Phasor Measurement Units Measurements Research Articles

Joint detection and state estimation based on GPS spoofing attack in smart grids

Phasor Measurement Units (PMUs) are widely used in power system state estimation due to its high sampling rate and real-time estimation of power state in power systems. However, it is also vulnerable to cyberattacks (GPS spoofing attacks) since it uses unencrypted GPS civil signals for synchronization. The GPS spoofing attacks (GSAs) will intentionally manipulate the time reference of PMUs, which is equivalent to falsifying the phase angle of the PMU measurements. In this paper, we consider the secure power state estimation and attacks detection with the unknown GSAs in the power systems. Particularly, we derived the PMU-based GSAs model in the power state estimation problem, which is formulated as a mixed maximum likelihood problem. In the formulated problem, the involved unknown parameters are coupled and the objective function is non-convex, which are of significant challenges in finding optimal solutions. To tackle these challenges, a joint maximum a posteriori and maximum likelihood (JMAP-ML) algorithm is proposed to securely estimate the power state and detect the GSAs in the mixed measurements of PMUs. Different testing scenarios in IEEE 14 bus system are simulated to show the proposed algorithm’ performance on GSAs detection and state estimation. Numerical examples demonstrate the improved accuracy of our algorithm compared with classical algorithms when GSAs are present. And we conclude that when a sufficient number of PMUs are deployed in the system, the impact of GSAs will be largely compensated in the estimation stage.

Real-time transient stability early warning system using Graph Attention Networks

In this paper, a classifier based early warning system is designed, trained and tested based on time-series of Phasor Measurement Unit (PMU) measurements at all buses in a power system. The classifier is based on a novel combination of Graph Attention Networks and Long Short-Term memories, and is trained to label power system data in the form of captured windows of PMU measurements. These labels are then used to provide early warning for transient instability. The classifier is trained and tested data from simulations of the Nordic44 test system, and includes extensive topological variations under two different load levels. It is found that accurate early warnings can be provided, but the quality of prediction is highly dependent on specific power system characteristics, such as how quickly the power system responds to transient disturbances.

AM-HNN based real-time voltage estimation method of distribution network using joint PMU and AMI data

A large amount of distributed energy access increases the risk of voltage fluctuation and off-limit voltage. Accurate voltage estimation is more and more important to ensure the safety of distribution networks. With the introduction of phasor measurement unit (PMU), multi-source measuring data with different time scales and measuring precision exist in distribution networks. How to fully integrate multi-source measurement data to achieve fast and accurate state estimation of distribution networks is an important prerequisite for efficient operation decision making. In this paper, a distribution network voltage state estimation method based on AM-HNN model is proposed. The attentional mechanism (AM) is introduced to mine the influence of PMU measurement data on voltage state estimation, and the feature weight is modified adaptively. The highway neural network (HNN) was used to fit the mapping relationship between the injected power of grid nodes and the voltage of key nodes. Taking the distribution network data of different scenes as an example, the superiority of the proposed optimal measurement model is verified by comparing with various voltage estimation methods.

Power System State Estimation Based on Fusion of PMU and SCADA Data

This paper introduces a novel hybrid filtering algorithm that leverages the advantages of Phasor Measurement Units (PMU) to address state estimation challenges in power systems. The primary objective is to integrate the benefits of PMU measurements into the design of traditional power system dynamic estimators. It is noteworthy that PMUs and Supervisory Control and Data Acquisition (SCADA) systems typically operate at different sampling rates in power system estimation, necessitating synchronization during the filtering process. To address this issue, the paper employs a predictive interpolation method for SCADA measurements within the framework of the Extended Kalman Filter (EKF) algorithm. This approach achieves more accurate estimates, closer to real observation data, by averaging the KL distribution. The algorithm is particularly well-suited for state estimation tasks in power systems that combine traditional and PMU measurements. Extensive simulations were conducted on the IEEE-14 and IEEE-30 test systems, and the results demonstrate that the fused estimator outperforms individual estimators in terms of estimation accuracy.

Enhancing voltage profile in islanded microgrids through hierarchical control strategies

This paper presents a novel approach aimed at enhancing the voltage profile of an islanded microgrid (MG) through the utilization of Phasor Measurement Units (PMUs) and a hierarchical control system for Distributed Generators (DGs). Recognizing the criticality of maintaining an optimal voltage profile for essential loads within an MG, we assume that PMUs are strategically placed across the MG based on existing placement methodologies to ensure the observability of load buses. The synchrophasor measurements captured by these PMUs are leveraged within an offline-designed tertiary control layer of the hierarchical framework, which in turn sets the voltage reference for the secondary control layer of DGs across the MG. This approach effectively enhances the voltage profile of vital load buses within the MG. The proposed hierarchical strategy encompasses primary, secondary, and tertiary levels of control, responsible for stabilizing voltage and frequency, computing power references, and managing power flow, respectively. PMU measurements play a crucial role in the secondary control level by continuously monitoring deviations. By ensuring the effective placement of PMUs, the proposed framework enables efficient control, leading to notable improvements in the voltage profile and power management. To evaluate the effectiveness of our approach, five test networks were used: 14-bus, 30-bus, 39-bus, 57-bus, and 118-bus test networks. Simulation results demonstrate an impressive over 80 % enhancement in the MG's voltage profile achieved by our proposed method. Additionally, our heuristic strategy efficiently assigns the closest load bus to each DG while aggregating equidistant bus deviations. Collectively, our research underscores the significant impact of PMU measurements and a well-structured hierarchical voltage control system in substantially improving the voltage profile of MGs.

Bias Analysis of PMU-Based State Estimation and Its Linear Bayesian Improvement

With the rapidly changing states of modern power systems, real-time state estimation based on phasor measurement units (PMUs) plays an increasingly important role in energy management systems (EMSs). However, due to the complicated distribution of PMU measurement errors, conventional state estimation methods such as the weighted least squares (WLS) estimator suffer from the estimation bias. Consequently, they do not represent the least variance unbiased estimators. To solve the estimation bias, a state estimation method combining the PMU linear measurement model and the linear Bayesian estimation theory is proposed. Specifically, considering the prior information on estimated parameters and the complicated probability distribution of PMU measurement errors, the linear Bayesian theory is applied to PMU-based state estimation to improve the performance of state estimation. To support this method, the correlation between real and imaginary errors is analyzed, and the prior information of estimated parameters is determined by the volatility of system states. When the real states of practical power systems are unavailable, performance indicators for state estimation are proposed based on the estimation residuals. The efficacies of the proposed estimation and evaluation methods are verified using IEEE 14 bus system and a large-scale power grid in China.

An online method for the accuracy level evaluation of the phasor measurement units

Online evaluation of the accuracy level of the phasor measurement unit (PMU) is very useful in assessing the accuracy ranges of PMU measurements. Such results can be applied to avoid the misoperation of power system protection and control and enhance the accuracy of power system state estimation. Because the theoretical values are unknown, the evaluation indices defined in the IEEE/IEC standard 60255-118-1, such as the total vector error, frequency error, and rate of change of frequency error, cannot be calculated online. To address this concern, a new index named the total waveform error (TWE) is proposed in this paper. It is defined as a ratio of fundamental root-mean-square (RMS) value to fundamental residual RMS, where harmonic components are excluded in the TWE calculation. For a specific window length, two TWE thresholds are set according to the IEEE standard C37.118.1 to divide the PMU measurement into 3 accuracy levels. Theoretical analysis and simulation tests show that the TWE is effective in accuracy-level evaluation. Two examples are given to illustrate the TWE applications of evaluating accuracy levels of PMU measurements.

Event Analysis in Transmission Systems Using Spatial Temporal Graph Encoder Decoder (STGED)

Phasor Measurement Units (PMUs) are located at different geographic positions in the transmission system, generating measurement data that can be analyzed to monitor and control the power grid. One utilization for such measurement data is monitoring based on machine learning based <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event analysis</i> in the transmission system, which includes <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">event detection, localization, and classification</i> . The approach developed in this work exploits the latent spatial and temporal features of PMU measurement data for event analysis. (1) For event detection, this research proposes a novel unsupervised <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">“Spatial Temporal Graph Encoder Decoder” (STGED)</i> deep learning model that concurrently/jointly exploits the spatial and temporal features of PMU measurements. STGED further supports downstream unsupervised event localization and classification. (2) For event localization, events are localized by estimating <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Turbulence and Proximity statistical scores</i> over predicted measurements/output from STGED. (3) For event classification, an unsupervised algorithm is developed with a classification scoring metric that leverages physics informed rules based on the fundamentals of power system. The proposed approach is evaluated on the IEEE test systems and other benchmark systems for diversified event scenarios. Additionally, performance of the developed approach has been compared with other techniques, and validated using real-world industry data. Experimental results show that the proposed approach outperforms other existing techniques for event analysis.

A novel multi-task learning method for evaluating short-term voltage stability with incomplete PMU measurements

Methods for short-term voltage stability (STVS) assessment based on phasor measurement unit (PMU) data have become quite abundant. However, most of them are challenged to deal with the commonly encountered incomplete PMU data. Existing models for STVS assessment of incomplete PMU data mostly have the disadvantages of high computational complexity and large impact from the level of data missing. This paper proposes a multi-task learning method that performs stability assessment and missing data completion in parallel. The Transformer Encoder is used as the shared feature extractor, a GRU structure is used to output complete PMU data sequences, and a BP neural network is used to output stability assessment results. The loss function used for the missing completion task considers the accuracy in both the shape and time domains. A comparison with relevant models shows that the model proposed in this paper achieves the best performance in all indicators and is minimally affected by the observation windows and the level of data loss, demonstrating good robustness.

Algebraic Approach to PMU Placement for Minimum Variance Linear State Estimation in Power Networks

Phasor Measurement Units (PMUs) are used to measure voltages and currents in a power network. Optimal PMU placement in a given network is an important problem since installing PMU at every node of a network is expensive. This paper proposes an algebraic approach to the PMU placement problem with a focus on complete voltage state estimation and PMU measurement noise, with the objective to minimize the variance of the state estimation. The approach determines the minimum number of PMUs needed for full voltage state observability in a network based on the number of buses with known nodal currents. Combined with the information on PMU measurement noise and the network admittance matrix, an optimal PMU placement algorithm is formulated that minimizes the variance of the voltage estimation. This algorithm groups nodes of the network into four different sets based on the nodal voltages and nodal/line currents measured by the PMUs deployed in the network. The proposed placement algorithm considers both single current-channel PMU case and multi-current channel PMU case. This proposed placement algorithm is tested on IEEE 14 bus and IEEE 39 bus network. The results show that optimal placement can significantly reduce the effects of PMU measurement noise on the estimated states.

Joint Detection and State Estimate with GSAs in PMU-Based Smart Grids

The Phasor Measurement Unit (PMU) with a GPS signal receiver is a synchronized sensor widely used for power system state estimation. While the GPS receiver ensures time accuracy, it is vulnerable to network attacks. GPS spoofing attacks can alter the phase angle of PMU measurement signals and manipulate system states. This paper derives a power system state model based on PMUs under GPS spoofing attacks, according to the characteristics of changes in bus voltages and branch currents after GSA. Based on the characteristics of this model, a detection and correction algorithm for attacked data is proposed to detect GSA and correct attacked measurements. The corrected measurements can be used for power system state estimation. Simulation results on the IEEE 14-bus system show that the proposed algorithm improves the accuracy of state estimation under one or multiple GSAs, especially when multiple GSAs are present, compared to classical Weighted Least Squares Estimation (WLSE) and Alternating Minimization (AM) algorithms. Further research indicates that this algorithm is also applicable to large-scale networks.

A Deep-Learning-Based Solution for Securing the Power Grid Against Load Altering Threats by IoT-Enabled Devices

The growing integration of high-wattage Internet-of-Things (IoT)-enabled electrical appliances at the consumer end has created a new attack surface that an adversary can exploit to disrupt power grid operations. Specifically, dynamic load-altering attacks (D-LAAs), accomplished by an abrupt or strategic manipulation of a large number of consumer appliances in a botnet-type attack, have been recognized as major threats that can potentially destabilize power grid control loops. This paper introduces a novel approach based a multi-output network (two-dimensional convolutional neural networks classifier and reconstruction decoder)-called “2DR-CNN”-to detect and localize D-LAAs with high resolution. To achieve this, we leverage the frequency and phase angle data of the generator buses monitored by phasor measurement units (PMUs) installed in the power grid. To verify the effectiveness of the proposed method, simulations are conducted on IEEE 14-and 39-bus systems. The performance of the 2DR-CNN method is compared against several benchmark machine learning-based approaches. The results confirm that the proposed method outperforms other techniques in detection and localizing D-LAAs with high resolution in a number of practical scenarios, including PMU measurement noises and missing measurements.

Transmission line parameters estimation in the presence of realistic PMU measurement error models

Proposals have been presented in literature to estimate line parameters and monitor their changes. Synchrophasor measurements from phasor measurement units (PMUs) have appeared as a possible breakthrough for accurate estimation. However, few methods consider a realistic measurement chain including PMUs and instrument transformers and their systematic and random error contributions. This paper proposes an improved method to simultaneously estimate line parameters and systematic measurement errors on multiple network lines. The algorithm is designed to deal with realistic PMU measurement errors and, in particular, with phase-angle errors caused by common time-base errors on multiple PMU channels. The impact of PMU measurement errors is investigated to achieve a comprehensive view of the performance under realistic conditions. The results obtained on an IEEE test network prove the advantages of the proposed method with respect to other recent methods and its robustness in the presence of mismatches in the error model.

An Agent-Based Distributed State Estimation Approach for Interconnected Power Systems

Phasor measurement units (PMUs) are becoming more popular in power systems and most of the distributed state estimation methods are based on the Gaussian measurement noise assumption. However, the PMU measurement noise has been demonstrated to be non-Gaussian. This article presents a distributed multiarea state estimation approach based on the quadratic and exponential functions for power systems to deal with the non-Gaussian measurement noise efficiently. The matrix splitting technique is utilized to implement a robust estimator in a fully distributed scheme. Based on the local measurements and the limited information exchanged between neighboring areas, each local area only estimates its local states and the computation time needed is further reduced. The effective and robust performance of the proposed distributed multiarea state estimation approach is demonstrated using the IEEE 30-, 118-, and 300-bus systems.

Detection and mitigation of GPS Spoofing Attacks on Phasor Measurement Units using deep learning

The widespread use of Phasor Measurement Units (PMUs) is considered one of the most important contributions to the quality of power system monitoring. PMUs are digital devices that provide synchronized phasor measurements time-referenced by the Global Positioning System (GPS). The lack of encryption in conventional GPS receivers used in PMUs makes them vulnerable to GPS Spoofing Attacks (GSAs) that cause the GPS receiver to lose track, resulting in a phase shift of all measurements of the affected PMU. Even small phase shifts can downgrade the performance of the state estimator, indicating their ability to propagate throughout the entire system. Therefore, ensuring the integrity of PMU measurements is of utmost importance. State-of-the-art statistical methods are insensitive to small phase shifts, and they become computationally intensive as the system size and the number of simultaneous attacks increase. This paper presents the first application of deep learning to simultaneously detect and mitigate the effects of GSAs against PMUs. The performance of the proposed method is evaluated on IEEE 14-, 57-, and 118-bus systems and compared to state-of-the-art statistical and deep learning methods.

Robust Event Classification Using Imperfect Real-World PMU Data

This paper studies robust event classification using imperfect real-world phasor measurement unit (PMU) data. By analyzing the real-world PMU data, we find it is challenging to directly use this dataset for event classifiers due to the low data quality observed in PMU measurements and event logs. To address these challenges, we develop a novel machine learning framework for training robust event classifiers, which consists of three main steps: data preprocessing, fine-grained event data extraction, and feature engineering. Specifically, the data preprocessing step addresses the data quality issues of PMU measurements (e.g., bad data and missing data); in the fine-grained event data extraction step, a model-free event detection method is developed to accurately localize the events from the inaccurate event timestamps in the event logs; and the feature engineering step constructs the event features based on the patterns of different event types, in order to improve the performance and the interpretability of the event classifiers. Based on the proposed framework, we develop a workflow for event classification using the real-world PMU data streaming into the system in real time. Using the proposed framework, robust event classifiers can be efficiently trained based on many off-the-shelf lightweight machine learning models. Numerical experiments using the real-world dataset from the Western Interconnection of the U.S power transmission grid show that the event classifiers trained under the proposed framework can achieve high classification accuracy while being robust against low-quality data.

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.

Distribution System State Estimation and False Data Injection Attack Detection with a Multi-Output Deep Neural Network

Distribution system state estimation (DSSE) has been introduced to monitor distribution grids; however, due to the incorporation of distributed generations (DGs), traditional DSSE methods are not able to reveal the operational conditions of active distribution networks (ADNs). DSSE calculation depends heavily on real measurements from measurement devices in distribution networks. However, the accuracy of real measurements and DSSE results can be significantly affected by false data injection attacks (FDIAs). Conventional FDIA detection techniques are often unable to identify FDIAs into measurement data. In this study, a novel deep neural network approach is proposed to simultaneously perform DSSE calculation (i.e., regression) and FDIA detection (i.e., binary classification) using real measurements. In the proposed work, the classification nodes in the DNN allow us to identify which measurements on which phasor measurement unit (PMU), if any, were affected. In the proposed approach, we aim to show that the proposed method can perform DSSE calculation and identify FDIAs from the available measurements simultaneously with high accuracy. We compare our proposed method to the traditional approach of detecting FDIAs and performing SE calculations separately; moreover, DSSE results are compared with the weighted least square (WLS) algorithm, which is a common model-based method. The proposed method achieves better DSSE performance than the WLS method and the separate DSSE/FDIA method in presence of erroneous measurements; our method also executes faster than the other methods. The effectiveness of the proposed method is validated using two FDIA schemes in two case studies: one using a modified IEEE 33-bus distribution system without DGs, and the other using a modified IEEE 69-bus system with DGs. The results illustrated that the accuracy and F1-score of the proposed method are better than when performing binary classification only. The proposed method successfully detected the FDIAs on each PMU measurement. Moreover, the results of DSSE calculation from the proposed method has a better performance compared to the regression-only method, and the WLS methods in the presence of bad data.

Fault Location in Distribution Network by Solving the Optimization Problem Based on Power System Status Estimation Using the PMU

Fault location is one of the main challenges in the distribution network due to its expanse and complexity. Today, with the advent of phasor measurement units (PMU), various techniques for fault location using these devices have been proposed. In this research, distribution network fault location is defined as an optimization problem, and the network fault location is determined by solving it. This is done by combining PMU data before and after the fault with the power system status estimation (PSSE) problem. Two new objective functions are designed to identify the faulty section and fault location based on calculating the voltage difference between the two ends of the grid lines. In the proposed algorithm, the purpose of combining the PMU in the PSSE problem is to estimate the voltage and current quantities at the branch point and the total network nodes after the fault occurs. Branch point quantities are calculated using the PMU and the governing equations of the π line model for each network section, and the faulty section is identified based on a comparison of the resulting values. The advantages of the proposed algorithm include simplicity, step-by-step implementation, efficiency in conditions of different branch specifications, application for various types of faults including short-circuit and series, and its optimal accuracy compared to other methods. Finally, the proposed algorithm has been implemented on the IEEE 123-node distribution feeder and its performance has been evaluated for changes in various factors including fault resistance, type of fault, angle of occurrence of a fault, uncertainty in loading states, and PMU measurement error. The results show the appropriate accuracy of the proposed algorithm showing that it was able to determine the location of the fault with a maximum error of 1.21% at a maximum time of 23.87 s.

High-Refresh-Rate Robust State Estimation Based on Recursive Correction for Large-Scale Power Systems

With the growing scale and complexity of power systems, the tracking performance of conventional state estimators has gradually been insufficient to support the reliable operation and control of large networks. This paper presents a novel multi-stage hybrid state estimator, which is capable of monitoring the large-scale power systems in an accurate and high-refresh-rate manner regardless of whether phasor measurement unit (PMU) data is available. To be specific, the state estimation results of the whole power system are real-time corrected by the proposed recursive correction strategy using triggering SCADA measurements and PMU measurements. Furthermore, a modified M-estimation method for the recursive correction strategy is proposed to timely eliminate the impact of bad data and non-Gaussian measurement noises. Comparative case studies conducted on the IEEE 14-bus, 118-bus, and Polish 2383-bus systems validate the effectiveness of the proposed method under various operation conditions.