Linear inequalities convex transformation for optimal reactive power flow model based on MISOCP relaxations

Abstract

A convex optimisation model for global optimum solution of optimal reactive power flow (ORPF) problem is proposed in this study, to solve the challenge of discrete variables of transformer taps involved in traditional ORPF models. Based on the second-order cone programming relaxation, a set of inequalities with 0-1 variables are introduced, to convexify the non-convex items that are products of discrete variables (or squares of discrete variables) and linear functions. After convexification, items containing second order of transformer ratio variables are dropped to the first order, and the non-convex non-linear nodal power equalities are equivalently transformed into linear equalities, thus formulating a mix-integer second-order cone programming (MISOCP) model of ORPF problem over feasible convex domain, which guarantees the global optimum theoretically. The results of IEEE-14, 30, 57, 118 bus systems show that, with stable numerical property and good optimum effect, the proposed model can give consideration to not only the quality of solution, but also the efficiency of calculation.