Power System Dynamic State Estimation Research Articles

Dynamic State Estimation of Synchronous Machines Using Iterated Square-Root Cubature Kalman Filter and Synchrophasor Measurements

Power system dynamic state estimation is the first prerequisite for control and stability prediction under transient conditions. For a stable and reliable power system, it is crucial and helpful to have accurate, precise, and up-to-date information on the states of the synchronous machines- rotor angle and rotor speed deviation. This paper proposes an application of the Iterated Square-root Cubature Kalman filter (ISCKF) to estimate these main states of synchronous generators. The ISCKF method consists of two step modification - one is the square-root step modification of CKF and the next step is the addition of iterative approach to the square-root CKF method. To demonstrate the performance of the proposed approach during a three-phase short circuit fault, the simulation results, are compared with that of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Cubature Kalman Filter (CKF). The test systems considered are a single machine infinite bus (SMIB) system, an IEEE 9-bus system and a 19-generator 42-bus test system. The estimation accuracy of the rotor angle using ISCKF method is increased by 6.8–36.54% when compared to that of the CKF method. Similarly, the improvement in accuracy is 4.4–28.57% for estimation of speed deviation.

Dynamic state estimation of power systems considering maximum correlation entropy and quadratic function

Uncertainties such as abnormal system inputs, strong model nonlinearities, outliers and impulsive noise unavoidably exist in the power system dynamic state estimation (SE) (DSE). The existing Kalman filter-based DSE methods cannot deal with the uncertainties well and can be improved further. In this paper, a robust DSE method based on the maximum correlation entropy (MCE), quadratic function (QF) and the cubature Kalman filter is proposed to reduce the effects caused by the uncertainties. The MCE-QF based estimator is robust and can alleviate the influence of uncertainties. A new SE error covariance is derived by using the robust statistical tool, influence function. The robustness and estimation precision of the proposed DSE method is demonstrated by conducting simulations on a synchronous generator under different cases.

Improved dynamic state estimation of power system using unscented Kalman filter with more accurate prediction model

Power system dynamic state estimation plays an important role. However, rapid changes in states cause state estimation to become very hard. To reduce the residual between pseudo and real measurement, prediction models are adopted, which are strongly associated with the convergence rates and accuracies of estimation methods. In this paper, to improve the estimation accuracy, a prediction model that consists of the convolutional neural network and long short-term memory (CNN-LSTM) is employed and then integrated into the unscented Kalman filter (UKF). In the proposed UKF with CNN-LSTM, state vectors are considered as time-series data, so CNN performs feature extraction for data pre-processing first, and then the features go through LSTM to improve its forecast accuracy in real-time. Next, online training and error normalization are introduced to UKF, which increases the estimation accuracy effectively. Finally, simulations are carried out on the IEEE 33-bus system. Simulation results show that the accuracies of the CNN-LSTM prediction model are much higher than those of conventional methods. Furthermore, compared to widely used state estimation methods, our method decreases RMSE and MAPE by about 2 multiples.

Square-root cubature Kalman filter based power system dynamic state estimation

The state estimator’s real-time state information plays a vital role in monitoring and control of the power system. As a result, one of the primary requirements of the estimator is to provide accurate state estimates with good convergence under varied system operating conditions. In this context, dynamic state estimation (DSE) consistently tracks the power system dynamics and delivers real-time system state evolution. In literature, this dynamic state estimation (SE) problem is generally solved using an extended Kalman filter (EKF). The EKF approach neglects the non-linear mathematical functions of network equations by linearly approximating the measurement equations. This leads to degradation of SE accuracy during a sudden change in load conditions. In this paper, a new derivative-free method based on square-root cubature Kalman filter (SCKF) is proposed to overcome the limitations of the EKF technique and achieves improved performance. The proposed SCKF technique has been tested on IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems under various operating conditions. The effectiveness of the SCKF technique has been compared with the traditional EKF and cubature Kalman filter (CKF) techniques using different performance indices. The obtained results demonstrate the versatility of the proposed SCKF technique.

Guest Editorial: Situational awareness of integrated energy systems

Guest Editorial: Situational awareness of integrated energy systems

A Robust Dynamic State Estimation Method for Power Systems Using Exponential Absolute Value-Based Estimator

Even though the noise model applied in power system dynamic state estimation is usually assumed to be Gaussian, this is not the case due to the unknown system inputs, influence from the communication channel noise and the outliers generated by phasor measurement units (PMUs). In this paper a robust power system dynamic state estimation (DSE) method combining a robust exponential absolute value based estimator and the unscented Kalman filter together is proposed under non-Gaussian noise. Based on the quadratic function and the exponential absolute value function, robust exponential absolute value based estimator is derived, further mitigating the effects of bad data or outliers. The influence function is utilized to calculate the state estimation error covariance of the proposed robust DSE method. The simulation results on the IEEE 39-bus system verify the robustness and effectiveness of the proposed dynamic state estimation method.

Observability Analysis of a Power System Stochastic Dynamic Model Using a Derivative-Free Approach

Serving as a prerequisite to power system dynamic state estimation, the observability analysis of a power system dynamic model has recently attracted the attention of many power engineers. However, because this model is typically nonlinear and large-scale, the analysis of its observability is a challenge to the traditional derivative-based methods. Indeed, the linear-approximation-based approach may provide unreliable results while the nonlinear-technique-based approach inevitably faces extremely complicated derivations. Furthermore, because power systems are intrinsically stochastic, the traditional deterministic approaches may lead to inaccurate observability analyses. Facing these challenges, we propose a novel polynomial-chaos-based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">derivative-free</i> observability analysis approach that not only is free of any linear approximations, but also accounts for the stochasticity of the dynamic model while bringing a low implementation complexity. Furthermore, this approach enables us to quantify the degree of observability of a stochastic model, what conventional deterministic methods cannot do. The excellent performance of the proposed method has been demonstrated by performing extensive simulations using a synchronous generator model with IEEE-DC1A exciter and the TGOV1 turbine governor.

Distributed Moving Horizon Estimation via Operator Splitting for Automated Robust Power System State Estimation

In this study, we present methods of optimization-based power system state estimation over sensor networks. By minimizing a composite loss function while ensuring that the state, disturbance, and measurement noise constraints are satisfied, the best or better state estimates are iteratively computed. The proposed distributed computational methods for power system state estimation are based on operator splitting. Our methods are computationally decomposable over sensor networks, so distributed and parallel computing can be applied. They can systematically handle the constraints of the state variables and noise as well as disturbances, such that the negative effects of bad data and parametric model uncertainty can automatically be reduced in the estimation. For demonstration, the IEEE 118-bus power system dynamic state estimation problem is considered. The results are compared to the ones obtained from a distributed extended Kalman filter. It is shown that compared with a distributed extended Kalman filter, the proposed method achieves improved robustness against adversarial data defection.

Roles of Dynamic State Estimation in Power System Modeling, Monitoring and Operation

Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today's synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems.

Robust Dynamic State Estimation of Synchronous Machines With Asymptotic State Estimation Error Performance Guarantees

A robust observer for performing power system dynamic state estimation (DSE) of a synchronous generator is proposed. The observer is developed using the concept of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stability for uncertain, nonlinear dynamic generator models. We use this concept to (i) design a simple, scalable, and robust dynamic state estimator and (ii) obtain a performance guarantee on the state estimation error norm relative to the magnitude of uncertainty from unknown generator inputs, and process and measurement noises. Theoretical methods to obtain upper and lower bounds on the estimation error are also provided. Numerical tests validate the performance of the L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> -based estimator in performing DSE under various scenarios. The case studies reveal that the derived theoretical bounds are valid for a variety of case studies and operating conditions, while yielding better performance than existing power system DSE methods.

A Decentralized H-Infinity Unscented Kalman Filter for Dynamic State Estimation Against Uncertainties

The widely used traditional Kalman filter-type power system dynamic state estimator is unable to address the unknown and non-Gaussian system process and measurement noise as well as dynamical model uncertainties. To this end, this paper proposes a decentralized H-infinity unscented Kalman filter that leverages the strength of the H-infinity criteria developed in robust control for handling system uncertainties with the advantage of the UKF for addressing strong model nonlinearities. Specifically, the statistical linerization approach is used to derive a linear-like batch-mode regression model similar to the linear Kalman filter. This allows us to resort to the linear H-infinity Kalman filter framework for the development of the proposed H-infinity UKF in the Krein space. An analytical form is also derived to tune the parameter of the H-infinity criterion. Two decoupled models are presented to enable the decentralized implementation of the H-infinity UKF using the local PMU measurements. Extensive simulation results carried out on the IEEE 39-bus system show that the proposed H-infinity UKF is able to bound the influences of various types of measurement and model uncertainties while obtaining accurate state estimates.

Power System Dynamic State Estimation: Motivations, Definitions, Methodologies, and Future Work

This paper summarizes the technical activities of the Task Force on Power System Dynamic State and Parameter Estimation. This Task Force was established by the IEEE Working Group on State Estimation Algorithms to investigate the added benefits of dynamic state and parameter estimation for the enhancement of the reliability, security, and resilience of electric power systems. The motivations and engineering values of dynamic state estimation (DSE) are discussed in detail. Then, a set of potential applications that will rely on DSE is presented and discussed. Furthermore, a unified framework is proposed to clarify the important concepts related to DSE, forecasting-aided state estimation, tracking state estimation, and static state estimation. An overview of the current progress in DSE and dynamic parameter estimation is provided. The paper also provides future research needs and directions for the power engineering community.

A Theoretical Framework of Robust H-Infinity Unscented Kalman Filter and Its Application to Power System Dynamic State Estimation

This paper presents a new theoretical framework that, by integrating robust statistics and robust control theory, allows us to develop a robust dynamic state estimator of a cyber-physical system. This state estimator combines the generalized maximum-likelihood-type (GM) estimator, the unscented Kalman filter (UKF), and the H -infinity filter into a robust H -infinity UKF filter in the Krein space, which is able to handle large system uncertainties as well as suppress outliers while achieving a good statistical efficiency under Gaussian and non-Gaussian process and observation noises. Specifically, we first use the statistical linearization approach to build a linearlike regression model in the Krein space. Then, we show that the H -infinity UKF is just the Krein space Kalman filter that exhibits a bounded estimation error in presence of system uncertainties while minimizing the least squares criterion; consequently, it suffers from a lack of robustness to outliers and non-Gaussian noise. Because the GM estimator is able to handle outliers, but it may yield large estimation errors in the presence of system uncertainties, we propose to combine it with the H -infinity UKF in a robust H -infinity UKF. We carry out a theoretical analysis to demonstrate the connections that our filter has with the H -infinity UKF and the GM-UKF. The good performance of the new filter is demonstrated via extensive simulation performed on the IEEE 39-bus power system.

An agent-based approach to power system dynamic state estimation through dual unscented Kalman filter and artificial neural network

This paper proposes a novel approach to the power system dynamic state estimation by using the concepts of dynamic artificial neural networks and dual unscented Kalman filter. A dynamic artificial neural network is applied for developing a discrete-time state transition model of power system which is used for one-step-ahead prediction of the state vector. The model is also applicable for the generation of pseudo-measurements while it is needed. The dual unscented Kalman filter estimates the state vector of power system and calculates the weights of the dynamic artificial neural network simultaneously. A multi-agent-based model is utilized to structure the computational architecture of the proposed approach. The autonomous agents are designed to carry out the complex computations needed in the power system dynamic state estimation. The agents distribute multiple execution tasks among themselves, and they share information interactively. The agent-based modeling of the proposed method enhances the computing efficiency through decomposition of the computations among several autonomous agents. The effectiveness of the proposed method is examined through comprehensive simulations. The results guarantee the performance of the proposed approach as a practical solution for the power system dynamic state estimation.

Fusion of Multirate Measurements for Nonlinear Dynamic State Estimation of the Power Systems

With the increasing availability of sensors, power system dynamic state estimation (PSDSE) is going to play a critical role in the reliable and efficient operation of power systems. The real-time measurements in today’s power grid are obtained through various types of sensors having different sampling rates, e.g., the traditional SCADA systems with low sampling rates (generally 0.5–2 samples per second), and different groups of phasor measurement units having high sampling rates (usually 30–60 samples per second). We propose a multi-rate multi-sensor data fusion -based PSDSE framework to utilize the measurements coming from sensors with two different sampling rates. The continuous time-domain nonlinear dynamical and measurement equations are discretized at appropriate sampling periods to obtain two discrete models. Two separate estimators are developed using these models. State information of the intermediate time steps of the estimation having coarser sampling period is evaluated using model-based prediction. These two estimations are optimally combined or fused using Bar–Shalom–Campo formula. The proposed algorithm tracks the dynamic states successfully during transient events such as faults. The method is demonstrated by using the standard IEEE-9, 39, 57, and 118 bus systems. The fusion -based state estimator is shown to perform better than the individual state estimators.

Power system dynamic state estimation considering correlation of measurement error from PMU and SCADA

SummaryIt is well known that measurements from phasor measurement unit (PMU) or supervisory control and data acquisition (SCADA) are not generally independent. Since the correlation of measurement error is a very representative feature of the actual measurement system, traditional assumptions on error independency are not adequate. In this paper, taking the correlation of measurement error of both PMU and SCADA measurements into consideration, a novel correlated extended Kalman filter (CEKF) is proposed. The actual measurement configurations are analyzed with the consideration of measurement error transfer characteristics. Then, the modified measurement error covariance matrix is calculated by using the point estimation method, which will replace the traditional diagonal variance matrix. At last, IEEE 14‐bus system and 57‐bus system are provided to illustrate the effectiveness and superiority of the method, respectively.

An extended Kalman particle filter for power system dynamic state estimation

PurposeThe purpose of this paper is to propose an extended Kalman particle filter (EPF) approach for dynamic state estimation of synchronous machine using the phasor measurement unit’s measurements.Design/methodology/approachEPF combines the extended Kalman filter (EKF) with the particle filter (PF) to accurately estimate the dynamic states of synchronous machine. EKF is used to make particles of PF transfer to the likelihood distribution from the previous distribution. Therefore, the sample impoverishment in the implementation of PF is able to be avoided.FindingsThe proposed method is capable of estimating the dynamic states of synchronous machine with high accuracy. The real-time capability of this method is also acceptable.Practical implicationsThe effectiveness of the proposed approach is tested on IEEE 30-bus system.Originality/valueIntroducing EKF into PF, EPF is proposed to estimate the dynamic states of synchronous machine. The accuracy of a dynamic state estimation is increased.

A multi-agent based approach to power system dynamic state estimation by considering algebraic and dynamic state variables

In this paper an agent-based modeling for the power system dynamic state estimation is proposed that is able to take advantages of hybrid measurement data. Multiple execution tasks are distributed among interacting agents which each agent is supposed to carry out a specific computation or functionality. The algebraic state variables of power system and the dynamic state variables of synchronous generators are considered in the proposed method. Artificial neural network is applied for deriving a parameterized process model of the algebraic state variables. The process model of the dynamic state variables is based on the fourth-order dynamic model of the synchronous generator. The dynamic state estimation problem is solved by using unscented Kalman filters. The effectiveness of the proposed method is confirmed through simulations while different scenarios are considered. The results are compared with some widely used approaches to power system dynamic state estimation. Further, since the proposed approach is benefited from agent based modeling, it is less time-consuming and can be implemented through modular configuration which is more desirable from software and hardware engineering points of view.

Dynamic State Estimation for Multi-Machine Power System by Unscented Kalman Filter With Enhanced Numerical Stability

In this paper, in order to enhance the numerical stability of the unscented Kalman filter (UKF) used for power system dynamic state estimation, a new UKF with guaranteed positive semidifinite estimation error covariance (UKF-GPS) is proposed and compared with five existing approaches, including UKF-schol, UKF-$\kappa$, UKF-modified, UKF-$\Delta Q$, and the square-root unscented Kalman filter (SR-UKF). These methods and the extended Kalman filter (EKF) are tested by performing dynamic state estimation on WSCC 3-machine 9-bus system and NPCC 48-machine 140-bus system. For WSCC system, all methods obtain good estimates. However, for NPCC system, both EKF and the classic UKF fail. It is found that UKF-schol, UKF-$\kappa$, and UKF-$\Delta Q$ do not work well in some estimations while UKF-GPS works well in most cases. UKF-modified and SR-UKF can always work well, indicating their better scalability mainly due to the enhanced numerical stability.

Comparing Kalman Filters and Observers for Power System Dynamic State Estimation With Model Uncertainty and Malicious Cyber Attacks

Kalman filters (KFs) and dynamic observers are two main classes of the dynamic state estimation (DSE) routines. The Power system DSE has been implemented by various KFs, such as the extended KF (EKF) and the unscented KF (UKF). In this paper, we discuss two challenges for an effective power system DSE: 1) model uncertainty and 2) potential cyber attacks and measurement faults. To address this, the cubature KF (CKF) and a nonlinear observer are introduced and implemented. Various KFs and the dynamic observer are then tested on the 16-machine 68-bus system given realistic scenarios under model uncertainty and different types of cyber attacks against synchrophasor measurements. It is shown that the CKF and the observer are more robust to model uncertainty and cyber attacks than their counterparts. Based on the tests, a thorough qualitative comparison is also performed for KF routines and observers.