Reactive Power Scheduling Using Quadratic Convex Relaxation

In this paper, quadratic convex relaxation (QCR) is used to relax AC optimal power flow (AC-OPF) used for reactive power scheduling (RPS) of power system. The objective function is system active power losses minimization to optimally determine the tap position of tap-changers, reactive power output of generating units, synchronous condensers, shunt capacitor banks and reactors. The nonlinear and non-convex terms due to trigonometric functions causes the problem to be non-convex which results in trapping in local minimum or even not converging in large size power systems. Therefore, in this paper the nonlinear terms and trigonometric function are relaxed by linear and quadratic functions. Furthermore, the product of two variables and multi-variables are relaxed by McCormick bilinear and multi-linear expressions, converting the AC-OPF of RPS to quadratic constraint programming (QCP) optimization problem. The proposed RPS method is studied based on IEEE RTS 24-bus test system. The results show the accuracy of the proposed (QCR) method to relax AC-OPF optimization problem of RPS.