Practicality of Nested Risk Measures for Dynamic Electric Vehicle Charging

Abstract

We consider the sequential decision problem faced by the manager of an electric vehicle (EV) charging station, who aims to satisfy the charging demand of the customer while minimizing cost. Since the total time needed to charge the EV up to capacity is often less than the amount of time that the customer is away, there are opportunities to exploit electricity spot price variations within some reservation window. We formulate the problem as a finite horizon Markov decision process (MDP) and consider a risk-averse objective function by optimizing under a dynamic risk measure constructed using a convex combination of expected value and conditional value at risk (CVaR). It has been recognized that the objective function of a risk-averse MDP lacks a practical interpretation. Therefore, in both academic and industry practice, the dynamic risk measure objective is often not of primary interest; instead, the risk-averse MDP is used as a computational tool for solving problems with predefined "practical" risk and reward objectives (termed the base model). In this paper, we study the extent to which the two sides of this framework are compatible with each other for the EV setting -- roughly speaking, does a "more risk-averse" MDP provide lower risk in the practical sense as well? In order to answer such a question, the effect of the degree of dynamic risk-aversion on the optimal MDP policy is analyzed. Based on these results, we also propose a principled approximation approach to finding an instance of the risk-averse MDP whose optimal policy behaves well under the practical objectives of the base model. Our numerical experiments suggest that EV charging stations can be operated at a significantly higher level of profitability if dynamic charging is adopted and a small amount of risk is tolerated.