A Modified Benders Decomposition Algorithm to Solve Second-Order Cone AC Optimal Power Flow

This paper proposes to speed up solving large-scale second-order cone ac optimal power flow (SOC-ACOPF) problem by decomposition and parallelization. First, we use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. Then a modified Benders decomposition algorithm (M-BDA) is proposed to solve the SOC-ACOPF problem iteratively. Taking the total power output of each subnetwork as the complicating variable, we formulate the SOC-ACOPF problem of tie-lines as the master problem and the SOC-ACOPF problems of the subnetworks as the subproblems in the proposed M-BDA. The feasibility and optimality (preserving the original optimal solution of the SOC-ACOPF model) of the proposed M-BDA are analytically and numerically proved. A GAMS grid computing framework is designed to compute the formulated subproblems of M-BDA in parallel. The numerical results show that the proposed M-BDA can solve large-scale SOC-ACOPF problem efficiently. Accelerated M-BDA by parallel computing converges within few iterations. The computational efficiency (reducing computation CPU time and computer RAM requirement) can be improved by increasing the number of partitioned subnetworks.