Optimal design of electric vehicle charging stations for commercial premises

Influx of plug-in electric vehicles (PEVs) creates a pressing need for careful charging infrastructure planning. In this paper, the primary goal is to devise a closed-form expression for the PEV charging station capacity problem. Two types of commercial charging stations are considered. The first problem is related to the calculation of the optimal service capacity for charging lots located at workplaces where PEV parking statistics are given as a priori. The second problem, on the other hand, is related to the optimisation of arrival rates for a given station capacity. In the second part, the mathematical models are expanded for the case where multiple charger technologies serve customer demand. This time the goal is to calculate the optimal customer load for each charger type according to its rate. Calculations are carried out for both social and individual optimality cases. Markovian queues are used to model the charging station system to capture the complex interactions between customer load, service waiting times, and electricity cost. The related optimisation problems are solved using convex optimisation methods. Closed-form expressions of station capacity and optimal arrival rates are explicitly derived. Both analytical calculations and discrete-event simulations are carried out and the results show that 60% of the waiting times and 42% of the queue length can be reduced by optimal capacity planning.