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L Mili - One of the best experts on this subject based on the ideXlab platform.

  • robust unscented kalman filter for power system dynamic State estimation with unknown noise statistics
    IEEE Transactions on Smart Grid, 2019
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    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.

  • a robust generalized maximum likelihood unscented kalman filter for power system dynamic State estimation
    IEEE Journal of Selected Topics in Signal Processing, 2018
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    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.

  • a robust iterated extended kalman filter for power system dynamic State estimation
    IEEE Transactions on Power Systems, 2017
    Co-Authors: Junbo Zhao, Marcos Netto, L Mili
    Abstract:

    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 power system dynamic State estimator with non gaussian measurement noise part i theory
    arXiv: Statistics Theory, 2017
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    This paper develops the theoretical framework and the equations of 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 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 (PS's) is proposed. The PS's are applied to a two-dimensional matrix that consists of 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. In the companion paper, extensive simulation results will be shown to verify the effectiveness and robustness of the proposed method.

Junbo Zhao - One of the best experts on this subject based on the ideXlab platform.

  • robust unscented kalman filter for power system dynamic State estimation with unknown noise statistics
    IEEE Transactions on Smart Grid, 2019
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    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.

  • robust forecasting aided power system State estimation considering State correlations
    IEEE Transactions on Smart Grid, 2018
    Co-Authors: Junbo Zhao, Gexiang Zhang, Zhao Yang Dong, Massimo La Scala
    Abstract:

    With the increase of load fluctuations and the integration of stochastic distributed generations (DGs), there have been more and more research interests in forecasting-aided State estimation. In this paper, we propose a robust generalized maximum likelihood (GM)-estimator based power system forecasting-aided State estimation, which integrates the statistical characteristics of both loads and DGs, i.e., spatial and temporal correlations. A first order vector auto-regressive model (VAR(1)) is developed to capture the statistical characteristics of load and DGs, facilitating short-term loads and DGs forecasting. These forecasted power injections are further combined with power balance equations to derive a new State transition model, where the relationship between forecasted State vector and Predicted power injections is expressed explicitly. After that, a redundant batch regression model that simultaneously processes Predicted State vector and received observations is derived, allowing the development of a robust estimator. To this end, we propose a robust GM-estimator that leverages modified projection statistics and a Huber convex score function, to bound the influence of observation outliers while maintaining its high statistical estimation efficiency. Finally, the iteratively reweighted least squares algorithm is adopted to solve the GM-estimator. Numerical comparisons on IEEE benchmark systems with DGs integration demonstrate the efficiency and robustness of the proposed method.

  • a robust generalized maximum likelihood unscented kalman filter for power system dynamic State estimation
    IEEE Journal of Selected Topics in Signal Processing, 2018
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    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.

  • a robust iterated extended kalman filter for power system dynamic State estimation
    IEEE Transactions on Power Systems, 2017
    Co-Authors: Junbo Zhao, Marcos Netto, L Mili
    Abstract:

    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 power system dynamic State estimator with non gaussian measurement noise part i theory
    arXiv: Statistics Theory, 2017
    Co-Authors: Junbo Zhao, L Mili
    Abstract:

    This paper develops the theoretical framework and the equations of 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 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 (PS's) is proposed. The PS's are applied to a two-dimensional matrix that consists of 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. In the companion paper, extensive simulation results will be shown to verify the effectiveness and robustness of the proposed method.

Mario Paolone - One of the best experts on this subject based on the ideXlab platform.

  • a prediction error covariance estimator for adaptive kalman filtering in step varying processes application to power system State estimation
    IEEE Transactions on Control Systems and Technology, 2017
    Co-Authors: Lorenzo Zanni, Jeanyves Le Boudec, Rachid Cherkaoui, Mario Paolone
    Abstract:

    In this paper, we present a new method for the estimation of the prediction-error covariances of a Kalman filter (KF), which is suitable for step-varying processes. The method uses a series of past innovations (i.e., the difference between the upcoming measurement set and the KF Predicted State) to estimate the prediction-error covariance matrix by means of a constrained convex optimization problem. The latter is designed to ensure the symmetry and the positive semidefiniteness of the estimated covariance matrix, so that the KF numerical stability is guaranteed. Our proposed method is straightforward to implement and requires the setting of one parameter only, i.e., the number of past innovations to be considered. It relies on the knowledge of a linear and stationary measurement model. The ability of the method to track State step-variations is validated in ideal conditions for a random-walk process model and for the case of power-system State estimation. The proposed approach is also compared with other methods that estimate the KF stochastic parameters and with the well-known linear weighted least squares. The comparison is given in terms of both accuracy and computational time.

Massimo La Scala - One of the best experts on this subject based on the ideXlab platform.

  • robust forecasting aided power system State estimation considering State correlations
    IEEE Transactions on Smart Grid, 2018
    Co-Authors: Junbo Zhao, Gexiang Zhang, Zhao Yang Dong, Massimo La Scala
    Abstract:

    With the increase of load fluctuations and the integration of stochastic distributed generations (DGs), there have been more and more research interests in forecasting-aided State estimation. In this paper, we propose a robust generalized maximum likelihood (GM)-estimator based power system forecasting-aided State estimation, which integrates the statistical characteristics of both loads and DGs, i.e., spatial and temporal correlations. A first order vector auto-regressive model (VAR(1)) is developed to capture the statistical characteristics of load and DGs, facilitating short-term loads and DGs forecasting. These forecasted power injections are further combined with power balance equations to derive a new State transition model, where the relationship between forecasted State vector and Predicted power injections is expressed explicitly. After that, a redundant batch regression model that simultaneously processes Predicted State vector and received observations is derived, allowing the development of a robust estimator. To this end, we propose a robust GM-estimator that leverages modified projection statistics and a Huber convex score function, to bound the influence of observation outliers while maintaining its high statistical estimation efficiency. Finally, the iteratively reweighted least squares algorithm is adopted to solve the GM-estimator. Numerical comparisons on IEEE benchmark systems with DGs integration demonstrate the efficiency and robustness of the proposed method.

Wu Yi-chen - One of the best experts on this subject based on the ideXlab platform.

  • Robust M–M unscented Kalman filtering for GPS/IMU navigation
    Journal of Geodesy, 2019
    Co-Authors: Cheng Yang, Wenzhong Shi, Wu Yi-chen
    Abstract:

    In this paper, a robust unscented Kalman filter (UKF) based on the generalized maximum likelihood estimation (M-estimation) is proposed to improve the robustness of the integrated navigation system of Global Navigation Satellite System and Inertial Measurement Unit. The UKF is a variation of Kalman filter by which the Jacobian matrix calculation in a nonlinear system State model is not necessary. The proposed robust M–M unscented Kalman filter (RMUKF) applies the M-estimation principle to both functional model errors and measurement errors. Hence, this robust filter attenuates the influences of disturbances in the dynamic model and of measurement outliers without linearizing the nonlinear State space model. In addition, an equivalent weight matrix, composed of the bi-factor shrink elements, is proposed in order to keep the original correlation coefficients of the Predicted State unchanged. Furthermore, a nonlinear error model is used as the dynamic equation to verify the performance of the proposed RMUKF with a simulation and field test. Compared with the conventional UKF, the impacts of measurement outliers and system disturbances on the State estimation are both controlled by RMUKF.