Understanding the Impact of Coalitions between EV Charging Stations (2404.03919v2)

Abstract: The rapid growth of electric vehicles (EVs) is driving the expansion of charging infrastructure globally. As charging stations become ubiquitous, their substantial electricity consumption can influence grid operation and electricity pricing. Naturally, \textit{some} groups of charging stations, which could be jointly operated by a company, may coordinate to decide their charging profile. While coordination among all charging stations is ideal, it is unclear if coordination of some charging stations is better than no coordination. In this paper, we analyze this intermediate regime between no and full coordination of charging stations. We model EV charging as a non-cooperative aggregative game, where each station's cost is determined by both monetary payments tied to reactive electricity prices on the grid and its sensitivity to deviations from a desired charging profile. We consider a solution concept that we call $\mathcal{C}$-Nash equilibrium, which is tied to a coalition $\mathcal{C}$ of charging stations coordinating to reduce their costs. We provide sufficient conditions, in terms of the demand and sensitivity of charging stations, to determine when independent (aka uncoordinated) operation of charging stations could result in lower overall costs to charging stations, coalition and charging stations outside the coalition. Somewhat counter to common intuition, we show numerical instances where allowing charging stations to operate independently is better than coordinating a subset of stations as a coalition. Jointly, these results provide operators of charging stations insights into how to coordinate their charging behavior, and open several research directions.

• The paper introduces the collusion-Nash equilibrium to model coordinated EV charging cost minimization.
• It employs rigorous game-theoretic analysis to demonstrate that coalitions may sometimes increase charging costs compared to independent operations.
• Findings provide actionable insights on operational strategies, highlighting trade-offs in grid coordination and pricing mechanisms.

Understanding Coalitions between Electric Vehicle (EV) Charging Stations: Insights from Game Theory

Introduction

The projected rise in electric vehicle (EV) adoption necessitates a concurrent expansion in EV charging infrastructure. Such an expansion, however, introduces significant challenges, particularly concerning its impact on the electricity grid's operations and pricing mechanisms. Coordination among EV charging stations offers a potential solution to optimize grid operations. However, achieving a comprehensive, global coordination is fraught with practical difficulties. This paper explores the dynamics and implications of forming coalitions among subsets of charging stations, providing a detailed game-theoretic analysis of whether such coalitions can indeed lead to optimal outcomes.

Modeling EV Charging Stations as Strategic Entities

The interaction among EV charging stations is modeled as a non-cooperative aggregative game, where the aim is to minimize the cost associated with charging. This cost is influenced by reactive electricity pricing and sensitivity to deviations from nominal charging profiles. Each charging station decides on its charging demand over a designated time horizon, with the total electricity price at any given time being reactive to the cumulative demand from all stations.

A new solution concept, the $\collusion$-Nash equilibrium, is introduced to assess the scenario where a coalition of stations coordinates to lower their collective charging costs. Analyzing this equilibrium sheds light on how such coalitions could theoretically lead to cost reductions, compared to a scenario where each charging station operates independently.

Analytical Characterization of $\collusion$-Nash Equilibrium

Through rigorous mathematical derivation, a unique and explicitly defined $\collusion$-Nash equilibrium is characterized for any given coalition of charging stations. This equilibrium incorporates both a uniformly distributed charging profile and a correction term accounting for coalition impacts and other parameters such as sensitivity and demand variations among the stations.

Surprisingly, the equilibrium condition suggests scenarios where forming a coalition may not always lead to the most favorable outcomes in terms of charging costs. Specifically, situations where independent operation (as modeled by the Nash equilibrium absent of any coalition) is more advantageous are identified, illuminating the nuanced nature of coordination among charging stations.

Implications of Coalitions: Practical and Theoretical Perspectives

A salient contribution of this paper is establishing conditions under which coalitions, or lack thereof, are preferred from different perspectives: societal, coalition, and non-coalition member viewpoints. These conditions are tied closely to the stations' demand and sensitivity characteristics, providing tangible insights into forming efficient operational strategies for EV charging stations.

We present numerical examples demonstrating instances where coalition formation leads to increased overall costs, challenging the intuitive notion that coordination among charging stations is universally beneficial. Such findings hold practical relevance for operators considering coordination strategies and highlight the theoretical intricacies of aggregative game models in the context of EV charging infrastructure.

Concluding Remarks and Future Directions

This paper pioneers in examining the dynamics of coalition formation among EV charging stations from a game-theoretic perspective. While it reveals potential drawbacks of indiscriminate coordination, it also opens up several avenues for future research. Future work could explore models incorporating demand feedback mechanisms, capacity constraints, and more complex coalition structures involving multiple EV charging operators. The insights from this work lay a foundational understanding, guiding the strategic operations of EV charging stations in an increasingly electrified automotive landscape.