Acceleration Framework and Solution Algorithm for Distribution System Restoration Based on End-to-End Optimization Strategy

The distribution system restoration (DSR) problem is traditionally modeled as a mixed-integer linear programming (MILP) model. However, a significant number of integer variables are introduced to describe the DSR process, which introduce additional complexities in both time and space dimensions. Moreover, an enormous number of constraints are constructed to establish a rational DSR decision, while some of them may not be considered tight in practice. The enormous number of binary variables and inactive constraints could make the DSR problem very hard to solve and apply in real-time. The DSR computation burden would be reduced significantly if binary variables and binding constraints are pre-determined. This paper proposes an acceleration framework and solution algorithm based on the end-to-end optimization, which applies deep neural network (DNN) and gradient boosting decision tree (GBDT) methods to DSR. The DSR problem, which is solved in offline and online stages, will accordingly be reduced to a linear programming problem which can be solved more efficiently and reliably. Case studies are carried out on the modified IEEE 33-bus and 123-bus systems and a practical 1069-bus system. The proposed results indicate that the DSR problem with the proposed end-to-end acceleration framework is solved more than tenfold faster than those of traditional solvers.