Solution of optimal power flow problems by operator splitting method

In recent years, interior point method combined with linear conic programming (LCP) has become a hot topic of solving optimal power flow (OPF) problem in power system. However, interior point method has been proved to be inefficient for a large-scale LCP problem as it can´t take advantage of the sparse characteristics in the original data matrix while solving the Schur complement equation. To this end, an operator splitting method, simplified alternating direction method of multipliers (SADMM) which is high-efficiency of solving LCP problems, is presented in this paper. In order to acquire the solvable form of SADMM, based on semidefinite-quadratic-linear programming (SQLP), the original OPF problem is transformed into an intermediate model called SQLP-OPF which consists of two semidefinite matrix variables and a non-negative conic variable. After forming the constraint coefficient matrix and the objective function coefficient of SADMM through the dual problem of SQLP-OPF, the solvable SADMM-based OPF could be formed. Four IEEE benchmark systems (IEEE 30, 57, 118, 300) and a 703 buses power system from Asia are employed in numerical experiments to demonstrate the effectiveness of the proposed method. The results indicate that the proposed SADMM-based algorithm possesses a high computational efficiency and accuracy, and applies to large-scale power system problems.