A two-stage robust power system state estimation method with unknown measurement noise

In practical applications like power system, the distribution of the measurement noise is unknown or frequently deviates from the assumed Gaussian model, often being characterized by heavy tails and sometimes generating impulse noise, named outliers. Under these conditions, the performances of the conventional state estimation (SE) methods that assume known and Gaussian noise, will be greatly degraded. To solve these problems, this paper proposes a two-stage robust power system SE method. In the first stage, a GM-estimator that uses conventional SCADA measurements is proposed by using the robust scale estimation, projection statistics and Huber-type M-estimator. Its result is further combined with the PMU measurement to achieve a linear robust estimation in the second stage. The projection statistics is used to identify and downweight the bad leverage measurements. The GM-estimator bounds the influences of bad data and the estimation residuals, yielding good statistical efficiency for Gaussian noise or even other non-Gaussian heavy tailed distributions, like Laplace, Gaussian mixture, etc. Numerical tests on the IEEE-30 bus system under various cases verify the effectiveness and robustness of the proposed method.