State Estimation of Power System Signal using Constrained Optimized Algorithms-Comparative Analysis

This paper presents two innovative algorithms constrained extended Kalman filter (CEKF) and recursive constrained convex optimization for parameters (amplitude, frequency, and phase) estimation of power system voltage/current signal in the presence of random noise and distortions. Under steady-state and dynamic conditions amplitude, frequency, and phase angle of the considered waveform vary within certain limits. In constrained state optimization problem, least mean squared error of a window of acquired voltage/current samples with respect to a given signal model and is considered for minimization to find the parameters. The objective function is further augmented with logarithmic barrier functions to include the constraints. An iterative algorithm has been proposed to minimize this augmented function. Further, a new algorithm of CEKF has been developed using interior point optimization where constraints are posed on states. Then, in order to examine the efficiency and robustness of both algorithms, two test cases with different signal conditions have been taken. The performed results are analyzed statistically by means of settling point and steady-state error. From the results, it can be concluded that CEKF is more reliable, effective technique to give a quick and correct estimation of the signal parameters.