Voltage-Instability Bus Identification in Power Transmission Networks Using an Improved Strength Pareto Evolutionary Algorithm

Voltage instability remains a major operational challenge in stressed transmission networks because reactive power deficiencies and contingency events can force bus voltages outside acceptable operating limits. This paper presents an Improved Strength Pareto Evolutionary Algorithm (ISPEA) for the identification of voltage-instability buses in transmission systems under steady-state and contingency loading. A Newton–Raphson load-flow model was first used to obtain the operating point of the network. Contingency severity is represented by a 90% increase in reactive demand at load buses, after which the ISPEA ranks buses using a multi-objective fitness structure based on voltage magnitude deviation, maximum loading capacity, and generator operating constraint penalties. ISPEA runs for 200 generations with a population of 100, an archive of 100, and a Newton–Raphson convergence tolerance of 10⁻⁵ p.u. The method was evaluated on the IEEE 30-bus and Nigerian 31-bus networks using MATLAB R2023a. Under base-case conditions, the IEEE 30-bus system reaches its minimum voltage at Bus 5 (0.9360 p.u.), whereas the Nigerian 31-bus system records its lowest voltage at Bus 21 (0.9430 p.u.). After contingency loading, the number of under-voltage buses increased from 2 to 8 in the IEEE system and from 2 to 9 in the Nigerian system. ISPEA identifies Buses 5, 7, and 23 as the most critical in the IEEE 30-bus system, and Buses 5, 11, and 21 in the Nigerian 31-bus system. Compared with LVSI and VCPI screening, ISPEA yields the lowest maximum loading capacity values across all evaluated buses, confirming the superior identification of genuinely vulnerable buses for reactive power compensation siting.

Voltage instability; weak-bus identification; contingency analysis; transmission networks; multi-objective optimization;

1. Adegoke, S. A., & Sun, Y. (2022). Power system optimization approach to mitigate voltage instability issues: A review. Cogent Engineering. https://doi.org/10.1080/23311916.2022.2153416 [Google Scholar] [Crossref]

2. Adetokun, B. B., Muriithi, C., Ojo, J., & Oghorada, O. (2023). Impact assessment of increasing renewable energy penetration on voltage instability tendencies of power system buses using a QV-based index. Scientific Reports, 13. https://doi.org/10.1038/s41598-023-36843-5 [Google Scholar] [Crossref]

3. Adeyemi, N. A., & Adebayo, I. (2025). Power System Stability Development and Application of Mathematical Model of Reactive Power Loss Index as a Measurement of Voltage Stability in Nigerian Transmission System. LAUTECH Journal of Engineering and Technology. https://doi.org/10.36108/laujet/5202.91.0302 [Google Scholar] [Crossref]

4. Alayande, A. S., Hassan, A., Olobaniyi, F., Osokoya, S. O., Adebeshin, A. I., & Ogundare, A. B. (2024). L-Index-Based Technique for Voltage Collapse Prediction and Voltage Stability Enhancement in Electrical Power Systems. ABUAD Journal of Engineering Research and Development (AJERD). https://doi.org/10.53982/ajerd.2024.0701.27-j [Google Scholar] [Crossref]

5. Angadi, R. V., Mangai, J. A., Manohar, V., Daram, S. B., & Rao, P. (2023). Ensemble-based data mining model for contingency analysis of power system under STLO. International Journal of Applied Power Engineering (IJAPE). https://doi.org/10.11591/ijape.v12.i4.pp349-358 [Google Scholar] [Crossref]

6. Babu, R., Raj, S., Dey, B., & Bhattacharyya, B. (2021). Optimal reactive power planning using oppositional grey wolf optimization by considering bus vulnerability analysis. Energy Conversion and Economics. https://doi.org/10.1049/enc2.12048 [Google Scholar] [Crossref]

7. Baleboina, G. M., & Rudramoorthy, M. (2024). Stability analysis of power system under n-1 contingency condition. Bulletin of Electrical Engineering and Informatics. https://doi.org/10.11591/eei.v13i4.6133 [Google Scholar] [Crossref]

8. Bharathi, Atla, C. S. R., & M. R. S. (2023). Power System Voltage Collapse Mitigation Employing Optimization-Based Dynamic Voltage Stability Analysis. U.Porto Journal of Engineering. https://doi.org/10.24840/2183-6493_009-003_001645 [Google Scholar] [Crossref]

9. Chi, Y.-Q., Tao, A., Xu, X., Wang, Q., & Zhou, N. (2023). Adaptive Many-objective Robust Optimization Model of Dynamic Reactive Power Sources for Voltage Stability Enhancement. Journal of Modern Power Systems and Clean Energy. https://doi.org/10.35833/mpce.2022.000431 [Google Scholar] [Crossref]

10. Hu, Y., Hu, W., Li, X., Shi, Y., Jin, J., Ren, X., Fan, X., & Yang, T. (2026). Optimal reactive power dispatch based on a multitask-assisted constrained multimodal multi-objective evolutionary algorithm. iScience, 29. https://doi.org/10.1016/j.isci.2026.115434 [Google Scholar] [Crossref]

11. Hu, Y., Hu, W., Li, X., Shi, Y., Jin, J., Ren, X., Fan, X., & Yang, T. (2026). Optimal reactive power dispatch based on a multitask-assisted constrained multimodal multi-objective evolutionary algorithm. iScience, 29. https://doi.org/10.1016/j.isci.2026.115434 [Google Scholar] [Crossref]

12. Ibrahim, M., & Jasim, A. (2021). Voltage Collapse Prediction of IEEE 30-Bus System. Tikrit Journal of Engineering Sciences. https://doi.org/10.25130/tjes.28.1.10 [Google Scholar] [Crossref]

13. Ismail, B., Wahab, N. A. A., Othman, M., Radzi, M., Vijyakumar, K. N., & Naain, M. N. M. (2020). A Comprehensive Review on Optimal Location and Sizing of Reactive Power Compensation Using Hybrid-Based Approaches for Power Loss Reduction, Voltage Stability Improvement, Voltage Profile Enhancement, and Loadability Enhancement. IEEE Access, 8, 222733-222765. https://doi.org/10.1109/access.2020.3043297 [Google Scholar] [Crossref]

14. Ismail, B., Wahab, N., Othman, M. L., Radzi, M., Vijayakumar, K. N., Rahmat, M., & Naain, M. M. (2022). New Line Voltage Stability Index (BVSI) for Voltage Stability Assessment in Power System: Comparative Studies. IEEE Access, 10, 103906-103931. https://doi.org/10.1109/access.2022.3204792 [Google Scholar] [Crossref]

15. Izzati, T. N., Soeprijanto, A., Syifa, B. N., Aryani, N. K., & Rahayu, P. (2025). Voltage Stability Enhancement Using NCPI-Based Optimal Reactive Power Compensation during Critical Line Outages. 2025 International Seminar on Intelligent Technology and Its Applications (ISITIA), 755-760. https://doi.org/10.1109/isitia66279.2025.11137457 [Google Scholar] [Crossref]

16. Kobibi, Y. D., Djehaf, M. A., Khatir, M., & Ouadafraksou, M. (2022). Continuation Power Flow Analysis of Power System Voltage Stability with a Unified Power Flow Controller. Journal of Intelligent Systems and Control. https://doi.org/10.56578/jisc010106 [Google Scholar] [Crossref]

17. Kyomugisha, R., Muriithi, C., & Nyakoe, G. (2022). Performance of Various Voltage Stability Indices in Stochastic Multiobjective Optimal Power Flow Using Mayfly Algorithm. J. Electr. Comput. Eng., 2022, 7456333:1-7456333:22. https://doi.org/10.1155/2022/7456333 [Google Scholar] [Crossref]

18. Luo, Y., & Liu, C. (2024). Power Systems Static Voltage Stability Assessment Considering N-1 Contingencies Based on Holo-morphic Embedding Method. 2024 IEEE Power & Energy Society General Meeting (PESGM), 01-05. https://doi.org/10.1109/pesgm51994.2024.10761098 [Google Scholar] [Crossref]

19. Luo, Y., & Liu, C. (2024). Power Systems Static Voltage Stability Assessment Considering N-1 Contingencies Based on Holo-morphic Embedding Method. 2024 IEEE Power & Energy Society General Meeting (PESGM), 01-05. https://doi.org/10.1109/pesgm51994.2024.10761098 [Google Scholar] [Crossref]

20. Mamari, A. S. A., Toha, S., Ahmad, S., & Mamari, A. (2021). Modal analysis based on reactive power compensation on 6-bus Oman electrical grid. International Journal of Power Electronics and Drive Systems (IJPEDS). https://doi.org/10.11591/ijpeds.v12.i2.pp757-764 [Google Scholar] [Crossref]

21. Miyazaki, M., Aoki, M., & Nakamura Y. (2025). Voltage Stability Estimation Considering Variability in Reactive Power Reserves Using Regression Trees. Energies. https://doi.org/10.3390/en18051260 [Google Scholar] [Crossref]

22. Mokred, S., Wang, Y., & Chen, T.-L. (2023). A novel collapse prediction index for voltage stability analysis and contingency ranking in power systems. Protection and Control of Modern Power Systems, 8, 1-27. https://doi.org/10.1186/s41601-023-00279-w [Google Scholar] [Crossref]

23. Mossie, M. A., Yetayew, T., Bitew, G. T., Yenealem, M. G., & Beza, T. M. (2025). Machine learning algorithms for voltage stability assessment in electrical distribution systems. Scientific Reports, 15. https://doi.org/10.1038/s41598-025-15791-2 [Google Scholar] [Crossref]

24. Nappu, M. B., Arief, A., Alam, N., & Zulfachri, M. (2020). Voltage stability assessment of the Southern Sulawesi power system in Indonesia for 2020 using modal analysis. IOP Conference Series: Earth and Environmental Science, 473. https://doi.org/10.1088/1755-1315/473/1/012097 [Google Scholar] [Crossref]

25. Nascimento, S., & Gouvêa, M. (2021). Multi-objective Adaptive Evolutionary Algorithm to Enhance Voltage Stability in Power Systems. International Journal of Control, Automation and Systems, 19, 2596 - 2610. https://doi.org/10.1007/s12555-020-0095-4 [Google Scholar] [Crossref]

26. Nascimento, S., & Gouvêa, M. (2021). Multi-objective Adaptive Evolutionary Algorithm to Enhance Voltage Stability in Power Systems. International Journal of Control, Automation and Systems, 19, 2596 - 2610. https://doi.org/10.1007/s12555-020-0095-4 [Google Scholar] [Crossref]

27. Okampo, E., Nwulu, N., & Bokoro, P. (2022). Optimization of Voltage Security with Placement of FACTS Device Using Modified Newton–Raphson Approach: A Case Study of Nigerian Transmission Network. Energies. https://doi.org/10.3390/en15124211 [Google Scholar] [Crossref]

28. Olasunkanmi, O. G., Barron, A. R., White, A. O., & Todeschini, G. (2024). Evaluation of HVDC Interconnection to Improve Voltage Stability of Nigerian Transmission Network. Journal of Electronics and Electrical Engineering. https://doi.org/10.37256/jeee.3120243799 [Google Scholar] [Crossref]

29. Puhan, S. S., Sharma, R., & Mallick, M. (2024). Ensuring grid resilience: Voltage stability analysis and contingency ranking in electric power systems. e-Prime - Advances in Electrical Engineering, Electronics and Energy. https://doi.org/10.1016/j.prime.2024.100696 [Google Scholar] [Crossref]

30. Puppala, V., & Chandrarao, D. T. P. (2018). Voltage stability assessment considering power system contingencies using continuation power flow method with regression. [Google Scholar] [Crossref]

31. Putranto, L. M., & Azhar, I. F. (2024). A proposed PMU-based voltage stability and critical bus detection method using an artificial neural network. Energy Informatics, 7. https://doi.org/10.1186/s42162-024-00302-w [Google Scholar] [Crossref]

32. Sobayo, A. S., Adejumobi, O. I., Adebisi, I. A., & Adams, D. O. (2024). Contingency Approach for Static Security Assessment on the Nigerian 330 Kv Electric Power Transmission Grid. Advances in Science and Technology, 154, 203 - 212. https://doi.org/10.4028/p-stvce4 [Google Scholar] [Crossref]

33. Valuva, C., Chinnamuthu, S., Khurshaid, T., & Kim, K.-C. (2023). A Comprehensive Review on the Modelling and Significance of Stability Indices in Power System Instability Problems. Energies. https://doi.org/10.3390/en16186718 [Google Scholar] [Crossref]

34. Zeitawyeh, R. A., & Faza, A. (2025). Optimal Reactive Power Planning Using FACTS Devices for Voltage Stability Enhancement in Power Transmission Systems. Energy Sci. Eng., 13. https://doi.org/10.1002/ese3.70064. [Google Scholar] [Crossref]

35. Zhang, M., & Li, Y. (2020). Multi-objective optimal reactive power dispatch of power systems by combining classification-based multi-objective evolutionary algorithm and integrated decision-making. IEEE Access, 8, 38198-38209. https://doi.org/10.1109/access. 2020.2974961, 1(5): 186–200. [Google Scholar] [Crossref]

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