Transient Stability Assessment Research Articles

Transient stability assessment combined model framework based on cost‐sensitive method

The real-time transient stability assessment (TSA) is critical for emergency control of power systems. Accurate and fast TSA can provide an important basis for post-fault control of power systems. At present, the accuracy of the evaluation model based on machine learning is very high, but there are still some misjudgements in the results. In order to build a high-accuracy evaluation model, a novel frame based on the cost-sensitive method is proposed. Firstly, a deep belief network (DBN) is applied to build a TSA frame. The DBN is effectively trained by means of pre-training and fine tuning. Secondly, two models with the opposite preference are constructed based on the cost-sensitive method. Based on the output results of the two models, the deterministic or uncertain evaluation results are obtained. The samples that may be misclassified are divided into uncertain evaluation results. Thus, the accuracy of the deterministic evaluation results can be improved greatly. Through this design, the practicability of the evaluation model based on machine learning is greatly improved. The effectiveness of the proposed scheme is verified by the simulation results in the IEEE-39 bus system and a realistic regional system.

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.

Transient stability assessment in large-scale power systems based on the sparse single index model

We apply a class of nonlinear semiparametric models to the problem of transient stability analysis of a large-scale power system. The mapping between the pre-contingency state and the transient stability boundary (TSB) is modelled by a block-oriented structure known as the single-index model (SIM). In this model one has a single dimensional projection that enters the unknown nonlinearity nonparametrically. Such models form a rich class of nonlinear mappings that includes classical models, e.g., linear and logistic regression, as special cases. The generalized case of the SIM is utilized that is taking into account the sparsity of the projection vector. This yields a low-dimensional nonlinear model suitable for high-dimensional data emerging in modern power systems. The parametric part of the model is obtained by the properly modified sparsity sensitive LASSO algorithm. The nonlinear nonparametric part of the model is estimated by the monotonically corrected kernel regression estimate. The precision of our modeling is verified for two fault cases of the 470-bus power system. It is shown that for the examined faults, the proposed modeling methodology exhibits a stronger prediction accuracy compared to the existing competing methods recently applied in the field, namely, kernel ridge regression, as well as LASSO linear modeling.

Qualitative and Quantitative Transient Stability Assessment of Stand-Alone Hybrid Microgrids in a Cluster Environment

Neighboring stand-alone hybrid microgrids with diesel generators (DGs) as well as grid-feeding photovoltaics (PV) and grid-forming battery storage systems (BSS) can be coupled to reduce fuel costs and emissions as well as to enhance the security of supply. In contrast to the research in control and small-signal rotor angle stability of microgrids, there is a significant lack of knowledge regarding the transient stability of off-grid hybrid microgrids in a cluster environment. Therefore, the large-signal rotor angle stability of pooled microgrids was assessed qualitatively and also quantitatively in this research work. Quantitative transient stability assessment (TSA) was carried out with the help of the—recently developed and validated—micro-hybrid method by combining time-domain simulations and transient energy function analyses. For this purpose, three realistic dynamic microgrids were modelled regarding three operating modes (island, interconnection, and cluster) as well as the conventional scenario “classical” and four hybrid scenarios (“storage”, “sun”, “sun & storage”, and “night”) regarding different instants of time on a tropical partly sunny day. It can be inferred that, coupling hybrid microgrids is feasible from the voltage, frequency, and also transient stability point of view. However, the risk of large-signal rotor angle instability in pooled microgrids is relatively higher than in islanded microgrids. Along with critical clearing times, new stability-related indicators such as system stability degree and corrected critical clearing times should be taken into account in the planning phase and in the operation of microgrids. In principle, a general conclusion concerning the best operating mode and scenario of the investigated microgrids cannot be drawn. TSA of pooled hybrid microgrids should be performed—on a regular basis especially in the grid operation—for different loading conditions, tie-line power flows, topologies, operating modes, and scenarios.

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.

Enhanced sensitivity‐based decentralised framework for real‐time transient stability assessment in bulk power grids with renewable energy resources

With the increasing trend in the integration and deployment of distributed energy resources, the real-time assessment of power system transient stability is becoming more and more challenging. This study presents an enhanced sensitivity-based decentralised transient stability assessment scheme, which first virtually decomposes the large-scale power network into several smaller areas. Then, a new sensitivity-based scheme is developed to derive and quantify the kinetic energy-based stability assessment index. This index allows taking into account the effects of both AC generators and power electronic-based generator units. In addition, thanks to the new sensitivity-based scheme, the transient stability can be assessed in a decentralised manner using only the boundary buses in each segmented area, which relaxes the need for massive data availability and transfer across the network and enables its applicability for online applications in large-scale power systems. Simulation results on the 48-machine IEEE 140-bus and 544-machine 2000-bus synthetic power grid test systems demonstrate the efficacy of the proposed method.

Recurrent Graph Convolutional Network-Based Multi-Task Transient Stability Assessment Framework in Power System

Reliable online transient stability assessment (TSA) is fundamentally required for power system operation security. Compared with time-costly classical digital simulation methods, data-driven deep learning (DL) methods provide a promising technique to build a TSA model. However, general DL models show poor adaptability to the variation of power system topology. In this paper, we propose a new graph-based framework, which is termed as recurrent graph convolutional network based multi-task TSA (RGCN-MT-TSA). Both the graph convolutional network (GCN) and the long short-term memory (LSTM) unit are aggregated to form the recurrent graph convolutional network (RGCN), where the GCN explicitly integrate the bus (node) states with the topological characteristics while the LSTM subsequently captures the temporal features. We also propose a multi-task learning (MTL) scheme, which provides joint training of stability classification (Task-1) as well as critical generator identification (Task-2) in the framework, and accelerate the process with parallel computing. Test results on IEEE 39 Bus system and IEEE 300 Bus system indicate the superiority of the proposed scheme over existing models, as well as its robustness under various scenarios.

Data-driven Transient Stability Assessment Model Considering Network Topology Changes via Mahalanobis Kernel Regression and Ensemble Learning

Transient stability assessment (TSA) is of great importance in power system operation and control. One of the usual tasks in TSA is to estimate the critical clearing time (CCT) of a given fault under the given network topology and pre-fault power flow. Data-driven methods try to obtain models describing the mapping between these factors and the CCT from a large number of samples. However, the influence of network topology on CCT is hard to be analyzed and is often ignored, which makes the models inaccurate and unpractical. In this paper, a novel data-driven TSA model combining Mahalanobis kernel regression and ensemble learning is proposed to deal with the problem. The model is a weighted sum of several sub-models. Each sub-model only uses the data of one topology to construct a kernel regressor. The weights are determined by both the topological similarity and numerical similarity between the samples. The similarities are decided by the parameters in Mahalanobis distance, and the parameters are to be trained. To reduce the model complexity, sub-models within the same topology category share the same parameters. When estimating CCT, the model uses not only the sub-model which the sample topology belongs to, but also other sub-models. Thus, it avoids the problem that there may be too few data under some topologies. It also efficiently utilizes information of data under all the topologies. Moreover, its decision-making process is clear and understandable, and an effective training algorithm is also designed. Test results on both the IEEE 10-machine 39-bus and a real system verify the effectiveness of the proposed model.

Comprehensive Validation of Transient Stability Calculations in Electric Power Systems and Hardware-Software Tool for Its Implementation

Reliability and survivability of electric power systems (EPS) depend on transient stability assessment (TSA). One of the most effective way to TSA is time-domain simulation. However, large-scale EPS mathematical model contains a stiff nonlinear system of high-order differential equations. Such system cannot be solved analytically. At the same time, numerical methods are imperfectly applied for such system due to limitation conditions. To make it appropriate, the EPS mathematical model is simplified and additional limitations are used. These simplifications and limitations reduce reliability of simulation results. Consequently, their validation is needed. The most reliable approach to provide it is to compare the simulation results with the field data. However, in practice, there are not enough data for such validation. This paper proposes an alternative approach for validation - the application of a reference model instead of field data. A hardware-software system HRTSim was used as a reference model. This power system simulator has all the necessary properties and capabilities to obtain reliable information required for comprehensive validation of transient stability calculations in EPSs. Main disturbances leading to instability in EPSs are investigated to conduct the validation (processes in cases of faults, single-phase auto-reclosing operation and power system interconnection). Fragments of corresponding experimental studies illustrate the efficiency of the proposed approach. Obtained results confirmed the possibility of the developed approach to identify the causes of numerical calculation errors and to determine disturbances calculated with the significant error. In addition, experimental studies have revealed that numerical calculations error depends on disturbances intensity.

Transient Stability Assessment of Power System Based on XGBoost and Factorization Machine

As the deployment of wide-area measurement systems (WAMS) expands, data-driven methods are playing an increasingly important role in transient stability assessment (TSA). However, if the measured data is disturbed by noise or the topological structure of the power system changes, the performance of the model based on data-mining would decline so that it could not meet the needs of real-world scenarios. In this paper, we develop a TSA methodology based on extreme gradient boosting (XGBoost) and factorization machine (FM). Utilizing XGBoost to complete automatically the feature construction and transform the power flow into a sparse matrix. The influence of noise can be reduce due to the sparsity of the new feature set. On this basis, FM algorithm, which has advantage in processing the large sparse matrix, is introduced into the model to complete fault classification. Furthermore, the feature crossing function of FM further mines the interactive information of the spatio-temporal features. For changed topology scenarios, we propose a extended-training set scheme. Adding some pivotal data of topology changes to the training set improves the robustness of the model. Compared with existing studies, the proposed assessment model based on XGBoost-FM not only has the better generalization performance in the case of noise interference or changed topology, but also has the least time consumption and complexity.

A Data-driven Method for Transient Stability Margin Prediction Based on Security Region

Transient stability assessment (TSA) based on security region is of great significance to the security of power systems. In this paper, we propose a novel methodology for the assessment of online transient stability margin. Combined with a geographic information system (GIS) and transformation rules, the topology information and pre-fault power flow characteristics can be extracted by 2D computer-vision-based power flow images (CVPFIs). Then, a convolutional neural network (CNN)-based comprehensive network is constructed to map the relationship between the steady-state power flow and the generator stability indices under the anticipated contingency set. The network consists of two components: the classification network classifies the input samples into the credibly stable/unstable and uncertain categories, and the prediction network is utilized to further predict the generator stability indices of the categorized samples, which improves the network ability to distinguish between the samples with similar characteristics. The proposed methodology can be used to quickly and quantitatively evaluate the transient stability margin of a power system, and the simulation results validate the effectiveness of the method.

Improved Deep Belief Network and Model Interpretation Method for Power System Transient Stability Assessment

The real-time transient stability assessment (TSA) and emergency control are effective measures to suppress accident expansion, prevent system instability, and avoid large-scale power outages in the event of power system failure. However, real-time assessment is extremely demanding on computing speed, and the traditional method is not competent. In this paper, an improved deep belief network (DBN) is proposed for the fast assessment of transient stability, which considers the structural characteristics of power system in the construction of loss function. Deep learning has been effective in many fields, but usually is considered as a black-box model. From the perspective of machine learning interpretation, this paper proposes a local linear interpreter (LLI) model, and tries to give a reasonable interpretation of the relationship between the system features and the assessment result, and illustrates the conversion process from the input feature space to the high-dimension representation space. The proposed method is tested on an IEEE new England test system and demonstrated on a regional power system in China. The result demonstrates that the proposed method has rapidity, high accuracy and good interpretability in transient stability assessment.

Anti-Jitter and Refined Power System Transient Stability Assessment Based on Long-Short Term Memory Network

In order to maintain the stable operation of power systems, quick and accurate transient stability assessment (TSA) after the fault clearance is important. Machine learning methods have been widely used in the transient stability analysis of power systems. However, how to make good use of time series data of PMUs and effectively balance the contradiction between rapidity and accuracy brings new challenges to TSA. To address this problem, we propose an anti-jitter dynamic evaluation method based on long-short term memory (LSTM) network. In this model, the trajectory cluster characteristics of generators power angles after fault clearance are taken as inputs, and an improved LSTM is used to learn the nonlinear mapping relationship between the input characteristics and the transient stability. Meanwhile, by the use of sliding time windows and anti-jitter mechanism, a hierarchical real-time prediction framework is constructed to effectively utilize the time series data of PMUs. The case studies on two systems indicate that the proposed method has superior evaluation accuracy and general performance. In addition, the proposed method can effectively evaluate the stability margin or instability degree of samples, which provides reliable reference information for emergency control.

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.

A Review of Machine Learning Approaches to Power System Security and Stability

Increasing use of renewable energy sources, liberalized energy markets and most importantly, the integrations of various monitoring, measuring and communication infrastructures into modern power system network offer the opportunity to build a resilient and efficient grid. However, it also brings about various threats of instabilities and security concerns in form of cyberattack, voltage instability, power quality (PQ) disturbance among others to the complex network. The need for efficient methodologies for quicker identification and detection of these problems have always been a priority to energy stakeholders over the years. In recent times, machine learning techniques (MLTs) have proven to be effective in numerous applications including power system studies. In the literature, various MLTs such as artificial neural networks (ANN), Decision Tree (DT), support vector machines (SVM) have been proposed, resulting in effective decision making and control actions in the secured and stable operations of the power system. Given this growing trend, this paper presents a comprehensive review on the most recent studies whereby MLTs were developed for power system security and stability especially in cyberattack detections, PQ disturbance studies and dynamic security assessment studies. The aim is to highlight the methodologies, achievements and more importantly the limitations in the classifier(s) design, dataset and test systems employed in the reviewed publications. A brief review of reinforcement learning (RL) and deep reinforcement learning (DRL) approaches to transient stability assessment is also presented. Finally, we highlighted some challenges and directions for future studies.

Development of Back-Propagation Neural Network for Transient Stability Assessment of Power Systems

Transient Stability Assessment (TSA) is aspect of the power system dynamic stability assessment, which includes measuring the capacity of the system to stay synchronized under extreme disturbances. This research work shows the transient stability status of the power system following a major disturbance, such as a faults, line switchings, generator voltages. It can be predicted early based on response trajectories of rotor angle. This early prediction of transient stability is achieved by training a Back Propagation Neural Network (BPNN) taking trajectory of rotor angles as training features. Transient stability index (TSI) proposed in [4] is utilized as a target feature. The proposed methodology is tested with wide range of fault data collected from simulated IEEE 39-Benchmark system. The simulation results shows, utilization of BPNN for transient stability prediction resulted in better performance when compared to Radial Basis Neural Network (RBFNN) [4]

The micro-hybrid method to assess transient stability quantitatively in pooled off-grid microgrids

In interconnected off-grid microgrids an in-depth knowledge of dynamic limits can be obtained by performing quantitative transient stability assessment. Quantitative stability results using the new hybrid method can be used for optimal generation dispatching, adjusting protection system settings, optimal clustering of microgrids etc. However, a discrepancy in the profiles of kinetic and potential energy has been noticed. Therefore, in this research work an improved new hybrid method, the so-called micro-hybrid method, was developed by adjusting the transient energy function, which is valid for transmission systems. Further, the new approach was validated and applied in a stand-alone multi-machine microgrid comprising detailed dynamic models of diesel generators with fast-reacting controllers. Finally, the transient stability of three clustered microgrids was assessed quantitatively. From the results it can be concluded that the profiles of the energies obtained by using the micro-hybrid method are exact mirror images. The critical fault clearing times can be corrected based on the profiles of the system stability degree and stability reserve degree of individual generators for different clearing times. Lastly, pooling of the investigated microgrids has a negative impact on the critical clearing times as well as on the profiles of system stability degree with respect to various clearing times.

Probabilistic transient stability assessment of power system considering wind power uncertainties and correlations

This paper proposes a simple yet effective method for power system probabilistic transient stability assessment considering the wind farm uncertainties and correlations. Specifically, the inverse Nataf transformation based three-point estimation method and the Cornish-Fisher expansion have been integrated together to deal with the uncertainties and the correlations among different wind farms. Then, by resorting to the extended dynamic security region approach, the transient stability criterion is derived as a linear combination of nodal injection vector under a given fault condition. New indices for the identification of critical lines have also been developed. Extensive simulation results carried out on four different systems, including the practical GZ power system in China show that the computational efficiency of the proposed method is much higher than the Monte Carlo-based method and other methods almost without the loss of accuracy. The effectiveness of the proposed method under different penetrations of wind power with different degree of correlations is also validated. It is shown that correlation among wind farms has a larger impact on the transient stability results with a higher penetration level of renewable energy.

Power System Transient Stability Study by Involving Higher Order Corrections in Improved Quadratic Lyapunov Function for Singular Perturbed Model of Synchronous Generator

The assessment of transient stability of multi-machine power system, in a post-fault scenario, is a very challenging task due to highly non-linear nature of the system equations. In this work, the physical concept of maximum relative acceleration of a machine at a fault scenario is related with the boundary of stability region. This approach is extended to develop a quadratic Lyapunov function using singular perturbed modelling. Unlike the conventional energy function methods, this Lyapunov function candidate is a more general energy function and has a decaying nature around an equilibrium point. Moreover, with higher order corrections, an improved Lyapunov function candidate is presented with simulation results of power system examples. The decaying nature of Lyapunov function candidate remains similar even without higher order corrections. However, the relevance of inclusion of higher order corrections is brought out in the cases of faults occurring at other than generator buses. Also, the upper bound of singular perturbation parameter in the model is within allowable limits and ensures the accuracy of results.