On the Stability of Strategic Energy Storage Operation in Wholesale Electricity Markets (Extended Version)

TL;DR

This work analyzes how strategic energy storage firms interact with a system operator in wholesale electricity markets under realistic constraints, revealing that competition can be unstable when renewable penetration is high and conventional plant flexibility is low. By reformulating the operator–ESS interaction as a quadratic program and employing a best-response dynamic, the authors derive analytical instability conditions (notably for the two-firm case) and demonstrate that imposing a price cap on storage bids can enforce convergence to a Nash equilibrium. Simulation on a CAISO-like case shows that stability improves with greater storage capacity and system flexibility, while higher solar penetration erodes arbitrage profitability. The findings inform market design by highlighting regulatory levers (price caps and alternative flexibility measures) to balance ESS profitability, price stability, and social welfare in high-renewable regimes.

Abstract

High shares of variable renewable energy necessitate substantial energy storage capacity. However, it remains unclear how to design a market that, on the one hand, ensures a stable and sufficient income for storage firms, and, on the other hand, maintains stable and affordable electricity costs for the consumers. Here, we use a game theoretic model to study storage competition in wholesale electricity markets. A main result is that these types of games are not necessarily stable. In particular, we find that under certain conditions, which imply a combination of a high share of variable renewable energy sources and low flexibility of conventional power plants, the system will not converge to an equilibrium. However, we demonstrate that a price cap on storage price bids can ensure convergence to a stable solution. Moreover, we find that when the flexibility of conventional power plants is low, while the storage usage for energy balancing increases with renewable energy generation, the profitability of using storage for the sole purpose of energy arbitrage decreases.

Figures (6)

• Figure 1: A flow chart of the game-theoretic model.
• Figure 2: Illustration of the optimal storage usage per storage price bids and the game's best-reply dynamics that lead to an infinite loop.
• Figure 3: Storage price bids at equilibrium for monopoly and duopoly market structures and for combinations of system flexibility and storage capacity values. Price instability means that the best reply dynamics do not converge to an equilibrium.
• Figure 4: Existence of a stable solution as a function of the share of solar energy and energy storage for low and high flexibility scenarios. The share of solar energy is expressed relative to the overall daily energy demand, while the share of storage capacity is expressed relative to the daily excess generated solar energy.
• Figure 5: The share of stable solutions as a function of the price cap on storage price bids for low and high flexibility scenarios.

Theorems & Definitions (16)

• Lemma 1
• proof
• Lemma 2
• proof
• Lemma 3
• proof
• Lemma 4
• proof
• Lemma 5
• proof