A joint optimisation model for charger locating and electric bus charging scheduling considering opportunity fast charging and uncertainties

The continuous improvement of charging technologies makes fast charging applicable to overcoming the limited driving range of electric vehicles by providing en-route opportunity charging. Fast chargers can be deployed at bus stops to top up the battery for an electric bus during its dwelling time when passengers board and alight, which allows the usage of small size battery and avoids deadheading trips to depot or charging station for recharging. This paper examines the joint optimisation problem of locating fast chargers at selected bus stops and developing charging schedule to support electric bus operation considering time-varying electricity price and penalty cost if passengers' extra waiting time, the delay time of starting a trip or the excessive travel time of completing a trip is caused by charging activities. To handle the uncertainties associated with the travel time and passenger demand, a robust model is proposed and formulated. The proposed methods are applied to multiple bus routes in Sydney in the numerical studies. The numerical results show that frequent charging activities occur at both intermediate and last stops during bus service trips, indicating that it is beneficial for buses to utilise passengers' boarding and alighting time at intermediate stops and resting time at the last stop between two adjacent trips to top up battery. Sensitivity analysis on a series of system parameters, such as the acquisition cost of chargers, amortized battery price and charging power, is conducted. The numerical results verify the feasibility of deployment of fast chargers and corresponding top-up charging activities at both intermediate and last stops. Electric buses outperform the conventional diesel buses regarding energy consumption cost, especially considering the increasing diesel fuel price and its costly environmental impacts. Moreover, charging activities at intermediate stops will become more common when passenger demand (the volume of boarding and alighting passengers) increases at intermediate stops.