Gaming on Coincident Peak Shaving: Equilibrium and Strategic Behavior

TL;DR

This paper models strategic peak demand shifting by customers under utility-imposed peak charges using game theory, revealing equilibrium behaviors, stability, and efficiency losses compared to centralized solutions.

Contribution

It introduces a game-theoretic framework for analyzing peak shaving with multiple agents, deriving equilibrium solutions, stability analysis, and efficiency comparisons.

Findings

Equilibrium solutions are derived for various demand-shifting scenarios.

System efficiency at equilibrium can be significantly lower than the optimal centralized outcome.

Customer flexibility and cost disparities influence the degree of efficiency loss.

Abstract

Power system operators and electric utility companies often impose a coincident peak demand charge on customers when the aggregate system demand reaches its maximum. This charge incentivizes customers to strategically shift their peak usage away from the system's collective peak, which helps reduce stress on electricity infrastructure. In this paper, we develop a game-theoretic model to analyze how such strategic behavior affects overall system efficiency. We show that depending on the extent of customers' demand-shifting capabilities, the resulting coincident peak shaving game can exhibit concavity, quasi-concavity with discontinuities, or non-concavity with discontinuities. In a two-agent, two-period setting, we derive closed-form Nash equilibrium solutions for each scenario and generalize our findings to multi-agent contexts. We prove the stability of the equilibrium points and propose an algorithm for computing equilibrium outcomes under all game configurations. Our results indicate that the peak-shaving outcome at the equilibrium of the game model is comparable to the optimal outcome of the natural centralized model. However, there is a significant loss in efficiency. Under quasi-concave and non-concave conditions, this inefficiency grows with increased customer flexibility and larger disparities in marginal shifting costs; we also examine how the number of agents influences system performance. Finally, numerical simulations with real-world applications validate our theoretical insights.