Voltage Stability Margin Research Articles

Transient voltage stability assessment and margin calculation based on disturbance signal energy feature learning

With the increasing variation of the network topology and the high complexity of the processing measurement data, the transient voltage stability assessment of the new power system is facing significant challenges in low accuracy and high time costs. To address the shortcomings of the existing method and apply it to online assessment, this paper proposes an assessment method based on feature learning for disturbance signal energy (DSE) from bus voltages. Firstly, the relationship between DSE and system transient voltage stability is established, and the calculation of DSE from bus voltage time series is detailed. Subsequently, a transient voltage stability assessment method based on the ID3 Decision Tree algorithm and DSE is proposed. Finally, by employing the Support Vector Machine (SVM) to construct the optimal boundary in the feature space formed by the key buses, the transient voltage stability margin (TVSM) for specific scenarios is proposed. Simulation results on the IEEE 39-bus system demonstrate that the proposed method can rapidly and accurately assess the transient voltage stability of the system and calculate the stability margin, providing intuitive and interpretable results with high engineering application value.

Comparative analysis of online voltage stability indices based on synchronized PMU measurements

The need for reliable real-time information on voltage stability margins of electrical power systems is an increasingly relevant concern within the current trend of electrification and deployment of power electronics-based devices. This paper conducts the assessment and comparison of four Voltage Stability Indices (VSIs) proposed for this application and based exclusively on synchronized phasor measurements. The robustness and accuracy of each method in identifying the point of maximum power transfer are evaluated as the correlation between load characteristics and consistent estimation of voltage stability margins is explored. In addition, the likelihood inherent to each VSI formulation of triggering false alarms under certain system dynamics is addressed in detail. The comparative analyses are derived from dynamic simulation data of a 3-bus test system, the IEEE 9-bus network and the IEEE 39-bus network, all modelled in the open-source Python-based power system simulator DynPSSimPy. Case studies cover placement of monitoring device, different load types, line disconnection events and presence of measurement noise. The results presented serve as a reference point for the development and/or enhancement of VSIs suitable for real-time applications, highlighting their most significant advantages and drawbacks and providing insights on potential trade-offs that need to be considered when employing such approaches within control center settings.

Application of cascaded neural network for prediction of voltage stability margin in a solar and wind integrated power system

Voltage stability is a paramount concern in the management of renewable-rich power systems. As the diffusion of renewable energy sources continues to increase, accurately estimating voltage stability margins becomes essential. This paper addresses the critical need for effective voltage stability margin estimation and presents a novel approach to predict the same on the solar and wind integrated power system. A new machine learning methodology is developed based on the cascaded neural network (CNN). The proposed CNN methodology effectively estimates the loadability margin in a renewable-rich power system under normal operating conditions, varied loading directions, and various contingency situations. The results of CNN are compared with different machine learning techniques and tested in the IEEE 30 bus system and IEEE 118 bus system under various operational circumstances. The results illustrate the efficiency of the suggested method for online assessment of a power system's Voltage Stability Margin. The proposed approach gives real-time insights into voltage stability margins by leveraging the power of data and powerful algorithms, allowing grid operators to proactively manage and optimize renewable energy integration while ensuring grid dependability and stability.

Multi-Objective optimal scheduling of energy Hubs, integrating different solar generation technologies considering uncertainty

For a few decades, operators of energy systems have sought to achieve appropriate frameworks due to energy crises and rapid growth in energy requirements. In this regard, this study presents a multi-objective optimization model for an energy hub (EH) designed to manage a diverse energy portfolio. The EH receives electricity, natural gas, hydrogen, seawater, and solar energy as inputs, aiming to satisfy electricity, heating, and freshwater demands at the output port while considering a limited available area. The model incorporates the selection of the optimal solar energy technology (photovoltaics, parabolic dish, or parabolic trough collector) through a comprehensive evaluation encompassing technical, economic, and environmental aspects. To achieve optimal scheduling of the EH’s production units, the model factors in forecasts of solar energy availability alongside electrical, heat, and water load demands. The evaluation of the EH’s performance is conducted through a multi-objective framework considering social welfare, CO2 emissions, voltage stability margin (VSM), a newly proposed simplified fast temperature stability index (SFTSI), and a similarly novel simplified fast pressure stability index (SFPSI). The optimization problem is formulated within a MATLAB environment and solved using a multi-objective Archimedes optimization algorithm across five distinct case studies, each characterized by a varying designated area for solar energy generation. The effectiveness of the proposed model and optimization technique is validated through test systems, with the obtained results demonstrating significant improvements compared to a baseline scenario. These improvements include a 36.18% reduction in CO2 emissions, a 14.22% increase in total social welfare, and reductions in the average values of VSM, SFTSI, and SFPSI when incorporating all solar energy technologies.

Stability analysis of power system under n-1 contingency condition

Several voltage stability indices (VSIs) have been developed to assess the potential for voltage collapse. However, certain indexes are computationally costly. Meanwhile, some have been noted to underperform across various conditions. This work proposes a novel line index called the super voltage stability index (SVSI) to calculate the system's voltage stability margin (VSM). The suggested approach is based on the transmission system's two bus systems. The reactive power loss and N-1 contingency conditions to voltage sensitivity is a unique calculation approach used in this study to identify voltage instability. Day to day, the demand for electric power is being increased due to incessant increments in technology and population growth. Therefore, the power system networks are under pressure. The operational conditions of transmission system networks are affected at this point, which may result in voltage collapse. Regular monitoring of power supply is essential to avert voltage collapse. The effectiveness of the suggested index has been assessed using the IEEE 5 and 30-bus systems across diverse operating scenarios, including variations in active and reactive power loading as well as single line losses. The findings indicate that SVSI provides a more reliable indication of the proximity to voltage collapse when compared to conventional line VSIs.

Improving islanded distribution system stability with adaptive decision-making framework

Abstract In an integrated distribution system incorporating distributed generation (DG), various technical challenges must be addressed when the grid becomes disconnected and transforms into an islanded system. The main focus in such circumstances revolves around ensuring the stability of the islanded network. This study presents an advanced decision-making framework for supporting islanded networks by integrating metaheuristic Black Widow Optimization (BWO) and the rate of change of the voltage stability index (RoCVSI). The Rate of Change of the Voltage Stability Index (RoCVSI) detects instability in islanded networks by continuously monitoring rapid changes in the voltage stability margin. Upon identifying potential instability, an advanced decision-making strategy utilizing the Black Widow Optimization (BWO) algorithm is deployed. BWO generates multiple load-shedding scenarios and evaluates their impact on system stability, iteratively refining the solutions through processes similar to selection and cannibalism in black widow spiders. The optimal load-shedding strategy is then implemented to selectively shed specific loads, thereby reducing demand and enhancing island stability. The proposed scheme’s effectiveness for islanded network stability is assessed by extensively analyzing the IEEE 33-bus system. The efficiency of the proposed approach is confirmed through a comparative analysis, with results indicating the better efficiency of the proposed method in the islanded network.

Research on a Distributed Photovoltaic Two-Level Planning Method Based on the SCMPSO Algorithm

In response to challenges such as voltage limit violations, excessive currents, and power imbalances caused by the integration of distributed photovoltaic (distributed PV) systems into the distribution network, this study proposes at two-level optimization configuration method. This method effectively balances the grid capacity and reduces the active power losses, thereby decreasing the operating costs. The upper-level optimization enhances the distribution network’s capacity by determining the siting and sizing of distributed PV devices. The lower-level aims to reduce the active power losses, improve the voltage stability margins, and minimize the voltage deviations. The upper-level planning results, which include the siting and sizing of the distributed PV, are used as initial conditions for the lower level. Subsequently, the lower level feeds back its optimization results to further refine the configuration. The model is solved using an improved second-order oscillating chaotic map particle swarm optimization algorithm (SCMPSO) combined with a second-order relaxation method. The simulation experiments on an improved IEEE 33-bus test system show that the SCMPSO algorithm can effectively reduce the voltage deviations, decrease the voltage fluctuations, lower the active power losses in the distribution network, and significantly enhance the power quality.

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.

Network equivalent-based VQ Curve method and its application in a novel real-time voltage stability assessment methodology

The PV and VQ curves have been widely accepted tools for monitoring voltage stability. Although these curves have been used in offline studies, their online applications are not trivial, involving specific issues and complexities concerning real-time environment. The literature presents some approaches to determine quantities related to voltage stability limit in real-time analysis of the PV curve. However, it does not occur with the corresponding quantities for the VQ curve, making it difficult to analyze these curves jointly. This work presents two significant innovative contributions, based on the use of real-time network equivalents estimated through measurement data. The first is a technique suitable for real-time applications to calculate the complete VQ curve, called Network Equivalent-based VQ Curve. The second is a methodology for determining voltage stability margins using information from both PV and VQ curves. Simulations were carried out in RVS Test System, and 9, 14, 30 and 118 Bus Test Cases available in MATPOWER. The results of Network Equivalent-based VQ Curve application were validated by power flow solution. The voltage stability assessment methodology proposed in this paper represents a significant advance, going beyond the traditional approaches.

Optimal location and operation of energy storage and transmission switching for minimizing wind power spillage

This paper proposes a bi-level multi-objective optimization model to improve the integration of wind power generators in electrical networks based on the optimal location and operation of the energy storage system and transmission switching strategies. The minimization of wind power spillage, load shedding, power losses, and the improvement of the voltage stability margin are the objectives of the upper-level subproblem. While the lower-level subproblem aims to maximize social welfare under different scenarios and overall system constraints. Under the uncertainty of the wind power and load demand, a collection of lower-level subproblems that represent the market clearing conditions is used to constrain the upper-level subproblem. The effectiveness of the proposed algorithm is examined on a modified IEEE 24-bus test system. The results show that the applicability of the proposed algorithm in aiding power system improvement planning for minimizing wind power spillage to integrate wind energy with maximizing the social welfare and improving the loadability and the voltage stability.

The Effect Pso/Abc, Abc/Bfo, Pso/Bfo and Cs/Bfo Hybrid Techniques on Power System Buses for Voltage Stability Margin Improvement

This paper presents and investigates new approaches inspired by nature to determine the optimal placement of UPFC for enhancing voltage stability margin of power system network. Voltage collapse phenomenon has remained an operational problem yet to be solved by power system engineers. To improve the voltage stability of the power system network, new optimisation techniques viz: PSO/ABC, ABC/BFO, PSO/BFO AND CS/BFO hybrids are investigated for their performance on power system buses for voltage stability improvement. The performance of the proposed hybrid methods are examined on the practical Nigerian 56 - bus network for voltage stability improvement. The simulation results has shown that ABC/BFO technique is better than BFO/PSO by 3.44 in improving voltage stability of margin of power system, gives additional improvement of 4.07, totalling 7.51% and lastly BFO/CS technique improved voltage stability margin of power system further by 5% totalling 12.51%. Also this research revealed that the smaller the gamma value the better the UPFC contribution to voltage stability enhancement. BFO/CS technique yielded the smallest gamma values of 0. 74532 and 0.830913 in both Nigerian practical network and IEEE – 14 bus network as shown in the analysis.

Study on Reactive Power Optimization Including DSSC for New Energy Access to the Power Grid

The vigorous development of new energy has effectively reduced carbon emissions, but it has also brought fluctuating impacts on the carrying capacity of the power grid. In order to improve the voltage stability after integrating new energy sources and promote the scientific consumption of more new energy, this paper proposes the use of Distributed Static Synchronous Compensator (DSSC) devices for flexible and controllable voltage regulation in new energy integration. An improved particle swarm optimization algorithm is then developed to optimize the reactive power considering the regulation of DSSC. The paper conducts power flow calculations based on the DSSC power injection model and establishes a reactive power optimization mathematical model with objectives of minimizing active power loss, minimizing node voltage deviation, and maximizing voltage stability margin in the grid with new energy integration. The improved particle swarm optimization algorithm is utilized to achieve the reactive power optimization. Experimental simulations are conducted using the IEEE 33-node system to analyze the voltage improvement before and after adopting the improved particle swarm optimization algorithm considering the DSSC device in the grid with new energy integration. It is found that the proposed method effectively reduces active power loss and stabilizes voltage fluctuations, demonstrating its practical value.

Voltage Stability Constrained Economic Dispatch for Multi-Infeed HVDC Power Systems

Multi-infeed LCC-HVDC decreases voltage stability margins due to its current source nature. Moreover, the high penetration of variable renewable energy makes it difficult to reserve enough margins for all periods. Therefore, voltage stability constraints need to be considered in the scheduling stage. However, the challenge is that the voltage stability margin is not analytic with respect to state variables. We propose a sparse support vector machine to extract the nonlinear voltage stability rule. To embed the rule into economic dispatch (ED), we apply a convex reformulating technique to the rule and then formulate a voltage stability constrained ED (VSCED) model by semi-definite programming. The model is tested on a modified IEEE-14 system and a real-world system from Jiangsu Province, China; and it is compared with other typical data-driven-based models in the Jiangsu system. The numerical experiments suggest that the stability margins can be effectively reserved above the required threshold within an acceptable computation time by the proposed VSCED model, which outperforms the other models.

Coordinated reactive power planning in an industrial park integrated energy system using support vector regression

In this study, we develop and present a comprehensive multi-objective optimization model for reactive power planning in industrial park integrated energy systems (IPIES), addressing the challenges posed by extensive inductive loads. Our model prioritizes enhancing system resilience through three key objectives: minimizing total costs, improving static voltage stability margins, and enhancing voltage recovery capabilities. We employ support vector regression (SVR) to estimate voltage recovery metrics effectively, using reactive power capacity as input. The optimization process leverages the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for efficient solution finding. Validation on the IEEE-39 bus system demonstrates the model’s effectiveness, with SVR significantly reducing computational demands while maintaining satisfactory accuracy.

Dynamic-Deep-Ensemble-Learning Scheme for Probabilistic Voltage Stability Margin Estimation to Enhance Resilient Power Grid Monitoring

Modern power grids are characterized by significant penetration of renewable energy sources (RES), variable power demand, and aging transmission infrastructure, all of which contribute to a high degree of operational uncertainty. Such uncertainty complicates the assessment of the static voltage stability in power grids. In response to this challenge, this paper proposes a novel deep ensemble learning-based approach to assess the probabilistic voltage stability margin (PVSM) for strengthening the resilience of power grid monitoring. First, the estimation of the PVSM is formulated as a quantile regression problem. Then, an improved deep quantile regression (iDQR) is utilized to generate a set of quantiles under specific nominal proportions. Next, a dynamic deep ensemble learning (D2EL) scheme based on diverse iDQR models and an improved Choquet fuzzy integral (iCFI) algorithm is proposed to enhance the overall performance of predictive quantiles for the PVSM. The proposed D2EL-based PVSM estimation approach is capable of accommodating system changes in a timely manner, thus providing higher estimation accuracy and stronger adaptability than conventional approaches. A comprehensive numerical study of several test systems is carried out, taking into account uncertain RES and loads, as well as topology changes. The results reveal the impressive performance of the proposed approach in the PVSM assessment.

Voltage Stability Constrained Operation Optimization: An Ensemble Sparse Oblique Regression Tree Method

Voltage stability remains a main challenge for high renewable penetrated power systems. In future power systems, the dispatch needs to consider the voltage stability margin. However, considering static and transient voltage stability is challenging because a complex relationship exists between voltage stability and operation state variables. This paper proposes an ensemble sparse oblique regression tree method for voltage stability constrained operation optimization. First, we train multiple oblique regression trees on voltage stability simulation datasets. The trained trees are then grouped into ensemble using a boosting method to extract accurate and understandable voltage stability rules. Finally, the rules are embedded as mixed-integer linear programming constraints in a linear optimal power flow model. Validation on the IEEE-14 case shows the interpretability and efficiency of the proposed algorithm. Case studies on the Qinghai power grid and IEEE-118 further show that the proposed strategy can effectively improve the voltage stability margin of optimized operation states.

Load Margin Assessment of Power Systems using Recurrent Neural Network and Greylag Goose Optimization

The complexity of operating power systems requires the development of methods capable of assisting in system monitoring. The Voltage Stability Margin or Load Margin (LM) represents an index that informs how much the system’s load level can increase without causing a case of instability. The LM is determined using voltage stability criteria, but low-frequency modes can arise with increasing load and can cause system instability. This article proposes a method based on Recurrent Neural Networks (RNNs) for monitoring LM. Furthermore, a metaheuristic called Greylag Goose Optimization is applied to choose the system buses whose measurements will be RNN inputs.

Identification of the Worst-Case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

Identification of the Worst-Case Static Voltage Stability Margin Interval of AC/DC Power System Considering Uncertainty of Renewables

A new index for the assessment of power system strength considering reactive power injection and interaction of inverter based resources

Power system strength evaluation is vital to maintain secure operation in power systems having huge dependence on Inverter Based Resources. This paper reviews the state-of-the-art power system strength assessment methodologies along with their research gaps. Further, this paper proposes a novel power system strength assessment index for power system strength assessment in the presence of Static Var Compensator. A modified IEEE 39 bus system with Inverter Based Resources was used for the validation. The proposed index is validated in positive sequence modelling software using voltage stability margin and is compared with existing indices. To verify the applicability of the proposed index along with other existing indices, Electro Magnetic Transient type simulations are presented, which illustrate the sensitivity of the voltage following a three phase to ground fault followed by transmission line tripping in the power system.