Fairness and Utilitarianism in Allocating Energy to EVs During Power Contingencies Using Modified Division Rules

Abstract

In order to maximize utilitarianism and fairness in allocating energy to electric vehicles (EVs) during outages, this study proposes an optimization method based on modified division rules. The idea of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">essential energy demand</i> is introduced in this paper to maximize the number of EVs that are served during power contingencies. For EVs carrying out the time-critical task(s), the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">essential energy demand</i> is defined as the amount of energy required by EVs to accomplish their upcoming task(s). For EVs carrying out delay-tolerant tasks, it is defined as the amount of energy required by EVs to travel to a nearby healthy charging station. To this end, an EV ranking mechanism is devised considering the full and essential energy demands along with the urgency of EVs. Subsequently, EVs with higher ranks are prioritized during energy allocation. The performance of the proposed method is compared with four existing division rules, i.e., proportional, constrained equal awards, constrained equal losses, and sequential priority rules. A utilitarianism index is proposed to analyze the performance of these methods and fairness is evaluated using existing indices, such as Jain's fairness index and cost of fairness index. The proposed method has outperformed existing division rules in both utilitarianism and fairness for the essential energy demand. Finally, a sensitivity analysis of uncertain parameters such as EV fleet size, available/required energy, and weight factors is carried out to analyze the performance of the proposed method under various conditions.