The optimal distribution of electric-vehicle chargers across a city

It has been estimated that the cumulative sales of Electric Vehicles (EVs) will be up to 5.9 million and the stock of EVs will be up to 20 million by 2020 [1]. As the number of EVs is expanding, there is a growing need for widely distributed, publicly accessible, EV charging facilities. The public EV Chargers (EVCs) are expected to be found and will be needed where there is on-street parking, at taxi stands, in parking lots at places of employment, hotels, airports, shopping centres, convenience shops, fast food restaurants, and coffee houses, etc.. In this work, we aim to optimize the distribution of public EVCs across the city such that (i) the overall revenue generated by the EVCs is maximized, subject to (ii) the overall driver discomfort (e.g., queueing time) for EV charging is minimized. This is the first study on EVC distribution where EVCs are assumed to be installed in almost all regions across a city. The problem is formulated using a bilevel optimization model. We propose an alternating framework to solve it and have proved that a local minima is achievable. Moreover, this work introduces novel methods to extract information to understand the discomfort of petroleum car drivers, EV charging demands, parking time and parking fees across the city. The source data explored include the trajectories of taxis, the distribution of petroleum stations and various local features. The empirical study uses the real data sets from Shenzhen City, one of the largest cities in China. The extensive tests verify the superiority of the proposed bilevel optimization model in all aspects.