Junbo Zhao

A Robust Iterated Extended Kalman Filter for Power System Dynamic State Estimation

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.

Robust Unscented Kalman Filter for Power System Dynamic State Estimation with Unknown Noise Statistics

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.

Calibrating Parameters of Power System Stability Models Using Advanced Ensemble Kalman Filter

With the ever increasing penetration of renewable energy, smart loads, energy storage, and new market behavior, todays power grid becomes more dynamic and stochastic, which may invalidate traditional study assumptions and pose great operational challenges. Thus, it is of critical importance to maintain good-quality models for secure and economic planning and real-time operation. Following the 1996 Western Systems Coordinating Council system blackout, North American Electric Reliability Corporation (NERC) and Western Electricity Coordinating Council (WECC) in North America enforced a number of policies and standards to guide the power industry to periodically validate power grid models and calibrate poor parameters with the goal of building sufficient confidence in model quality. The PMU-based approach using online measurements without interfering with the operation of generators provides a low-cost alternative to meet NERC standards. This paper presents an innovative procedure and tool suites to validate and calibrate models based on a trajectory sensitivity analysis method and an advanced ensemble Kalman filter algorithm. The developed prototype demonstrates excellent performance in identifying and calibrating bad parameters of a realistic hydro power plant against multiple system events.

Dynamic State Estimation With Model Uncertainties Using

When implementing Kalman filters to track system dynamic state variables, the dynamical model is assumed to be accurate. However, this assumption may not hold true as power system dynamical model is subjected to various uncertainties, such as varying generator transient reactance in different operation conditions, uncertain inputs, or noise statistics. As a result, the performance of Kalman-type filters can be degraded significantly. To bound the influence of these uncertainties, this letter proposes an

H_\infty

H_\infty

Extended Kalman Filter

extended Kalman filter (HEKF) based on the robust control theory. An approach to tune the parameter of HEKF is presented as well. Numerical results on the IEEE 39-bus system demonstrate the effectiveness of the HEKF.

A robust extended Kalman filter for power system dynamic state estimation using PMU measurements

This paper develops a robust extended Kalman filter to estimate the rotor angles and the rotor speeds of synchronous generators of a multimachine power system. Using a batch-mode regression form, the filter processes together predicted state vector and PMU measurements to track the system dynamics faster than the standard extended Kalman filter. Our proposed filter is based on a robust GM-estimator that bounds the influence of vertical outliers and bad leverage points, which are identified by means of the projection statistics. Good statistical efficiency under the Gaussian distribution assumption of the process and the observation noise is achieved thanks to the use of the Huber cost function, which is minimized via the iteratively reweighted least squares algorithm. The asymptotic covariance matrix of the state estimation error vector is derived via the covariance matrix of the total influence function of the GM-estimator. Simulations carried out on the IEEE 39-bus test system reveal that our robust extended Kalman filter exhibits good tracking capabilities under Gaussian process and observation noise while suppressing observation outliers, even in position of leverage. These good performances are obtained only under the validity of the linear approximation of the power system model.

Sparse State Recovery Versus Generalized Maximum-Likelihood Estimator of a Power System

This letter shows that the sparse state recovery optimization method is equivalent to the well-known Huber M-estimator, and then justifies its robustness to bad data. We derive the total influence functions of the Huber M-estimator and the generalized maximum-likelihood (GM)-estimator, and give a formal proof that the Huber M-estimator is vulnerable to bad leverage points while the GM-estimator can handle them. Numerical results carried out on various IEEE systems validate our theoretical results.

A Framework for Robust Hybrid State Estimation With Unknown Measurement Noise Statistics

In practical applications like power systems, the distribution of the measurement noise is usually unknown and frequently deviates from the assumed Gaussian model, yielding outliers. Under these conditions, the performances of the existing state estimators that rely on Gaussian assumption can deteriorate significantly. In addition, the sampling rates of measurements from supervisory control and data acquisition (SCADA) system and phasor measurement unit (PMU) are quite different, causing time skewness problem. In this paper, we propose a robust state estimation framework to address the unknown non-Gaussian noise and the measurement time skewness issue. In the framework, robust Mahalanbis distances are proposed to detect system abnormalities and assign appropriate weights to each chosen buffered PMU measurements. Those weights are further utilized by the Schweppe-type Huber generalized maximum-likelihood (SHGM) estimator to filter out non-Gaussian PMU measurement noise and help suppress outliers. In the meantime, the SHGM estimator is used to handle unknown noise of the received SCADA measurements, yielding another set of state estimates. We show that the state estimates provided by the SHGM estimator follow an asymptotical Gaussian distribution. This nice property allows us to obtain the optimal state estimates by resorting to the data fusion theory for the fusion of the estimation results from two independent SHGM estimators. Extensive simulation results carried out on the IEEE 14, 30 and 118-bus test systems demonstrate the effectiveness and robustness of the proposed method.