Time-of-use (TOU) electricity rate for vehicle-to-grid (V2G) to minimize a charging station capacity

• An optimization framework is introduced to determine the new electricity rate, considering demand-side power capacity limitations. • An EV connection matrix was developed to make charging/discharging scheduling algorithm implementation much easier. • The modified particle swarm optimization (PSO) algorithm increases the convergence rate of the algorithm. • Simulation results revealed that the TOU rates should be applied according to a specific pattern, depending on the location. This paper introduces a framework to yield an electricity rate for vehicle-to-grid (V2G) charging station (CS) to minimize installation capacity of a charging station considering electric vehicle (EV) arrival/departure time distribution. Two different layers are designed to avoid an obstacle encountered when formulating the problem as a convex optimization and to represent an EV aggregator and an electricity rate decision maker – a regulator. The EV aggregator layer focuses on increasing the profit and the regulator minimizes the peak load of the V2G CS. Linear programming was formulated for the former layer, and a modified particle swarm optimization (PSO) method was developed for the latter. Modification of the PSO approach allowed for easier escape of local minima, resulting in a new electricity rate for the V2G CS based on the EV arrival/departure time distribution data. The algorithm employs new matrices devised in this paper to accommodate EV information in the optimization process. In a simulation study, two distinct CSs with V2G operations were evaluated, each with a different EV arrival/departure time distribution. The simulation revealed that the peak load and the profit of the aggregator vary dramatically depending on the arrival/departure time distributions.