Convex Optimal Power Flow Based on Second-Order Cone Programming: Models, Algorithms and Applications

Abstract: Optimal power flow (OPF) is the fundamental mathematical model to optimally operate the power system. Improving the solution quality of OPF can help the power industry save billions of dollars annually. Past decades have witnessed enormous research efforts on OPF since J. Carpentier proposed the fully formulated alternating current OPF (ACOPF) model which is nonconvex. This thesis proposes three convex OPF models (SOC-ACOPF) based on second-order cone programming (SOCP) and McCormick envelope. The underlying idea of the proposed SOC-ACOPF models is to drop assumptions of the original SOC-ACOPF model by convex relaxation and approximation methods. A heuristic algorithm to recover feasible OPF solution from the relaxed solution of the proposed SOC-ACOPF models is developed. The quality of solutions with respect to global optimum is evaluated using MATPOWER and LINDOGLOBAL. A computational comparison with other SOC-ACOPF models in the literature is also conducted. The numerical results show robust performance of the proposed SOC-ACOPF models and the feasible solution recovery algorithm. We then propose to speed up solving large-scale SOC-ACOPF problem by decomposition and parallelization. We use spectral factorization to partition large power network to multiple subnetworks connected by tie-lines. 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 of the proposed M-BDA is analytically proved. A GAMS grid computing framework is designed to compute the formulated subproblems 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.Finally, various applications of our SOC-ACOPF models and M-BDA including distribution locational marginal pricing (DLMP), wind power integration and ultra-large-scale power network or super grid operation are demonstrated.