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Mixed-Integer SDP Relaxation-based Volt/Var Optimization for Unbalanced Distribution Systems

This paper aims to conduct volt/var optimization for unbalanced distribution systems considering discrete tap changers, such as voltage regulators (VRs). There are two challenges to tackle this mixed-integer nonlinear optimization problem, namely, the difficulty to judge the quality of the solution and the lack of an effective solver. In this paper, we tackle both challenges. A sparse convex relaxation of branch flow model for multiphase distribution systems is adopted for the underlying optimal power flow problem. The overall problem becomes a mixed-integer semidefinite programming (MISDP) problem. Further, an effective generalized Benders decomposition (GBD) algorithm is developed in this paper to solve the problem. Boundtightening technique is employed in this research to reduce the search region of the main problem, which renders a significantly faster convergence. Numerical tests on an IEEE 37-bus system demonstrate the convergence of the GBD and success in finding a global optimal setting of VR taps while abiding by the system's constraints.