Optimal Power Flow for AC Power System based on Convex Relaxtion with Semi-Definite Programming

In this paper, the classical AC-OPF model is firstly introduced, and then it is relaxed into semi-definite (SD) OPF and second-order cone (SOC) OPF by the convex relaxation technique. Linear, SOC and SD OPF are compared in the example analysis. The high accuracy of SD OPF is verified. Compared with the classical AC OPF, the SD OPF model does not have the rank-one constraint, so the optimal solution may be outside the feasible area of the original OPF problem which is nonlinear and non-convex. This paper introduces two methods to obtain the exact solution, namely the penalty function method and the iterative algorithm based on convex-concave procedure principle, and then applies these two approaches to the case30 test system in the following part, where the feasibility of the two methods is verified.