A distributed restoration framework for distribution systems incorporating electric buses

•Electric buses are employed for the restoration of distribution systems.•A distributed restoration framework for distribution systems is proposed.•A novel electric bus scheduling model incorporating passenger demand is built.•An improved ADMM is used to solve the restoration problem efficiently. Electric buses can enhance the restoration of distribution systems. However, existing studies have focused on centralized restoration between the electric bus and the distribution system, ignoring the subjectivity and privacy of the electric bus company. This paper proposes a distributed restoration framework for distribution systems incorporating electric buses to address the problem. Firstly, a mixed-integer linear scheduling model of electric buses is constructed considering the bus service requirements, space–time characteristics, and energy characteristics. Secondly, a bi-level distributed restoration framework is proposed. The upper level aims to decide the energy restoration tasks of the electric bus company, and the lower level introduces a control center, using a sequential iterative approach to determine each electric bus's energy and bus service tasks. Thirdly, the distributed restoration model is developed using the augmented Lagrangian method and solved via the improved alternating direction multiplier method (ADMM). The improved ADMM can adaptively change the penalty factor to speed up the convergence. Finally, numerical simulations are performed by the IEEE 33-node distribution system. The results show that the participation of electric buses can enhance the restoration of distribution systems and the proposed distributed restoration framework has good convergence and high optimization efficiency.