.

Abstract

Grid edge resources refer to distributed energy resources (DERs) located on the consumer side of the electrical grid, controlled by consumers rather than utility companies. Integrating DERs with real-time electricity pricing can better align distributed supply with system demand, improving grid efficiency and reliability. However, DER owners, known as prosumers, often lack the expertise and resources to directly participate in wholesale energy markets, limiting their ability to fully realize the economic potential of their assets. Meanwhile, as DER adoption grows, the number of prosumers participating in the energy system is expected to increase significantly, creating additional challenges in coordination and market participation. To address these challenges, we propose a mean-field game framework that enables prosumers to autonomously learn optimal decision policies based on dynamic market prices and their variable solar generation. Our framework is designed to accommodate heterogeneous agents and demonstrates the existence of a mean-field equilibrium (MFE) in a wholesale energy market with many prosumers. Additionally, we introduce an algorithm that automates prosumers' resource control, facilitating real-time decision-making for energy storage management. Numerical experiments suggest that our approach converges towards an MFE and effectively reduces peak loads and price volatility, especially during periods of external demand or supply shocks. This study highlights the potential of a fully decentralized approach to integrating DERs into wholesale markets while improving market efficiency.

Decentralized Integration of Grid Edge Resources into Wholesale Electricity Markets via Mean-field Games

TL;DR

The paper addresses the challenge of integrating distributed energy resources into wholesale electricity markets in a fully decentralized manner. It develops a discrete-time mean-field game framework where prosumers with solar and storage optimize bids and storage actions under real-time LMPs, proving the existence of a mean-field equilibrium for infinite populations and an -Markov-Nash equilibrium for large finite populations. An online, single-loop learning algorithm enables prosumers to adapt their strategies using observed prices without centralized coordination, including mechanisms to handle demand and supply shocks. Numerical experiments on a IEEE 14-bus system with thousands of DERs show convergence of price beliefs, reduced price volatility, and lower energy costs, demonstrating the framework's potential to enhance grid efficiency while preserving prosumer autonomy.

Abstract

Grid edge resources refer to distributed energy resources (DERs) located on the consumer side of the electrical grid, controlled by consumers rather than utility companies. Integrating DERs with real-time electricity pricing can better align distributed supply with system demand, improving grid efficiency and reliability. However, DER owners, known as prosumers, often lack the expertise and resources to directly participate in wholesale energy markets, limiting their ability to fully realize the economic potential of their assets. Meanwhile, as DER adoption grows, the number of prosumers participating in the energy system is expected to increase significantly, creating additional challenges in coordination and market participation. To address these challenges, we propose a mean-field game framework that enables prosumers to autonomously learn optimal decision policies based on dynamic market prices and their variable solar generation. Our framework is designed to accommodate heterogeneous agents and demonstrates the existence of a mean-field equilibrium (MFE) in a wholesale energy market with many prosumers. Additionally, we introduce an algorithm that automates prosumers' resource control, facilitating real-time decision-making for energy storage management. Numerical experiments suggest that our approach converges towards an MFE and effectively reduces peak loads and price volatility, especially during periods of external demand or supply shocks. This study highlights the potential of a fully decentralized approach to integrating DERs into wholesale markets while improving market efficiency.

Paper Structure

This paper contains 19 sections, 7 theorems, 38 equations, 11 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Wholesale Energy Market Operations
  4. A Prosumer's Markov Decision Process
  5. Assumptions on the Agents
  6. Single-agent's Dynamic Optimization
  7. Dynamic Optimization and Optimal Policy
  8. Multiagent Mean-field Games
  9. Mean-Field Equilibrium: Definition and Existence
  10. Finite Agents and Approximate Markov-Nash Equilibrium
  11. Learning in a Mean-Field Game: An Algorithmic Approach
  12. Numerical Results
  13. Test Case
  14. Result Analysis
  15. Conclusion and Future Research
  16. ...and 4 more sections

Key Result

Proposition 1

Assume that the generation cost function $C_n(\cdot)$ in obj1 is a strongly convex quadratic function in the form of $C_n(g) = \frac{1}{2}\alpha_n g^2 + \beta_n g + \gamma_n$, with $\alpha_n > 0$ for all $n = 1, \ldots, N$. Under Assumption assump:LICQ, with $\mathbf{B}_t\in\mathcal{F}_B$, the LMP a

Figures (11)

  • Figure 1: Conceptual framework of a wholesale energy market with aggregators participation
  • Figure 2: Experimental results showing the dependency of charging efficiency on the charging rate for a Li-ion cell ($C$ represents battery capacity)amoroso2012advantages
  • Figure 3: IEEE-14 test bus system
  • Figure 4: Daily load shapes for agents
  • Figure 5: Relative difference between the belief and true LMP: mean-field learning without prior shock information
  • ...and 6 more figures

Theorems & Definitions (12)

  • Proposition 1
  • Proposition 2
  • Definition 1
  • Proposition 3: Existence of an MFE
  • Definition 2
  • Proposition 4: $\epsilon$-Markov-Nash Equilibrium
  • proof
  • Theorem 1
  • Definition 3
  • Lemma 1
  • ...and 2 more