Gaming on Coincident Peak Shaving: Equilibrium and Strategic Behavior

TL;DR

The paper addresses coincident peak shaving by modeling customer responses as a game between agents shifting demand across a two-period horizon under a fixed peak charge. It introduces a two-agent, two-period CP shaving game with a discontinuous payoff arising from a CP-indicator, and derives NE under concave, quasiconcave, and non-concave regimes, proving global stability of the switched dynamics and providing a gradient-based method to compute equilibria. It then extends the analysis to multi-agent settings, showing NE existence and, under standard conditions, uniqueness, while establishing that the peak shaving effectiveness at equilibrium matches the centralized optimum, but with efficiency losses that grow with agent flexibility and cost disparities. Numerical experiments and a Texas ERCOT 4CP case validate the theoretical results, revealing that higher agent participation can substantially reduce CP charges while introducing modest efficiency losses in non-concave/quasiconcave regimes. Overall, the work provides a tractable, stable framework for decentralized CP shaving with clear guidance for policy design and system planning.

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.

Figures (6)

• Figure 1: Convergence performance of two-agent quasiconcave CP shaving game.
• Figure 2: Convergence of two-agent non-concave CP shaving game.
• Figure 3: Convergence performance of two-agent concave CP shaving game.
• Figure 4: Convergence performance of multi-agent non-concave CP shaving game.
• Figure 5: Agent number impacts on efficiency loss. Each box contains 1000 samples, the circle denotes the outlier, the box upper and lower line denotes the quartiles, and the short blue line inside the box is the median value.

Theorems & Definitions (42)

• Definition 1
• Definition 2
• Definition 3
• Proposition 1
• proof : Sketch of the proof
• Theorem 1
• proof : Sketch of the proof
• Theorem 2
• proof : Sketch of the proof
• Theorem 3