Power System State Estimation Research Articles

Critical Data Visualization to Enhance Protection Schemes for State Estimation

Intelligent electrical power grids, widely referred to as smart grids (SGs), rely on digital technology resources, especially communication and measurement devices, becoming a cyber-physical energy system. Massive data flow between grid elements makes smart grids more vulnerable to cyber-attacks. Power system state estimation (SE)—an essential function of energy management systems—is one of these data integrity attacks’ targets. Integrity validation routines can fail when insufficient redundancy levels are reached, and spurious data occur. These levels are associated with critical data, i.e., those whose unavailability makes the grid unobservable. Data redundancy is a metric that gives a precarious indication that SE can run. Alternatively, it is more appropriate to quantify this function strength concerning its results’ reliability, which can be achieved by criticality analysis (CA). This paper proposes a novel approach to visualize the results of an extensive CA through representative graphs; they facilitate understanding the usefulness of CA. Critical sets of measurements are generalized, and several metrics are proposed to reveal measuring system vulnerabilities, assisting the design of protection schemes to resist cyber-attacks. Simulations attained on the IEEE-30bus system evince significant improvements in the interpretation/use of CA.

A Real-Time Recursion Correction Hybrid Linear State Estimator Using Stream Processing

This study intends to improve the accuracy, efficiency, and timeliness of state estimation (SE) for large-scale electric power systems by presenting a recursion correction hybrid linear state estimator that utilizes all the field measurements received from supervisory control and data acquisition (SCADA) systems and phasor measurement units (PMUs). We present a novel reformulation of the SE problem, where the SCADA and PMU measurements are processed asynchronously. Here, the PMU measurements along with the previous SE results are utilized during the time gap between two successive SCADA measurement sets to run a recursion correction, and thereby, provide real-time updates of the system state estimates. Moreover, the efficiency of this process is guaranteed through multithreaded stream processing. The effectiveness of the proposed method is demonstrated based on simulations involving IEEE 14-bus, 118-bus, and Polish 2383-bus systems.

System State Estimation Using Weighted Least Square Method

State estimation is an essential part of every energy control management system. Accurate estimation of state or operating state is essential for security control and monitoring of power systems. Power system state estimation is a procedure to estimate true state from the inexact state of a power system. The conventional state estimator provides estimates of the power system states, i.e., bus voltages and angles which is obtained. State estimation is a computational technique for electrical power system. It empowers the calculation of the power flows of the electrical power system which are not observed or not directly measured. State estimation is a computer program that detects, isolate and eliminate the incorrect or bad measurement data and estimates the accurate state. The magnitudes of bus voltage and phase angle are the states variables for an electrical power system. This paper outlines Weighted Least Square (WLS) estimation techniques and simulated estimation for standard IEEE systems.

Power System State Estimation using Weighted Least Square Method

State estimation is an essential part of every energy control management system. Accurate estimation of state or operating state is essential for security control and monitoring of power systems. Power system state estimation is a procedure to estimate true state from the inexact state of a power system. The conventional state estimator provides estimates of the power system states, i.e., bus voltages and angles which is obtained. State estimation is a computational technique for electrical power system. It empowers the calculation of the power flows of the electrical power system which are not observed or not directly measured. State estimation is a computer program that detects, isolate and eliminate the incorrect or bad measurement data and estimates the accurate state. The magnitudes of bus voltage and phase angle are the states variables for an electrical power system. This paper outlines Weighted Least Square (WLS) estimation techniques and simulated estimation for standard IEEE systems.

Robust Power System State Estimation Method Based on Generalized M-Estimation of Optimized Parameters Based on Sampling

Robustness is an important performance index of power system state estimation, which is defined as the estimator’s capability to resist the interference. However, improving the robustness of state estimation often reduces the estimation accuracy. To solve this problem, this paper proposes a power system state estimation method for generalized M-estimation of optimized parameters based on sampling. Compared with the traditional robust state estimator, the generalized M-estimator based on projection statistics improves the robustness of state estimation, and the proposed optimized parameter determination method improves the overall accuracy of state estimation by appropriately adjusting its robustness. Considering different degrees of non-Gaussian distributed measurement noises and bad data, the estimation accuracy the proposed method is demonstrated to be up to 23% higher than the traditional generalized M-estimator through MATLAB simulations in IEEE 14, 118 bus test systems, and Polish 2736 bus system.

Grey Wolf Optimizer and Cuckoo Search Algorithm for Electric Power System State Estimation with Load Uncertainty and False Data

State estimate serves a crucial purpose in the control centre of a modern power system. Voltage phasor of buses in such configurations is referred to as state variables that should be determined during operation. A precise estimation is needed to define the optimal operation of all components. So many mathematical and heuristic techniques can be used to achieve the aforementioned objective. An enhanced power system state estimator built on the cuck search algorithm is described in this work. Several scenarios, including the influence of load uncertainty and the likelihood of false data injection as significant challenges in electrical energy networks, are proposed to analyse the operation of estimators. The ability to identify and correct false data is also assessed in this regard. Additionally, the performance of the presented estimator is compared to that of the weighted least squares, Cuckoo Search algorithm and grey wolf Optimizer. The findings demonstrate that the grey wolf Optimizer overcomes the primary shortcomings of the conventional approaches, including accuracy and complexity, and is also better able to identify and rectify incorrect data. On IEEE 14-bus and 30-bus test systems, simulations are run to show how well the method works.

Dynamic State Estimation of Power Systems with Uncertainties Based on Robust Adaptive Unscented Kalman Filter

Dynamic State Estimation of Power Systems with Uncertainties Based on Robust Adaptive Unscented Kalman Filter

Widely-Linear MMSE Estimation of Complex-Valued Graph Signals

In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can achieve a lower mean-squared-error (MSE) than that of the linear minimum MSE (LMMSE) estimator for the estimation of improper complex-valued signals. Inspired by the WLMMSE estimator, in this paper we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes the MSE among estimators that are represented as a two-channel output of a graph filter, i.e. widely-linear GSP estimators. We discuss the properties of the proposed GSP-WLMMSE estimator. In particular, we show that the MSE of the GSP-WLMMSE estimator is always equal to or lower than the MSE of the GSP-LMMSE estimator. The GSP-WLMMSE estimator is based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">diagonal</i> covariance matrices in the graph frequency domain, and thus has reduced complexity compared with the WLMMSE estimator. This property is especially important when using the sample-mean versions of these estimators that are based on a training dataset. We state conditions under which the low-complexity GSP-WLMMSE estimator coincides with the WLMMSE estimator. In simulations, we investigate a synthetic linear estimation problem and the nonlinear problem of state estimation in power systems. For these problems, it is shown that the GSP-WLMMSE estimator outperforms the GSP-LMMSE estimator and achieves similar performance to that of the WLMMSE estimator. Moreover, the sample-mean version of the GSP-WLMMSE estimator outperforms the sample-mean WLMMSE estimator for a limited training dataset and is more robust to topology changes.

Unscented Trainable Kalman Filter Based on Deep Learning Method Considering Incomplete Information

Rapid changes of states and occurrence of data missing in power systems cause accurate state estimation very hard. In this paper, an unscented trainable Kalman filter (UTKF) with a deep learning prediction model is proposed to provide accurate state estimation under incomplete information. First, the CNN-LSTM architecture, a typical deep learning model, is applied to form a trainable prediction model (TPM), which offers more accurate prediction of states. However, sometimes states are incomplete due to data losses in transmissions. To deal with incomplete information, historical time-series states are employed and fed to the TPM in order to develop a missing data filling method. In this way, the prediction errors can be lower through the online training and parameter adjustment of the TPM. Combining with the TPM and the missing data filling method, an unscented trainable Kalman filter (UTKF) is proposed to improve the state estimation of power systems when incomplete information is involved. Finally, three cases are designed, and the simulation results show that for the prediction of states, the root mean square error (RMSE), an indicator of accuracies, is reduced by about 3 multiples, if our missing data filling method is added. Furthermore, the accuracy of state estimation is improved about 5 multiples by the proposed UTKF method, even if incomplete information is involved.

A New Dynamic State Estimation Approach Including Hard Limits on Control Devices

This paper puts forward a comprehensive formulation for the wide area dynamic state estimation of power systems. This is a problem of great current interest in the power systems community, where significant progress has been achieved in recent years. This proposal builds on the existing work and formulates a novel approach to estimate dynamic and algebraic state variables of the entire power system in a simultaneous solution method. In contrast to existing formulations, the proposed approach simultaneously co-estimates the transient evolution of the transmission grid's nodal voltages and the dynamic states associated with synchronous machines and their associated controllers. Since controllers with hard limits are always present in a power system, the proposal also estimates when and how hard limits constrain the time evolution of the power system operating state. In this case, constrained dynamic variables associated with non-windup and windup limiters are automatically handled in the estimation process by transforming the inequality constraints of hard limits into equality constraints using the complementarity theory and the Fischer-Burmeister merit function. The feasibility of the proposed method is demonstrated on the WSCC 9-bus power system and the Mexican 190-bus power system.

Analysis of Targeted Coordinated Attacks on Decomposition-Based Robust State Estimation

The impact of false data injection (FDI) attacks on static state estimation of power systems has been actively studied in the past decade. In this paper, we consider an estimation method that first decomposes the system into islands and then implements robust regression estimators at the island level as well as the system level. We carry out an analysis to establish its advantages in terms of state estimation accuracy and attack detections. In particular, we focus on highly adversarial cases where the attacker can attack both the measurement vector and the regressor matrix and attempts to manipulate the states to targeted values. Our estimation approach employs a system decomposition method capable to generate islands small in their sizes and applies the robust estimation method of least trimmed squares. We make comparisons with methods using other decompositions and other robust estimators. To this end, we analyze the structure of the system topology and measurements and perform extensive simulations using the IEEE 14- and 118-bus systems. Furthermore, we investigate robustness improvement when phasor measurement units (PMUs) are available and hybrid state estimation can be employed.

Detection of False Data Injection Attacks in Smart Grid Based on Joint Dynamic and Static State Estimation

Power system state estimation is an essential component of the modern power system energy management system (EMS), and accurate state estimation is an indispensable basis for subsequent work. However, the attacker can inject biases into measurements to launch false data injection attacks (FDIAs) in smart grids, which ultimately cause state estimates to deviate from security values. This paper proposed the joint use of static state estimation and dynamic state estimation to detect the FDIA, i.e. the joint use of weighted least squares (WLS) and extended Kalman filter (EKF) with exponential weighting function (WEKF), which improves the robustness of state estimation. Since the WLS estimation considers only the measurements at the current moment, the recursive feature of the WEKF enables the estimation process to involve both historical state and current measurements. Therefore, consistency tests and residual tests were performed using the estimations of WLS and WEKF to effectively detect FDIA. In addition, a cluster partitioning approach with approximate equal redundancy of subsystems is proposed to locate the FDIA. The detection of FDIA triggers the partitioning of the network system, and then the chi-square test is used separately in each sub-network to determine the location of FDIA. Finally, the experimental results in the IEEE-14 bus system and the IEEE-30 bus system demonstrate that the approach can effectively detect and locate FDIAs.

Advances in Algorithms for Power System Static State Estimators: An Improved Solution for Bad Data Management and State Estimator Convergence

More than 50 years have passed since the first state estimator was introduced to power system operations, by Fred Schweppe, in 1969. Today, state estimation is the most important function in the energy management system (EMS) because the solution of the state estimator is the basis of other functions, including contingency analysis, security assessment, dynamitic security analysis, optimal power flow, and so on. Numerous research papers and reports have been published about trying to improve the performance of the power system state estimator since 1969. After the efforts of several decades by researchers and power engineers, today’s state estimator can be found in almost every power system control center worldwide. Power system state estimation was considered a mature area until the occurrence of a 14 August 2003 blackout in the northeastern United States. The state estimator at the control center crashed due to a single topology error in the system model, and the system operator could not take appropriate actions to avoid the occurrence of the blackout.

Robust Moving Target Defence Against False Data Injection Attacks in Power Grids

Recently, moving target defence (MTD) has been proposed to thwart the false data injection (FDI) attacks in power system state estimation by proactively triggering the distributed flexible AC transmission system (D-FACTS) devices. One of the key challenges for MTD in power grid is to design its real-time implementation with performance guarantees against unknown attacks. Converting from the noiseless assumptions in the literature, this paper investigates the MTD design problem in a noisy environment and proposes, for the first time, the concept of robust MTD to guarantee the worst-case detection rate against all unknown attacks. We theoretically prove that, for any given MTD strategy, the minimal principal angle between the Jacobian subspaces corresponds to the worst-case performance against all potential attacks. Based on this finding, robust MTD algorithms are formulated for the systems with both complete and incomplete configurations. Extensive simulations using standard IEEE benchmark systems demonstrate the improved average and worst-case performances of the proposed robust MTD against state-of-the-art results.

Assessment on power systems non-deterministic state estimation algorithms

Power systems are operated in a deterministic way. However, the increase in uncertainties (caused by measurement and communication errors or the absence of complete knowledge of the measured quantity) requires algorithms capable of assessing randomness in real-time monitoring and operation of energy management systems. Among them, state estimation is a fundamental element that provides complete and reliable information about the current network state. This paper offers a review of non-deterministic algorithms, used to assess the randomness caused by the uncertainties in power system state estimation. Depending on the uncertainty modeling method, different static and dynamic non-deterministic state estimation algorithms for transmission and distribution systems are reviewed. Also, four of the most relevant algorithms are implemented and results are compared for distribution networks. The relevance of such models, as well as their motivation, are addressed. • This paper offers a review of methods employed for power system uncertainty modeling. • Review of state estimation algorithms based on uncertainty modeling methods. • Non-deterministic state estimation algorithms in transmission and distribution grids. • Non-deterministic state estimators in low voltage networks have been implemented. • Future research lines on non-deterministic state estimation are proposed.

Time-domain Dynamic State Estimation for Unbalanced Three-phase Power Systems

In this paper, we present a time-domain dynamic state estimation for unbalanced three-phase power systems. The dynamic nature of the estimator stems from an explicit consideration of the electromagnetic dynamics of the network, i.e., the dynamics of the electrical lines. This enables our approach to release the assumption of the network being in quasi-steady state. Initially, based on the line dynamics, we derive a graph-based dynamic system model. To handle the large number of interacting variables, we propose a port-Hamiltonian modeling approach. Based on the port-Hamiltonian model, we then follow an observer-based approach to develop a dynamic estimator. The estimator uses synchronized sampled value measurements to calculate asymptotic convergent estimates for the unknown bus voltages and currents. The design and implementation of the estimator are illustrated through the IEEE 33-bus system. Numerical simulations verify the estimator to produce asymptotic exact estimates, which are able to detect harmonic distortion and sub-second transients as arising from converter-based resources.

Parameter visibility: Next-generation energy management [Guest Editorial

In the aftermath of the 1965 blackout, the need for robust power system state estimators became apparent. Edward Teller, a member of the task force investigating the 1965 blackout, wrote “the electric power system is a dinosaur with a large body and a small brain.” The committee recognized the need to have a way of knowing the operating conditions of the power system in real time. Work following the 1965 blackout established many engineering principles by which we presently operate the electric power system. It is clear that the control and operation of power systems are primarily model based. State estimation provides the operating conditions as well as the real-time model of the system. Using the model and operating conditions, we compute control actions, including economic operation; the maximization of operational security; and other important operational controls.

Attack Power System State Estimation by Implicitly Learning the Underlying Models

False data injection attacks (FDIAs) are a real and latent threat in modern power systems networks due to the unprecedented integration of data acquisition systems. It is of utmost importance to understand attacking mechanisms to design countermeasures. To successfully deploy a FDIA, most past FDIA strategies need privileged power system information, which is carefully held by the power system operator. Newer approaches circumvent this issue by solely relying on intercepted measurement data, but they lack mathematical warranties of succeeding. This paper exposes power systems’ vulnerability by showing that it is possible to deploy an attack without confidential information and, at the same time, to have a high probability of being successful. We present a scheme that learns (1) the implicit power system measurement distribution and (2) a surrogate of the unknown state estimator model. The proposed framework utilizes a Wasserstein generative adversarial network to learn the measurement distribution and an autoencoder to learn the unknown state estimator model. Additionally, we present a convergence proof that ensures that the proposed framework converges to the power system measurement distribution. The proposed method is demonstrated to be successful via extensive simulation on IEEE 9-, 14-, 57-, 118-, and 300-bus test cases.

Robust forecasting-aided state estimation of power system based on extended Kalman filter with adaptive kernel risk-sensitive loss

State estimation (SE) plays a pivotal role in the development of modern power system. Accurate forecasting-aided state estimation (FASE) can track the sudden changes of power system state and maintain the safe operation of modern power system. However, the performance of existing FASE methods is affected by anomalies in real power system, such as sudden state changes and bad data. To address this problem, a robust algorithm based on extended Kalman filter (EKF) with the kernel risk-sensitive loss (KRSL) (called KRSL-EKF) is proposed for FASE. The KRSL-EKF, taking KRSL as the cost function of the original EKF algorithm, can overcome the limitations of the EKF to perform higher estimation accuracy under non-Gaussian noise cases. In addition, an adaptive method is further introduced into the proposed KRSL-EKF algorithm to adjust the covariance matrices of process noise and measurement noise, and we denote it as AKRSL-EKF. The novel AKRSL-EKF algorithm can effectively adapt the noise to system state variations and achieves better estimation accuracy. The effectiveness of the proposed algorithms for FASE is verified on IEEE 14-bus, IEEE 30-bus, and IEEE 57-bus systems. The results show that the estimation accuracy of the proposed algorithms is 30% higher than other traditional algorithms, with high estimation accuracy.

Joint Adversarial Example and False Data Injection Attacks for State Estimation in Power Systems.

Although state estimation using a bad data detector (BDD) is a key procedure employed in power systems, the detector is vulnerable to false data injection attacks (FDIAs). Substantial deep learning methods have been proposed to detect such attacks. However, deep neural networks are susceptible to adversarial attacks or adversarial examples, where slight changes in inputs may lead to sharp changes in the corresponding outputs in even well-trained networks. This article introduces the joint adversarial example and FDIAs (AFDIAs) to explore various attack scenarios for state estimation in power systems. Considering that perturbations added directly to measurements are likely to be detected by BDDs, our proposed method of adding perturbations to state variables can guarantee that the attack is stealthy to BDDs. Then, malicious data that are stealthy to both BDDs and deep learning-based detectors can be generated. Theoretical and experimental results show that our proposed state-perturbation-based AFDIA method (S-AFDIA) can carry out attacks stealthy to both conventional BDDs and deep learning-based detectors, while our proposed measurement-perturbation-based adversarial FDIA method (M-AFDIA) succeeds if only deep learning-based detectors are used. The comparative experiments show that our proposed methods provide better performance than state-of-the-art methods. Besides, the ultimate effect of attacks can also be optimized using the proposed joint attack methods.