Electric Bus Charging Schedules Relying on Real Data-Driven Targets Based on Hierarchical Deep Reinforcement Learning

A Markov Decision Process (MDP) is conceived, where the time horizon includes multiple charging and operating periods in a day, while each period is further divided into multiple time steps. To overcome the challenge of long-range multi-phase planning with sparse reward, we conceive Hierarchical DRL (HDRL) for decoupling the original MDP into a high-level Semi-MDP (SMDP) and multiple low-level MDPs. The Hierarchical Double Deep Q-Network (HDDQN)-Hindsight Experience Replay (HER) algorithm is proposed for simultaneously solving the decision problems arising at different temporal resolutions. As a result, the high-level agent learns an effective policy for prescribing the charging targets for every charging period, while the low-level agent learns an optimal policy for setting the charging power of every time step within a single charging period, with the aim of minimizing the charging costs while meeting the charging target. It is proved that the flat policy constructed by superimposing the optimal high-level policy and the optimal low-level policy performs as well as the optimal policy of the original MDP . Since jointly learning both levels of policies is challenging due to the non-stationarity of the high-level agent and the sampling inefficiency of the low-level agent, we divide the joint learning process into two phases and exploit our new HER algorithm to manipulate the experience replay buffers for both levels of agents. Numerical experiments are performed with the aid of real-world data to evaluate the performance of the proposed algorithm. Index T erms Deep Reinforcement Learning; Electric Bus; Hierarchical Reinforcement learning; Charging Control A CRONYMS DDQN Double Deep Q Network DNN Deep Neural Network DQL Double Q-learning DQN Deep Q Network DRL Deep Reinforcement Learning EB Electric Bus EBCSP Electric Bus Charging Scheduling Problem GA Genetic Algorithm GHG GreenHouse Gas HAC Hierarchical Actor-Critic HDDQN Hierarchical Double Deep Q Network HDRL Hierarchical Deep Reinforcement Learning HER Hindsight Experience Replay HRL Hierarchical Reinforcement Learning IA Immune Algorithm MDP Markov Decision Process MILP Mixed Integer Linear Programming ML Machine Learning MRP Markov Reward Process RES Renewable Energy Source RL Reinforcement Learning RO Robust Optimization RTEM Real Time Energy Market 1 J. Qi and L. Lei are with the School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada, jiaju@uoguelph.ca;