Voltage Stability Evaluation Research Articles

A probabilistic distributed digital twins approach for short-term stability and islanding of smart grid

The simultaneous evaluation of voltage, frequency, and transient stability enhances the reliability of the power systems, due to the transient effect of stability aspects on each other. However, different quantitative and qualitative parameters in the aspect and nonlinear structural analysis of the system make simultaneous and accurate predictions difficult. For this reason, the simultaneous probabilistic prediction of the stability state of three aspects with high certainty can be considered the most accurate method. This study presents a simultaneous prediction method for the stability aspect states by means of the decision theory and the game theory matrix on the basis of distributed digital twins (DDTs). The decision matrix weighs the aspect states in each bus using the distributed structure measurement and prioritizes the weak buses. In addition, the stability of different bus aspects is predicted using the game matrix. Furthermore, the changes in the system stability are predicted with high probability and certainty in the digital twins (DTs) graph, and if required, islanding is performed on the basis of the weak buses' priorities. The effects of the three aspects on each other, and the use of real-time data of the DDTs, have contributed to the high accuracy and speed of the proposed method. Simulations were performed on IEEE 14-bus, 39-bus, and 118-bus systems by means of MATLAB and DIgSILENT. The results show the advantages of the proposed method over other methods.

SE-CNN based emergency control coordination strategy against voltage instability in multi-infeed hybrid AC/DC systems

For receiving-end power systems with multi-infeed HVDCs and large-scale renewable energy generation, the challenges of weak reactive power support and limited anti-interference capacity pose a threat to the power system voltage stability. To enhance the voltage stability under large disturbances, this paper proposes a data-driven method for coordinated emergency control strategy against voltage instability in multi-infeed hybrid AC/DC systems based on the squeeze and excitation (SE) module and convolutional neural network (CNN). Firstly, the SE module and CNN are integrated to intuitively capture correlations among various feature channels and extract key features related to voltage stability levels. Secondly, a voltage stability evaluation method is proposed based on the SE-CNN model, utilizing a dual channel structure to unveil the quantitative relationship between key response characteristics and voltage stability margin. Finally, regarding the control measures containing load shedding and DC modulation, the emergency control sensitivity index is proposed to assess the stability margin improvement effect of various control objects, and the optimal emergency control strategy is formulated to coordinate multiple voltage stability emergency control measures. Case studies were conducted on a typical China local region receiving-end power grid test system with voltage instability problems, and the simulation results verified the effectiveness of the proposed method. © 2017 Elsevier Inc. All rights reserved.

L-Index-Based Technique for Voltage Collapse Prediction and Voltage Stability Enhancement in Electrical Power Systems

Recent years have witnessed a notable increase in the occurrence of blackouts, especially in developing nations, attributed to the continuously growing demand on modern power networks. Given that the demand shows no signs of abating and is projected to increase further in the coming years, additional research on power system stability is imperative. This study, therefore, investigates voltage stability assessment in power systems using the L-index methodology, focusing on the Nigerian 28-bus system and the IEEE system. The L-index offers a practical means of identifying weak buses and evaluating voltage stability margins. Calculating L-index values for load buses under diverse conditions identifies critical points, with higher values indicating vulnerability. The research investigates injecting reactive power at load buses to prevent collapse, comparing outcomes with and without compensation. Analyzing the L-index's performance across varied loading scenarios confirms its precision in predicting breakdown points and identifying critical buses. Load flow analysis of the Nigerian 28-Bus system reveals that only bus 16 exceeds voltage limits, while line analysis shows total power losses. Increasing loadability exposes bus 16 as the weakest, supported by its low voltage magnitude. The research confirms bus 16 as the system's weakest point, guiding corrective measures to enhance stability and prevent collapse. Utilizing Matlab for implementation, this study contributes valuable insights into system vulnerability and provides a framework for improving voltage stability in power systems.

Voltage stability index: a review based on analytical method, formulation and comparison in renewable dominated power system

In an interconnected complex power system network voltage stability evaluation is indispensable to guarantee secure power system operation. To further increase the system performance and to make the system safer assessment, the voltage stability improvement is obligatory. In the various literature different voltage security assessment method using the voltage stability index has been presented. Different lists proposed in literature can be utilized to realize the weak buses and weak transmission lines to enacting the countermeasures against issues of voltage insecurity. Additionally, the arrangement and measuring of inexhaustible assets, on the web and disconnected observing of force framework and the measure of load to be shed at whatever point essential. This paper shows a survey on the different voltage stability index from various perspectives. The audit results on various record gives a far and wide logical to perceive the impending works in this field and to choose the best index for variety of applications such as voltage security assessment, renewable energy integration, distributed generation (DG) placement and sizing, online monitoring of the power system, and shedding of load.

Investigation on voltage stability evaluation indicators and algorithms for power systems based on neural network algorithms

Abstract In order to avoid the occurrence of unstable phenomena in the Power Grid (PG), it is necessary to have a thorough understanding of the current operating status of the PG. Research on voltage stability evaluation indicators and algorithms in the power system can assist power system operators in making effective decisions. In this paper, an improved continuous power flow scheme based on Lagrange quadratic interpolation was adopted. Secant method and Lagrange quadratic interpolation method were used for prediction comparison, and Newton method was used to correct the predicted results. This article utilized an online voltage safety assessment and warning model to ensure the safe operation of the PG and reduce the occurrence of faults. To ensure the integrity and accuracy of network dynamic information, a least squares fitting method based on orthogonal functions was adopted to improve the fitting accuracy without increasing communication volume. As the step size increases from 2 to 3, the number of power flow solutions decreased and the solution time increased. The effectiveness of the voltage stability evaluation algorithm in this paper was verified through simulation of two node systems: New England 39 and IEEE118.

Evaluation of Voltage Variations Arising from the Increase in Photovoltaic Insertion in the Transmission Network: Case Study Coremas-PB Power Plant

The objective of this work was to analyze the impacts on the transmission network due to the increase in centralized photovoltaic (PV) generators’ incorporation. A study was carried out in a high-voltage (HV) transmission network, considering adjustments in the simulation environment for more realistic results. ANAREDE software and the static voltage stability evaluation method were used. The simulation was carried out in a steady state, considering an average load and the power of the PV generators corresponding to the base case (70.6 MW), with an increase of 100% of the predicted total (270 MW) for the future. The results showed that, under normal and contingency conditions, small disturbances caused voltage instability. It was observed that the incorporation of PV generators contributes to the improvement of the voltage stability in the bars close to their insertion. However, the greater the PV distribution and generation was, the greater the influence on the attenuations of the voltage profiles through the transmission system was.

A Comprehensive Review on the Modelling and Significance of Stability Indices in Power System Instability Problems

Many technological advancements in the modern era have made actual use of electrical power and the constrained operating of power systems within stability limits. Some expeditious load variations and rising power demands initiate complications in voltage stability and can put stress on performance, leading to voltage instability. Voltage Stability Indices can be used to perform voltage stability assessment. This review evaluates various VSIs based on mathematical derivations, assumptions, critical values, and methodology. VSIs determine the maximum loadability, voltage collapse proximity, stability margin, weak areas, and contingency ranking. Stability indices can also specify the optimal placing and sizing of Distributed Generators. Thus, VSIs play a vital role in power system voltage stability. This review is a comprehensive survey of various indices and analyses their accuracy in determining the instability of power systems. Voltage stability is a crucial concern in operating a reliable power system, and the systematic evaluation of voltage stability is essential in a power system. This review considered and analyzed 34 indices from 138 articles from the literature for their significant performance in various power system stability problems. Of 33 indices, were 22 derived from transmission line parameters, referred to as line indices, and 12 from bus and line parameters, referred to as bus indices.

Evaluation of Voltage Stability in Microgrid-Tied Photovoltaic Systems

These days, with the significant increase in the use of renewable energy sources as additional energy sources connected to the distribution network, many challenges and difficulties arise in ensuring sustainability and reliability. The generation, transmission and distribution, in the current state of the electricity system, are facing quite dynamic changes. They are the result of the liberalization of the energy market, the increased use of renewable energy sources such as photovoltaic systems, wind turbines and the charging stations for hybrid and electric vehicles. The most important factors are related to the balancing of the energy system, the analysis of voltage stability, overcoming the consequences of the increase in short-circuit currents, increasing the transmission capacities of the system forming and distribution networks, as well as the accurate forecasting of the development of loads and consumption over the coming years. This article presents an analysis of the voltage stability in a smart microgrid for two different scenarios. The studied cases describe a linear low-voltage p-type microgrid with loads connected to it at different nodes. Data on the type and cross-section of the conductors of the studied power line are presented. Simulation studies were carried out to determine the limits of grid voltage stability when connecting photovoltaic plants with a set power. The simulation results are commented on and an analysis of the optimal operating mode of the system is realized. The model studies were implemented in the NEPLAN program environment. The research carried out allows an evaluation of the permissible limits for network stability when connecting photovoltaic plants. Through this evaluation, it can be determined how many and at which node the loads should be connected without causing an imbalance in the network. This is useful from the point of view of ensuring the sustainability and reliability of electrical energy in a microgrid.

Multi-task transient stability assessment of power system based on graph neural network with interpretable attribution analysis

Transient power angle stability analysis and voltage stability analysis are the key basis of power system security and stability control. The diversified operation modes of power system put forward higher requirements for real-time and topology generalization of transient stability assessment. Based on Convolution Neural Network (CNN) and Graph Attention Networks (GAT), this paper uses the wide-area transient response features to evaluate the transient angle stability and voltage stability of power system. Firstly, CNN is used to encode the temporal variation characteristics of transient features of electrical components in hidden layer space. Secondly, the encoded hidden layer features are mapped into graph data samples according to the spatial topological correlation of electrical components, so as to train and build a multi-task transient stability assessment model based on GAT. The model can adaptively capture the interaction relationship between encoded hidden layer features of topologically correlated components, and realizes real-time evaluation of transient angle stability and transient voltage stability by perceiving the temporal–spatial correlation of transient features. Finally, Shapley additive explanation (SHAP) method is used to explain the decision-making mechanism of the model and extract the key features that affect the transient stability, so as to enhance the ability of power grid operators to perceive the transient stability situation. The results of IEEE-39 system show that the transient stability assessment model has good accuracy and topology generalization, and the results of interpretable analysis are in line with the conclusions of traditional mechanism cognition, which helps to improve the credibility of the model results.

Data Domain Adaptation for Voltage Stability Evaluation Considering Topology Changes

Data Domain Adaptation for Voltage Stability Evaluation Considering Topology Changes

Static voltage stability influence evaluation method of distribution network including electric vehicles based on LHS-PPF

The temporal and spatial distribution of electric vehicle charging load (EVCL) is closely related with the drivers’ trip behavior, which has a highly uncertainty. The access of EVCL will increase the risk of safe and stable operation of the distribution network. To evaluate the impact of EVCL access to system’s static voltage stability, we propose a novel probability evaluation method based on the combination of static voltage stability evaluation model and probabilistic power flow (PPF). Firstly, considering steady state operation, dynamic operation and ultimate operation of the distribution network, the three different static voltage stability evaluation models are established respectively. Then, the probabilistic power flow model is adopted to simulate the impact of EVCL on the power flow of the distribution network. To improve the low calculation efficiency of the PPF model based on the Monte Carlo sampling method, the Latin hypercube sampling (LHS) is used. The LHS-PPF model not only ensures calculation accuracy but also improves calculation efficiency. Finally, based on MATLAB 2020a simulation software, the proposed method is programmed in M language. The results show that the access of EVCL will obviously decrease the system anti-interference capability, and increase the risk of the system approaching limit operation state. The case studies verify the correctness and effectiveness of the proposed method.

LCC-HVDC's Systematical Impact on Voltage Stability: Theoretical Analysis and a Practical Case Study

Line-commutated-converter HVDC (LCC-HVDC) is generally believed to impair voltage stability. While in a China's practical power grid, increase of HVDC power unexpectedly enhances the stability. The phenomenon reveals that existing studies overlook HVDC's systematical impact on the receiving AC system. This paper empirically elaborates how the phenomenon arises, theoretically clarifies the mechanism, and demonstrates its effect on practical system operating. In this paper, systematical features of power grid are visually depicted by two vectors, i.e., network structural vector and power-flow conditional vector. A unified burden rate is proposed to evaluate voltage stability of any AC bus. Impact of HVDC is explicitly expressed by two positive-definite terms and one negative-definite term. The latter of them is overlooked by most existing literatures, and enhances voltage stability by reducing the burden rate. The proposed methodology is validated by simulations with a practical power system in Asia with tens of HVDC infeed and tens of thousands of AC nodes.

Static voltage stability analysis and evaluation of vector controlled offshore wind farm considering cable capacitance parameters

Voltage stability region assessment is the key to ensuring the reliable operation of offshore wind farms However, the traditional analysis method, which treats the WFs as a PQ node and directly connected to the infinite power grid, fails to take the cable capacitance and the dynamics of the converter into account, resulting an inaccurate evaluation of voltage stability. The contribution of this paper is to propose a more accurate method for assessing the voltage stability of OWFs. Firstly, based on the equivalent circuit method, the point of common coupling (PCC) and internal voltage characterization models of OWF considering the cable capacitance parameters are derived. Then, the coupling interface between the dynamic of the converter and the voltage characteristics of the system is designed, and the transfer function of the power injection from the DC side of the converter to the voltage of the collector system is established, which fully reflects the OWF Pin→Udc→Id→Upcc→Pout transitive relationship. Finally, a voltage stability criterion based on dPw, out/dId&dUdc/dt direction discrimination is proposed, and the influence of cable parameters, output power, and grid impedance on the voltage stability margin is analyzed. The accuracy of the proposed method is verified based on the RT-LAB platform.

Fast Calculation Method for Continuous Power Flow of Microgrid Based on Levenberg-Marquardt Algorithm

There are possible non-convergence problems at load power critical value while using conventional continuous power flow methods. Generally, the step control method is used in the calculation to perform the calculation in small steps at the convergence to the load power critical value, and this method sacrifices the speed of the calculation although the calculation accuracy is high. In this paper, the Levenberg-Marquardt algorithm is used to search for the load power critical value firstly, and after that the step control algorithm is designed to perform fast power flow finding with known load power critical value, which takes into account the computational accuracy and computational efficiency. The case shows that the fast calculation method for continuous power flow of microgrid based on Levenberg-Marquardt algorithm proposed in this paper can guarantee the accuracy while effectively improving the calculation speed, and is suitable for online real-time evaluation of voltage stability and preventive control aided decision online calculation of isolated microgrid with high requirements for real-time.

Transient voltage stability assessment of renewable energy grid based on residual SDE-Net

For the purpose of assessing the transient voltage stability of renewable energy grid more effectively and to measure the epistemic uncertainty of the evaluation results, a power system transient voltage stability assessment method based on residual stochastic differential equation network (SDE-Net) is proposed in this paper. Considering the transient stability characteristics is chronological, the proposed network takes the time series of the basic physical quantity measurement data of the power system as the input. The internal features of time series data are extracted by residual convolution block based stochastic differential equation network in this paper. Meanwhile, the proposed method introduces the focal loss function to eliminate the imbalance of the samples and improve the accuracy of transient stability assessment. In particular, the drift network for learning prediction of stability and the diffusion network for learning uncertainty measurement in residual SDE-Net are trained respectively. As a result, case study on modified IEEE 30- bus system demonstrate the residual SDE-Net’s superior performances on both transient voltage stability assessment and stability evaluation result confidence estimation.

Enhancement of Voltage Stability by Optimal Placement of Shunt Compensation using Bus Voltage Stability Indices and Reactive Power Margin

Voltage stability problem has caused several blackouts in many countries in recent years. Impending voltage instability has been a significant threat to modern power system's security and reliability. Moreover, the operation and planning of large interconnected power systems is becoming increasingly complex as power demand rises, posing a security risk to the grid. Appropriate efforts to improve power system security and increase voltage stability margin should be planned to keep the system secure. This work investigates the voltage stability of a power system with and without a shunt capacitor. The bus voltage stability index, L index, is used to measure the distance of the power system to its stability limit in order to assign the shunt capacitor. The L-index for a particular load state is computed for all load buses, and the greatest L-index indicates the system's approach to voltage collapse. The system's load ability margin is being traced utilizing a static voltage stability evaluation approach, i.e., PV and QV curve analysis. The minimal power loss approach is used to calculate the optimal capacitor size. The effect of shunt compensation was simulated, and the results with and without compensation were compared. The IEEE-9 bus system was employed in this work, and the system was simulated using MATLAB and Power World Simulator. The result demonstrates that the shunt capacitor enhances voltage stability by injecting the appropriate reactive power.

Incorporating Complex Inter-Inverter Interactions Into Strength Assessment for Emerging Hierarchical-Infeed LCC-UHVDC Systems

The strength concept is an important tool for voltage stability evaluation of emerging hierarchical-infeed LCC-UHVDC (HIDC) systems. However, the complex inter-inverter interactions in such systems have caused significant difficulties for the strength assessment. This makes the accuracy of earlier strength assessment indices limited due to empirical analysis rather than rigorous theoretical reasoning. Thus in this paper, the hierarchical-infeed voltage interaction factor (HVIF) index is firstly utilized to quantitatively depict the complex inter-inverter interactions in HIDC systems. The use of the HVIF enables these interactions to be effectively incorporated into the subsequent strength assessment by proposing the hierarchical-infeed interactive effective short-circuit ratio (HIESCR) strength index. The critical HIESCR (CHIESCR) defined to delineate the voltage stability limit also evaluates to consistently 1.0 such that the distance between the HIESCR and CHIESCR is naturally an accurate stability margin. Since the HIESCR is developed based on the rigorous theoretical reasoning, it is more accurate than earlier indices for voltage stability evaluation. Moreover, the parametric dependence analysis of the HIESCR versus various system parameters and rated operation variables is conducted. This offers a comprehensive perspective for better understanding of the strength variation characteristics. Finally, case study on the modified IEEE 118-bus system validates the HIESCR.

Monitoring Data Factorization of High Renewable Energy Penetrated Grids for Probabilistic Static Voltage Stability Assessment

The increasing integration of large number of renewable energy sources (RESs) generates multiple kinds of uncertainties in power grids, which heavily challenges traditional deterministic approaches for voltage stability assessment (VSA). Under this circumstance, this paper proposes a high-dimensional spatial-temporal matrix factorization (STMF) approach for monitoring data to separate the deterministic part and uncertain elements caused by RESs, and presents a probabilistic index to online evaluate voltage stability. Specifically, this method explores the eigenvalue distribution of measurement data when penetrating multiple distributed wind and solar generations, as well as a learning-based STMF model is accordingly used to iteratively extract the random elements due to RESs. Unlike traditional matrix factorization approaches, this STMF method uses an adaptive and analytical model to depict the eigenvalue distribution of random components. Subsequently, a probabilistic index is designed to measure the voltage stability degree as well as provide quantiles to indicate its potential fluctuations. Numerous cases verify the effectiveness and advantages of the proposed method using different load changing models and various RES penetration levels, as well as other probabilistic and deterministic indicators are compared.

Online Monitoring of Voltage Stability Margin in Kosovo Power System Using Local Measurements

This paper presents an analysis of the voltage stability of the Kosovo power system. The first part of the study has included a detailed analysis of the Kosovo power system by using the continuous power flow method, with an emphasis on the determination of the P–V curve of voltage stability. Thus, it has identified the weak and critical points of the power system in terms of voltage stability and has defined the margin of instability. In order to achieve online monitoring of voltage stability in the power system, it is proposed to place phasor measurement units in the weakest critical buses. Furthermore, the Thevenin equivalent method has been applied to evaluate voltage stability in the critical buses. The maximum transmissible real power to the weak buses in the system can be achieved when load impedance is equal to the Thevenin impedance. The load and Thevenin impedance values have been obtained from the relevant PMU data. Following online monitoring of voltage stability in the power system, the developed voltage stability load bus index can be used as useful information by system operators in order to undertake appropriate countermeasures to prevent voltage collapse.

Comprehensive Review of Short-Term Voltage Stability Evaluation Methods in Modern Power Systems

The possibility to monitor and evaluate power system stability in real-time is in growing demand. Whilst most stability-related studies focus on long-term voltage stability and frequency stability, very little attention is given to the issue of short-term (voltage) instability. In this paper, the most common evaluation methods present in the literature are summarized, with a focus on their applicability to modern power systems with a large amount of renewable energy integration. The paper presents a first-of-a-kind structured review of this topic. We find that all existing methods have noteworthy limitations that necessitate further improvements. Additionally, the need of having an inclusive short-term instability prediction method is demonstrated, due to strong interactions between various short-term instability mechanisms. These findings provide a good foundation for further research and advancement in the field of real-time stability monitoring.