On-line Transient Stability Assessment Research Articles

Maximum Lyapunov Exponent Based Nearest Neighbor Algorithm For Real-Time Transient Stability Assessment

In power systems, ensuring transient stability is paramount to prevent unforeseen blackouts and power failures. Transient stability assessment is crucial for the early detection and mitigation of instabilities, providing a rapid response to severe fault situations. The concept of the maximum Lyapunov exponent facilitates fast predictions for transient stability assessment after severe disturbances. This paper introduces an efficient maximum Lyapunov exponent algorithm for online transient stability assessment, representing the primary contribution of this work. This approach uses the time series data from the rotor angles of generators or the phase angles of generator terminal buses. Case studies are conducted on the Nordic Power System, with simulations performed in DigSilent PowerFactory. This study contributes by offering insights into the performance and adaptability of the proposed algorithm.

Predictive Online Transient Stability Assessment for Enhancing Efficiency

Predictive Online Transient Stability Assessment for Enhancing Efficiency

Integrated Data-Driven Power System Transient Stability Monitoring and Enhancement

While many promising data-driven power system transient stability assessment (TSA) studies have been recently reported, very few of them further propose efficient data-driven solutions for follow-up control actions, e.g., generator tripping, against potential instability. To address this inadequacy, this work develops an integrated data-driven transient stability monitoring and enhancement (TSMAE) approach that can reliably and efficiently handle various emergency situations in real time. First, by introducing the emerging spatial-temporal synchronous graph convolutional network (STSGCN), wide-area spatial-temporal features w.r.t. system stability are sufficiently learned to reliably implement online TSA. Then, to handle impending instability in a tractable manner, remedial actions are quickly taken based on intelligent critical generator identification (CGI). Specifically, with the help of the STSGCN again, the potential effects of tripping individual generators on system stabilization are efficiently predicted from the spatial-temporal perspective. Based upon that, the most critical generators for tripping are adaptively selected to enhance system stability. Numerical test results on a realistic provincial power grid of China illustrate the efficacy of the proposed TSMAE approach.

Deep learning-based framework for real-time transient stability prediction under stealthy data integrity attacks

Cyber-attacks can degrade the performance of online transient stability prediction (TSP) and assessment functions offered for power systems. This paper proposes a cyber-resilient real-time TSP framework created by considering both perspectives, of the attacker, and of the smart grid operator. From the attacker’s viewpoint, to minimize the attack cost, a model-free data-driven algorithm for finding the measurements to which the TSP function is vulnerable is considered. The attack vector that maximizes the TSP classifier’s inaccuracy reduces the performance of TSP significantly. From the perspective of the system operator and to defend the system against data integrity attacks, two unsupervised learning algorithms which are principal component analysis and fuzzy c-means clustering, are combined and employed to detect the falsified phasor measurement units (PMUs) in the system. In the proposed framework, a denoising autoencoder model is also developed to eliminate the effect of stealthy cyber-attacks. When a cyber-attack is detected, the denoising autoencoder-based model is triggered to recover the damage of the cyber-attack, while a well-tuned long short-term memory model is implemented for the TSP application. The proposed framework is tested on two IEEE test systems, including 39-bus and 127-bus systems, with various attack scenarios. Results show that the developed system is more resilient to the attacks than the existing well-established TSP functions.

A data-driven method for online transient stability monitoring with vision-transformer networks

Online transient stability assessment (TSA) plays an important role in power system planning and operation. The massive integration of renewable energy sources into the grids increases the risks of relay malfunction; however, the existing TSA approaches only apply to scenarios where the fault could be successfully cleared, and are not applicable under relay failure scenarios. Besides, the post-fault TSA methods normally rely on the accurate fault clearance information, which would be affected by the clock synchronization errors in relays. Thus, this paper proposes an online monitoring system that assesses transient stability based on the current operating condition, which is independent of the accurate moments of fault occurrence and clearance provided by fault indicators or relays signals; the transient stability prediction during the fault duration provides the system operators with an early warning of system instability in the event of relay failures. Moreover, an adaptively adjusted criterion for instability is proposed to balance the false alarm and misclassification rates. Furthermore, novel Vision-Transformer-based models for both TSA and unstable generators identification are built in this paper. Compared with other networks, the self-attention structure in the Transformer leads to a global receptive field and higher resolution for capturing time-series information in each sample. Our experiments on the IEEE-39 system show that the proposed method can assess transient stability at each moment in different operation states. It outperforms existing machine learning-based models in terms of accuracy and robustness in TSA and unstable generators identification tasks.

An online power system transient stability assessment method based on graph neural network and central moment discrepancy

The increasing penetration of renewable energy introduces more uncertainties and creates more fluctuations in power systems. Conventional offline time-domain simulation-based stability assessment methods may no longer be able to face changing operating conditions. In this work, a graph neural network-based online transient stability assessment framework is proposed, which can interactively work with conventional methods to provide assessment results. The proposed framework consists of a feature preprocessing module, multiple physics-informed neural networks, and an online updating scheme with transfer learning and central moment discrepancy. The t-distributed stochastic neighbor embedding is used to virtualize the effectiveness of the proposed framework. The IEEE 16-machine 68-bus system is used for case studies. The results show that the proposed method can achieve accurate online transient stability assessment under changing operating conditions of power systems.

An Automated and Interpretable Machine Learning Scheme for Power System Transient Stability Assessment

Many repeated manual feature adjustments and much heuristic parameter tuning are required during the debugging of machine learning (ML)-based transient stability assessment (TSA) of power systems. Furthermore, the results produced by ML-based TSA are often not explainable. This paper handles both the automation and interpretability issues of ML-based TSA. An automated machine learning (AutoML) scheme is proposed which consists of auto-feature selection, CatBoost, Bayesian optimization, and performance evaluation. CatBoost, as a new ensemble ML method, is implemented to achieve fast, scalable, and high performance for online TSA. To enable faster deployment and reduce the heavy dependence on human expertise, auto-feature selection and Bayesian optimization, respectively, are introduced to automatically determine the best input features and optimal hyperparameters. Furthermore, to help operators understand the prediction of stable/unstable TSA, an interpretability analysis based on the Shapley additive explanation (SHAP), is embedded into both offline and online phases of the AutoML framework. Test results on IEEE 39-bus system, IEEE 118-bus system, and a practical large-scale power system, demonstrate that the proposed approach achieves more accurate and certain appropriate trust solutions while saving a substantial amount of time in comparison to other methods.

A fast sequential transient stability preventive control approach driven by model interpretation

Transient stability preventive control (TSPC), regarded as generation rescheduling, plays an important role in maintaining secure and economic dispatch of power systems. To accommodate the increasing uncertainty of operation conditions, online TSPC is urgently required in real power systems. To this end, a new sequential online TSPC strategy driven by transient stability assessment (TSA) model interpretation is proposed in this paper. In this strategy, two data-driven TSA models, namely full-feature-trained and controllable-feature-trained models, are deployed for online TSA and generation rescheduling, respectively. To identify the control generators for TSPC, an instance-based model interpretation tool, Local Interpretable Model-agnostic Explanations (LIME), is introduced to interpret the unstable operation detected by online TSA. In addition, a pair-wise generator regulation strategy and a continual prediction method are used to quickly search the TSPC operating point while ensuring the power shift balance of the system during regulation. The adaptability of the strategy to the online applications is demonstrated on the IEEE 3-machine 9-bus system and the IEEE 10-machine 39-bus system. • Sequential framework speeds up transient stability preventive control (TSPC). • TSA model trained by controllable features locates the origin of system instability. • Model interpretation breaks up the opacity of TSA model’s predictions.

Risk assessment of power system transient instability incorporating renewable energy sources

Transient stability affected by renewable energy sources integration due to reductions of system inertia and uncertainties associated with the expected generation. The ability to manage relation between the available big data and transient stability assessment (TSA) enables fast and accurate monitoring of TSA to prepare the required actions for secure operation. This work aims to build a predictive model using Gaussian process regression for online TSA utilizing selected features. The critical fault clearing time (CCT) is used as TSA index. The selected features map the system dynamics to reduce the burden of data collection and the computation time. The required data were collected offline from power flow calculations at different operating conditions. Therefore, CCT was calculated using electromagnetic transientsimulation at each operating point by applying self-clearance three phase short circuit at prespecified locations. The features selection was implemented using the neighborhood component analysis, the Minimum Redundancy Maximum Relevance algorithm, and K-means clustering algorithm. The vulnerability of selected features tends to result great variation on the best features from the three methods. Hybrid collection of the best common features was used to enhance the TSA by refining the final selected features. The proposed model was investigated over 66-bus system.

Time-Adaptive Transient Stability Assessment Based on the Gating Spatiotemporal Graph Neural Network and Gated Recurrent Unit

With the continuous expansion of the UHV AC/DC interconnection scale, online, high-precision, and fast transient stability assessment (TSA) is very important for the safe operation of power grids. In this study, a transient stability assessment method based on the gating spatiotemporal graph neural network (GSTGNN) is proposed. A time-adaptive method is used to improve the accuracy and speed of transient stability assessment. First, in order to reduce the impact of dynamic topology on TSA after fault removal, GSTGNN is used to extract and fuse the key features of topology and attribute information of adjacent nodes to learn the spatial data correlation and improve the evaluation accuracy. Then, the extracted features are input into the gated recurrent unit (GRU) to learn the correlation of data at each time. Fast and accurate evaluation results are output from the stability threshold. At the same time, in order to avoid the influence of the quality of training samples, an improved weighted cross entropy loss function with the K-nearest neighbor (KNN) idea is used to deal with the unbalanced training samples. Through the analysis of an example, it is proved from the data visualization that the TSA method can effectively improve the assessment accuracy and shorten the assessment time.

Deep learning-based transient stability assessment framework for large-scale modern power system

When severe disturbance occurs in power system, lack of efficacious information about transient stability state is a key challenge for power network operator. Especially for the system operating in boundary of security constraints due to economic reasons, it becomes more prominent. With the extensive deployment of phasor measurement units (PMUs), abundant historical data of power system have been collected and the data driven method based on machine learning model has become important tool to solve transient stability assessment (TSA) problem. However, the implementation of data-driven TSA method is difficult due to the characteristics of huge feature number and variable network topology of large-scale modern power system. In order to address this issue, a novel deep learning-based online TSA framework is proposed in this article. Firstly, parallel convolution algorithms are employed to address redundant input features. secondly, a novel machine learning model, deep forest is employed to train a TSA model. Some improvements are implemented for better assessment performance: 1) The internal feature transmission of deep forest is adjusted for higher assessment accuracy. 2) A fast update scheme is proposed based on active learning technique and graded strategy. 3) The cost-based method is employed to address class-imbalance training data. The test results on three power systems show that the proposed TSA framework has advantages in prediction accuracy, training speed, and update time. It is suitable for application of large-scale modern power system.

Networked Time Series Shapelet Learning for Power System Transient Stability Assessment

While many machine learning approaches have been widely applied to power system online dynamic stability assessment, how to sufficiently learn spatial-temporal correlations from system transients without losing the interpretability is still a challenging issue. In this paper, a novel networked time series shapelet learning approach is proposed to learn spatial-temporal correlations for transient stability assessment (TSA) in an interpretable manner. Specifically, a network impedance-based adjacency matrix is first introduced to characterize spatial networked correlations. Based on graph structural regularization, this matrix is effectively incorporated into the subsequent learning procedure as spatial constraints. Taking time series trajectories acquired from multiple buses as the inputs, networked shapelet learning is heuristically performed to learn critical sequential features, i.e., networked shapelets, for TSA model derivation. With the learning procedure strategically guided by inherent spatial-temporal correlations of the system, the obtained data-driven TSA model is able to perform highly reliable and interpretable online TSA. Numerical test results on the IEEE 39-bus test system and the realistic GD Power Grid in China verify the superior performances of the proposed approach.

Risk-Constrained Minimization of Combined Event Detection and Decision Time for Online Transient Stability Assessment

This paper addresses the problem of `quickest possible' online transient stability assessment, by minimizing the decision time of combined event detection that might lead to a system split and unstable generator group prediction, from real-time wide area power system measurements. More importantly it does so by respecting predefined probabilistic error constraints for the prediction. The statistical theory of optimal detection is applied, firstly to choose the detection threshold and secondly to select a flexible assessment time, after using probabilistic neural networks to provide a temporal representation of the data. On simulated wide area measurements from the interconnected New England test system and New York power system this approach is between two and three times faster on average than strategies based on fixed assessment times, despite having comparable error rates.

Hybrid analytical and data-driven modeling based instance-transfer method for power system online transient stability assessment

Data-driven methods are widely concerned and show good effects in online transient stability assessment. However, tedious and time-consuming sample collection process is always neglected. In power systems, continuous changes in operation mode require repetitive sample collection process, underlining importance of collection efficiency. To achieve high sample collection efficiency after operation mode change, a new instance-transfer method based on compressing and matching strategy is proposed, by which useful previous samples are inherited directly for new sample base construction. Further, a hybrid model is put forward to guarantee rationality in sample similarity comparison and selection, where high-importance features of analytical models are introduced to data-driven methods. Meanwhile, data-driven method is also utilized to realize fast error correction of analytical models in the hybrid model, helping achieve fast and accurate post-disturbance transient stability assessment. As a paradigm, scheme for online critical clearing time (CCT) estimation is concerned, where integrated extended equal area criterion (IEEAC) and extreme learning machine (ELM) are used as analytical model and data-driven error correction model part respectively. Results validate effectiveness of the proposed method.

Entropy based prioritization strategy for data-driven transient stability batch assessment

Transient stability batch assessment (TSBA) is essential for dynamic security check in both power system planning and day-ahead dispatch. It is also a necessary technique to generate sufficient training data for data-driven online transient stability assessment (TSA). However, most existing work suffers from various problems including high computational burden, low model adaptability, and low performance robustness. Therefore, it is still a significant challenge in modern power systems, with numerous scenarios (e.g., operating conditions and N-k contingencies) to be assessed at the same time. The purpose of this work is to construct a data-driven method to early terminate timedomain simulation (TDS) and dynamically schedule TSBA task queue a prior, in order to reduce computational burden without compromising accuracy. To achieve this goal, a time-adaptive cascaded convolutional neural networks (CNNs) model is developed to predict stability and early terminate TDS. Additionally, an information entropy based prioritization strategy is designed to distinguish informative samples, dynamically schedule TSBA task queue and timely update model, thus further reducing simulation time. Case study in IEEE 39-bus system validates the effectiveness of the proposed method.

Construction of Multi-State Transient Stability Boundary Based on Broad Learning

This paper presents a novel methodology for the construction of a transient stability boundary (TSB) that overcomes the lack of TSB analytical description for multiple operating states and contingencies in power systems. The proposed approach models the TSB as a nonlinear mapping between the system parameters of interest and the corresponding critical clearing time (CCT). This compact mathematical expression is built based on an efficient discriminative network, broad learning system (BLS). While keeping a high accuracy and generalization ability, the newly introduced construction method provides an efficient update strategy that does not require an entire retraining cycle. These properties make this method suitable for online transient stability assessment (TSA). The prospects of the developed method are verified via case studies by employing the IEEE 9-bus, IEEE 39-bus (New England) test systems and a real system of China Southern Power Grid. In comparison with existing methods, the newly introduced algorithm has a higher prediction accuracy and improved robustness. The demonstrated characteristics indicate that the proposed method may serve as a valuable tool in the framework of online TSA.

An Improved Power System Transient Stability Prediction Model Based on mRMR Feature Selection and WTA Ensemble Learning

Fast online transient stability assessment (TSA) is very important to maintain the stable operation of power systems. However, the existing transient stability assessment methods suffer the drawbacks of unsatisfactory prediction accuracy, difficult applicability, or a heavy computational burden. In light of this, an improved high accuracy power system transient stability prediction model is proposed, based on min-redundancy and max-relevance (mRMR) feature selection and winner take all (WTA) ensemble learning. Firstly, the contributions of four different series of raw sampled data from all of the three-time stages, namely the pre-fault, during-fault and post-fault, to transient stability are compared. The new feature of generator electromagnetic power is introduced and compared with three conventional types of input features, through a support vector machine (SVM) classifier. Furthermore, the two types of most contributive input features are obtained by the mRMR feature selection method. Finally, the prediction results of the electromagnetic power of generators and the voltage amplitude of buses are combined using the WTA ensemble learning method, and an improved transient stability prediction model with higher accuracy for unstable samples is obtained, whose overall prediction accuracy would not decrease either. The real-time data collected by wide area monitoring systems (WAMS) can be fed into this model for fast online transient stability prediction; the results can also provide a basis for the future emergency control decision-making of power systems.

MVMO-Based Identification of Key Input Variables and Design of Decision Trees for Transient Stability Assessment in Power Systems With High Penetration Levels of Wind Power

Unlike synchronous generators, wind turbines cannot directly respond to large disturbances, which may cause transient instability, due to their power electronic-based interface and maximum power control strategy. To effectively monitor the influence of wind turbines, this paper proposes an approach that combines decision trees (DTs), and a newly developed variant of the Mean-Variance Mapping Optimization (MVMO) algorithm, to simultaneously tackle the problem of selecting the key variables that properly reflect the transient stability performance of a system dominated by wind power, and designing the DTs for reliable online assessment of transient stability. The notion of key variables refers to the set of variables that are closely related to the modified power system transient stability performance as a consequence of the replacement of conventional power plants by wind generators. The selection of key variables is formulated as a non-linear optimization problem with weight factors as decision variables and is tackled by MVMO. A weight factor is assigned to each key variable candidate, and its value is considered to reflect the degree of influence of the key variable candidate on the splitting property and estimation accuracy of the DTs. The samples of the key variable candidates and the initialized weight factors are used to build the first group of DTs. Then, MVMO iteratively evolves the weight factors according to its special mapping function with minimizing DTs' estimation error. According to the final list of optimized weight factors, system operators can select a reduced set of variables with the largest weight factors as key variables, depending on the resulting accuracy of the DTs. Meanwhile, DTs built by using key variables are considered as the optimal performance trees for transient stability estimation. In this way, the selection of key variables and the development of DTs are made jointly and automatically, without the interference of the users of the DTs. Test results on the modified IEEE 9 bus system and a synthetic model of a real power system show that the proposed method can correctly identify the set of key variables related to wind turbine dynamics, as well as its ability to provide a reliable estimation of the transient stability margin.

Convolutional neural network-based power system transient stability assessment and instability mode prediction

Online transient stability assessment (TSA) is vital for power system control as it provides the basis for operators to decide emergency control actions. But none of previous TSA research has taken into consideration the difference between two instability modes (aperiodic instability and oscillatory instability), which may threaten secure operation of power system. To address this problem, a TSA and instability mode prediction method based on convolutional neural network is proposed. The method takes the bus voltage phasor sampled by phasor measurement units (PMUs) during a short observation window after disturbance as input, and outputs the prediction result promptly: stable, aperiodic unstable or oscillatory unstable. The end-to-end model automatically extracts needed features from the raw measurement data, thus freeing itself from reliance on expertise. At the offline training stage, stochastic gradient descent with warm restart (SGDR) optimization algorithm is employed so that the model tends to converge to 'flat' and 'wide' minima with better generalization ability. Case studies conducted on New England 39-bus system and Western Electricity Coordinating Council (WECC) 179-bus system demonstrate superior accuracy, adaptability and scalability of the proposed method compared with conventional machine learning methods. Furthermore, the proposed model is empirically proven to be robust to PMU noise and loss.

Online Assessment of Transient Stability of Grid Connected PV Generator With DC Link Voltage and Reactive Power Control

The proliferation of Photovoltaic (PV) generation has brought several changes in the transient stability analysis of power systems. The rotor angle dynamics based stability analysis used for synchronous generators may not be applicable for PV generators. In the existing literature, the transient stability of a grid connected PV generator with dc link voltage and reactive power control ( $V_{dc}$ and $Q$ control) is analyzed from the coupled nonlinear functions corresponding to PV control loops, Phase Locked Loop (PLL) and network dynamics. The existing method may not be suitable for online transient stability assessment because it is computationally heavy. This paper proposes an online transient stability criterion for a PV generator (with $V_{dc}$ and $Q$ control) connected to grid modelled as infinite bus. The PV generator is considered to have Low Voltage Ride Through (LVRT) capability, but does not provide voltage support. In this study, the relation between the ac and dc side dynamics is explored. A stability criterion is proposed to assess the transient stability by monitoring the swing in the energy of the dc link capacitor. The proposed criterion requires the dc link voltage trajectory only till the first swing of the dc link voltage. As a result, the proposed assessment criterion is computationally less demanding and less prone to measurement errors in comparison to existing methods. Thus, the proposed criterion is suitable for online transient stability assessment. The effectiveness of the proposed criterion is verified for single-stage as well as two-stage converter configurations of PV generator. The proposed criterion is also verified on a modified IEEE 39 bus system. Time-domain simulations are carried out to validate the proposed criterion. The proposed approach is compared with an existing transient stability criterion for $V_{dc}$ and $Q$ control based grid connected PV generator. The advantages of the proposed method as compared to the existing method are discussed.