Simplified Stability Assessment of Power Systems with Variable-Delay Wide-Area Damping Control

This paper presents transient stability assessment of a large actual power system using the probabilistic neural network (PNN) with enhanced feature selection and extraction method. The investigated large power system is divided into five smaller areas depending on the coherency of the areas when subjected to disturbances. This is to reduce the amount of data sets collected for the respective areas. Transient stability of the power system is first determined based on the generator relative rotor angles obtained from time domain simulations carried out by considering three phase faults at different loading conditions. The data collected from the time domain simulations are then used as inputs to the PNN. An enhanced feature selection and extraction methods are then incorporated to reduce the input features to the PNN which is used as a classifier to determine whether the power system is stable or unstable. It can be concluded that the PNN with enhanced feature selection and extraction methods reduces the time taken to train the PNN without affecting the accuracy of the classification results.

Modern electric power systems are large and complicated, and, in many regions, the generation and transmission systems are operating near their limits. Eigenanalysis is one of the tools used to analyze the behavior of these systems. Standard eigenvalue methods require that simplified models be used for these analyses; however, these simplified models do not adequately model all of the characteristics of large power systems. Thus, new eigenanalysis methods that can analyze detailed power system models are required. The primary objectives of the work described in this report were I) to determine the availability of eigenanalysis algorithms that are better than methods currently being applied and that could be used an large power systems and 2) to determine if vector supercomputers could be used to significantly increase the size of power systems that can be analyzed by a standard power system eigenanalysis code. At the request of the Bonneville Power Administration, the Pacific Northwest Laboratory (PNL) conducted a literature review of methods currently used for the eigenanalysis of large electric power systems, as well as of general eigenanalysis algorithms that are applicable to large power systems. PNL found that a number of methods are currently being used for the this purpose, and all seem to work fairly well. Furthermore, most of the general eigenanalysis techniques that are applicable to power systems have been tried on these systems, and most seem to work fairly well. One of these techniques, a variation of the Arnoldi method, has been incorporated into a standard power system eigenanalysis package. Overall, it appears that the general purpose eigenanalysis methods are more versatile than most of the other methods that have been used for power systems eigenanalysis. In addition, they are generally easier to use. For some problems, however, it appears that some of the other eigenanalysis methods may be better. Power systems eigenanalysis requires the computation of eigenvalues of nonsymmetric matrices. Such computations are fairly difficult, however, and they constitute an area of active research. Thus, research in this area should be closely monitored, and, as new methods become available, they should be tested on large power systems. PNL also investigated the use of vector supercomputers to enlarge the size of power systems that can be analyzed by MASS, a standard power system eigenanalysis code. MASS was converted to run on a Cray supercomputer. On a conventional computer, MASS is limited to power system problems with about 500 states because of computer time constraints. Running MASS on a Cray X-MP EA/232, however, PNL found that a problem with about 2200 states could be solved in about 26 minutes. Furthermore, by moving to a larger Cray, it should be possible to use MASS to analyze power systems with 5,000 to 10,000 states. Problems with 5,000 states would probably take about 5 Cray hours, while a problem with 10,000 states would probably take about 43 Cray hours, though the actual execution times will depend on the type of Cray used. Problems requiring 5 Cray hours are not uncommon. Problems requiring 43 Cray hours, however, would be fairly expensive. Thus, power systems with about 5000 states probably represent an upper limit on the size of problems that one would want to routinely solve using a Cray version of MASS.

Modern power systems are large in size and complex in features; the data collected by Phasor Measurement Units (PMUs) are often noisy and contaminated; and the machine learning models that have been applied to the transient stability assessment (TSA) of power systems are not sufficiently capable of capturing long-distance dependencies. All these issues make it difficult for data mining-based power system TSA methods to have sufficient accuracy, timeliness, and robustness. To solve this problem, this paper proposes a power system TSA model based on the transformer and neighborhood rough set. The model first uses the neighborhood rough set to deal with the redundant features of the power system trend data and then uses the transformer model to train the TSA model, in which various normalization methods such as Batch Normalization and Layer Normalization are introduced in the process to obtain better evaluation performance and speed up the convergence rate of the model. Finally, the model is evaluated by two evaluation indicators, F1−measure and accuracy, with values of 99.61% for accuracy and 0.9972 for F1−measure, as soon as the tests on noise contamination and missing data test results on the IEEE39 system show that the NRS-Transformer model proposed in this paper is superior in terms of prediction accuracy, training speed, and robustness.

Achieving clean energy goals will require significant advances in regard to addressing the computational needs for next-generation renewable-dominated power grids. One critical obstacle that lies in the way of transitioning today’s power grid to a renewable-dominated power grid is the lack of a faster-than-real-time stability assessment technology for operating a fast-changing power grid. This paper proposes an artificial intelligence (AI) -based method that predicts the system’s stability margin information (e.g., the frequency nadir in the frequency stability assessment and the critical clearing time (CCT) value in the transient stability assessment) directly from the system operating conditions without performing the conventional time-consuming time-domain simulations over detailed dynamic models. Since the AI method shifts the majority of the computational burden to offline training, the online evaluation is extremely fast. This paper has tested the AI-based stability assessment method using multiple dispatch cases that are converted and tuned from actual dispatch cases of the Western Electricity Coordinating Council (WECC) system model with more than 20,000 buses. The results show that the AI-based method could accurately predict the stability margin of such a large power system in less than 0.2 milliseconds using the offline-trained AI agent. Therefore, the proposed method has great potential to achieve faster-than-real-time stability assessment for practical large power systems while preserving sufficient accuracy.

Transient stability assessment is playing a vital role in modern power systems. For this purpose, machine learning techniques have been widely employed to find critical conditions and recognize transient behaviors based on massive data analysis. However, an ever increasing volume of data generated from power systems poses a number of challenges to traditional machine learning techniques, which are computationally intensive running on standalone computers. This paper presents a MapReduce based high performance neural network to enable fast stability assessment of power systems. Hadoop, which is an open-source implementation of the MapReduce model, is first employed to parallelize the neural network. The parallel neural network is further enhanced with HaLoop to reduce the computation overhead incurred in the iteration process of the neural network. In addition, ensemble techniques are employed to accommodate the accuracy loss of the parallelized neural network in classification. The parallelized neural network is evaluated with both the IEEE 68-node system and a real power system from the aspects of computation speedup and stability assessment.

Voltage stability assessment in power system has recently been a growing concern to power system utilities due to blackout experienced in a couple of years in some developed and underdeveloped nations. This paper presents an alternative method which is based on the topology of the power network to identify weak load buses that are susceptible to voltage instability. The method makes use of the critical mode and the eigenvectors to determine the weak bus of the system. To determine the critical mode of the system, eigenvalue decomposition technique is used. Comparison analysis with the power flow based voltage collapse proximity index (VCPI) is performed to show the significance of the suggested approach. Results obtained show that voltage stability assessment in power system could as well be done using the structurally based approach as it saves time and reduces the computational burden compared with the traditional power flow based approach of VCPI.

Based upon a modeling technique of power systems, called the component oriented modeling technique (COMT), this paper applies the small gain theorem and /spl mu/-analysis to establish a stability assessment method for interconnected power systems. Although the stability criterion provides only the sufficient conditions, it permits a direct and fast stability assessment of power systems that may be nonlinear time variant and unbalanced in three phase structure. >

Modern power systems are pushed to operate close to their secure limits due to increased system complexity and high penetration of renewable energy sources (RES). Conventional stability assessment (SA) and control methods face significant adaptiveness and robustness issues under highly uncertain and variable modern power systems. In recent years, with advanced real-time system monitoring and communication techniques like phasor measurement unit (PMU) devices, huge volumes of network-wide time-synchronized measurements can be collected and utilized. Under this new reality, data-driven methods have been identified as powerful tools for online and real-time stability assessment and control. This Ph.D. research aims to develop data-analytic methodologies online and real-time assess the system stability status and provide intelligent control actions when the power system is subject to a severe contingency. Specifically, this research covers a series of new methods in pre-fault SA, post-fault real-time SA and power system emergency control. Special efforts are devoted to enhancing the accuracy and robustness of data-driven methods under some extreme scenarios and practical problems, and a confidence-aware data-driven control scheme to manage the potential prediction error better. In data-driven SA, the point and consecutive data missing at both offline and online stages are studied, and two missing data-robust methods are developed, respectively for pre-fault SA and post-fault SA. For the pre-fault method, to enhance the robustness of SA against incomplete PMU measurements, a hybrid ensemble learning-based online SA method is proposed with feature-validation-based missing data estimators. Considering the possibility that some features may have a low correlation with other measurements, a feature validation process detects the potentially inaccurately estimated features to ensure the model performance and data restoration quality. Further, a novel spatial-temporal recurrent imputation network, SRIN, is proposed for time-series data missing at both sensor and PMU levels. The proposed SRIN method jointly learns the imputation for missing values and prediction output through an integrated multi-task recurrent network model, where the imputed values and the SA output can be simultaneously and effectively updated during backpropagation. In this way, the proposed method can be effectively trained by incompletely recorded datasets, which is immensely valuable for practical applications without high-quality historical data. Moreover, by learning shared representations or features across tasks, multi-task models can better exploit the information present in the data and improve the overall performance of both tasks. In addition, considering the time-varying and location-varying missing data patterns, the imputations of SRIN are derived by an intelligent combination of history-based and feature-based estimations through a trainable weighting component. Thereby, the proposed method is highly adaptive to various data missing scenarios, including both spatial and temporal consecutive missing patterns. In emergency control, data-driven methods for event-based load shedding (ELS) and response-based load shedding (RLS) are developed. Specifically, a hierarchical data-driven method is proposed for real-time prediction of ELS to mitigate fault-induced delayed voltage recovery (FIDVR). First, a novel adaptive trajectory sensitivity analysis is developed to optimize the ELS solutions offline and construct the ELS database. Then, by hierarchically modelling the ELS problem as a multi-output classification subproblem and a regression subproblem, the critical load buses mainly responsible for the delayed voltage recovery can be identified, and the over-shedding buses can be effectively reduced. Moreover, based on an improved weighted kernel extreme learning machine (WKELM) method, the direct mapping between system pre-fault operating conditions and corresponding control variables is constructed. Meanwhile, the established weighted learning scheme can extract the decision-making knowledge from the highly sparse and imbalanced dataset and emphasize on the rare yet critical cases. Therefore, the risk of insufficient load shedding is reduced, and better ELS effectiveness can be achieved. Subsequently, a probabilistic confidence-aware method for real-time RLS is developed to manage the potential prediction error better. The method is based on a two-stage process where a scalable Gaussian process (SGP) method determines the average load shedding amount at the first stage. The upper bound of the prediction interval is considered supplementary in the second stage. In parallel, if an RLS case is identified as unconfident, the conservative rule-based load shedding is taken as a backup plan rather than adopting LS estimations that cannot be trusted. Guided by the probabilistic information, the potential prediction error can be fully considered, and the confidence information can be incorporated into the control process, thereby more accurate and reliable load shedding actions can be taken. Leveraging confident predictions-based 2-stage RLS process, the excessive load loss can be reduced while ensuring high control effectiveness. All the proposed methods have been well verified on simulation experiments over standard power system models.

Transient stability assessment (TSA) is a cornerstone for resilient operations of today’s interconnected power grids. This paper is a confluence of quantum computing, data science and machine learning to potentially address the power system TSA issue. We devise a quantum TSA (QTSA) method to enable efficient data-driven transient stability prediction for bulk power systems, which is the first attempt to tackle the TSA issue with quantum computing. Our contributions are three-fold: 1) A high expressibility, low-depth quantum circuit (HELD) is designed for accurate and noise-resilient TSA; 2) A quantum natural gradient descent algorithm is developed for efficient HELD training and 3) A systematical analysis on QTSA’s performance under various quantum factors is performed. QTSA underpins a foundation of quantum machine learning-enabled power grid stability analytics. It renders the intractable TSA straightforward and effortless in the Hilbert space, and therefore provides stability information for power system operations. Extensive experiments on quantum simulators and real quantum computers verify the accuracy, noise-resilience, scalability and universality of QTSA.

Power system is tending to form a large scale network with numerous interconnected subsystems. In order to maintain the reliability and stability of the power grid, multiple analysis systems with specific hardware platforms are implemented in the electrical power dispatching centre, which makes the software maintenance and hardware management more complicated and ponderous. This paper describes a common task based parallel platform for power system analysis and stability assessment, in which multiple analysis systems and applications can be implemented respectively by sharing the same hardware and support software. The computers in the platform are assigned as data server, computation workstations or console workstations. There are two roles for the computation workstations, one is assumed the manager, and the others are assumed the node. The support software includes 9 programs: file transfer service, configuration service, database service, raw data service, task partitioning interface, task dispatching service, calculation interface, result processing interface and computation management service. Analysis systems and applications can easily be integrated into the platform by development of 3 programs: the task partitioning program, the calculation program and the result processing program. The parallel platform is designed to meet the needs of different applications, by which the hardware costs are reduced and the development cycle is shortened. It is also beneficial to enhance the reliability of power system operations.

Missing data caused by phasor measurement unit (PMU) faults and communication errors leads to power system unobservability, making transient stability assessment (TSA) challenging. To address this issue, a source-free domain adaptation method based on embedding space recovery is presented for TSA. First, an end-to-end multi-task learning framework is proposed, which ensures the integrity of transient features and the distinguishability of system states by sharing spatio-temporal features to recover missing feature spaces and align transient features across domains. Next, a spatio-temporal variational autoencoder (STVAE) is introduced, which avoids the accumulation of imputation errors by recovering the feature space of missing data, using spatial modeling from the power system topology and graph convolutional networks to guide temporal feature recovery. Additionally, an evaluation metric approximation mechanism is proposed to address sample imbalance by converting confusion matrix-based metrics into differentiable loss functions, allowing for direct optimization and improved model performance. This method enables the stability assessment of power systems with missing data, ensuring both rapid assessment and data privacy. Finally, simulation results using the 39-bus and 145-bus systems validate the effectiveness of the proposed method.

The paper presents a comprehensive methodology for voltage stability assessment of power systems using modern analytical tools. The paper also highlights the importance of proper power system component modeling, especially dynamic loads, for achieving higher accuracy. A case study for a practical system is presented and simulation results are discussed.

This chapter presents the small‐signal stability of power systems operating in “steady state,” that is, the system stability of an equilibrium point. The ability of the power system to track the load changes requires the power system to be small‐signal stable, that is, a power system can stably move from one operating condition to a slightly different operating condition. The chapter discusses electromechanical modes in power systems and techniques to compute and identify the frequency and damping of these modes. The approach used is to develop linearized system models that are valid in a region about the equilibrium operating point. Electromechanical modes in a practical power system can be divided into three types: intraplant modes; local modes; and interarea modes. The chapter provides an overview of the development of linear models for nonlinear systems. There are two methods commonly used for generating linearized models: using analytical expressions, and using a numerical perturbation method.

The present work is based on developing a control strategy to mitigate the impact of reduced inertia due to significant DFIG penetration in a large power system. The paper aims to design a supplementary control for the DFIG power converters such that the effective inertia contributed by these wind generators to the system is increased. The paper also proposes the idea of adjusting pitch compensation and maximum active power order to the converter in order to improve inertial response during the transient with response to drop in grid frequency. Results obtained on a large realistic power system indicate that the frequency nadir following a large power impact in the form of generators dropping out is effectively improved with the proposed control strategy. The proposed control is also validated against the sudden wind speed change in the form of wind gust downs and wind ramp downs occurring in conjunction with the generators dropping out. A beneficial impact in terms of damping power system oscillations is also observed, which is validated by eigenvalue analysis. The affected mode is then excited with a large disturbance in time domain. The damping improvement observed in time domain and subsequent Prony analysis support the result obtained from eigenvalue analysis.

Dear Editor, Machine learning (ML) approaches have been widely employed to enable real-time ML-based stability assessment (MLSA) of large-scale automated electricity grids. However, the vulnerability of MLSA to malicious cyber-attacks may lead to wrong decisions in operating the physical grid if its resilience properties are not well understood before deployment. Unlike adversarial ML in prior domains such as image processing, specific constraints of power systems that the attacker must obey in constructing adversarial samples require new research on MLSA vulnerability analysis for power systems. In this letter, we propose a novel evaluation framework to analyze the robustness of MLSA against adversarial samples with key considerations for damage (i.e., the ability of the adversarial data to cause ML misclassification), bad data detection, physical consistency, and limited attacker's capacity to corrupt data. Extensive experiments are conducted to evaluate the robustness of MLSA under different settings.