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Due to the communication channel noises, GPS synchronization process, changing environment temperature and different operating conditions of the system, the statistics of the system process and measurement noises may be unknown and they may not follow Gaussian distributions. As a result, the traditional Kalman filter-based dynamic state estimators may provide strongly biased state estimates. To address these issues, this paper develops a robust generalized maximum-likelihood unscented Kalman filter (GM-UKF). The statistical linearization approach is presented to derive a compact batch-mode regression form by processing the predicted state vector and the received measurements simultaneously. This regression form enhances the data redundancy and allows us to detect bad phasor measurement unit measurements and incorrect state predictions, and filter out unknown Gaussian and non-Gaussian noises through the generalized maximum likelihood-estimator. The latter minimizes a convex Huber function with weights calculated via the projection statistics (PS). Particularly, the PS is applied to a proposed 2-dimensional matrix that consists of temporally correlated innovation vectors and predicted states. Finally, the total influence function is used to derive the error covariance matrix of the GM-UKF state estimates, yielding the robust state prediction at the next time instant. Extensive simulations carried out on the IEEE 39-bus test system demonstrate the effectiveness and robustness of the proposed method. [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 new robust generalized maximum-likelihood-type unscented Kalman filter (GM-UKF) that is able to suppress observation and innovation outliers while filtering out non-Gaussian process and measurement noise. Because the errors of the real and reactive power measurements calculated using phasor measurement units (PMUs) follow long-tailed probability distributions, the conventional UKF provides strongly biased state estimates since it relies on the weighted least squares estimator. By contrast, the state estimates and residuals of our GM-UKF are proved to be roughly Gaussian, allowing the sigma points to reliably approximate the mean and the covariance matrices of the predicted and corrected state vectors. To develop our GM-UKF, we first derive a batch-mode regression form by processing the predictions and observations simultaneously, where the statistical linearization approach is used. We show that the set of equations so derived are equivalent to those of the unscented transformation. Then, a robust GM-estimator that minimizes a convex Huber cost function while using weights calculated via projection statistics (PSs) is proposed. The PSs are applied to a two-dimensional matrix that consists of a serially correlated predicted state and innovation vectors to detect observation and innovation outliers. These outliers are suppressed by the GM-estimator using the iteratively reweighted least squares algorithm. Finally, the asymptotic error covariance matrix of the GM-UKF state estimates is derived from the total influence function. Extensive simulation results carried out on IEEE New England 39-bus 10-machine test system verify the effectiveness and robustness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper develops a robust iterated extended Kalman filter (EKF) based on the generalized maximum likelihood approach (termed GM-IEKF) for estimating power system state dynamics when subjected to disturbances. The proposed GM-IEKF dynamic state estimator is able to track system transients in a faster and more reliable way than the conventional EKF and the unscented Kalman filter (UKF) thanks to its batch-mode regression form and its robustness to innovation and observation outliers, even in position of leverage. Innovation outliers may be caused by impulsive noise in the dynamic state model while observation outliers may be due to large biases, cyber attacks, or temporary loss of communication links of PMUs. Good robustness and high statistical efficiency under Gaussian noise are achieved via the minimization of the Huber convex cost function of the standardized residuals. The latter is weighted via a function of robust distances of the two-time sequence of the predicted state and innovation vectors and calculated by means of the projection statistics. The state estimation error covariance matrix is derived using the total influence function, resulting in a robust state prediction in the next time step. Simulation results carried out on the IEEE 39-bus test system demonstrate the good performance of the GM-IEKF under Gaussian and non-Gaussian process and observation noise. [ABSTRACT FROM AUTHOR]