A game-theoretic, market-based approach to extract flexibility from distributed energy resources

TL;DR

The paper tackles coordinating distributed energy resources (DERs) owned by autonomous agents through a market design that combines a consumer-level market (CMO/CMAs) with a Stackelberg game where the CMO sets prices $(\mu,\widetilde{\mu})$ to steer aggregate injections toward a target $\widetilde{P}$. Each CMA first solves a multiperiod optimization to compute a baseline injection $P_i^0$ and a feasible flexibility range $[\underline{P}_i,\overline{P}_i]$ for its DER mix, then bids a flexible injection $P_i^*$ in response to prices; the CMO aggregates bids, ensures budget balance, and computes the optimal prices via closed-form expressions. The authors derive analytical, closed-form solutions for CMA bids and market prices, prove the existence and uniqueness of a Nash equilibrium among CMAs and a Stackelberg equilibrium with the CMO, and demonstrate the approach on a small system using realistic data. The results highlight how price signals shape DER participation and the associated cost implications, and point to directions for scaling to larger systems and relaxing information assumptions in future work.

Abstract

We propose a market designed using game theory to optimally utilize the flexibility of distributed energy resources (DERs) like solar, batteries, electric vehicles, and flexible loads. Market agents perform multiperiod optimization to determine their feasible flexibility limits for power injections while satisfying all constraints of their DERs. This is followed by a Stackelberg game between the market operator and agents. The market operator as the leader aims to regulate the aggregate power injection around a desired value by leveraging the flexibility of their agents, and computes optimal prices for both electricity and flexibility services. The agents follow by optimally bidding their desired flexible power injections in response to these prices. We show the existence and uniqueness of a Nash equilibrium among all the agents and a Stackelberg equilibrium between all agents and the operator. In addition to deriving analytical closed-form solutions, we provide simulation results for a small example system to illustrate our approach.

Figures (3)

• Figure 1: Overall schematic of the CM (see \ref{['sec:overall_flow']}). All variables will be described in the following sections.
• Figure 2: CMO power injections and prices.
• Figure 3: DER power injections and states for CMA 1.