Phân tích so sánh các thuật toán metaheuristic trong bài toán bù công suất phản kháng tối ưu trên lưới phân phối 34 nút
,
và
Article Sidebar
Full Text: 
PDF
Abstract
This study presents a comprehensive comparison and analysis of the performance of three metaheuristic algorithms: Differential Evolution (DE), Particle Swarm Optimization (PSO), and Grey Wolf Optimizer (GWO) for determining the optimal location and size of shunt capacitors in the IEEE 34-bus distribution system. The objective is to minimize active power loss and annual operating costs while maintaining bus voltages within permissible limits. Two scenarios are considered: continuous compensation, allowing any size within the boundaries, and discrete compensation, using standard 150 kVAr steps. The results show that PSO achieves superior performance, particularly in the discrete case, reducing active power loss from 221.72 kW to 160.85 kW and saving more than 10,000 USD per year. Meanwhile, DE and GWO yield lower investment savings and more limited loss reduction. The study provides practical insights for selecting suitable optimization methods based on specific grid operation objectives.
Tóm tắt
Nghiên cứu này được thực hiện nhằm trình bày kết quả so sánh và phân tích tổng quát về hiệu quả của ba thuật toán metaheuristic, bao gồm Differential Evolution (DE), Particle Swarm Optimization (PSO) và Grey Wolf Optimizer (GWO) được áp dụng trong bài toán xác định vị trí và dung lượng tụ bù tối ưu trên lưới phân phối IEEE 34 nút. Mục tiêu là giảm tổn thất công suất tác dụng và chi phí vận hành hàng năm, đồng thời duy trì điện áp nút trong giới hạn cho phép. Hai kịch bản đã được triển khai bao gồm bù liên tục để chọn dung lượng bất kỳ trong giới hạn và bù rời rạc theo cấp 150 kVAr. Kết quả cho thấy PSO đạt hiệu suất vượt trội, đặc biệt là ở kịch bản rời rạc giúp giảm tổn thất công suất từ 221,72 kW xuống 160,85 kW và tiết kiệm chi phí hơn 10.000 USD/năm. Trong khi đó, DE và GWO có kết quả tiết kiệm đầu tư thấp hơn nhưng hiệu quả giảm tổn thất hạn chế hơn. Kết quả nghiên cứu đã giúp cung cấp cơ sở thực tiễn để lựa chọn thuật toán phù hợp với mục tiêu vận hành lưới.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Tài liệu tham khảo
Abdelsalam, M., Diab, H. Y., & El-Bary, A. A. (2021). A Metaheuristic Harris Hawk Optimization Approach for Coordinated Control of Energy Management in Distributed Generation Based Microgrids. Applied Sciences 2021, 11(9), 4085. https://doi.org/10.3390/APP11094085
Abou El-Ela, A. A., El-Sehiemy, R. A., Kinawy, A. M., & Mouwafi, M. T. (2016a). Optimal capacitor placement in distribution systems for power loss reduction and voltage profile improvement. IET Generation, Transmission & Distribution, 10(5), 1209–1221. https://doi.org/10.1049/IET-GTD.2015.0799
Abou El-Ela, A. A., El-Sehiemy, R. A., Kinawy, A. M., & Mouwafi, M. T. (2016b). Optimal capacitor placement in distribution systems for power loss reduction and voltage profile improvement. IET Generation, Transmission & Distribution, 10(5), 1209–1221. https://doi.org/10.1049/IET-GTD.2015.0799
Abul’Wafa, A. R. (2013). Optimal capacitor allocation in radial distribution systems for loss reduction: A two stage method. Electric Power Systems Research, 95, 168–174. https://doi.org/10.1016/J.EPSR.2012.09.004
Águila Téllez, A., López, G., Isaac, I., & González, J. W. (2018). Optimal reactive power compensation in electrical distribution systems with distributed resources. Review. Heliyon, 4(8), e00746. https://doi.org/10.1016/J.HELIYON.2018.E00746
Ahmadi Kamarposhti, M., Ghandour, R., Abdel-Aty, M., Hafez, M., Alfiras, M., Alkhazaleh, S., Colak, I., & Solyman, A. (2025a). Optimizing capacitor bank placement in distribution networks using a multi-objective particle swarm optimization approach for energy efficiency and cost reduction. Scientific Reports, 15(1), 12332. https://doi.org/10.1038/S41598-025-96341-8
Ahmadi Kamarposhti, M., Ghandour, R., Abdel-Aty, M., Hafez, M., Alfiras, M., Alkhazaleh, S., Colak, I., & Solyman, A. (2025b). Optimizing capacitor bank placement in distribution networks using a multi-objective particle swarm optimization approach for energy efficiency and cost reduction. Scientific Reports, 15(1). https://doi.org/10.1038/S41598-025-96341-8
Asabere, P., Sekyere, F., Ayambire, P., & Ofosu, W. K. (2025). Optimal capacitor bank placement and sizing using particle swarm optimization for power loss minimization in distribution network. Journal of Engineering Research, 13(2), 1307–1315.
https://doi.org/10.1016/J.JER.2024.03.007
Askarzadeh, A. (2016a). Capacitor placement in distribution systems for power loss reduction and voltage improvement: a new methodology. IET Generation, Transmission & Distribution, 10(14), 3631–3638.
https://doi.org/10.1049/IET-GTD.2016.0419
Askarzadeh, A. (2016b). Capacitor placement in distribution systems for power loss reduction and voltage improvement: A new methodology. IET Generation, Transmission and Distribution, 10(14), 3631–3638.
https://doi.org/10.1049/iet-gtd.2016.0419;website:website:ietresearch;journal:journal:17518695;wgroup:string:publication
Bilal, M., Shahzad, M., Arif, M., Ullah, B., Hisham, S. B., & Ali, S. S. A. (2021). Annual Cost and Loss Minimization in a Radial Distribution Network by Capacitor Allocation Using PSO. Applied Sciences 2021, Vol. 11, Page 11840, 11(24), 11840. https://doi.org/10.3390/APP112411840
Bolufé-Röhler, A., & Tamayo-Vera, D. (2025). Machine Learning for Enhancing Metaheuristics in Global Optimization: A Comprehensive Review. Mathematics 2025, Vol. 13, Page 2909, 13(18), 2909. https://doi.org/10.3390/MATH13182909
Chiou, J. P., Chang, C. F., & Su, C. T. (2006). Capacitor placement in large-scale distribution systems using variable scaling hybrid differential evolution. International Journal of Electrical Power & Energy Systems, 28(10), 739–745. https://doi.org/10.1016/J.IJEPES.2006.03.022
Chis, M., & Salama, M. M. A. (1997). Capacitor placement in distribution systems using heuristic search strategies. IEE Proceedings - Generation, Transmission and Distribution, 144(3), 225–230. https://doi.org/10.1049/IP-GTD:19970945
Duan, D. L., Ling, X. D., Wu, X. Y., & Zhong, B. (2015). Reconfiguration of distribution network for loss reduction and reliability improvement based on an enhanced genetic algorithm. International Journal of Electrical Power & Energy Systems, 64, 88–95. https://doi.org/10.1016/J.IJEPES.2014.07.036
Farzin, H., & Monadi, M. (2022a). A meta-heuristic capacitor placement framework for distribution grids using modal resonance analysis. IET Renewable Power Generation, 16(13), 2921–2933. https://doi.org/10.1049/RPG2.12548
Farzin, H., & Monadi, M. (2022b). A meta-heuristic capacitor placement framework for distribution grids using modal resonance analysis. IET Renewable Power Generation, 16(13), 2921–2933.
https://doi.org/10.1049/RPG2.12548;PAGE:STRING:ARTICLE/CHAPTER
Gali, V., Gupta, N., Jamwal, P. K., Kumawat, M., & Babu, B. C. (2025). Real-time performance enhancement of battery energy storage system in sustainable microgrids using Harris Hawks Optimization. Sustainable Computing: Informatics and Systems, 46, 101110. https://doi.org/10.1016/J.SUSCOM.2025.101110
Gholinezhad, J., Noroozian, R., & Bagheri, A. (2017). Optimal Capacitor Allocation in Radial Distribution Networks for Annual Costs Minimization Using Hybrid PSO and Sequential Power Loss Index Based Method. Journal of Operation and Automation in Power Engineering, 5(2), 117–130. https://doi.org/10.22098/joape.2017.2760.1233
Jamil, U. (2023). Power Loss Minimization of Distribution Network using Different Grid Strategies. https://arxiv.org/pdf/2307.06275
Jayabarathi, T., Raghunathan, T., Sanjay, R., Jha, A., Mirjalili, S., & Cherukuri, S. H. C. (2022). Hybrid Grey Wolf Optimizer Based Optimal Capacitor Placement in Radial Distribution Systems. Electric Power Components and Systems, 50(8), 413–425. https://doi.org/10.1080/15325008.2022.2132556
Jones, E. S., Jewell, N., Liao, Y., & Ionel, D. M. (2023). Optimal Capacitor Placement and Rating for Large-Scale Utility Power Distribution Systems Employing Load-Tap-Changing Transformer Control. https://doi.org/10.1109/ACCESS.2023.3244572
Karri, C., & Avv, S. (2017). Invasive Weed Optimization for Optimal Capacitor Placement on a Radial Distribution System. International Journal of Electrical Engineering & Technology, 8(5), 9–19. www.jifactor.comttp://iaeme.com
Kasaei, M. J., Gandomkar, M., & Dadfar, S. (2014). IJTPE Journal OPTIMAL CAPACITOR PLACEMENT AND SIZING WITH CONSIDERATION OF COSTS AND LOSSES IN RADIAL DISTRIBUTION SYSTEMS USING ANT COLONY ALGORITHM. International Journal on “Technical and Physical Problems of Engineering” (IJTPE) Issue, 21, 56–60. www.iotpe.com
Kazmi, S. A. A., Altamimi, A., Khan, Z. A., Shin, D. R., Shahroz, M., Ali, S., Kazmi, A., Altamimi, A., Khan, Z. A., & Shin, D. R. (2023). Multi-Objective Optimization-Based Approach for Optimal Allocation of Distributed Generation Considering Techno-Economic and Environmental Indices. Sustainability 2023, Vol. 15, Page 4306, 15(5), 4306. https://doi.org/10.3390/SU15054306
Mohamed Shuaib, Y., Surya Kalavathi, M., & Christober Asir Rajan, C. (2015). Optimal capacitor placement in radial distribution system using Gravitational Search Algorithm. International Journal of Electrical Power & Energy Systems, 64, 384–397. https://doi.org/10.1016/J.IJEPES.2014.07.041
Montazeri, M., & Askarzadeh, A. (2020). A new analytical index for solving capacitor placement problem of distribution networks in bi-level framework: Total loss index. International Transactions on Electrical Energy Systems, 30(10), e12532. https://doi.org/10.1002/2050-7038.12532
Mtonga, T. P. M., Kaberere, K. K., & Irungu, G. K. (2021). Optimal Shunt Capacitors’ Placement and Sizing in Radial Distribution Systems Using Multiverse Optimizer. IEEE Canadian Journal of Electrical and Computer Engineering, 44(1), 10–21.
https://doi.org/10.1109/ICJECE.2020.3012041
Nguyen, P. T., Anh, T. N., Vo Ngoc, D., Le Thanh, T., Chi, H., City, M., Ward, L. T., District, D., & Minh, H. C. (2020). A Cost-Benefit Analysis of Capacitor Allocation Problem in Radial Distribution Networks Using an Improved Stochastic Fractal Search Algorithm. Complexity, 2020(1), 8811674. https://doi.org/10.1155/2020/8811674
Sadovskaia, K., Bogdanov, D., Honkapuro, S., & Breyer, C. (2019). Power transmission and distribution losses – A model based on available empirical data and future trends for all countries globally. International Journal of Electrical Power & Energy Systems, 107, 98–109. https://doi.org/10.1016/J.IJEPES.2018.11.012
Salman, I., Mohammed, K., Shaker, K., & Shaker, H. (2019). Optimal Capacitor Placement in Radial Distribution System Using Moth Flame Optimization Algorithm. Journal of Southwest Jiaotong University, 54(3). https://doi.org/10.35741/ISSN.0258-2724.54.3.21
Selvam, R., Hiremath, P., Cs, S. K., Ramakrishna Bhat, R., Tomar, V., Bansal, M., & Singh, P. (2024). Metaheuristic Algorithms for Optimization: A Brief Review. Engineering Proceedings 2023, Vol. 59, Page 238, 59(1), 238.
https://doi.org/10.3390/ENGPROC2023059238
Sharma, S., & Ghosh, S. (2019a). FIS and hybrid ABC-PSO based optimal capacitor placement and sizing for radial distribution networks. Journal of Ambient Intelligence and Humanized Computing 2019 11:2, 11(2), 901–916. https://doi.org/10.1007/S12652-019-01216-2
Sharma, S., & Ghosh, S. (2019b). FIS and hybrid ABC-PSO based optimal capacitor placement and sizing for radial distribution networks. Journal of Ambient Intelligence and Humanized Computing 2019 11:2, 11(2), 901–916. https://doi.org/10.1007/S12652-019-01216-2
Storn, R., & Price, K. (1997). Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces. Journal of Global Optimization, 11(4), 341–359. https://doi.org/10.1023/A:1008202821328/METRICS
Su, C. T., Chang, C. F. U., & Chiou, J. I. P. (2005). Optimal Capacitor Placement in Distribution Systems Employing Ant Colony Search Algorithm. Electric Power Components and Systems, 33(8), 931–946. https://doi.org/10.1080/15325000590909912
Sultana, S., & Roy, P. K. (2014). Optimal capacitor placement in radial distribution systems using teaching learning based optimization. International Journal of Electrical Power & Energy Systems, 54, 387–398. https://doi.org/10.1016/J.IJEPES.2013.07.011
Sundhararajan, S., & Pahwa, A. (1994). Optimal Selection of Capacitors for Radial Distribution Systems using A Genetic Algorithm. IEEE Transactions on Power Systems, 9(3), 1499–1507. https://doi.org/10.1109/59.336111
Ul Haq, I., Shams ur Rehman, M., Yousaf, A., & Noor, J. (2023). Optimal Placement of Capacitor in Distribution System using Particle Swarm Optimization.
https://arxiv.org/pdf/2311.08728