Application of Kalman Filter to Bad-Data Detection in Power System

This paper presents a new approach for detection and identification of ultiple bad data --- estimation-identification approach which has been developed in order to improve the performance of static-state estimators of power systems. It describes the important function of detection and identification of bad data which is of crucial importance in designing a static-state estimator as a basic element in power system real-time control; it also discusses tthe basic principle, method of solution and programing technique of so called "Estimation-Identificaition Approach" which is based on the better utilization of the resources of residues and the analysis of the property of its sensitivity matrix; and some test results of simulation on a model system and a practical searching system of doubtful data are given. Test results of identifying bad data is good, it is usually successful especially in the case of the occurence of multi-bad data. At the end of this paper comments concerning the advantages of this approach and its recommendation as a prospective practical approach in real-time applications are given.

Due to the insufficient measurements in the distribution system state estimation (DSSE), full observability and redundant measurements are difficult to achieve without using the pseudo measurements. The matrix completion state estimation (MCSE) combines the matrix completion and power system model to estimate voltage by exploring the low-rank characteristics of the matrix. This paper proposes a robust matrix completion state estimation (RMCSE) to estimate the voltage in a distribution system under a low-observability condition. Tradition state estimation weighted least squares (WLS) method requires full observability to calculate the states and needs redundant measurements to proceed a bad data detection. The proposed method improves the robustness of the MCSE to bad data by minimizing the rank of the matrix and measurements residual with different weights. It can estimate the system state in a low-observability system and has robust estimates without the bad data detection process in the face of multiple bad data. The method is numerically evaluated on the IEEE 33-node radial distribution system. The estimation performance and robustness of RMCSE are compared with the WLS with the largest normalized residual bad data identification (WLS-LNR), and the MCSE.

In this paper a new remote terminal unit (RTU) placement algorithm is presented. The objective of this algorithm is to place a minimum set of RTUs which satisfies three important constraints of the problem-observability, absence of critical measurements, and reliability requirements defined in terms of RTU loss. The problem is solved in a single stage. The results of this algorithm are interfaced with a linear programming (LP) state estimator. This estimator only uses the voltage measurements, and the active and reactive power flows in the lines for the development of the coupled state-estimation Jacobian H-matrix. The injection measurements are not currently included, though in practice they can be easily added to the estimator model. The inclusion of the injection measurements will enlarge the use of the presented algorithm. The RTU placement algorithm and its link with the LP estimator are tested on IEEE standard bus systems. Using the proposed RTU set, the test results presented show that the LP estimator has very good filtering capabilities when operated with or without bad data, and that the loss of any RTU does not have any significant impact on the solution.

Decoupled State-Estimation in Energy Control Centres

Bad data in a power system fail to accurately reflect its state of operation. Cleaning bad data is thus necessary for the situational analysis of a data-based power system. Methods for the identification and modification of bad data based on state estimation may fail to converge in iterative calculations, and yield poor results when the errors are significant. State estimation also involves non-linear computation, which incurs a significant computational overhead and makes it difficult to efficiently handle large volumes of data. To solve these problems, this paper proposes a method for the detection and identification of bad data based on constraints on spatial–temporal correlation. In the spatial domain, we fix the equivalent power balance condition through the topology of the network. In sequential distribution, we establish data constraints based on the similarity of data among temporal sections. We then check the data in combination with the spatial–temporal correlation constraints. The proposed method was applied to an IEEE 14-bus system and a provincial grid, and the results show that it can reliably detect and modify bad data to significantly improve their quality. The proposed approach avoids non-linear calculations, is computationally efficient, and can quickly detect and modify bad data.

Guest Editorial: Situational awareness of integrated energy systems

The quality of measurement data directly determines the accuracy of the state estimation. In practice, erroneous measurement may exist due to various physical factors, and they are known as bad data. Moreover, the measured data may also be attacked by hackers. The existence of bad data and cyber attacks could cause the state estimation unable to estimate the actual system states. Therefore, it is of great significance to detect and differentiate bad data and cyber attacks in power system state estimation. To this end, a support vector machine was proposed in this paper. It was validated using IEEE 118 bus and IEEE 30 bus systems. Numerical results prove the effectiveness of the proposed method in identifying bad data and false data injection data.

With the development of smart grids and the continuous penetration of new energy power generation, the scale of the power grid has increased, and the structure and operation methods have become increasingly complex. In order to more accurately grasp the operating status of the power grid, it is necessary to estimate the operating status of the power system. In recent years, with the development of artificial intelligence and data mining technology, neural networks have also been widely used in the field of state estimation. However, there are few researches on artificial intelligence algorithms in active distribution network state estimation, and the small amount of data in the bad data detection link that needs to be carried out before state estimation also limits the application of many artificial intelligence algorithms that require a large number of training samples. A small sample learning method applied to the detection of bad data for power system state estimation is proposed, which successfully solves the problem of the lack of available training data in building a neural network model for bad data detection, and solves the traditional method calculation speed brought by the massive increase of grid data. The problem of serious decline, and the accuracy of the traditional state estimation method is improved by more than 47%.

Phasor measurement units (PMUs) are power system devices placed at various locations in electrical power network that provide the measurement of phasors of voltages and currents from the respective meters or instruments placed at locations. Data provided by the PMUs are used for system analysis and also help to analyze the sequence of events that may have contributed to the failure of the power system. The presence of bad data in PMUs is increasing in today’s power system due to the system complexity and associated issues. This will lead to inaccurate measurement of voltage magnitude and phase angle. Hence, it is important to detect the presence of bad data and identify the PMU which contains the error. In order to identify the bad data, state estimation is carried out to obtain the true state variables by the application of Load Flow Analysis (LFA). The application of Engineering Optimization is called into this work for improving the detection of bad data and its correction. Firefly optimization and particle swarm optimization techniques are developed for the above problem, and later results are compared with respect to the accuracy of results. The system is modeled in MATLAB platform.

The state estimator is a fundamental algorithm used in modern power industry to estimate the steady state of the system. The gross errors in input data of power system SE algorithm can considerably effect the accuracy of estimated measurements. Although, the commonly used state estimator algorithms utilize some statistical tests to detect the bad data, they are unable to properly deal with the gross errors with smaller magnitude and higher probabilities. This paper develops a new procedure based on the GLR test to effectively detect the bad measurements in the SE algorithm. The proposed strategy can detect, identify and to estimate the size of gross errors. This method is implemented on both single and multiple bad measurements cases to comparatively investigate the abilities of this algorithm. The obtained results confirm that the proposed algorithm has greater power of detecting and identifying the bad measurements compared to the estimator based on the conventional Chi-square and normalized residual test statistics. The IEEE-14 bus test system has been used to validate the theoretical results in this work and its practical implementation in state estimation problems.

State estimation is critical for the normal operation of power system. However, due to the aging of electric infrastructures, the power grid become more vulnerable to cyber-attack. Therefore, in this paper, scenario-based two-stage sparse cyber-attack models for smart grid with complete and incomplete network information are proposed. In previous traditional state estimator, bad data detector (BDD) is used to prevent power systems from the smearing effect of the unsteady power system caused by the bad data. However, the researches have pointed out that BDD can't recognize the abnormal state which launch by the hackers who know the topologies of the power system. Then, in order to detect false data effectively, we proposed a new detect mechanism based on extreme learning machine (ELM). In the proposed defense mechanism, we combine numbers of ELM whit certain rules, which objective is to improve the precision of the detection. Finally, the effectiveness and validation of the proposed method is verified on standard IEEE14-bus AIEEE57-bus system.

In this paper, we consider the problem of state estimation through observations possibly corrupted with both bad data and additive observation noises. A mixed $\ell_1$ and $\ell_2$ convex programming is used to separate both sparse bad data and additive noises from the observations. Through using the almost Euclidean property for a linear subspace, we derive a new performance bound for the state estimation error under sparse bad data and additive observation noises. Our main contribution is to provide sharp bounds on the almost Euclidean property of a linear subspace, using the "escape-through-a-mesh" theorem from geometric functional analysis. We also propose and numerically evaluate an iterative convex programming approach to performing bad data detections in nonlinear electrical power networks problems.

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 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.

The transition from passive to active distribution networks has led to a growing use of state estimators (SEs), particularly in applications that require high quality data (e.g., demand management and fault detection). To ensure accurate estimations, a bad data detection (BDD) algorithm capable of detecting errors is needed. While these algorithms exist, network operators require understanding the benefits and limitations of these approaches before adopting a solution for their SEs. This paper compares three Chi-square-based BDD algorithms (conventional and two residual covariance matrix-based) to evaluate their performance in terms of speed and effectiveness. Comparisons are carried out using the IEEE 37-bus test feeder with different bad data scenarios. Results highlight that the conventional algorithm is faster, but its filtering capabilities is more limited. On the other hand, they show that the residual covariance matrix-based algorithms require on average 1594% and 2661% more time to achieve a detection that in certain conditions can be 1.56 and 1.67 times better.