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While the Lyapunov exponents used in previous studies require embedded dimensions and/or multiple initial conditions, our previously proposed instantaneous Lyapunov exponent (ILE) and Malthusian parameter estimator (MPE) directly estimate the rate of increase or decrease by time series data in real-time. The MPE uses adaptive control algorithms to estimate the rate of increase or decrease of the system. Our previously proposed MPE tends to have larger errors for fast-varying parameters and requires a PE condition, but the MPE in the case of a stable system does not satisfy the persistency of excitation (PE) condition. In this paper, we apply recently proposed parameter estimation algorithms effective for time-varying parameters to MPE. Moreover, the other MPE using the generalized parameter estimation-based observer (GPEBO) and the energy pumping-and-damping injection construction is proposed, that does not require the PE condition. The proposed methods allow us to monitor the transient stability in real-time. We compare the estimation performance of ILE and four MPE's by using two power system examples. [ABSTRACT FROM AUTHOR]

From time to time, a series of unpredictable and conflicting contingencies can lead to angular instability of the power system and even blackouts if not adequately handled by an out-of-step (OOS) protection system. The key contribution of this research work, to the theory of out-of-step protection, is the identification and isolation after a given disruption of many unstable swings. This paper presents a proposed method to avoid false operation for distance function by out-of-step blocking to improve the system stability by using optimally placed PMUs for the fast detection of system analogue quantities. The studies were performed on a modified Eskom transmission network in the Western Cape with 765 kV and 400 kV voltage levels. The aim is to investigate the IEC 61850-90-5 standard for predictive dynamic stability maintaining systems using PMUs for out-of-step conditions of synchronous generators. The power system modelling and simulation are performed in the RSCAD-FX for the proposed multi-area power system network. An experimental lab-scale implementation is built to test the proposed out-of-step algorithm in a real-time digital simulator. Software-based PMU is incorporated to test and validate the IEC 61850-90-5 standard sampled values. Simulation and experimental results are presented. [ABSTRACT FROM AUTHOR]

This manuscript proposes a hybrid technique for determining the optimal positioning of phasor measurement units (PMUs) in power systems. The PMUs play a crucial role in power system control, wide-area monitoring, and protection. The proposed hybrid method is the joint execution of the Lichtenberg algorithm (LA) and the heap-based optimization (HBO) technique. Hence, it is named the LA-HBO technique. The objective of the proposed method is to place the PMUs in the power system for observability. The goal is to enhance the efficiency and accuracy of PMU placement, ensuring optimal positioning for improved grid monitoring capabilities. The Lichtenberg Algorithm (LA) enhances PMU placement by addressing system observability challenges and ensuring that selected locations provide comprehensive coverage of the power grid. The heap-based approach optimizes PMU placement by efficiently managing the selection process, considering factors like computational efficiency and scalability. The proposed hybrid technique is implemented in IEEE-30 and -14 bus systems. The MATLAB-based simulation results are compared with the various existing methods, such as Sea Lion Optimization (SLO), Particle Swarm Optimization (PSO), and Ant Bee Colony Optimization (ABC). By then, the outcome reveals the efficacy of the proposed method for defining the optimum PMU locations. The proposed method shows a low computational time of 0.02348 sec for the IEEE-14 bus, and 0.03565 sec for the IEEE-30 bus compared with other existing methods. [ABSTRACT FROM AUTHOR]

Renewable energy resources have increasingly been integrated into electric power grids. Moreover, new challenges constantly arise, showing the need for modernization in monitoring, control, and protection. Transmission and distribution systems have explored the use of phasor measurement units (PMUs) in an attempt to meet these requirements. The decreasing cost of hardware components of PMUs, similar to what occurred with digital relays, is an important factor in terms of their worldwide use in different applications. Low-cost variations of PMUs focused on distribution systems, such as micro- and D-PMUs, are growing in number. Thus, this survey article presents significant and recent research conducted in the field of power systems using PMUs. Firstly, it briefly describes the characteristics of PMUs concerning hardware and phasor estimation algorithms. Afterward, recent studies related to transmission and distribution system protection based on PMUs are presented, such as fault detection and location, stability, and wide-area protection. Finally, the article also provided important guidelines, which certainly can be useful for future research in the years to come. [ABSTRACT FROM AUTHOR]

The paper presents the performance enhancement of band-pass filter-based M-class phasor estimation. The performance of the M-class phasor estimation using a band-pass FIR filter is enhanced with a magnitude correction factor for the off-nominal frequency range. The band-pass filter is implemented for the phasor estimation with various window functions Tukey, Rife Vincent class-I order-2 (RV2), Hamming, Hanning, Blackman, and Flat-top (FT) and its performance are evaluated under the steady and dynamic state tests prescribed by the standard. A rigorous performance analysis of enhanced phasor estimation using band-pass FIR filter with various window functions is presented with the accuracy indices of total vector error (TVE), frequency error (FE), and rate of change of frequency error (RFE). The result analysis reveals that the performance enhanced phasor estimation using band-pass FIR filter offers significantly less error than reported work at the low sampling rate. The design and performance analysis of the phasor estimation using the band-pass FIR filter is performed in the MATLAB platform. [ABSTRACT FROM AUTHOR]

Challenges in the operation of power systems arise from several factors such as the interconnection of large power systems, integration of new energy sources and the increase in electrical energy demand. These challenges have required the development of fast and reliable tools for evaluating the operation of power systems. The load margin (LM) is an important index in evaluating the stability of power systems, but traditional methods for determining the LM consist of solving a set of differential-algebraic equations whose information may not always be available. Data-Driven techniques such as Artificial Neural Networks were developed to calculate and monitor LM, but may present unsatisfactory performance due to difficulty in generalization. Therefore, this article proposes a design method for Physics-Informed Neural Networks whose parameters will be tuned by bio-inspired algorithms in an optimization model. Physical knowledge regarding the operation of power systems is incorporated into the PINN training process. Case studies were carried out and discussed in the IEEE 68-bus system considering the N-1 criterion for disconnection of transmission lines. The PINN load margin results obtained by the proposed method showed lower error values for the Root Mean Square Error (RMSE), Mean Square Error (MSE) and Mean Absolute Percentage Error (MAPE) indices than the traditional training Levenberg-Marquard method. [ABSTRACT FROM AUTHOR]

Voltage stability assessment (VSA) is invariably an essential step in the satisfactory operation of power system. For this, several Voltage Stability Indices (VSIs) based on 1) Existence of solution for voltage equations, 2) Maximum power transfer (MPT) through a line, 3) MPT theorem/maximum loadability limit, 4) P-V curve, 5) Energy function and 6) Jacobian matrix can be found in the literature. VSIs assist in identifying weak lines and buses, voltage collapse proximity, maximum loadability, voltage stability margin, and prompting countermeasures against voltage instability. This article examines 78 different VSIs based on their concepts, assumptions, thresholds, and formulae. Additionally, mathematical proofs for 29 indices have been elaborated upon so that researchers may familiarize themselves with the underlying concepts of the other existing indices and find newer indices in modern power systems composed of intermittent power generation and dynamic loads. Also, a novel qualitative comparative analysis of VSIs is tabulated. Further, a novel framework has been proposed to aid researchers in shortlisting VSIs for a particular application. This article intends to serve as a meaningful reference to various researchers and individuals working in domains like Distributed Generation (DG) placing and rating, Voltage Stability Assessment (VSA), and power system planning.

Power system balancing authorities are routinely affected by sudden frequency fluctuations. These frequency events can take the form of negligible frequency deviations or more severe emergencies that can precipitate cascading outages, depending on the severity of the disturbance and efficacy of remedial action schema. It is imperative to arrest such disturbances quickly by activating primary frequency control measures. This manuscript proposes a configurable event detection framework using optimization methods to tune a detection algorithm to detect events as specified by experts from a Balancing Authority. The utility of the detection framework is demonstrated using a regression-based frequency event detection algorithm with tunable parameters. Two swarm intelligence-based optimization algorithms, Grey Wolf Optimization and Particle Swarm Optimization, are applied to tune the parameters of the detection algorithm according to the definition of frequency events specified by experts. The performances of the GWO and PSO algorithms are analyzed, and the efficacy of the proposed system is demonstrated using an algorithm evaluation environment and a suite of evaluation metrics. The proposed event detection framework is capable of detecting events in real-time with high accuracy and speed using real-world, real-time phasor measurement unit data.

The availability of phasor measurement unit (PMU) data enables dynamic state estimation (DSE) of synchronous generators (SGs) via nonlinear Kalman filters. The mechanical power input of an SG is not measured by PMUs. This input can be treated as three types in DSE: an unknown input, a static state variable, and a dynamic state variable that requires a first-order governor-turbine model. To properly apply DSE to power systems, the DSE accuracies for the three types of input must be compared. In this paper, an identification method for a first-order governor-turbine model is developed using frequency-domain PMU data. Then, three DSE methods corresponding to the three types of mechanical power are designed using the cubature Kalman filter. Their accuracies under PMU measurement noise and SG model parameter uncertainties are evaluated by simulating DSE of the IEEE 39-bus system. The simulation results show that all three methods provide similar estimation accuracies for the SG state but exhibit different behaviors in tracking the mechanical power. The method with the static variable is shown to have a long transient time in DSE for ambient data.

Online transient stability assessment (TSA) is essential for the reliable operation of power systems. The increasing deployment of phasor measurement units (PMUs) across power systems provides a wealth of fast, accurate, and detailed transient data, offering significant opportunities to enhance online TSA. Unlike conventional data-driven methods that require large volumes of transient PMU data for accurate TSA, this paper develops a new TSA method that requires significantly less data. This data reduction is enabled by generative and adversarial networks (GAN), which predict voltage time-series data following a transient event, thereby minimizing the need for extensive data. A classifier embedded in the generative network deploys the predicted data to determine the stability of the system. The developed method preserves the temporal correlations in the multivariate time series data. Hence, compared to the state-of-the-art methods, it is more accurate using only one sample of the measured PMU data and has a shorter response time.

Fault location has significant importance in energy management system and has been used for many years. Recently, wide-area fault location using phasor measurement units (PMU) has attracted many attentions. However, measurement uncertainties decrease the accuracy of available methods. In this paper, a wide-area fault location method based on weighted maximum exponential squares (WMES) algorithm is proposed which has high robustness against measurement uncertainties. In this method, the measurements are weighted appropriately based on the uncertainty propagation theorem. Using WMES algorithm guarantees the robustness of the proposed method against bad data resulted from measurement uncertainty. In the previous methods, only voltage measurements are used in fault location; however, the formulation in this paper is developed to consider the current measurements provided by PMUs in addition to voltage ones for detecting the fault location. Results of simulation on the standard IEEE 57-bus network illustrates the efficiency of proposed fault location method based on the WMES compared to the other methods.

This paper proposes a novel method for estimating the inertia, damping, and mechanical power variation of power systems using short-term phasor measurement data during transient events. The method applies a linear least square optimization technique to the generator swing equation and utilizes a pair of sliding windows to capture the dynamic changes of the system. The method can estimate the inertia under different types of disturbances in real-time and track the inertia changes caused by secondary disturbances. The method is validated using simulations in the IEEE New England 10-machine system and compared with existing methods.

Wide Area Monitoring System (WAMS) using Phasor Measurement Unit (PMU) have been widely implemented in power systems. Due to its voltage and current measurements accuracy and precision, PMU can be adopted into power system defense plan as well as WAMS. However, there are considerations of the PMU data acquisition to be able to deliver performing analysis of the electrical power system, i.e.: the synchronization of data acquisition time, reporting rate effect, data sample acquisition, and data acquisition range. This paper addresses problems in PMU data collection and method to solve them prior to carrying out analysis to achieve reliable results. Further, the proposed method has been exercised and implemented in actual power systems accordingly the data collection issues in PMU for WAMS analysis have been solved. In contrast to other studies, this research offers insight into data collections and its solutions before they are examined. [ABSTRACT FROM AUTHOR]

In recent decades, because of the rapid population growth of the world, considerable changes in climate, the reduction of fossil fuel sources to consume the traditional power plants and their high depreciation, and the increase in fuel prices. Due to the increased penetration of DG units which have a random nature into the power system, the ordinary equations of power flow must be changed. For the power system to operate in a stable condition estimating future demand and calculating the important and operational indexes such as losses of the power system is an important duty that must be done precisely and rapidly. In this paper, the Improved Taguchi method and phasor measurement unit are used to model the uncertainties of DGs and estimate the error of voltage, respectively. The results show that the magnitude error and the angle error of voltage are decreased using PMU. The applied optimal power flow and state estimations are analyzed and verified using standard IEEE 30-bus and 14-bus test power systems by MATLAB, and MINITAB softwares. The Made Strides Taguchi strategy appears to have modeled the DG units precisely and successfully, and using the PMU, the mistake of the point and greatness estimation is exceptionally moot. The values that were evaluated are very close to the values that were done by the Newton-Raphson stack stream. [ABSTRACT FROM AUTHOR]

The power grid operators collect the data on a smart grid via the phasor measurement unit (PMU), which is placed at several points on the bus. However, the data at the PMU is prone to bad data; to classify that data, a detection scheme must be executed in the server system. The events in PMU data were subjected to several transmission conditions in the distribution system, and detecting those conditions is the major need for research. Hence to cope with that, a multi-level classification of synchrophasor's data is proposed in this paper. An agglomerative clustering-based extreme gradient boosting (AXGBoost) classifier is proposed for a multi-level classification. The puzzle optimization method updates the probability of a data line point to the agglomerative cluster detector. The model is analyzed on IEEE 14 and 39 bus system PMU data for classification and evaluation of a model. As a result, the classification accuracy of 99.49% is obtained for IEEE 14 bus, while the accuracy for IEEE 39 bus is 99.74%, which is comparably higher than the 14 bus system. The obtained result on both systems is compared with state-of-the-art techniques such as isolation forest classifier, weighting and imbalance bagging and PMUNET. [ABSTRACT FROM AUTHOR]

In this paper, a customizable low-cost voltage waveform generator based on a real-time desktop PC and embedded data acquisition card synchronized with Coordinated Universal Time (UTC) is presented. A software approach to phase-locked loop synchronization with an external Global Positioning System (GPS) pulse signal is utilized to achieve a time uncertainty of ± 1 μ s. This avoids expensive hardware modules for synchronization and timing purposes, which are commonly presented in literature. Besides the application for controlling the test platform, our own phasor data concentrator (PDC) application is running concurrently on the host PC. The latter is used for collecting and comparing the syncrophasor data from the test platform against the syncrophasor data measured by phasor measurement units (PMUs) under the test. The paper describes all procedures for generating reference test signals. Numerous case studies were performed, and experimental results for steady-state compliance as well as frequency ramp and phase modulation tests for dynamic compliance are presented in detail. All tests confirm that customizable test platform meets the requirements of IEEE/IEC standards. Compared to other calibrators, the cost as well as the specifications and point-by-point concept of data processing makes the described test platform suitable for performance analysis of PMU algorithms implemented on various development boards. [ABSTRACT FROM AUTHOR]

Small‐signal stability is an important task and key research in electrical engineering for networks. This research article focuses on the implementation of a multi‐objective approach for choosing an optimal location for Phasor Measurement Units (PMUs) to quantify a power system's small‐signal stability by maximizing the signal‐to‐noise ratio (SNR) in the system. The novelty of this research lies in the implementation of Dingo Optimization (DOX) technique along with the Prony Analysis (PA) approach for the assessment of small‐signal stability in standard grid networks. The voltage angle, amplitude and the range of frequencies are measured by the optimal placement of PMUs, which primarily focus on the multi‐signal PA. To achieve the objective of this research, DOX integrated with the multi‐signal PA approach is used to determine the ideal position for PMU placement by considering maximum redundancy and optimizing the signal to noise ratio to a maximum level. The effectiveness of the DOX strategy is established with improved accuracy and fewer disturbances by optimizing the electromechanical oscillations of the system. The implementation of the DOX approach for attaining the best value of the maximized SNR is obtained by analyzing a wide set of conditions, perturbations, and additive noise, which provides an accurate assessment of damping ratio (DR) and frequency (f) of electromechanical oscillations. Numerical results obtained from the standard IEEE test systems (14, 39, 57, 118, and 300 bus systems) are compared with the existing methods in the literature. The statistical indices demonstrate that under the highly limited optimization context selected, the intended optimizer functions satisfactorily. [ABSTRACT FROM AUTHOR]

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Using PMU data, the fault location algorithm has gradually been trended in the literature. Besides the optimality of the algorithm, the fault location application should directly receive the data of the faulty line from the PMU devices to have the best performance; using state estimation to create the input data of fault location algorithm not only wastes the golden time, but it also decreases the reliability. Given, it is not possible to install PMU devices in all buses of the system, it is better to install them for the lengthy lines having the most probability of the failure. Although various approaches have been presented in the literature to solve optimal PMU placement (OPP), the fault location observability has less been considered in OPP formulation Accordingly, this paper considers a new index, named fault location observability (FLO), as a second objective function in its OPP formulation. Using this index, in addition to minimizing PMU installation cost, the number of lengthy lines being directly observable are also maximized. Using the ɛ-constraint method, the multi-objective problem has been solved several times as single-objective optimizations. Given the constraints and objective functions are linear, the work presents a mixed integer linear programming (MILP) formulation for the placement problem. Using the GAMS under CPLEX solver, the global optimal solutions of MILP model corresponding to the various ɛ-constraints yields to a Pareto optimal front. The simulation results, next, implements the proposed method on the IEEE 300 bus test system as well as the practical OMAN grid to prove the effectiveness of the proposed method.

Smart grid networks face several cyber-attacks, where distributed denial-of-service (DDoS) attacks distract the grid network. The synchrophasor technique protects the wide-area measurement system (WAMS) from the complex problem and addresses different issues in a grid. The DDoS attack detection strategy is complicated due to attack complexities, vendor specifications, and communication standard protocols. Attacker target phasor measurement unit (PMU) data on the phasor data concentrator (PDC) database in WAMS. However, during the cyber-attack, the framework ensures the end application uses the normal PDC datastream. The proposed attack detection technique efficiently verifies PMU-generated data in WAMS. However, numerous machine learning algorithms are used to detect DDoS attacks, but the best detection model is still given open choices. The motivation of this study: (a) which machine learning algorithm will be suitable for DDoS attack detection and (b) what would be the accuracy of training algorithms. This study presents a machine learning-based hybrid technique that achieves 83.23% accuracy. Python compiler is used to execute the proposed model, and the result shows that the proposed detection approach efficiently improves the DDoS attack detection accuracy.

From time to time, a series of unpredictable and conflicting contingencies can lead to angular instability of the power system and even blackouts if not adequately handled by an out-of-step (OOS) protection system. The key contribution of this research work, to the theory of out-of-step protection, is the identification and isolation after a given disruption of many unstable swings. This paper presents a proposed method to avoid false operation for distance function by out-of-step blocking to improve the system stability by using optimally placed PMUs for the fast detection of system analogue quantities. The studies were performed on a modified Eskom transmission network in the Western Cape with 765 kV and 400 kV voltage levels. The aim is to investigate the IEC 61850-90-5 standard for predictive dynamic stability maintaining systems using PMUs for out-of-step conditions of synchronous generators. The power system modelling and simulation are performed in the RSCAD-FX for the proposed multi-area power system network. An experimental lab-scale implementation is built to test the proposed out-of-step algorithm in a real-time digital simulator. Software-based PMU is incorporated to test and validate the IEC 61850-90-5 standard sampled values. Simulation and experimental results are presented.

Today, creating a smart grid that is resistant to cyberattacks is a subject of utmost significance. One of the components of the smart grid that is most susceptible to a cyber-attack is the phasor measuring unit (PMU). The reason is that PMU employs IEEE C37.118.2 communication standards, which specify the structure and sequencing of data packets but offer no security measures. Users must implement the security techniques to ensure the protection of PMU data. Additionally, PMU communicates via a public wide-area network, raising the risk to security. In addition, PMU is a crucial component of the smart grid, enabling different crucial choices for the reliable functioning of the smart grid to be made using its data. This research suggests a chaos-based data encryption solution to close the knowledge gap and reduce the confidentiality assault on PMU data. For this, a brand-new boost converter logarithmic map (BCLM), a one-dimensional (1D) chaotic map, has been presented. The research demonstrates how the suggested chaotic map has better chaotic qualities than conventional chaotic maps. The pseudorandom generator is the chaotic BCLM system. The PMU data are encrypted using the random sequence produced by the BCLM chaotic system. The suggested chaotic map is not computationally demanding, making it simple to implement in a PMU device with limited resources. [ABSTRACT FROM AUTHOR]

The sampling rate of the wide-area synchronous phasor measuring device (D-PMU) in the distribution network is insufficient, and the localization sensitivity of the traditional localization method based on the time-domain Bergeron equation in the distribution network is insufficient. In this paper, an accurate location method of the distribution line grounding fault based on the time-domain' synchronous information calculation is proposed to solve the problem of limited location accuracy caused by a low sampling rate and the insufficient sensitivity of traditional methods. The method preprocesses the measurement data through low-frequency time-domain signal reconstruction and cubic spline interpolation. The fault current's different location criterion is constructed by using the voltage and current constraints at the fault point. By calculating the fault current difference at a limited number of calculated points, the accurate fault location under a low sampling rate is realized, which is beneficial to the rapid maintenance of faults and the shortening of the power outage time. [ABSTRACT FROM AUTHOR]

Modern power systems have increasingly high requirements for real-time and accurate network topology analysis, and phasor measurement devices are widely used in power systems. The correlation between plant and station busbars was analyzed. A method for evaluating the number of equivalent nodes and evaluating the running status of lines was proposed, thereby the topology structure of the entire network was obtained. The results show that the proposed algorithm can effectively use analog information from synchronized phasor measurements to quickly obtain new network topology when the switch changes. The accuracy and applicability of the proposed method are verified by different types of simulation scenarios, and the validation using the actual field data shows that the proposed method can play an important role in the actual power grid. [ABSTRACT FROM AUTHOR]

Abstract Large-scale power grid observability is still a challenge because of deteriorating infrastructure and the incorporation of renewable energy sources. A smart grid that makes use of cutting-edge technology, such as a phasor measurement unit (PMU), is an excellent option for monitoring and bringing networks up to speed with the latest information. Latterly, the considerable investment required for the deployment locations has slowed down the adoption of PMU. Therefore, because PMUs are expensive, it is necessary to deploy them in the best possible places on large-scale power grids. The most significant share of optimal PMU placement problems (OPPP) is defined as 0–1 knapsack problems. Considering this, the development of an effective optimization technique that can handle difficulties has emerged as an appealing topic in recent years. In this paper, a meta-heuristic algorithm based on the binary particle swarm algorithm (BPSO), a binary accelerated particle swarm optimization (BAPSO), is offered for solving OPPP. Since earlier research has shown that BPSO is likely to stick to local optima, the majority of them evaluated their suggested technique using small-scale test systems. The technique that has been suggested searches for the optimal solution by employing two topologies—one global and one local—that are analogous to BPSO. This work determines the optimal PMU position for a large network in a reasonable amount of time by fine-tuning the acceleration factor. Additionally, in order to employ fewer PMUs, an integration strategy was put into place for the radial buses. The OPPP solutions are provided by the suggested method within a reasonable period with prior solutions published in reliable publications, according to computational findings.

Background Smart grid systems require high-quality Phasor Measurement Unit (PMU) data for proper operation, control, and decision-making. Missing PMU data may lead to improper actions or even blackouts. While the conventional cubic interpolation methods based on the solution of a set of linear equations to solve for the cubic spline coefficients have been applied by many researchers for interpolation of missing data, the computational complexity increases non-linearly with increasing data size. Methods In this work, a modified recurrent equation-based cubic spline interpolation procedure for recovering missing PMU data is proposed. The recurrent equation-based method makes the computations of spline constants simpler. Using PMU data from the State Load Despatch Center (SLDC) in Madhya Pradesh, India, a comparison of the root mean square error (RMSE) values and time of calculation (ToC) is calculated for both methods. Results The modified recurrent relation method could retrieve missing values 10 times faster when compared to the conventional cubic interpolation method based on the solution of a set of linear equations. The RMSE values have shown the proposed method is effective even for special cases of missing values (edges, continuous missing values). Conclusions The proposed method can retrieve any number of missing values at any location using observed data with a minimal number of calculations.

Wide-Area Power System Stabilizers (WAPSSs) are damping controllers used in power systems that employ data from Phasor Measurement Units (PMUs). WAPSSs are capable of providing high damping rates for the low-frequency oscillation modes, especially the inter-area modes. Oscillation modes can destabilize power systems if they are not correctly identified and adequately damped. However, WAPSS communication channels may be subject to failures or cyber-attacks that affect their proper operation and may even cause system instability. This research proposes a method based on an optimization model for the design of a WAPSS robust to multiple permanent communication failures. The results of applications of the proposed method in the IEEE 68-bus system show the ability of the WAPSS design to be robust to a possible number of permanent communication failures. Above this value, the combinations of failures and processing time are high and they make it difficult to obtain high damping rates for the closed-loop control system. The application and comparison of different optimization techniques are valid and showed a superior performance of the Grey Wolf Optimizer in solving the optimization problem.

Background Smart grid systems require high-quality Phasor Measurement Unit (PMU) data for proper operation, control, and decision-making. Missing PMU data may lead to improper actions or even blackouts. While the conventional cubic interpolation methods based on the solution of a set of linear equations to solve for the cubic spline coefficients have been applied by many researchers for interpolation of missing data, the computational complexity increases non-linearly with increasing data size. Methods In this work, a modified recurrent equation-based cubic spline interpolation procedure for recovering missing PMU data is proposed. The recurrent equation-based method makes the computations of spline constants simpler. Using PMU data from the State Load Despatch Center (SLDC) in Madhya Pradesh, India, a comparison of the root mean square error (RMSE) values and time of calculation (ToC) is calculated for both methods. Results The modified recurrent relation method could retrieve missing values 10 times faster when compared to the conventional cubic interpolation method based on the solution of a set of linear equations. The RMSE values have shown the proposed method is effective even for special cases of missing values (edges, continuous missing values). Conclusions The proposed method can retrieve any number of missing values at any location using observed data with a minimal number of calculations.

Voltage stability is a critical aspect of power system operation, ensuring the reliable and efficient delivery of electrical energy to consumers. Recently, voltage stability in the power system has received much attention. The primary cause of voltage instability is the lack of real and reactive power generation to cope with the continuous demand increment. Maintaining voltage stability while planning, controlling, and assessing the system’s security is a difficult task for power system engineers. From knowledge of past incidents, a lack of reactive power is identified as the primary cause of voltage instability, which may further lead to the total collapse of the system. The importance of voltage stability assessment is essential to maintain the integrity of power systems. It helps prevent voltage instability, which can lead to cascading failures and widespread outages. This paper uses various parameters, including load demand, generator capacity, and system impedance, to develop voltage stability indices (VSIs). The paper mainly focuses on the idea of VSIs that have been developed in order to monitor and control the criticality of the power system. The voltage stability indices for transmission and distributed systems, as well as their subclasses, are thoroughly reviewed in this study. Furthermore, traditional voltage stability methods, as well as various software tools for monitoring the voltage stability problems, are also discussed. In addition, the development of VSIs and its related concepts are clearly described in this paper. This comprehensive survey provides a decent groundwork for future work in this area, and assists professionals in selecting the optimal VSI for various applications. Moreover, it provides a concise overview of methods and the importance of voltage stability assessment in both transmission and distribution systems.

Large-scale power grid observability is still a challenge because of deteriorating infrastructure and the incorporation of renewable energy sources. A smart grid that makes use of cutting-edge technology, such as a phasor measurement unit (PMU), is an excellent option for monitoring and bringing networks up to speed with the latest information. Latterly, the considerable investment required for the deployment locations has slowed down the adoption of PMU. Therefore, because PMUs are expensive, it is necessary to deploy them in the best possible places on large-scale power grids. The most significant share of optimal PMU placement problems (OPPP) is defined as 0–1 knapsack problems. Considering this, the development of an effective optimization technique that can handle difficulties has emerged as an appealing topic in recent years. In this paper, a meta-heuristic algorithm based on the binary particle swarm algorithm (BPSO), a binary accelerated particle swarm optimization (BAPSO), is offered for solving OPPP. Since earlier research has shown that BPSO is likely to stick to local optima, the majority of them evaluated their suggested technique using small-scale test systems. The technique that has been suggested searches for the optimal solution by employing two topologies—one global and one local—that are analogous to BPSO. This work determines the optimal PMU position for a large network in a reasonable amount of time by fine-tuning the acceleration factor. Additionally, in order to employ fewer PMUs, an integration strategy was put into place for the radial buses. The OPPP solutions are provided by the suggested method within a reasonable period with prior solutions published in reliable publications, according to computational findings. [ABSTRACT FROM AUTHOR]

The development of modern power systems is directly related to changes in the traditional principles of management, planning, and monitoring of electrical modes. The mass introduction of renewable energy sources and control devices based on power electronics components contributes to changing the nature of the flow of transient and quasi-established electrical modes. In this area, the problem arises of conducting a more accurate and rapid assessment of the parameters of the electrical regime using synchronized vector measurement devices. The paper presents an extensive meta-analysis of the modern applications of phasor measurement units (PMUs) for monitoring, emergency management and protection of power systems. As a result, promising research directions, the advantages and disadvantages of the existing approaches to emergency management, condition assessment, and relay protection based on PMUs are identified. [ABSTRACT FROM AUTHOR]

The phasor measurement unit (PMU) is an essential instrument for surveillance, control, and protection of power grids because it has the ability to provide critical time-synchronized real-time voltage, current, frequency, and phase data. PMUs are being deployed for real-time behaviour monitoring of power grids. The exactness and reliability of data obtained from PMUs can be ensured if the PMUs are calibrated from a traceable PMU calibrator. The facility of Phasor Measurement Unit Calibration System (PMU-CAL) has been established at the CSIR-National Physical Laboratory, New Delhi, in 2018 and is traceable to the national standards. By testing and calibrating PMUs according to the latest IEEE standard, PMU-CAL provides the best solution for PMU users, manufacturers, and energy suppliers. This paper presents the results of reference standard PMU calibrated for the measurement class carried out in the last five years from 2018 to 2022. The results show that the reference standard is highly stable and complies with the IEEE standard. With traceable measurements, once calibration is complete, all PMUs deployed in a country's grid will provide precise and reliable data that will help to increase efficiency, improve reliability, and enhance the quality of the power grid. [ABSTRACT FROM AUTHOR]

Harmonic and interharmonic content in power system signals is increasing with the development of renewable energy generation and power electronic devices. These multiple signal components can seriously degrade power quality, trip thermal generators, cause oscillations, and threaten system stability, especially the interharmonic tones with positive damping factors. The first step to mitigate these adverse effects is to accurately and quickly monitor signal features, including frequency, damping factor, amplitude, and phase. This paper proposes a concise and robust index to identify the number of modes present in the signal using the singular values of the Hankel matrix and discusses the scope of its application by testing the influence of various factors. Next, the simplified matrix pencil theory is employed to estimate the signal component frequency and damping factor. Then their estimates are considered in the modified least-squares algorithm to extract the wideband multi-component phasors accurately. Finally, this paper designs a series of scenarios considering varying signal frequency, damping factor, amplitude, and phase to test the proposed algorithm thoroughly. The results verify that the proposed method can achieve a maximum total vector error of less than 1.5%, which is more accurate than existing phasor estimators in various signal environments. The high accuracy of the proposed method is because it considers both the estimation of the frequency number and the effect of signal damping. [ABSTRACT FROM AUTHOR]

The operation of modern power systems must meet stability requirements to guarantee the supply of electrical energy. One of these requirements is to ensure that the low-frequency oscillation modes have high damping ratios to avoid angular instability and future power system blackouts. Advances in phasor measurement units (PMUs) have contributed to the development and improvement of wide-area damping controllers (WADCs) capable of increasing the damping rates of the oscillation modes of the system, especially the inter-area modes. Nevertheless, the operation of WADCs is vulnerable to communication failures and cyber-attacks, and if not properly designed the WADC can affect the stability of the entire system. This research proposes a procedure for designing a WADC robust to permanent communication failures using a linear quadratic regulator (LQR) and genetic algorithms. Case studies conducted on an IEEE 68-bus test power system show the effectiveness of the WADC designed by the proposed procedure even when communication failures are occurring in the system. The use of genetic algorithms improves the convergence and results of the LQR-based method. [ABSTRACT FROM AUTHOR]

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This paper describes an open-source library of transmission-level synchrophasor measurements, curated with the aim of accelerating data-driven research and development in the power systems domain. This dataset contains measurements describing both disturbances and ambient conditions, spans two years in time, and is sourced from electric utilities across the United States. Comprised of 1694 unique events, this is the largest open-source repository of real transmission-level phasor measurement unit (PMU) data to date, and will be invaluable for benchmarking new algorithms, testing tools and approaches developed by vendors and researchers, and developing educational tools for university students and control room operators. This paper additionally highlights several potential applications of the dataset that may be useful to the research community.

To completely eliminate the time delays caused by phasor data compressions for real-time synchrophasor applications, a real-time synchrophasor data compression (RSDC) is proposed in this paper. The two-way rotation characteristic and elliptical trajectory of dynamic synchrophasors are introduced first to enhance the compressions along with a fast solving method for elliptical trajectory fitting equations. The RSDC for phasor data compression and reconstruction is then proposed by combining the interpolation and extrapolation compressions. The proposed RSDC is verified by both the actual phasor measurement data recorded in a two-phase short-circuit incident and a subsynchronous oscillation incident, and the synthetic dynamic synchrophasors. It is also compared with two previous real-time phasor data compression techniques, i.e., phasor swing door trending (PSDT) and exception and swing door trending (SDT) data compression (ESDC). The verification results demonstrate that RSDC can achieve significantly higher compression ratios for offline applications with the interpolation and the zero-delay phasor data compression with the extrapolation for real-time applications simultaneously.

In this work, a robust subspace clustering algorithm is developed to exploit the inherent union-of-subspaces structure in the data for reconstructing missing measurements and detecting anomalies. Our focus is on processing an incessant stream of large-scale data such as synchronized phasor measurements in the power grid, which is challenging due to computational complexity, memory requirement, and missing and corrupt observations. In order to mitigate these issues, a low-rank representation (LRR) model-based subspace clustering problem is formulated that can handle missing measurements and sparse outliers in the data. Then, an efficient online algorithm is derived based on stochastic approximation. The convergence property of the algorithm is established. Strategies to maintain a representative yet compact dictionary for capturing the subspace structure are also proposed. The developed method is tested on both simulated and real phasor measurement unit (PMU) data to verify the effectiveness and is shown to significantly outperform existing algorithms based on simple low-rank structure of data.

This paper develops a forecasting-based missing value replacement model for Phasor Measurement Unit (PMU) data during power system events. The proposed forecasting model leverages a sequence-to-sequence (Seq2Seq) long short-term memory (LSTM) network with an attention mechanism, which is trained with both pre-event and post-event data. The trained forecasting model is utilized to accurately estimate and recover missing measurements in PMU data. To improve the accuracy of the proposed model, we introduced two novel techniques: 1) integrating a prior knowledge matrix into the attention mechanism that effectively preserves correlations within PMU data, and 2) decoupling the magnitude and trend components of the residual forecast so that such forecasting models are separately trained, which boosts the resistance to the noisy signal. Numerical studies on real-world PMU data collected from the North American electric power grid demonstrate that our proposed model achieves 5% to 30% error reduction compare to the baseline models for all key power grid measurements in both root mean square error and mean absolute error metrics. Furthermore, our model exhibits robust missing data recovery performance even when nearly all of the grid event data is missing.

Real-time power system algorithms are necessary for grid advancement, but few practical applications have been demonstrated in a research usability context. The work in this paper consists of implementing a data correction algorithm, its deployment within realistic substation equipment, and the design of a testbed to demonstrate the overall framework and its usability. A digital simulator is used to generate Phasor Measurement Unit (PMU) data for the algorithm. The algorithm corrects data that has been perturbed by GPS spoofing attacks. Finally, the entire system is visualized on power-utility software, SEL Synchrowave Operations. Considerations and potential issues are discussed and are applicable to digital Hardware-in-the-Loop (HIL) systems as well as to field-deployed systems. The system is demonstrated with 11 simultaneously GPS-spoofing attacked PMUs in a 21 PMU system. The HIL testbed developed in this paper provides a valuable tool for easily testing a variety of real-time power system algorithms and the communications and control necessary for them operate successfully.

Accurate fault location on transmission lines is paramount for ensuring the reliable and efficient operation of the electricity grid, which underpins every aspect of modern society. Existing fault localization methods for transmission lines often face shortcomings, particularly in scenarios involving multi-terminal transmission lines, where complexities arise due to dispersed generations and intricate network configurations. Traditional approaches may struggle to provide accurate fault localization, impacting the reliability and efficiency of the electricity grid. Research provide a unique fault localization technique in this article depends on Phasor Measurement Units (PMUs) and Bidirectional Gradient Boost Random Forest (BDGB-RF) machine learning technique to address these challenges. The proposed method offers several advantages over traditional methods, including enhanced accuracy and efficiency. By leveraging PMU data and BDGB-RF, the method provides a two-phase fault localization strategy, incorporating fault line selection based on nodal current imbalance and subsequent fault distance determination. Simulation results demonstrate the effectiveness of the proposed approach, achieving up to 97% accuracy in the majority of studied scenarios, even under different tapping configurations. The adoption of this approach could significantly impact the practices of experts in the field, facilitating more reliable fault detection and localization in complex transmission line networks. This, in turn, can contribute to the resilience and stability of power systems, ultimately improving grid reliability and minimizing downtime.

Phasor measurement units (PMUs) have gained significant interest in recent decades. These instruments are used to measure synchronized phasor data. PMUs are gradually but definitely taking over power grids because of the significant phasor information that they generate for both regular and irregular conditions for the purpose of maintaining safety and control. PMUs may be used for a variety of purposes, including state estimation, which is a common task. In order to make state estimation more reliable, a variety of approaches have been looked into, and one of them is the positioning of PMUs. This paper provides a plan for the implementation of the PMUs, taking into account the potential for failure and vulnerability posed by PMU-equipped buses. Two separate studies were carried out and evaluated with the goal of solving the optimum PMU placement problem (OPPP), which pertains to the grids. The findings of the first study show that the maximum bus observability may be accomplished with the fewest possible number of PMUs, even while taking into consideration the fact that there is a risk that one or more PMUs would malfunction. This investigation was carried out with common measures such as zero injection bus (ZIB) and branch flow measurements, both with and without them, in order to assess the outcomes. The second research focused on selecting the PMU-equipped bus’s vulnerability analysis as its primary area of investigation. All of the tests were completed by using binary integer linear programming. Specifically, the described method is meant to be used with an existing PMU framework and in the case that new locations for new PMUs are necessary to be furnished with existing PMUs. This results confirm that the recommended strategy can be implemented successfully on the IEEE benchmark test systems.

To ensure the reliability of power supply, ultra-fast and reliable fault classification of the transmission line is the critical stage of the wide-area transmission network protection. As the distributed generation (DG) current injection to the transmission line, the amplitude characteristic of the break current protection reduces and the system reliability decreases. With the wide-area measurement generated to the power system, an online fault classification method with the global and local discriminant analysis (GLDA) is proposed to enhance the phase characteristic and decrease calculation load. In the single line to ground (SLG) fault process, the local current phase shift is analyzed to enhance the spatiotemporal characteristic. To fully measure the ordering degree of the spatiotemporal characteristic, the axiomatic definition for the characteristic entropy (CE) of the grid impedance in the individual bus in the wide-area transmission network is proposed according to the characteristic distribution. Based on the current spatiotemporal characteristic analysis, a multi-priority GLDA classifies the fault phase in a coordinating way using with the phasor measurement unit (PMU). The multi-priority GLDA-CE fault classification method reduces the computational load, ensures resilience against measurement noise and the transition resistance effect. Compared with the statistical entropy and neural network method, the classification accuracy and response speed of the GLDA-CE fault classification method are validated in the IEEE 39-bus system with 10 PMUs. Compared with the conventional statistical entropy and neural network methods, the GLDA-CE method is able to classify 226 entire power outages and 600 single phase outages within 1.621 s.

Wide-Area Power System Stabilizers (WAPSSs) are damping controllers used in power systems that employ data from Phasor Measurement Units (PMUs). WAPSSs are capable of providing high damping rates for the low-frequency oscillation modes, especially the inter-area modes. Oscillation modes can destabilize power systems if they are not correctly identified and adequately damped. However, WAPSS communication channels may be subject to failures or cyber-attacks that affect their proper operation and may even cause system instability. This research proposes a method based on an optimization model for the design of a WAPSS robust to multiple permanent communication failures. The results of applications of the proposed method in the IEEE 68-bus system show the ability of the WAPSS design to be robust to a possible number of permanent communication failures. Above this value, the combinations of failures and processing time are high and they make it difficult to obtain high damping rates for the closed-loop control system. The application and comparison of different optimization techniques are valid and showed a superior performance of the Grey Wolf Optimizer in solving the optimization problem. [ABSTRACT FROM AUTHOR]