The Effect of Nonlinear Charging Function and Line Change Constraints on Electric Bus Scheduling

Aijia Zhang
School of Transportation, Southeast University, Nanjing, China

Tiezhu Li
School of Transportation, Southeast University, Nanjing, China

Ran Tu
School of Transportation, Southeast University, Nanjing, China

Changyin Dong
School of Transportation, Southeast University, Nanjing, China

Haibo Chen
Institute for Transport Studies, University of Leeds, UK

Jianbing Gao
Institute for Transport Studies, University of Leeds, UK

Ye Liu
Institute for Transport Studies, University of Leeds, UK

Abstract

The recharging plans are a key component of the electric bus schedule. Since the real-world charging function of electric vehicles follows a nonlinear relationship with the charging duration, it is challenging to accurately estimate the charging time. To provide a feasible bus schedule given the nonlinear charging function, this paper proposes a mixed integer programming model with a piecewise linear charging approximation and multi-depot and multi-vehicle type scheduling. The objective of the model is to minimise the total cost of the schedule, which includes the vehicle purchasing cost and operation cost. From a practical point of view, the number of line changes of each bus is also taken as one of the constraints in the optimisation. An improved heuristic algorithm is then proposed to find high-quality solutions of the problem with an efficient computation. Finally, a real-world dataset is used for the case study. The results of using different charging functions indicate a large deviation between the linear charging function and the piecewise linear approximation, which can effectively avoid the infeasible bus schedules. Moreover, the experiments show that the proposed line change constraints can be an effective control method for transit operators.