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Understanding the Impact of Coalitions between EV Charging Stations

Sukanya Kudva, Kshitij Kulkarni, Chinmay Maheshwari, Anil Aswani, Shankar Sastry

TL;DR

The paper analyzes the impact of partial coordination among EV charging stations by formulating a non-cooperative aggregative game in which charging prices are endogenous to aggregate demand. It introduces a relaxed equilibrium, the $\mathcal{C}$-Nash equilibrium, capturing a coalition of stations that coordinate to reduce their costs, and proves existence and uniqueness of this equilibrium with a closed-form solution that decomposes into a time-uniform base term plus a coalition-specific correction term. The authors derive sufficient conditions under which coordinating a subset of stations can be worse than independent operation, using welfare metrics that compare societal, in-coalition, and out-of-coalition costs, and develop results for special cases with uniform price fluctuations and uniform desired demand. Numerical experiments illustrate that coalitions can be counterproductive, depending on heterogeneity in demand and sensitivity, thereby challenging the intuition that any coordination improves outcomes. The work provides practical guidance for EV charging operators on when to coordinate and opens avenues for extending the model to multiple coalitions, nonlinear pricing, and operational constraints.

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.

Understanding the Impact of Coalitions between EV Charging Stations

TL;DR

The paper analyzes the impact of partial coordination among EV charging stations by formulating a non-cooperative aggregative game in which charging prices are endogenous to aggregate demand. It introduces a relaxed equilibrium, the -Nash equilibrium, capturing a coalition of stations that coordinate to reduce their costs, and proves existence and uniqueness of this equilibrium with a closed-form solution that decomposes into a time-uniform base term plus a coalition-specific correction term. The authors derive sufficient conditions under which coordinating a subset of stations can be worse than independent operation, using welfare metrics that compare societal, in-coalition, and out-of-coalition costs, and develop results for special cases with uniform price fluctuations and uniform desired demand. Numerical experiments illustrate that coalitions can be counterproductive, depending on heterogeneity in demand and sensitivity, thereby challenging the intuition that any coordination improves outcomes. The work provides practical guidance for EV charging operators on when to coordinate and opens avenues for extending the model to multiple coalitions, nonlinear pricing, and operational constraints.

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 -Nash equilibrium, which is tied to a coalition 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.
Paper Structure (18 sections, 9 theorems, 26 equations, 5 figures)

This paper contains 18 sections, 9 theorems, 26 equations, 5 figures.

Table of Contents

  1. Introduction
  2. Related Works
  3. Model
  4. Charging stations as strategic entities
  5. Coalition between charging stations
  6. Results
  7. Analytical Characterization of $\mathcal{C}-$Nash equilibrium
  8. When is $\mathcal{C}-$Nash equilibrium beneficial?
  9. Case A: Exogeneous price fluctuations $a^t$ are uniform across time
  10. Case B: The desired demand $\bar{x}^t$ is uniform across time
  11. Coalitions may not be always beneficial.
  12. Discussion
  13. Impact of simultaneous variations in $a^t$ and $\alpha^t$
  14. Impact of the composition of coalitions
  15. Conclusion
  16. ...and 3 more sections

Key Result

Theorem 4.1

For any arbitrary coalition $\mathcal{C}\subset[N]$, when $b>0$ and $\mu_i > 0 \; \forall i\in N$, the $\mathcal{C}-$Nash equilibrium exists, is unique, and takes the following form where $\delta^{tt'}$ is the Kronecker delta function ($\delta^{tt'} = 1$ when $t = t'$ and is $0$ otherwise), $\mu= \textsf{diag}([\mu_1, \cdots,\mu_{N}])$ and $\textbf{C} = .$

Figures (5)

  • Figure 1: A schematic depiction of charging stations located in different areas (e.g. residential, downtown, highway) and owned by different EVCCs. Charging stations that are contained in the same red box are owned by same company (i.e. form a coalition). Each charging station demands charge from the grid, which determines the prices.
  • Figure 2: Setting $\eta_1=0.4/T, \eta_2 = 1.6/T$ and $\delta=0$
  • Figure 3: Setting $\eta_1=1/T, \eta_2 = 1/T$ and $\delta=0.4$
  • Figure 4: Comparison between Nash equilibrium and $\mathcal{C}-$Nash equilibrium with respect to \ref{['eq: Eval-Metric']} under different size of coalition.
  • Figure 5: Comparison of societal (overall) cost, coalitional cost, and the cost of the station outside the coalition in the three station game.

Theorems & Definitions (19)

  • Remark 3.1
  • Definition 3.2
  • Definition 3.3
  • Theorem 4.1
  • proof
  • Lemma 4.2
  • Remark 4.3
  • Remark 4.4
  • Corollary 4.5
  • Proposition 4.6
  • ...and 9 more