Virtual-Voltage Partition-Based Approach to Mixed-Integer Optimal Power Flow Problems

This paper deals with optimal power flow (OPF) problems with discrete variables that capture binary decisions about network topology configurations and capacitor bank settings. We adopt a semidefinite programming formulation for the OPF problem which, however, remains nonconvex due to the presence of discrete variables and bilinear products between the decision variables. To tackle the latter, we introduce a novel physically-inspired, virtual-voltage approximation that leads to provable lower and upper bounds on the solution of the original problem. To deal with the exponential complexity caused by the discrete variables, we introduce a graph partition-based algorithm which breaks the problem into several parallel mixed-integer subproblems of smaller size. Simulations on the IEEE 30, 118, 300 bus test cases demonstrate the high degree of accuracy and affordable computational requirements of our approach.