Adaptive and Robust Distribution System State Estimator Handling Unknown Noise Statistics

State estimation (SE) is a vital monitoring tool for active distribution networks (ADNs). Conventional cubature Kalman filter (CKF)-based ADN-SE delivers deteriorated estimates due to fast state variations caused by intermittency in injections from distributed energy resources (DERs). With the nature of DER outputs being unknown, the process noise covariance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {Q}$</tex-math></inline-formula>) adaptation is essential, and Q-scaled adaptive CKF (QS-CKF) is initially proposed for forecasting aided ADN-SE to deliver improved accuracy. Thereafter, performance assessment with unknown non-Gaussian measurement noise statistics using QS-CKF indicates an inferior accuracy. To overcome this limitation, a Mahalanobis distance (MD)-based outlier detection and robustification of QS-CKF (RQS-CKF) is proposed, where the outliers are detected via MD criterion, and robustness is achieved by measurement noise covariance (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {R}$</tex-math></inline-formula>) inflation. The scaling factor for inflating <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {R}$</tex-math></inline-formula> remains unknown initially and is determined via Newton’s method, which is also numerically stable for different non-Gaussian noise distributions. Testing these estimators on IEEE benchmark systems reveals that RQS-CKF delivers fast and superior estimates, thereby ensuring adaptability and robustness.