An alternating direction method of multipliers-based approach to solve mixed-integer nonlinear volt/var optimization problems in distribution systems

This paper presents a tailored version of the alternating direction method of multipliers to achieve a centralized voltage and VAR optimization (VVO) in the electric distribution system. The adopted VVO model is a mixed-integer nonlinear optimization problem derived from the generic optimal power flow problem. A novel generalized and decomposable version of the VVO model is developed first to establish the proposed approach. The approach accounts for load tap-changers and switchable capacitor banks for illustration. However, it can be expanded to a broad range of controllable VVO equipment with discrete/integer settings. The approach performance is validated on different distribution networks. Results are compared with current leading heuristic approaches used to solve nonconvex mixed-integer nonlinear problems such as the Branch-and-Bound method. Furthermore, a comparison vs the branch flow model-based mixed integer second-order conic programming model is conducted to illustrate the proposed model's advantages. Moreover, to benchmark the proposed approach optimality, a direct search scheme is developed to capture guaranteed globally optimal results. Experiments show the superiority of the proposed approach with noteworthy convergence rates and promising optimal solution allocation.