A two-stage stochastic programming model of coordinated electric bus charging scheduling for a hybrid charging scheme

This paper proposes a coordinated charging scheduling approach for battery electric buses (BEBs) in a hybrid charging scheme, i.e., both plug-in fast charging and battery-swapping charging modes are incorporated in a single charging station. To accommodate the uncertain battery energy consumption during bus operation, a two-stage stochastic program is formulated, where the first stage decision determines the battery inventory level of each station and the second stage determines the charging mode and designs when, where, and how long each bus should be charged. Future uncertainties associated with energy consumption are captured by a set of possible discrete scenarios from historical data. A progressive hedging algorithm is developed to decompose the two-stage stochastic program into sub-problems. A case study is conducted to verify the proposed models and solution algorithms.