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Real-time state information provided by the state estimator plays a major role in power system monitoring and control. As a result, the convergence of the estimator under various system operating conditions becomes one of the key requirements. In this paper, a state estimation framework that achieves both statistical and numerical robustness is proposed. This estimation framework also generalizes several well-known estimators, including the weighted least squares estimator, the least absolute value estimator, the Huber Maximum-likelihood-estimator, and the Schweppe-type Huber generalized Maximum-likelihood (SHGM)-estimator. The statistical robustness of each estimator has been studied analytically through the total influence function. In addition, the dependence between the statistical robustness of an estimator and the numerical robustness of the iterative algorithm is investigated. To enhance the numerical robustness of the iterative algorithm that solves the SHGM-estimator, a fourth-order Levenberg–Marquardt approach-based SHGM (LM-SHGM) estimator is proposed. It integrates the statistical robustness of that estimator to address various types of bad data and the numerical robustness of the LM approach to handle highly stressed operating conditions. Numerical results carried out on the IEEE test systems demonstrate the good convergence and robustness of the proposed approach under various operating conditions. [ABSTRACT FROM AUTHOR]

This paper develops a robust generalized maximum-likelihood Koopman operator-based Kalman filter (GM-KKF) to estimate the rotor angle and speed of synchronous generators. The approach is data driven and model independent. Its design phase is carried out offline and requires estimates of the synchronous generators’ rotor angle and speed, along with active and reactive power at the generators’ terminal; in real-time operation, only measurements of the rotor speed, active, and reactive power are used. We first investigate the probability distribution of the transformed dynamic states by means of Q–Q plots and verify that the states of the GM-KKF approximately follow a Student's t-distribution with 20 degrees of freedom when the initial state vector is normally distributed. Under this assumption, our filter presents high statistical efficiency. Numerical simulations carried out on the IEEE 39-bus test system reveal that the GM-KKF has a faster convergence rate than the non-robust Koopman operator-based Kalman filter thanks to the adoption of a batch-mode regression formulation. They also show that the computing time of the GM-KKF is roughly reduced by one-third as compared to the one taken by our previously developed robust GM-extended Kalman filter. [ABSTRACT FROM AUTHOR]

This paper develops a robust power system state estimation framework that accounts for correlations and imperfect time synchronization of the measurements. In this framework, correlations of the measurements obtained from the supervisory control and data acquisition (SCADA) system and the phasor measurement units (PMUs) are separately calculated through the unscented transformation and a vector auto-regression (VAR) model. Specifically, the PMU measurements during the waiting period of two successive SCADA measurement scans are buffered via a VAR model whose parameters are robustly estimated using the projection statistics. The latter take into account their temporal and spatial correlations and provide the needed measurement redundancy to suppress bad data and mitigate imperfect time synchronization. In the case where the SCADA and the PMU measurements do not arrive simultaneously at the control center, yielding imperfect measurement time synchronization, either the forecasted PMU measurements or the prior SCADA measurements from the latest state estimation run are leveraged to restore system observability. Finally, a robust generalized maximum-likelihood (GM)-estimator is extended to integrate the measurement error correlations and to handle the outliers, also known as bad data. Simulation results that stem from a comprehensive comparison with other alternatives under various conditions demonstrate the benefits of the proposed framework. [ABSTRACT FROM AUTHOR]