Jinghe Zhang

A Two-Stage Kalman Filter Approach for Robust and Real-Time Power System State Estimation

As electricity demand continues to grow and renewable energy increases its penetration in the power grid, real-time state estimation becomes essential for system monitoring and control. Recent development in phasor technology makes it possible with high-speed time-synchronized data provided by phasor measurement units (PMUs). In this paper, we present a two-stage Kalman filter approach to estimate the static state of voltage magnitudes and phase angles, as well as the dynamic state of generator rotor angles and speeds. Kalman filters achieve optimal performance only when the system noise characteristics have known statistical properties (zero-mean, Gaussian, and spectrally white). However, in practice, the process and measurement noise models are usually difficult to obtain. Thus, we have developed the adaptive Kalman filter with inflatable noise variances (AKF with InNoVa), an algorithm that can efficiently identify and reduce the impact of incorrect system modeling and/or erroneous measurements. In stage one, we estimate the static state from raw PMU measurements using the AKF with InNoVa; then in stage two, the estimated static state is fed into an extended Kalman filter to estimate the dynamic state. The simulations demonstrate its robustness to sudden changes of system dynamics and erroneous measurements.

Observability and estimation uncertainty analysis for PMU placement alternatives

The synchronized phasor measurement unit (PMU), developed in the 1980s, is considered to be one of the most important devices in the future of power systems. While PMU measurements currently cover fewer than 1% of the nodes in the U.S. power grid, the power industry has gained the momentum to advance the technology and install more units. However, with limited resources, the installation must be selective. Previous PMU placement research has focused primarily on the network topology, with the goal of finding configurations that achieve full network observability with a minimum number of PMUs. Here we present a new approach that also includes stochastic models for the signals and measurements, to characterize the observability and corresponding uncertainty of any given configuration of PMUs, whether that configuration achieves full observability or not. We hope that this approach can provide planning engineers with a new tool to help choose between PMU placement alternatives.

Optimal PMU placement evaluation for power system dynamic state estimation

The synchronized phasor measurement unit (PMU), developed in the 1980s, is considered to be one of the most important devices in the future of power systems. The recent development of PMU technology provides high-speed, precisely synchronized sensor data, which has been found to be useful for dynamic state estimation of the power grid. While PMU measurements currently cover fewer than 1% of the nodes in the U.S. power grid, the power industry has gained the momentum to advance the technology and install more units. However, with limited resources, the installation must be selective. Previous PMU placement research has focused primarily on network topology, with the goal of finding configurations that achieve full network observability with a minimum number of PMUs. Recently we introduced an approach that utilizes stochastic models of the signals and measurements, to characterize the observability and corresponding uncertainty of power system static states (bus voltage magnitudes and phase angles), for any given configuration of PMUs. Here we present a new approach to designing optimal PMU placement according to estimation uncertainties of the dynamic states. We hope the approach can provide planning engineers with a new tool to help in choosing between PMU placement alternatives.

Analyzing Invariants in Cyber-Physical Systems using Latent Factor Regression

The analysis of large scale data logged from complex cyber-physical systems, such as microgrids, often entails the discovery of invariants capturing functional as well as operational relationships underlying such large systems. We describe a latent factor approach to infer invariants underlying system variables and how we can leverage these relationships to monitor a cyber-physical system. In particular we illustrate how this approach helps rapidly identify outliers during system operation.

LoDiM: A novel power system state estimation method with dynamic measurement selection

For decades, state estimation has been a fundamental aspect of power systems. However for large-scale and wide-area interconnected power systems, the required computation makes real-time on-line estimation a major challenge. In this paper we present a new method we call Lower Dimensional Measurement-space (LoDiM) state estimation. LoDiM is based on the Extended Kalman filter — popular because of its efficiency, robustness, and typical accuracy. LoDiM, which can take advantage of modern parallel computation techniques, may be useful for other large-scale, real-time on-line and computationally-intensive state tracking systems beyond the power systems, such as weather forecasting or gas-pipeline state estimation. Although LoDiM is presented in the context of the Kalman filter, the associated measurement selection procedure is not filter-specific, i.e. it can be used with other state estimation methods such as particle and unscented filters. If desired, robust estimation techniques can also be employed to detect and eliminate outlier measurements.

Reduced Measurement-space Dynamic State Estimation (ReMeDySE) for power systems

Applying Kalman filtering techniques to dynamic state estimation is a developing research area in modern power systems. Compared to traditional steady state estimators, the Kalman filter is able to track dynamic state variables both efficiently and accurately. However, in large-scale and wide-area interconnected power systems, the combination of computational complexity—primarily due to the very large number of measurements—and slow processing speeds present a significant challenge. To help address this challenge we have developed an approach we call Reduced Measurement-space Dynamic State Estimation (ReMeDySE). We present the method in the context of the Kalman filter, however it can also be applied to other state estimation methods such as particle filters. In addition, although we present the method in the context of power systems, it is suitable for real-time and massive calculations in any large-scale state tracking systems. Finally, the method lends itself well to modern parallel computation techniques for further improvements.

Power system state estimation with dynamic optimal measurement selection

Power system measurement devices continue to evolve towards higher accuracy and update rate. On the other hand, the computation required for processing the enormous amounts of measurement data associated with large complex power systems makes real-time estimation a major challenge. In this paper we present the Lower Dimensional Measurement-space (LoDiM) state estimation method for large-scale and wide-area interconnected power systems. We present the method in the context of the Kalman filter and Extended Kalman filter, however our measurement selection procedure is not filter-specific, i.e. it can also be applied on other state estimation methods such as particle filters and unscented filters. Our method can also take advantage of large-scale parallel computation techniques for further improvement. Moreover, the concept of LoDiM should be applicable to other large-scale, real-time and computationally-intensive state tracking systems beyond the power systems, such as weather forecasting systems, gas-pipeline systems, and other critical infrastructure.

Secure and adaptive state estimation for a PMU-equipped smart grid

Modern power systems are constantly subjected to various disturbances, device failures, as well as data attacks. To improve the quality of monitoring and control in smart grid, researchers have conducted extensive studies in exploring the advantages of real-time digital meters such as the Phasor Measurement Units, combining with dynamic estimation methods such as Kalman filters. Standard Kalman filter assumes we have statistical knowledge regarding the uncertainty of the system under study. The reality is, the accurate system model is almost impossible to obtain, especially with the existence of malicious data attack. A lightweight and efficient adaptive Kalman filter algorithm is presented in this paper for its ability to alleviate the impact of incorrect system models and/or measurement data. Simulations demonstrate that it is resilient to suboptimal system modeling, sudden system dynamic changes and bad data injection.