Short-term Voltage Stability Research Articles

Short-term voltage stability analysis in power systems: A voltage solvability indicator

This paper presents an analytical study for short-term voltage stability based on a novel indicator. First, it is shown that the reduced Jacobian matrix of network equations can be transformed to obtain an approximately symmetric matrix which is usually positive definite when the system under study is stable. The minimum eigenvalue of the matrix is suggested as a short-term Voltage Solvability Indicator (VSI). Then, properties of the reduced conductive matrix and susceptance matrix which have significant impacts on VSI are examined. The focus of the study is power systems with multiple constant power injections, while VSI can also be applied to analyze the impact of generic power system models. It is shown that as the penetration level of constant power injections increases, VSI decreases and the system becomes more vulnerable to voltage collapse. Finally, the relationship between the eigenvalues of the reduced Jacobian matrix and the structure-preserving Jacobian matrix is established. As a result, the suggested VSI can be efficiently computed by exploring the sparsity of structure-preserving Jacobian matrix of network equations. Case studies of several test systems including a simplified 575-machine 8117-bus East China power system are reported, demonstrating the effectiveness and practicability of the proposed method.

A novel deep learning approach for estimating and classifying short-term voltage stability events in modern power systems with composite load and distributed energy resources

A novel deep learning approach for estimating and classifying short-term voltage stability events in modern power systems with composite load and distributed energy resources

Dynamic voltage safety measurement and assessment index considering short-term voltage stability

Dynamic voltage safety measurement and assessment index considering short-term voltage stability

Robust Representation Learning for Power System Short-Term Voltage Stability Assessment Under Diverse Data Loss Conditions.

With the help of neural network-based representation learning, significant progress has been recently made in data-driven online dynamic stability assessment (DSA) of complex electric power systems. However, without sufficient attention to diverse data loss conditions in practice, the existing data-driven DSA solutions' performance could be largely degraded due to practical defective input data. To address this problem, this work develops a robust representation learning approach to enhance DSA performance against multiple input data loss conditions in practice. Specifically, focusing on the short-term voltage stability (SVS) issue, an ensemble representation learning scheme (ERLS) is carefully designed to achieve data loss-tolerant online SVS assessment: 1) based on an efficient data masking technique, various missing data conditions are handled and augmented in a unified manner for lossy learning dataset preparation; 2) the emerging spatial-temporal graph convolutional network (STGCN) is leveraged to derive multiple diversified base learners with strong capability in SVS feature learning and representation; and 3) with massive SVS scenarios deeply grouped into a number of clusters, these STGCN-enabled base learners are distinctly assembled for each cluster via multilinear regression (MLR) to realize ensemble SVS assessment. Such a divide-and-conquer ensemble strategy results in highly robust SVS assessment performance when faced with various severe data loss conditions. Numerical tests on the benchmark Nordic test system illustrate the efficacy of the proposed approach.

Hybrid model-data-driven dynamic VAR planning for wind-penetrated power system using spectral surrogate techniques

The increasing wind power penetration and proliferation of induction motor loads, of which dynamic impact cannot be revealed through steady-state analysis, bring challenges to the short-term voltage stability of modern power systems. This study proposes a hybrid model-data-driven approach for dynamic VAR source planning to enhance the short-term voltage stability of wind-penetrated power systems to reduce the computation burden of electro-mechanical transient models. Firstly, the theoretical background of Stochastic Spectral Embedding (SSE) is introduced. Then, a surrogate model for the electromechanical transient model is established using SSE following efficient expansion coefficient calculation and a designed partition strategy for the studied problem. Furthermore, a hybrid model-data-driven VAR deployment optimization model is established with 3 objectives, which is solved by a dual-population-based evolutionary algorithm (DPEA). The accuracy and effectiveness of the model are verified on a modified New England 39-bus system. Simulation results prove that the computational cost is reduced significantly in comparison with conventional model-based method without a compromise in accuracy and the proposed method is also more accurate than methods based on other surrogate models. The proposed SSE-based model can be applied to other power system analysis with electro-mechanical transient models to alleviate the computational cost.

Online assessment of short-term voltage stability based on hybrid model and data-driven approach

With the continuously increasing integration of renewable energy sources into power grids, the dynamic response of a power system is becoming more complex. For example, the interaction between the dynamic loads and low-voltage ride-through of renewable energy generators makes the voltage response more rapid and unpredictable. Ensuring the accuracy and speed of traditional voltage stability assessment methods is difficult. This study developed a novel hybrid model and data-driven voltage stability assessment approach. First, the equivalent parameters of a power system were calculated based on the measured data, and the parameters were constantly modified based on the response data. To further improve the accuracy of the approach, a data-driven method was introduced to correct the assessment results using a Thevenin equivalent-based assessment. The difference between the Thevenin and system impedances, which better reflects the system stability, was included in the data-driven input data. Finally, by combining the clear physical mechanism of the model-driven method and high accuracy of the data-driven method, the final the assessment process was a serial combination of the model- and data-driven methods. The effectiveness of the method was verified using an IEEE New England 10-generator 39-bus test system and a 100-bus actual system in China. The results showed that the method developed was more accurate and had higher robustness under data loss and noise conditions than other methods.

Grid Strength Impedance Metric: An Alternative to SCR for Evaluating System Strength in Converter Dominated Systems

Short circuit ratio is an outdated measure of system strength in converter dominated systems as the useful behaviour of inverter-based resources is not represented. While still useful for determining fault current provision, converter connected generation contributes to short circuit level and system strength in a different way to traditional synchronous generation. Additionally, traditional measures only account for system strength at the fundamental frequency while converters possess complex interactions across a frequency range. A novel method of determining system strength across this frequency range from the network impedances is proposed in this paper. The approach known as the Grid Strength Impedance Metric, calculates the system strength independently from short circuit level. The unique contribution of grid-following and grid-forming converters is represented by including the multiple-input multiple-output converter output impedances in the calculation. Small-signal impedance models are employed, and the metric is largely concerned with short-term voltage stability, but some inferences can be made for longer timescales. The approach is validated using time domain simulations to check for any identified areas of weakness in the frequency range. The Grid Strength Impedance Metric successfully represents the useful behaviour of grid-forming converters, indicating an enhancement in voltage stiffness in locations of deployment.

ANN based smart sensing of short-term voltage stability assessment of modern power system

This study addresses the critical challenge of Short-term Voltage Stability (STVS) in the contemporary electric grid system, characterized by diverse static loads, induction motors, electronic loads, electric vehicle charging stations, and renewable energy sources. High-power sensing elements are identified for power system stability and transient measurements, and the existing system is explored for fault measurement and stability maintenance. The analysis employs an IEEE 14-bus dynamic model with two distinct load configurations. In the first configuration, the static load at bus 14 is replaced with a composite load, encompassing static loads, induction motors, electronic loads, and EV charging stations. For the second novel configuration at bus 14, the static load is substituted with a composite load and a solar photovoltaic (PV) generator operating in reactive power compensation mode. This addition of the PV generator compensates for elevated reactive power demand in the 14-bus system. The study conducts voltage stability analysis in two phases, evaluating the voltage profile and transmission line load ability in both scenarios during the first phase. In the second phase, STVS is simulated by briefly opening the circuit breaker in bus 2. The results reveal notable improvements in the voltage profile of all buses, a 6 % enhancement in power factor at bus 14 in the dynamic model with the novel configuration, and a 3 % increase in the loading factor of the IEEE Bus 14 system. The dynamic model incorporating a PV generator and composite load in bus 14 demonstrates superior STVS performance compared to the setup with only a composite load. The abstract concludes by highlighting the development of real-time voltage profile assessment using Artificial Neural Network (ANN) topology, leveraging results from the Continuous Power Flow (CPF) analysis of the novel model with a PV generator and composite load in the far end bus. This restructuring ensures a logical and clear organization, encompassing an introduction to the problem, a description of methods employed, presentation of results, and a succinct conclusion summarizing the key findings.

Short-term voltage instability prediction using pre-identified voltage templates and machine learning classifiers

System operators use different procedures to detect disturbances which can lead to short-term voltage instability. These schemes are designed using the domain knowledge and generally specific for the corresponding system. The design procedure of such schemes is heuristic and cannot be directly applied to any other power system. This paper proposes a data-driven approach to predict short-term voltage stability using set of post-disturbance voltage templates and a machine learning-based classifier. In this scheme, a set of voltage templates corresponding to stable/unstable events is identified for selected buses using a suitably generated training data set. The proximity of real-time voltage trajectory to each of the template is computed and input to a trained machine learning classifier to predict the short-term voltage stability status. The proposed approach is validated using IEEE Nordic test system. The investigations show that this method provides accurate short-term voltage stability predictions. Furthermore, impact of adverse phenomena such as measurement noise and missing data on the proposed method is analyzed to confirm the robustness of this scheme in particle environments. © 2017 Elsevier Inc. All rights reserved.

Optimal Grid-Support Strategy With Inverter-Interfaced Distributed Generators for Short-Term Voltage Stability Improvement

Optimal Grid-Support Strategy With Inverter-Interfaced Distributed Generators for Short-Term Voltage Stability Improvement

Short-Term Voltage Stability Assessment Based on Heterogeneous Edge-Integrated Graph Attention Network

Short-Term Voltage Stability Assessment Based on Heterogeneous Edge-Integrated Graph Attention Network

Hydrogenated TiO2 Carbon Support for PtRu Anode Catalyst in High-Performance Anion-Exchange Membrane Fuel Cells.

The availability of durable, high-performance electrocatalysts for the hydrogen oxidation reaction (HOR) is currently a constraint for anion-exchange membrane fuel cells (AEMFCs). Herein, a rapid microwave-assisted synthesis method is used to develop a core-shell catalyst support based on a hydrogenated TiO2/carbon for PtRu nanoparticles (NPs). The hydrogenated TiO2 provides a strong metal-support interactionwith the PtRu NPs, which improves the catalyst's oxophilicity and HOR activity compared to commercial PtRu/C and enables greater size control of the catalyst NPs. The as-synthesized PtRu/TiO2/C-400 electrocatalyst exhibits respectable performance in an AEMFC operated at 80 °C, yielding the highest current density (up to 3× higher) within the catalytic region (compared at 0.80-0.90V) and voltage efficiency (68%@ 0.5 A cm-2) values in the compared literature. In addition, the cell demonstrates promising short-term voltage stability with a minor voltage decay of 1.5mV h-1. This "first-of-its-kind in alkaline" work may open further research avenues to develop rapid synthesis methods to prepare advanced core-shell metal-oxide/carbon supports for electrocatalysts for use in the next-generation of AEMFCs with potential applicability to the broader electrochemical systems research community.

Probabilistic steady-state and short-term voltage stability assessment considering correlated system uncertainties

As correlated uncertainties in power grids become more prevalent, modeling of stochastic dependencies is becoming increasingly necessary. Independent probability distributions disregard these correlated uncertainties, potentially leading to significant errors, underscoring the necessity of dependence structures. This paper presents a probabilistic approach for modeling uncertain system parameters with their inherent correlations. The proposed approach is validated through various aspects of system voltage measures, including voltage profile and static and dynamic voltage stability. In total, nine alternative sampling generation techniques are employed, and their accuracy is measured based on real-world data using root mean square error (RMSE) and coefficient of determination (R2) criteria. The result suggests that multivariate (Gaussian and Student's) copula techniques accurately represent the real system data, consistently achieving high accuracy rates of 98 % for voltage profiles, 97 % for static voltage stability, and 93 % for dynamic voltage stability. In contrast, the independent sampling technique failed to follow the real-world system data for the different aspects of system voltage measures.

Deep learning based on Transformer architecture for power system short-term voltage stability assessment with class imbalance

Most existing data-driven power system short-term voltage stability assessment (STVSA) approaches presume class-balanced input data. However, in practical applications, the occurrence of short-term voltage instability following a disturbance is minimal, leading to a significant class imbalance problem and a consequent decline in classifier performance. This work proposes a Transformer-based STVSA method to address this challenge. By utilizing the basic Transformer architecture, a stability assessment Transformer (StaaT) is developed as a classification model to reflect the correlation between the operational states of the system and the resulting stability outcomes. To combat the negative impact of imbalanced datasets, this work employs a conditional Wasserstein generative adversarial network with gradient penalty (CWGAN-GP) for synthetic data generation, aiding in the creation of a balanced, representative training set for the classifier. Semi-supervised clustering learning is implemented to enhance clustering quality, addressing the lack of a unified quantitative criterion for short-term voltage stability. Numerical tests on the IEEE 39-bus test system extensively demonstrate that the proposed method exhibits robust performance under class imbalances up to 100:1 and noisy environments, and maintains consistent effectiveness even with an increased penetration of renewable energy. Comparative results reveal that the CWGAN-GP generates more balanced datasets than traditional oversampling methods and that the StaaT outperforms other deep learning algorithms. This study presents a compelling solution for real-world STVSA applications that often face class imbalance and data noise challenges.

Coordinated Optimization for Multi-Infeed LCC-HVDCs Transient Control Considering Short-Term Voltage Stability of Receiving-End Grid

With local synchronous generators in receiving-end grids being replaced by multi-infeed line-commutated converter-based (LCC) high-voltage direct currents (HVDCs), the dynamic voltage supportability of the power grid decreases. Moreover, the reactive power consumption of LCC-HVDCs during the recovery process brings risks to voltage stability. Hence, the transient control of LCC-HVDCs should be optimized coordinately to support short-term voltage stability under credible contingencies. In this paper, the dynamic reactive power characteristics between AC/DC systems are derived mathematically. Based on the coupling mechanism among the voltage-dependent current order limiter (VDCOL), AC dynamic voltage, and HVDC power recovery, an “autonomous-synergic” optimization strategy incorporating short-term voltage stability constraints is proposed for multi-infeed LCC-HVDCs. To handle the problem of large-scale differential-algebraic equations (DAEs), the optimization is iteratively solved based on time-domain simulation (TDS) and trajectory sensitivities. The stability is quantified by an indicator and the trajectory sensitivity analysis is utilized to relax stability constraints. The effectiveness and feasibility of the proposed methods are verified with a benchmark system and a real system in China. The short-term voltage stability under all credible contingencies can be guaranteed, while the total power recovery of LCC-HVDCs is improved.

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

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

A Novel Centralized Load Shedding Approach to Assess Short-Term Voltage Stability: A Model-Free Using Time Series Forecasting

In the wake of ever-growing integration of dynamic loads and power electronics-interfaced devices, power systems are becoming more complex with growing nonlinear behaviors, and preserving these systems' dynamic stability is a crucial challenge more than ever. Under voltage load shedding (UVLS) is one of the protection schemes adopted to enhance stability of the system at the events jeopardizing the system voltage. Despite underway efforts to design UVLS using analytical approaches/models, it is barely possible to estimate their various parameters with sufficient accuracy. Also, due to steady changes in characteristics of elements, especially loads, the estimated model at a time is not legitimate long lasting. Eluding these difficulties, this paper presents a novel data-driven UVLS scheme with a centralized design to enhance short-term voltage stability during fault-induced delayed voltage recovery (FIDVR) events. The proposed methodology utilizes time series forecasting in conjunction with the long short-term memory neural network. In order to quantize FIDVR severity, a novel dynamic index called short-term voltage index (STVI) is introduced for motor-load buses. STVI is a function of both voltage magnitude and load angle. The proposed approach is successfully verified on an actual power system model.

A short-term voltage stability online assessment based on multi-layer perceptron learning

In this paper, a deep learning-based approach is used to analyze short-term voltage stability of power systems in order to completely learn the hidden timely dependencies from post fault behavior of the system. The direct measurements from the PMU, which did not require any significant amount of computation, have been used, and the results will be accurate. The proposed approach makes considerable use of a Multi-Layer Perceptron-based deep learning model in order to make the most accurate prediction feasible regarding the short-term voltage stability status. Rapid prediction of voltage stability allowed system operators sufficient time to take effective corrective action against large disturbances. In-depth offline simulations will be executed against various fault types, with the results being fed into the classifier as inputs. After the classifier has been trained using the results of the offline simulations, the online application will be applied to the test samples. The effectiveness of the suggested method will be evaluated based on the results of tests conducted on both small and large-scale test systems.

Weighted ensemble learning for real‐time short‐term voltage stability assessment with phasor measurements data

AbstractVoltage stability assessment based on machine learning has become an important challenge in power systems. This paper presents real‐time short‐term voltage stability (STVS) assessment based on phasor measurement unit (PMU) data and machine learning (ML). The database is created through time series of measurement data to involve system time‐temporal and dynamics. Then multiple operating states of the power system are classified through the calculation of the Lyapunov exponent and dynamic voltage index according to the database. This paper presents a weighted combination of random forest (RF) and LightGBM (LGBM) classifiers to train a time‐series database. One of the main advantages of this paper is using the gradient concept in data preprocessing, which has enhanced performance metrics and reduced the defect of data noise. Also, hyperparameter optimization is conducted to improve machine performance. Studies on the IEEE 118bus and a real local grid (RLG) demonstrate that the proposed method improves the performance metrics such as accuracy and F1‐score. Also, this approach is robust against PMU data noise and topology changes in the network.

A Data-Driven Method for Power System Emergency Control to Improve Short-Term Voltage Stability

The power system contains a variety of uncertainties of different types of sources and loads, as well as random contingencies. Under these uncertainties and rapidly changing operating conditions, traditional rule-based methods cannot dynamically handle short-term voltage instability. To alleviate this situation, this paper proposes a novel power system emergency control scheme using a data-driven method, which combines edge-conditioned graph convolutional networks and deep reinforcement learning. The edge-conditioned graph convolutional network is utilized to extract the characteristics from not only power system nodes but also transmission lines. Deep reinforcement learning is introduced to perform load shedding actions, so as to guarantee the safety and stability of the electric power system. The IEEE 39-bus network is utilized for simulations to validate the effectiveness of the proposed data-driven method. The outcomes demonstrate the proposed method can generate a superior strategy in a number of the short-term voltage instability(STVI) circumstances.