A two-stage stochastic programming model of locating fast chargers at stops for battery electric buses

With the development of charging technology, chargers with dropped price and increased charging power make fast charging more applicable and competitive to provide efficient and effective charging solution to electric vehicles. Compared to normal chargers, fast chargers can top up battery in a short time, which enables battery electric buses to get top-up charging at selected bus stops when the buses load and unload passengers. Such en-route charging solution can avoid deadhead trips during daily operation and further reduce energy consumption due to smaller size of battery required. In this paper, we develop a two-stage stochastic programming model to locate fast chargers at selected bus stops considering uncertainties of passenger demand and energy consumption during bus operation. A modified L-shaped method is proposed to solve the challenging problem since its size grows expo-nentially with the increasing number of scenarios. Numerical results show that the en-route top-up charging time keeps in line with passengers\u27 boarding and alighting time at intermediate stops when the bus loads and unloads passengers, which causes negligible passengers\u27 extra waiting time and corresponding penalty cost caused by charging activities. The modified L-shaped method is further compared to the commercial solver Gurobi with better performance and higher efficiency