Set-Valued Power System State Estimation Based on McCormick Relaxation

Power system state estimation (PSSE) is one of important tools for efficient operations of power systems. PSSE uses mathematical relation between the measured data and the power system’s network structure to estimate the state variables, i.e. voltage phasor of all buses. Uncertainty in the measured data affects the accuracy and reliability of estimation. In case that the uncertainty is given in the form of measurements’ bounds, the set-valued PSSE can be applied to estimate a set of all possible values of state variables. The problem can be expressed as a nonlinear constrained optimization problem. In this paper, a solution technique based on McCormick relaxation is proposed. The state variables are represented in rectangular forms. The nonlinear terms are substituted by auxiliary variables with linear inequalities. The linear programming technique is then applied to improve bounds of the estimated values. The proposed algorithm has been implemented based on the YALMIP toolbox. The preliminary results from testing with IEEE 14-bus show that the proposed approach provides the results with similar accuracy but uses less computation time than solving by the global nonlinear optimization.