Robust adaptive Unscented Kalman Filter with gross error detection and identification for power system forecasting-aided state estimation

To solve the complex scenarios, such as multimodal noise, bad measurement data and sudden load changes, in the power system, the enhanced generalised cross correlation entropy unscented Kalman filter (EnGCCE‐UKF) method is proposed in this paper. This method replaces the mean square error (MSE) criterion of the traditional UKF with the generalised cross correlation entropy (GCCE) criterion and obtains the optimal solution by optimising the state estimation cost function, significantly improving the robustness and estimation accuracy in the non‐Gaussian noise environment. Considering the interference of bad measurement data on the information matrix, the strong filtering tracking (SFT) theory is further embedded in the GCCE‐UKF framework. By dynamically adjusting the information matrix to suppress the influence of abnormal factors, the anti‐interference ability of the algorithm is enhanced. This method integrates the state and measurement error into the cost function of the EnGCCE by using the statistical linearisation technique and recursively updates the posterior estimation and covariance matrix with the help of the fixed‐point iterative algorithm. Verified through multiscenario experiments and comparative analysis, the proposed method has shown good effectiveness in power systems of three scales.

The robust Kalman filter with correntropy loss has received much attention in recent years for forecasting-aided state estimation in power systems, since it efficiently reduces the negative influence of various abnormal situations, such as non-Gaussian communication, changing environment, and instrument failures, and obviously improves the stability of power systems. However, the existing correntropy-based robust Kalman filters usually use the Gaussian function with a fixed center as the kernel function in correntropy, which may not be a suitable choice in practical applications of power system forecasting-aided state estimation (PSSE). To address this issue, a new and robust unscented Kalman filter, called the maximum correntropy with variable center unscented Kalman filter (MCVUKF), is proposed in this paper for PSSE. Specifically, MCVUKF adopts an extended version of correntropy, whose center can be located at any position, to replace the original correntropy in an unscented Kalman filter to improve the performance in PSSE. Moreover, by using an exponential function of the innovation vector to adjust a covariance matrix, an enhanced MCVUKF (En-MCVUKF) method is also developed for suppressing the influence of bad data to the innovation vector and further improving the accuracy of PSSE. Finally, extensive simulations have been conducted on IEEE 14-bus, 30-bus, and 57-bus test power systems, and the simulation results have shown the superiority of the proposed MCVUKF and En-MCVUKF methods compared with several related state-of-the-art Kalman filter methods.

The Kalman-filter-based algorithms as the mainstream algorithms of dynamic state estimation of power systems have been extensively used to provide accurate data for power system applications. However, few comparisons are made to show their advantages and disadvantages. In this paper, four Kalman-filter-based algorithms (i.e., extended Kalman filter, unscented Kalman filter, cubature Kalman filter, and ensemble Kalman filter) are compared to show their differences from implementation complexity, estimation accuracy and calculation efficiency, the resistance to measurement errors, and the sensitivity to system scales. Finally, the simulation results on the 3-machine, 10-machine, and 48-machine power systems show their advantages and disadvantages.

In this paper, a topological/geometrical based approach is used to define an index, undetectability index (UI), which provides the distance of a measurement from the range space of the Jacobean matrix of the power system. The higher the value of this index, for a measurement, the closer it will be to the range space of that matrix, that is, the error in measurements with high UI is not reflected in their residuals, thus masking a possible gross error those measurements might have. Using the UI of a measurement, the possible gross error the state estimation process might mask is recovered; then the total gross error of that measurement is composed and used to the gross error detection and identification test. The gross error processing turns out to be very simple to implement, requiring only a few adaptations to the existing state estimation software. The IEEE-14 bus system is used to validate the proposed gross error detection and identification test.

According to the contradiction between the static power system state estimation and the actual operation of power system, based on the study of the classical algorithms of power system state estimation, apply the gray system theory of power system based on GM (1, 1) mode to the state estimation of power system, and create a new dynamic power system state estimation algorithm, for example to a four-node power system network test for State estimation simulation. Measurement of a known algorithm used to predict the gray system theory. On the other hand, measurement of unknown quantity, using the result that come from the known quantity, then get all parameters with character of power system state through statistical analysis of simulation results that the normal measurement system, the method is feasible and has a good filtering effect. The power system state estimation algorithm based on the gray system theory of Power System based on GM (1, 1) model has high estimating precision, fast calculation, use small memory and the adaptability of the measurement system is very strong, so it has good prospects.

Data concerning actual temperatures of line conductors constitutes essential information for the power system operator. The temperature of the power lines can be used to improve the accuracy of the power system model, thereby increasing the accuracy of the state estimation. This article presents a two-step algorithm for the power system state and line temperature estimation. In its second stage, the proposed method searches for a line temperatures vector, which corrects the uncertain power system base model and allows for further minimization of an objective function. As a result, a more accurate estimation is obtained along with a more precise model of the estimated system. The derived model can then be used for more accurate optimization. The presented method enhances standard procedures of power system state estimation, and its advantage is that it does not require direct measurements performed by phasor measurement units or measurements of line conductor temperatures and weather conditions realized by dynamic line rating systems. The results of simulations made on various test models have been examined, confirming the convergence of the procedure to the point at which the average temperature of the line wires together with the voltage values and phase angles are achieved. The algorithm’s performance and improvement method have also been presented. An advantage of the investigated approach is the possibility to calculate the temperature of line wires with the use of primary measurements in the power system. The presented and examined method, however, is sensitive to the measuring device errors. Additionally, an analysis of the method’s errors and ways of reducing them has been performed.

This paper presents an algorithm for state estimation in power systems that include FACTS devices and PMUs. The FACTS devices are equipments of special purpose capable of changing the natural behavior of transmission systems. They may be able to influence the voltage, the active power or the reactive power flows based on predefined targets so that the classical power flow and steady state calculations must be adapted. Furthermore, PMU measurements are increasing in number so that the accuracy in steady state calculations can be improved. A state estimation algorithm was developed by considering the behavior of TCSC and SVC devices, while including some improvements due to the integration of synchronized measurements. A Matlab application was developed and simulations were performed on various test networks. In this paper, results obtained on the IEEE 30 bus test system only will be presented.

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.

The measurement values would be affected by different types of gross errors, which will reduce the accuracy of state estimation of power system. To solve these problems, this paper proposes a generalized Correntropy loss based unscented Kalman filter combined with gross error detection and identification (UKF-GCL-GEDI).UKF-GCL-GEDI method can monitor the gross error in the measurement data in real time, classify the types of gross errors, estimate the true measured values, and then compensate the abnormal measurement points, so as to improve the accuracy of state estimation. Compared with unscented Kalman filter with generalized Correntropy loss and unscented Kalman filter, UKF-GCL-GEDI has higher robustness and can handle different types of gross errors in measurement data. The simulations on IEEE 6-bus test system show that UKF-GCL-GEDI can effectively suppress the influence of gross error.

Guest Editorial: Situational awareness of integrated energy systems

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.

Joint outage identification and state estimation in power systems is studied. A Bayesian framework is employed, and a Gaussian prior distribution of the states is assumed. The joint posterior of the outage hypotheses and the network states is developed in closed form, which can be applied to obtain the optimal joint detector and estimator under any given performance criterion. Employing the minimum probability of error as the performance criterion in identifying outages with uncertain states, the optimal detector is obtained. Efficiently computable performance metrics that capture the probability of error of the optimal detector are developed. Under simplified model assumptions, closed-form expressions for these metrics are derived, and these lead to a mixed integer convex programming problem for optimizing sensor locations. Using convex relaxations, a branch and bound algorithm that finds the globally optimal sensor locations is developed. Significant performance gains from using the optimal detector with the optimal sensor locations are observed from simulations. Furthermore, performance with greedily selected sensor locations is shown to be very close to that with globally optimal sensor locations.

The quadratic cost function J(xˆ) and the normalized residuals rN are used conventionally for identifying the presence and location of bad measurements in power system state estimation. These are "post estimation" tests and therefore require the complete re-estimation of system states whenever bad data is identified. This paper presents a pre-estimation filter for detection and identification of gross measurement errors. The basic function of this filter is to compare the measured value of a system variable with its predicted value obtained using an autoregressive (AR) model. If the difference exceeds a pre-determined threshold, the measured value is discarded in favor of the predicted value. Each measurement is processed by an AR filter before being used in the state estimation. The performance of the AR filter is tested against that of the J(xˆ) and rN tests and the results are reported in this paper. The principal advantage of the AR filtering scheme is its speed in bad data identification. Furthermore, it can be used to complement other bad data processing methods.

Power system state estimation is one of the most important functions of power system control centers. In recent years, the complexity of power system state estimation has significantly increased due to the growing number of distributed, including renewable energy sources, electric vehicles, the demand response technologies, and the increased risk of cyber-attacks. Under these conditions, state estimation methods, which consider information about the time-correlation of the power system states have a great potential. The correlation is described by a transition model. The well-known state estimation methods usually use one single model. However, in case of stochastic behavior of the load and generation, it is impossible to assert the adequacy of the chosen model over the entire observation interval. Therefore, the paper proposes a multi-model forecasting power system state estimation method, which has lower errors in comparison with a single-model assessment at the moments of the lowest accuracy of the latter. Multi-model parameter estimation is used based on three procedures of the single-model Kalman filtering estimation and various transition models based on autoregressive and vector autoregressive analyzes, as well as Holt's exponential smoothing. Uniting the single-model estimation has been carried out according to the criterion of the minimum of variance of the resulting estimate. An algorithm of multi-model power system state estimation has been developed. Its version has been analyzed using a three-model forecasting-aided estimation using linear transition models. The state of the IEEE 30-bus test power system has been assessed by the means of simulation modeling. The maximum accuracy increase of the multi-model estimation in comparison with the single model is set up. 26,1 % is for autoregressive analysis; 16,9 % is for vector regression analysis and 37,7 % is for Holt’s exponential smoothing. The proposed method of multi-model state estimation has higher robustness and accuracy at the moments of the lowest accuracy of single-model estimation. It is advisable to use the method to solve control tasks of power systems with rapidly changing dynamic modes.

Boosting efficiency in state estimation of power systems by leveraging attention mechanism