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Increasing demand for electricity and the modernization of power systems within competitive markets has induced power systems to operate close to their stability limits. Therefore, the continuous monitoring and control of power systems through voltage stability indices is urgently needed. This is the first-ever effort to examine more than 40 voltage stability indices based on their formulation, application, performance, and assessment measures. These indices are sorted based on a logical and chronological order considering the most recent indices to be applied worldwide. However, the generalizability of these indices in terms of multivariable objectives is limited. Despite its limitation, this study systematically reviews available indices in the literature within the past three decades to compile an integrated knowledge base with an up-to-date exposition. This is followed by a comparative analysis in terms of their similarity, functionality, applicability, formulation, merit, demerit, and overall performance. Also, a broad categorization of voltage stability indices is addressed. This study serves as an exhaustive roadmap of the issue and can be counted as a reference for planning and operation in the context of voltage stability for students, researchers, scholars, and practitioners.

In this study, a novel approach is proposed for fast prediction of dynamic voltage instability occurrence (as a short term phenomenon and/or a long term one) and voltage stability stiffness of the system, against load disturbances. The main contribution of this paper is in introducing a procedure for generating novel features to be applied to a pattern classifier, by which dynamic voltage stability status of a power system can be predicted. The proposed feature generation procedure only needs measured pre-disturbance variables and disturbance severity provided by phasor measurement units as inputs whereas a set of output variables are derived from an unconstrained power flow program. Since the proposed method does not need any measured post disturbance data, the prediction task can be performed just after the disturbance. Thus, corrective actions can be executed in a short time after the disturbance to inhibit voltage instability. Moreover as no measured post-disturbance data are needed, the proposed method can also be employed in preventive procedures for voltage stability enhancement and/or decreasing possibility of voltage instability occurrence. Training a decision tree based classifier with the proposed features and testing the method on a modified version of Nordic32 test system, the simulation results have demonstrated that the proposed method effectively predicts the status of dynamic voltage stability in the test system.

The increasing integration of solar and wind energy into modern power grids introduces challenges in maintaining voltage and frequency stability due to their intermittent and uncertain nature. This study evaluates the performance of three advanced state observers: extended Kalman filter (EKF), unscented Kalman filter (UKF), and cubature Kalman filter (CKF) for real-time monitoring and stability assessment in solar and wind-integrated grids (SAWIG). The analysis focuses on estimation accuracy, convergence speed, and classification performance under varying phasor measurement unit (PMU) sampling rates. Simulation results reveal that the CKF achieves the lowest root mean square error (RMSE) of 0.005 at a 10 Hz sampling rate, outperforming the UKF (0.007) and EKF (0.010). In terms of dynamic performance, CKF stabilizes within 0.1 s, while UKF and EKF require 0.2 and 0.4 s, respectively. Classification evaluation shows that CKF achieves the highest accuracy of 99.5%, with precision, recall, and F1-score of 99.2, 99.3, and 99.4%, respectively. In contrast, UKF reports values of 98.8, 98.5, 98.7, and 98.6%, while EKF records 97.6, 96.9, 97.1, and 97.3%. Confusion matrix analysis further confirms a classification accuracy of 95% for CKF. These results demonstrate its robustness, speed, and precision in ensuring reliable state estimation for voltage and frequency stability in renewable-integrated smart grids.

Numerous optimization techniques have recently been employed in the literature to enhance various electric power systems. Optimization algorithms help system operators determine the optimal location and capacity of any renewable energy source (RES) connected to a system, enabling them to achieve a specific goal and improve its performance. This study presents a novel statistical evaluation of 20 famous metaheuristic optimization techniques based on 10 performance measures. The performance measures comprise five power loss indices, three voltage profile indices, load flow calling frequency, and execution time. The evaluation involves 10 distribution systems of varying sizes to ensure an equitable comparison of the algorithm. The Friedman Ranking method evaluates algorithms based on performance metrics, yielding a specific score. Upon modeling all distribution systems, a composite ranking methodology is employed to categorize the algorithms into only four categories: excellent, very good, good, and fair. The study finalizes the ranking of all algorithms according to their overall assessment. The AEO, GWO, JS, PSO, MVO, BO, and GNDO algorithms attain ranks below 25%, thereby placing them in the highest category. The ALO, DA, FPA, SSA, YAYA, and SPO algorithms fall into the second category, with rankings ranging from 25 to 50%. The SMA and CGO algorithms are classified in the third group, with rankings between 50 and 75%. The analysis ultimately reveals that the algorithms CStA, HHO, AOA, GOA, and AOS are positioned in the lowest group, each achieving rankings beyond 75%. As comparison case studies, the proposed algorithms achieved a power loss of 87.164 kW for the 33-bus system, which is less than or equal to the published work. The same result is achieved with the 69-bus system, which has a power loss of 71.644 kW for most of the studied algorithms. Using the appropriate algorithms with distribution systems saves time and effort for the system operator, enhances performance, and increases the usability of optimization algorithms.

This paper proposes an innovative approach for predicting faults in synchronous condensers in ultra-high voltage direct current (UHVDC) transmission systems. The framework combines Wavelet Packet Transform (WPT) for intelligent feature extraction with an enhanced Gated Recurrent Unit (GRU) network augmented by multi-head attention mechanisms. WPT is employed for efficient decomposition of fault signals into multiple frequency sub-bands, facilitating the extraction of fault features such as energy, entropy, and statistical moments. By applying Large Language Models (LLM) to WPT, an intelligent feature selection mechanism significantly improves both detection accuracy and processing efficiency. The Multi-Head Attention GRU (MHA-GRU) network architecture is designed to capture complex temporal dependencies in fault signals while maintaining computational efficiency. Comprehensive experimental results demonstrate that our framework consistently outperforms state-of-the-art methods across all performance metrics, including classification accuracy, detection time, and false alarm rate. The system exhibits robust stability under varying load conditions with particularly significant improvements in air-gap eccentricity fault detection. The proposed approach provides a reliable solution for early fault prediction in UHVDC synchronous condensers, enabling timely maintenance intervention before minor issues develop into critical failures.

The incessant power outages that characterize the Nigerian power network (NGP), as in all developing countries, are not limited to the shortage of fuel for power generation. However, differential power shortages between the generated power and the load demand are alarming. In this study, we propose a new voltage stability pointer (NVSP) based on a reduced one-line power network to act as a classifier. The NVSP was trained with a support vector machine (SVM) using a medium Gaussian kernel classification toolbox (mGkCT) in the MATLAB environment. This classification is based on the power network susceptibility to voltage instability. NGP 28-bus 330 kV data were extracted and modeled in the MATLAB environment and tested with the NVSP-mGkCT classifier. The NVSP-mGkCT was able to classify the lines viz. stable and unstable lines for the base and contingency cases. Similarly, the linear load dynamics and non-linear load dynamics were evaluated on the basis of critical buses using the NVSP. The aim of this work was to help the Transmission Company of Nigeria (TCN) and the National Control Centre (NCC) to be pre-emptive with respect to possible voltage collapse due to voltage instability. The simulation results show that NVSP was able to flag vulnerable lines in the NGP.

The growing attention to environmental issues is leading to an increasing integration of renewable energy sources into electrical grids. This integration process could contribute to power system decarbonization, supporting the diversification of primary energy sources and enhancing the security of energy supply, which is threatened by the uncertain costs of conventional energy sources. Despite these environmental and economical benefits, many technological and regulatory problems should be fixed in order to significantly increase the level of penetration of renewable power generators, which are connected to power transmission and distribution systems via power electronic interfaces. Indeed, these converter-interfaced generators (CIGs) perturb grid operation, especially those fueled by non-programmable energy sources (e.g., wind and solar generators), affecting the system stability and making power systems more vulnerable to dynamic perturbations. To face these issues, the conventional operating procedures based on pre-defined system conditions, which are currently adopted in power system operation tools, should be enhanced in order to allow the “online” solution of complex decision-making problems, providing power system operators with the necessary measures and alerts to promptly adjust the system. A comprehensive analysis of the most promising research directions and the main enabling technologies for addressing this complex issue is presented in this paper.

Within the framework of this study, the inductive analysis of voltage stability indices’ theoretical formulation, functionality, and overall performances are introduced. The prominence is given to investigate and compare the original indices from three main dimensions (formulation, assessment, and application) standpoints, which have been frequently used and recently attracted. The generalizability of an exhaustive investigation on comparison of voltage stability indices seems problematic due to the multiplicity of the indices, and more importantly, their variety in theoretical foundation and performances. This study purports the first-ever framework for voltage stability indices classification for power system analysis. The test results found that indices in the same category are coherent to their theoretical foundation. The paper highlights the fact that each category of the indices is functional for a particular application irrespective of the drawback ranking, and negated the application of the Jacobian matrix-based indices for online application. Finally, the research efforts put forward a novel classification of voltage stability indices within the main three aspects of formulation, assessment, and behavior analysis in a synergistic manner as an exhaustive reference for students, researchers, scholars, and practitioners related to voltage stability analysis. The simulation tools used were MATLAB® and PowerWorld®.

The ongoing development of renewable energy and microgrid technologies has gradually transformed the conventional energy infrastructure and upgraded it into a modernized system with more distributed generation and localized energy storage options. Compared with power grids utilizing synchronous generation, inverter-based networks cannot physically provide large amounts of inertia, which means that more advanced and extensive studies regarding stability considerations are required for such systems. Therefore, appropriate analytical methods are needed for the voltage stability analysis of renewable-dominated power systems, which incorporate a large number of inverters and distributed energy sources. This paper provides a comprehensive literature review of voltage stability analyses of power systems with high levels of renewable energy penetration. A series of generalized evaluation schemes and improvement methods relating to the voltage stability of power systems integrated with various distributed energy resources are discussed. The existing voltage stability analysis methods and corresponding simulation verification models for microgrids are also reviewed in a systematic manner. The traditional and improved voltage stability analysis methods are reviewed according to the microgrid operation mode, the types of distributed generators, and the microgrid configurations. Moreover, the voltage stability indices, which play a crucial role in voltage stability assessments, are critically evaluated in terms of the applicable conditions. The associated modeling and simulation techniques are also presented and discussed. This contribution presents guidelines for voltage stability analysis and instability mitigation methods for modern renewable-rich power systems.