DOI: https://doi.org/10.61435/ijred.2026.62157
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A multi-objective metaheuristic framework for reactive power market optimization in distributed renewable systems

1University of Burgos, Department of Applied Economics, Burgos, 09001, Spain

2MOEVE, Exploration and Production, Madrid, 28046, Spain

Received: 25 Dec 2025; Revised: 18 May 2026; Accepted: 5 Jul 2026; Available online: 17 Jul 2026; Published: 1 Sep 2026.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2026 The Author(s). Published by Centre of Biomass and Renewable Energy (CBIORE)
Creative Commons License This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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Abstract

The increasing integration of renewable energy sources into the electrical grid demands specific ancillary services, particularly for reactive power supply and voltage control. This study introduces an optimization framework integrated with a reactive power market under a high penetration of distributed generation (DG). The methodology formulates a multi-objective optimization problem with five technical and economic objective functions, solved using a multi-objective metaheuristic algorithm (MOPSO) and selecting the operating point from the Pareto front through TOPSIS. It also integrates a VCG auction mechanism to allocate the reactive power demanded by the system operator, promoting truthful bidding under the usual VCG assumptions. Validation is performed on a modified IEEE-30 test system with 50 MW DG units at buses 19, 21 and 30 and a stressed load condition at the same buses. The TOPSIS selected operating point under scenario S3 achieves active power losses of 2.382 MW, voltage deviation of 0.194 p.u., and conventional generation cost of 7648 $, while the S3 Pareto front reaches a hypervolume of 0.823. In the reactive power auction based on 20.2 MVAr demand, VCG allocates 100 % of the procurement to renewable units for total payments of 60.71 $. The results confirm that the proposed model significantly improves the technical operation of the system while providing an economically viable framework for the integration of reactive power ancillary services into electricity distribution, supporting the transition towards more efficient, stable and sustainable electrical networks.

Keywords: Distributed generation; Electrical grid integration; Reactive power; Renewable energy sources; Voltage regulation;

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Section: Original Research Article
Language : EN
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  1. Acosta, M. N., Gonzalez-Longatt, F., Andrade, M. A., Torres, J. L. R., & Chamorro, H. R. (2021). Assessment of daily cost of reactive power procurement by smart inverters. Energies, 14(16), Article 4834. https://doi.org/10.3390/en14164834
  2. Anaya, K. L., & Pollitt, M. G. (2020). Reactive power procurement: A review of current trends. Applied Energy, 270, Article 114939. https://doi.org/10.1016/j.apenergy.2020.114939
  3. Bamikole, O. J., Jibril, Y., Jimoh, B., Okorie, P. U., & Adamu, S. A. (2024). Optimal transmission voltage deviation based on fractional kinetic gas molecular optimization symbiotic organism search algorithm for network operational stability improvement. Materials Today: Proceedings, 105, 50–55. https://doi.org/10.1016/j.matpr.2023.07.005
  4. Behzadian, M., Otaghsara, S. K., Yazdani, M., & Ignatius, J. (2012). A state-of-the-art survey of TOPSIS applications. Expert Systems with Applications, 39(17), 13051–13069. https://doi.org/10.1016/j.eswa.2012.05.056
  5. Blaabjerg, F., Yang, Y., Yang, D., & Wang, X. (2017). Distributed power-generation systems and protection. Proceedings of the IEEE, 105(7), 1311–1331. https://doi.org/10.1109/JPROC.2017.2696878
  6. Bozionek, J., Wolgast, T., & Nieße, A. (2022). Design and evaluation of a multi-level reactive power market. Energy Informatics, 5(1), Article 6. https://doi.org/10.21203/rs.3.rs-1389372/v1
  7. Bukhsh, W. A., Grothey, A., McKinnon, K. I., & Trodden, P. A. (2013). Local solutions of the optimal power flow problem. IEEE Transactions on Power Systems, 28(4), 4780–4788. https://doi.org/10.1109/tpwrs.2013.2274577
  8. Candra, O., Alghamdi, M. I., Hammid, A. T., Alvarez, J. R. N., Staroverova, O. V., Hussien Alawadi, A., Marhoon, H. A., & Shafieezadeh, M. M. (2024). Optimal distribution grid allocation of reactive power with a focus on the particle swarm optimization technique and voltage stability. Scientific Reports, 14(1), Article 10889. https://doi.org/10.1038/s41598-024-61412-9
  9. Chen, S.-J., & Hwang, C.-L. (1992). Fuzzy multiple attribute decision making methods. In Fuzzy multiple attribute decision making: Methods and applications (pp. 289–486). Springer. https://doi.org/10.1007/978-3-642-46768-4_5
  10. Coello, C. A. C., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Transactions on Evolutionary Computation, 8(3), 256–279. https://doi.org/10.1109/TEVC.2004.826067
  11. Cramton, P. C., Shoham, Y., Steinberg, R., & Smith, V. L. (2006). Combinatorial auctions (Vol. 1). MIT Press. https://doi.org/10.7551/mitpress/9780262033428.003.0001
  12. Eladl, A. A., Basha, M. I., & ElDesouky, A. A. (2022). Multi-objective-based reactive power planning and voltage stability enhancement using FACTS and capacitor banks. Electrical Engineering, 104(5), 3173–3196. https://doi.org/10.1007/s00202-022-01542-3
  13. Gandhi, O. (2020). Reactive power support using photovoltaic systems: Techno-economic analysis and implementation algorithms. Springer Nature. https://doi.org/10.1007/978-3-030-61251-1_1
  14. Halbhavi, S. B., Karki, S., & Kulkarni, S. G. (2012). Reactive power pricing framework problems and a proposal for a competitive market. International Journal of Innovations in Engineering and Technology, 1(2), 22–27
  15. Häselbarth, S., Winkels, O., & Strunz, K. (2023). Blockchain-based market procurement of reactive power. IEEE Access, 11, 36106–36119. https://doi.org/10.1109/access.2023.3263669
  16. Hasanvand, S., Sobhani, H., & Khooban, M.-H. (2025). Distribution network clustering for reactive power planning and distributed voltage control. IET Generation, Transmission & Distribution, 19(1), Article e70002. https://doi.org/10.1049/gtd2.70002
  17. Huang, Y.-S., & Li, W.-H. (2012). A study on aggregation of TOPSIS ideal solutions for group decision-making. Group Decision and Negotiation, 21, 461–473. https://doi.org/10.1007/s10726-010-9218-2
  18. Iweh, C. D., Gyamfi, S., Tanyi, E., & Effah-Donyina, E. (2021). Distributed generation and renewable energy integration into the grid: Prerequisites, push factors, practical options, issues and merits. Energies, 14(17), Article 5375. https://doi.org/10.3390/en14175375
  19. Javed, A. H., Nguyen, P. H., Morren, J., & Slootweg, J. G. H. (2023). Using smart PV inverters for reactive power management in distribution grids. In 2023 IEEE PowerTech Belgrade. IEEE
  20. Ji, Y., Chen, X., He, P., Liu, X., Wu, X., & Zhao, C. (2023). A novel voltage/var sensitivity calculation method to partition the distribution network containing renewable energy. Recent Advances in Electrical & Electronic Engineering, 16(4), 380–394. https://doi.org/10.2174/2352096516666221130150549
  21. Li, Z., & Xiong, J. (2024). Reactive power optimization in distribution networks of new power systems based on multi-objective particle swarm optimization. Energies, 17(10), Article 2316. https://doi.org/10.3390/en17102316
  22. Liu, X., Zhang, P., Fang, H., & Zhou, Y. (2021). Multi-objective reactive power optimization based on improved particle swarm optimization with ε-greedy strategy and Pareto archive algorithm. IEEE Access, 9, 65650–65659. https://doi.org/10.1109/access.2021.3075777
  23. Liu, Y., Chen, M., Fan, Y., Ying, L., Cui, X., & Zou, X. (2024). Design of a stochastic electricity market mechanism with a high proportion of renewable energy. Energies, 17(12), Article 3044. https://doi.org/10.3390/en17123044
  24. Malik, S., Thakur, S., Duffy, M., & Breslin, J. G. (2023). Comparative double auction approach for peer-to-peer energy trading on multiple microgrids. Smart Grids and Sustainable Energy, 8(4), Article 21. https://doi.org/10.1007/s40866-023-00178-x
  25. Miraftabzadeh, S. M., Colombo, C. G., Longo, M., & Foiadelli, F. (2023). K-means and alternative clustering methods in modern power systems. IEEE Access, 11, 119596–119633. https://doi.org/10.1109/access.2023.3327640
  26. Mohammed, A., Sakr, E. K., Abo-Adma, M., & Elazab, R. (2024). A comprehensive review of advancements and challenges in reactive power planning for microgrids. Energy Informatics, 7(1), Article 63. https://doi.org/10.1186/s42162-024-00341-3
  27. Molzahn, D. K., Dörfler, F., Sandberg, H., Low, S. H., Chakrabarti, S., Baldick, R., & Lavaei, J. (2017). A survey of distributed optimization and control algorithms for electric power systems. IEEE Transactions on Smart Grid, 8(6), 2941–2962. https://doi.org/10.1109/TSG.2017.2720471
  28. Mugemanyi, S., Qu, Z., Rugema, F. X., Dong, Y., Bananeza, C., & Wang, L. (2020). Optimal reactive power dispatch using chaotic bat algorithm. IEEE Access, 8, 65830–65867. https://doi.org/10.1109/ACCESS.2020.2982988
  29. Musirin, I., & Rahman, T. K. A. (2002). Novel fast voltage stability index (FVSI) for voltage stability analysis in power transmission system. In Student Conference on Research and Development (pp. 265–268). IEEE. https://doi.org/10.1109/scored.2002.1033108
  30. Nkalo, U. K., Inya, O. O., Obi, P. I., Bola, A. U., & Ewean, D. I. (2024). A modified multi-objective particle swarm optimization (M-MOPSO) for optimal sizing of a solar–wind–battery hybrid renewable energy system. Solar Compass, 12, Article 100082. https://doi.org/10.1016/j.solcom.2024.100082
  31. Potter, A., Haider, R., Ferro, G., Robba, M., & Annaswamy, A. M. (2023). A reactive power market for the future grid. Advances in Applied Energy, 9, Article 100114. https://doi.org/10.1016/j.adapen.2022.100114
  32. Prioste, F. B. (2021). Optimal power flow using genetic algorithm. In Anais do 15 Congresso Brasileiro de Inteligência Computacional (pp. 1–6). https://doi.org/10.21528/cbic2021-144
  33. Qiu, D., Baig, A. M., Wang, Y., Wang, L., Jiang, C., & Strbac, G. (2024). Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach. Applied Energy, 361, Article 122929. https://doi.org/10.1016/j.apenergy.2024.122929
  34. Ruan, H., Gao, H., Liu, Y., Wang, L., & Liu, J. (2020). Distributed voltage control in active distribution network considering renewable energy: A novel network partitioning method. IEEE Transactions on Power Systems, 35(6), 4220–4231. https://doi.org/10.1109/tpwrs.2020.3000984
  35. Sachan, S., Mishra, S., Øyvang, T., & Bordin, C. (2025). Minimizing active power losses and voltage deviations for reactive power planning considering bus vulnerability. Next Research, Article 100633. https://doi.org/10.1016/j.nexres.2025.100633
  36. Safari, A., Salyani, P., & Hajiloo, M. (2020). Reactive power pricing in power markets: A comprehensive review. International Journal of Ambient Energy, 41(13), 1548–1558. https://doi.org/10.1080/01430750.2018.1517675
  37. Siahroodi, H. J., Mojallali, H., & Mohtavipour, S. S. (2022). A new stochastic multi-objective framework for the reactive power market considering plug-in electric vehicles using a novel metaheuristic approach. Neural Computing and Applications, 34(14), 11937–11975. https://doi.org/10.1007/s00521-022-07081-z
  38. Singh, K., Padhy, N. P., & Sharma, J. (2011). Transmission expansion planning including reactive power procurement in deregulated environment. Electric Power Components and Systems, 39(13), 1403–1423. https://doi.org/10.1080/15325008.2011.584110
  39. Tesfatsion, L. (2020). A new swing-contract design for wholesale power markets. John Wiley & Sons. https://doi.org/10.1002/9781119670155
  40. Wolgast, T., Ferenz, S., & Nieße, A. (2022). Reactive power markets: A review. IEEE Access, 10, 28397–28410. https://doi.org/10.1109/ACCESS.2022.3141235
  41. Wood, A. J., Wollenberg, B. F., & Sheblé, G. B. (2013). Power generation, operation, and control. John Wiley & Sons
  42. Wu, J., Li, N., He, L., Yin, B., Guo, J., & Liu, Y. (2010). Research on multi-objective reactive power optimization based on modified particle swarm optimization algorithm. In 2010 Chinese Control and Decision Conference (pp. 477–480). IEEE. https://doi.org/10.1109/ccdc.2010.5499012
  43. Xu, B., Zhang, G., Li, K., Li, B., Chi, H., Yao, Y., & Fan, Z. (2022). Reactive power optimization of a distribution network with high-penetration of wind and solar renewable energy and electric vehicles. Protection and Control of Modern Power Systems, 7(1), Article 51. https://doi.org/10.1186/s41601-022-00271-w
  44. Zhang, J., Tang, Q., Li, P., Deng, D., & Chen, Y. (2016). A modified MOEA/D approach to the solution of multi-objective optimal power flow problem. Applied Soft Computing, 47, 494–514. https://doi.org/10.1016/j.asoc.2016.06.022
  45. Zhang, X., Chen, Y., Wang, Y., Ding, R., Zheng, Y., Wang, Y., Zha, X., & Cheng, X. (2020). Reactive voltage partitioning method for the power grid with comprehensive consideration of wind power fluctuation and uncertainty. IEEE Access, 8, 124514–124525. https://doi.org/10.1109/access.2020.3004484
  46. Zimmerman, R. D., Murillo-Sánchez, C. E., & Thomas, R. J. (2010). MATPOWER: Steady-state operations, planning, and analysis tools for power systems research and education. IEEE Transactions on Power Systems, 26(1), 12–19. https://doi.org/10.1109/TPWRS.2010.2051168

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