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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.

Voltage stability improvement is a challenging issue in planning and security assessment of power systems. As modern systems are being operated under heavily stressed conditions with reduced stability margins, incorporation of voltage stability criteria in the operation of power systems began receiving great attention. This study presents a novel voltage stability constrained optimal power flow (VSC-OPF) approach based on static line voltage stability indices to simultaneously improve voltage stability and minimise power system losses under stressed and contingency conditions. The proposed methodology uses a voltage collapse proximity indicator (VCPI) to provide important information about the proximity of the system to voltage instability. The VCPI index is incorporated into the optimal power flow (OPF) formulation in two ways; first it can be added as a new voltage stability constraint in the OPF constraints, or used as a voltage stability objective function. The proposed approach has been evaluated on the standard IEEE 30-bus and 57-bus test systems under different cases and compared with two well proved VSC-OPF approaches based on the bus voltage indicator L-index and the minimum singular value. The simulation results are promising and demonstrate the effectiveness of the proposed VSC-OPF based on the line voltage stability index.

The fast growth of the world’s energy demand in the modernized world has stirred many countries around the globe to focus on power generation by abundantly available renewable energy resources. Among them, wind energy has attained significant attention owing to its environment-friendly nature along with other fabulous advantages. However, wind-integrated power systems experience numerous voltage instability complexities due to the sporadic nature of wind. This paper comprehensively reviews the problems of voltage instability in wind-integrated power systems, its causes, consequences, improvement techniques, and implication of grid codes to keep the operation of the network secure. Thorough understanding of the underlying issues related to voltage instability is necessary for the development of effective mitigation techniques in order to facilitate wind integration into power systems. Therefore, this review delves into the origin and consequences of voltage instability, emphasizing its adverse impacts on the performance and reliability of power systems. Moreover, it sheds light on the challenges of integrating wind energy with existing grids. This manuscript provides a comprehensive overview of the essential features required for critical analysis through a detailed examination of Voltage Stability Indices (VSIs). To address voltage stability issues in wind-integrated power systems, this review examines diverse techniques proposed by researchers, encompassing the tools utilized for assessment and mitigation. Therefore, in the field of power system operation and renewable energy integration, this manuscript serves as a valuable resource for researchers by comprehensively addressing the complexities and challenges associated with voltage instability in wind-integrated power systems.

Voltage stability is crucial for power systems, ensuring that electrical grids maintain voltages within acceptable limits with increasing demand, renewable energy integration, and changing network topology. This paper reviews the voltage stability phenomena, voltage stability indices (VSIs) (line and bus), and offline/online voltage stability assessment considering load variations, uncertain renewable energy, and network structures. Multiple VSIs and algorithms quantify voltage stability, providing information on the system’s resilience to disruptions. A systematic review encompassing the essential aspects of mathematical formulation, expressions, constraints, and applicability of VSIs is presented. Also discussed is the voltage stability control strategy employing flexible AC transmission system (FACTS) devices, considering the incorporation of the power generated from renewable resources. A comparison of voltage stability analysis methodologies is performed. The study offers power system researchers and practitioners a comprehensive summary of voltage stability assessment methods and control strategies for integrating various FACTS devices with renewable energy sources. Finally, the challenges and limitations of voltage stability assessment and control are discussed, as are further research directions.

Voltage instability is a serious phenomenon that can occur in a power system because of critical or stressed conditions. To prevent voltage collapse caused by such instability, accurate voltage collapse prediction is necessary for power system planning and operation. This paper proposes a novel collapse prediction index ( NCPI ) to assess the voltage stability conditions of the power system and the critical conditions of lines. The effectiveness and applicability of the proposed index are investigated on the IEEE 30-bus and IEEE 118-bus systems and compared with the well-known existing indices ( L mn , FVSI , LQP , NLSI , and VSLI ) under several power system operations to validate its practicability and versatility. The study also presents the sensitivity assumptions of existing indices and analyzes their impact on voltage collapse prediction. The application results under intensive case studies prove that the proposed index NCPI adapts to several operating power conditions. The results show the superiority of the proposed index in accurately estimating the maximum load-ability and predicting the critical lines, weak buses, and weak areas in medium and large networks during various power load operations and contingencies. A line interruption or generation unit outage in a power system can also lead to voltage collapse, and this is a contingency in the power system. Line and generation unit outage contingencies are examined to identify the lines and generators that significantly impact system stability in the event of an outage. The contingencies are also ranked to identify the most severe outages that significantly cause voltage collapse because of the outage of line or generator.

This paper proposes utilizing a recent metaheuristic technique, artificial rabbits’ optimization (ARO), enhanced with the quasi-opposition-based learning (QOBL) technique to improve global search capabilities. Furthermore, the novel line stability index (NLSI) is used to show weak buses in radial distribution systems (RDSs), aiding in the optimal placement and sizing of renewable energy sources (RES) such as photovoltaic (PV) systems. This enhanced algorithm, named the hybrid quasi-oppositional ARO (Hybrid QOARO) algorithm, addresses both single-objective and multi-objective functions. The single-objective approach focuses on reducing active power loss in the RDS, while the multi-objective function seeks to minimize active power loss with total voltage deviation (VD) and maximize the voltage stability index (VSI). This multi-objective approach helps determine the appropriate sizing of PV and battery energy storage systems (BESS) over 96 h (four seasons), considering the variability of photovoltaic power generation. To evaluate the effectiveness of the proposed approach compared to different optimization strategies, the IEEE 33-bus RDS is used. The highest reduction in energy losses and VD, at 92.48% and 99.78%, respectively, is achieved by applying PV + BESS at optimal power factor (PF) compared to PV only, PV + BESS at unity PF, and PV + BESS at 0.95 lagging PF.

This paper propounds a new metaheuristic optimization algorithm to obtain the optimum site and size of distributed generation (DG) in radial distribution system (RDS). This problem is concomitant with reducing the active power loss, the total voltage deviation and the voltage stability index of the RDS considering different types of load models (such as constant power (CP), industrial (IL), residential (RES) as well as commercial (COM)). To solve this weighting factor-based multi-objective DG allocation problem, a novel metaheuristic optimization algorithm, student psychology-based optimization (SPBO), is suggested in this article. A multi-criteria approach (such as the analytic hierarchy process) is employed to optimize the weighting factors involved. To the best of the authors’ knowledge, this is the first time that this novel SPBO algorithm is being used for optimal siting and sizing of DGs in the RDS for different types of load models (like CP, IL, RES and COM) for IEEE 33-bus, IEEE 69-bus and practical Brazil 136-bus RDS. The simulation results attained by the proposed SPBO algorithm are compared with the results provided by recently surfaced Harris hawks optimization (HHO) algorithm and other state-of-the-art algorithms. The outcomes prove that the suggested SPBO algorithm is more efficient to solve the optimal multiple DG allocation problem with minimum real power loss, less computational time and prominent convergence rate.

The fast-response feature from a superconducting magnetic energy storage (SMES) device is favored for suppressing instantaneous voltage and power fluctuations, but the SMES coil is much more expensive than a conventional battery energy storage device. In order to improve the energy utilization rate and reduce the energy storage cost under multiple-line power distribution conditions, this paper investigates a new interline DC dynamic voltage restorer (IDC-DVR) scheme with one SMES coil shared among multiple compensating circuits. In this new concept, an improved current-voltage (I/V) chopper assembly, which has a series of input/output power ports, is introduced to connect the single SMES coil with multiple power lines, and thereby satisfy the independent energy exchange requirements of any line to be compensated. Specifically, if two or more power lines have simultaneous compensating demands, the SMES coil can be selectively controlled to compensate the preferable line according to the priority order of the line. The feasibility of the proposed scheme is technically verified to maintain the transient voltage stability in multiple-line voltage swell and sag cases caused by either output voltage fluctuations from external power sources or power demand fluctuations from local sensitive loads. The simulation results provide a technical basis to develop a cost-effective SMES-based IDC-DVR for use in various DC distribution networks.

Voltage instability poses a significant challenge by limiting power system operation and transmission capacity. Rapid detection and effective corrective actions are essential to prevent voltage collapse. However, traditional methods for assessing voltage security margins are computationally intensive and often impractical for real-time applications. This study addresses voltage stability assessment in power systems using machine learning (ML) to overcome the computational limitations of traditional methods. By employing Linear Regression (LR), Random Forest (RF), Gradient Boosting (GB), and Support Vector Machine (SVM), we predict Fast Voltage Stability Indices (FVSI) at nominal load as well as under varying loads (10–150%) in 15 kV Ethiopian distribution networks: a 35-bus Bata feeder system and a 53-bus Papyrus feeder system. RF and GB models achieved superior accuracy with R² values of 0.999 and 0.9998 respectively, significantly outperforming LR and SVM which exhibited substantial deviations. The GB model achieves the highest accuracy, with RMSE values of 0.0002 (53-bus) and 2.419e-05 (35-bus), while RF yields RMSE values of 0.0039 (53-bus) and 0.00120 (35-bus), demonstrating strong predictive performance. The FVSI threshold analysis revealed critical stability limits, with values approaching 1.0 indicating proximity to voltage collapse. The analysis identified buses 36, 32, and 21 in the 53-bus system (FVSI values: 0.087, 0.082, and 0.080) and buses 27 and 16 in the 35-bus system (FVSI values: 0.085 and 0.082) as critical instability risk points requiring immediate monitoring. These findings underscore the efficacy of ensemble methods for rapid voltage stability assessment and emphasize the need for targeted interventions in high-risk areas to bolster grid resilience in Ethiopian distribution networks.

In this paper , a Reactive Power Planning (RPP) approach based on a proposed voltage stability index is introduced to allocate and size reactive power compensators. The proposed index is employed to identify the weakest bus for compensator placement, while the compensator rating is determined using a sensitivity-based approach to satisfy reactive power requirements under normal operating conditions, ( N  − 1) contingency scenarios, and light-load conditions. Unlike many existing voltage stability indices that rely on solving vector or differential equations and computing Jacobian matrices, the proposed index is formulated as a simple algebraic expression and is efficiently evaluated using a single load-flow solution implemented in tools such as MATLAB script. Based on the proposed index, a sequential RPP framework is developed to systematically allocate and size Static VAr Compensators (SVCs) in order to enhance the system voltage profile and maintain all bus voltages within permissible limits, while achieving the minimum required SVC capacity and the corresponding minimum overall investment cost. The performance of the proposed RPP methodology is benchmarked against metaheuristic optimization techniques, namely Particle Swarm Optimization (PSO) and Grey Wolf Optimization (GWO). A comprehensive performance assessment is conducted using quantitative indices related to voltage profile improvement and economic performance. The proposed voltage stability index is validated using the standard IEEE 9, 14, and 39-bus test systems. The sequential RPP strategy is applied to modified IEEE 14 and 39-bus systems incorporating renewable energy sources such as hydro, wind, and photovoltaic (PV) solar generation. The comparative results, including voltage profile enhancement and cost analysis, demonstrate that the proposed RPP approach effectively compensates reactive power requirements, achieves improved voltage profile and minimum investment costs. All simulation studies are carried out using DIgSILENT PowerFactory and MATLAB.