skip to main content

Maximize the total electric sale profit for a hybrid power plant with fifteen thermal units and a 100-MW solar photovoltaic farm under a 20-year power generation project

Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 700000, Viet Nam

Received: 11 Dec 2024; Revised: 15 Mar 2025; Accepted: 16 Apr 2025; Available online: 25 Apr 2025; Published: 1 May 2025.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2025 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.

Citation Format:
Abstract

This study investigates the effectiveness of two recently proposed meta-heuristic methods, the Weighted Average Algorithm (WAA) and Electric Eel Foraging Optimization (EEFO), to maximize the total profit of a hybrid power system. The considered system comprises fifteen thermal generating units (TGUs) and a 100-MW solar photovoltaic farm (SPP) operating over a 20-year period. Initially, the problem is solved under conditions of fixed load demand and rated power supply from the renewable energy source while accounting for prohibited operating zone constraint and system power losses. Comparative results obtained from both algorithms demonstrate that EEFO exhibits superior performance in terms of stability and convergence speed. Specifically, EEFO demonstrates a lower fluctuation in overall electricity generation cost (OEGC) across multiple independent runs compared to WAA. Furthermore, EEFO achieves better minimum, mean, and maximum OEGC values of $0.266, $58.890, and $214.225, respectively. Subsequently, EEFO is reapplied to maximize the profit of the hybrid power system, incorporating load demand variations and real solar radiation data. This analysis includes the evaluation of initial capital expenditure (CAPEX) and operation and maintenance (O&M) costs for the SPP over the 20-year period. Current electricity and solar power prices are utilized to illustrate the cumulative profit over time. The results indicate that the hybrid system experienced the highest loss in the first year, with the minimum loss occurring after 9 years for the TGUs and 7 years for the SPP. Profitability is achieved after 10 years for the TGUs and 7 years for the SPP. The cumulative profit over 20 years amounts to $14.2 billion for the TGUs and $0.207 billion for the SPP, representing approximately 83% and 127% of their respective total costs.

Fulltext View|Download
Keywords: Economic load dispatch; thermal power plants; prohibited operating zones; fuel cost; total revenue; total profit

Article Metrics:

  1. Ahmed, I., Rehan, M., Basit, A., Malik, S. H., Ahmed, W., & Hong, K. S. (2024). Adaptive salp swarm algorithm for sustainable economic and environmental dispatch under renewable energy sources. Renewable Energy, 223, 119944. https://doi.org/10.1016/j.renene.2024.119944
  2. Ali, A., Aslam, S., Mirsaeidi, S., Mugheri, N. H., Memon, R. H., Abbas, G., & Alnuman, H. (2024). Multi‐objective multiperiod stable environmental economic power dispatch considering probabilistic wind and solar PV generation. IET Renewable Power Generation. https://doi.org/10.1049/rpg2.13077
  3. Alkoffash, M. S., Awadallah, M. A., Alweshah, M., Zitar, R. A., Assaleh, K., & Al-Betar, M. A. (2021). A non-convex economic load dispatch using hybrid salp swarm algorithm. Arabian Journal for Science and Engineering, 46(9), 8721-8740. https://doi.org/10.1007/s13369-021-05646-z
  4. Arezki, R., Djankov, S., Nguyen, H., & Yotzov, I. (2022). The political costs of oil price shocks. CESifo Working Paper Series 9763, CESifo. https://dx.doi.org/10.2139/ssrn.4123823
  5. CAPEX and O&M of SPP from National Renewable Energy Laboratory's https://atb.nrel.gov/electricity/2023/utility-scale_pv
  6. CAPEX and O&M of TGU from National Renewable Energy Laboratory's. https://atb.nrel.gov/electricity/2023/fossil_energy_technologies
  7. Chaudhary, V., Dubey, H. M., Pandit, M., & Salkuti, S. R. (2024). A chaotic Jaya algorithm for environmental economic dispatch incorporating wind and solar power. AIMS Energy, 12(1). https://doi.org/10.3934/energy.2024001
  8. Chen, C., Zou, D., & Li, C. (2020). Improved jaya algorithm for economic dispatch considering valve-point effect and multi-fuel options. IEEE Access, 8, 84981-84995. https://doi.org/10.1109/ACCESS.2020.2992616
  9. Cheng, J., & De Waele, W. (2024). Weighted average algorithm: a novel meta-heuristic optimization algorithm based on the weighted average position concept. Knowledge-Based Systems, 112564. https://doi.org/10.1016/j.knosys.2024.112564
  10. Dasgupta, K., & Banerjee, S. (2014). An analysis of economic load dispatch using different algorithms. 2014 1st International Conference on Non-Conventional Energy (ICONCE 2014). IEEE. https://doi.org/10.1109/ICONCE.2014.6808722
  11. Duong, M. P., Vo, D. N., Nguyen, T. T., & Phan, V. D. (2021). Optimal Power Flow in Power System Considering Wind Power Integrated into Grid. GMSARN International Journal, 15(4), 287-300
  12. Duong, M. Q., Nguyen, T. T., & Nguyen, T. T. (2021). Optimal placement of wind power plants in transmission power networks by applying an effectively proposed meta-heuristic algorithm. Mathematical Problems in Engineering, 2021. https://doi.org/10.1155/2021/1015367
  13. Farag, A., Al-Baiyat, S., & Cheng, T. C. (1995). Economic load dispatch multiobjective optimization procedures using linear programming techniques. IEEE Transactions on Power Systems, 10(2), 731-738. https://doi.org/10.1109/59.387910
  14. Fesanghary, M., & Ardehali, M. M. (2009). A novel meta-heuristic optimization methodology for solving various types of economic dispatch problem. Energy, 34(6), 757-766. https://doi.org/10.1016/j.energy.2008.12.015
  15. Guaita-Pradas, I., & Blasco-Ruiz, A. (2020). Analyzing profitability and discount rates for solar PV plants. A Spanish case. Sustainability, 12(8), 3157. https://doi.org/10.3390/su12083157
  16. Ha, P. T., Hoang, H. M., Nguyen, T. T., & Nguyen, T. T. (2020). Modified moth swarm algorithm for optimal economic load dispatch problem. TELKOMNIKA (Telecommunication Computing Electronics and Control), 18(4), 2140-2147. http://doi.org/10.12928/telkomnika.v18i4.15032
  17. Hassan, M. H., Houssein, E. H., Mahdy, M. A., & Kamel, S. (2021). An improved manta ray foraging optimizer for cost-effective emission dispatch problems. Engineering Applications of Artificial Intelligence, 100, 104155. https://doi.org/10.1016/j.engappai.2021.104155
  18. Jarosławska-Sobór, S. (2021). Decarbonisation–Origins and Evolution of the Process on the European Level. Journal of Sustainable Mining, 20(4), 250-259. https://doi.org/10.46873/2300-3960.1323
  19. Jiriwibhakorn, S., & Wongwut, K. (2024). Evaluation of the Power Demand for Economic Load Dispatch Problem Using Adaptive Neuro-Fuzzy Inference System and Artificial Neural Network. IEEE Access. https://doi.org/10.1109/ACCESS.2024.3458149
  20. Karimi, N., & Khandani, K. (2020). Social optimization algorithm with application to economic dispatch problem. International Transactions on Electrical Energy Systems, 30(11), e12593. https://doi.org/10.1002/2050-7038.12593
  21. Kaur, A., Singh, L., & Dhillon, J. S. (2022). Modified Krill Herd Algorithm for constrained economic load dispatch problem. International Journal of Ambient Energy, 43(1), 4332-4342. https://doi.org/10.1080/01430750.2021.1888798
  22. Kherfane, N., Kherfane, R. L., Younes, M., & Khodja, F. (2014). Economic and emission dispatch with renewable energy using HSA. Energy Procedia, 50, 970-979. https://doi.org/10.1016/j.egypro.2014.06.116
  23. Kheshti, M., Ding, L., Ma, S., & Zhao, B. (2018). Double weighted particle swarm optimization to non-convex wind penetrated emission/economic dispatch and multiple fuel option systems. Renewable Energy, 125, 1021-1037. https://doi.org/10.1016/j.renene.2018.03.024
  24. Kubicek, K., Cech, M., & Strelec, M. (2024). A Robust Distributed Algorithm for Solving the Economic Dispatch Problem with the Penetration of Renewables and Battery Systems. Applied Sciences, 14(5), 1991. https://doi.org/10.3390/app14051991
  25. Kumar, B. S., Rastogi, A. K., Rajani, B., Mehbodniya, A., Karunanithi, K., & Devarapalli, D. (2021, August). Optimal solution to economic load dispatch by modified jaya algorithm. In 2021 International Conference on Recent Trends on Electronics, Information, Communication & Technology (RTEICT) (pp. 348-352). IEEE. https://doi.org/10.1109/RTEICT52294.2021.9574009
  26. Kumar, M., & Dhillon, J. S. (2018). Hybrid artificial algae algorithm for economic load dispatch. Applied Soft Computing, 71, 89-109. https://doi.org/10.1016/j.asoc.2018.06.035
  27. Mishra, S., & Shaik, A. G. (2024). Solving bi-objective economic-emission load dispatch of diesel-wind-solar microgrid using African vulture optimization algorithm. Heliyon, 10(3). https://doi.org/10.1016/j.heliyon.2024.e24993
  28. Mokarram, M.J., Niknam, T., Aghaei, J., Shafie-khah, M., & Catalao, J.P. (2019). Hybrid optimization algorithm to solve the nonconvex multiarea economic dispatch problem. IEEE Systems Journal, 13(4), 3400-3409. https://doi.org/10.1109/JSYST.2018.2889988
  29. Nagarajan, K., Rajagopalan, A., Bajaj, M., Sitharthan, R., Dost Mohammadi, S. A., & Blazek, V. (2024). Optimizing dynamic economic dispatch through an enhanced Cheetah-inspired algorithm for integrated renewable energy and demand-side management. Scientific Reports, 14(1), 3091. https://doi.org/10.1038/s41598-024-53688-8
  30. Nguyen, T. T., & Vo, D. N. (2015). The application of one rank cuckoo search algorithm for solving economic load dispatch problems. Applied Soft Computing, 37(1), 763-773. https://doi.org/10.1016/j.asoc.2015.05.048
  31. Nguyen, T. T., Nguyen, T. T., & Le, B. (2022). Artificial ecosystem optimization for optimizing of position and operational power of battery energy storage system on the distribution network considering distributed generations. Expert Systems with Applications, 208, 118127. https://doi.org/10.1016/j.eswa.2022.118127
  32. Nguyen, T. T., Quynh, N. V., & Van Dai, L. (2018). Improved firefly algorithm: a novel method for optimal operation of thermal generating units. Complexity, 2018. https://doi.org/10.1155/2018/7267593
  33. Pandit, N., Tripathi, A., Tapaswi, S., & Pandit, M. (2012). An improved bacterial foraging algorithm for combined static/dynamic environmental economic dispatch. Applied Soft Computing, 12(11), 3500-3513. https://doi.org/10.1016/j.asoc.2012.06.011
  34. Pham, L. H., Duong, M. Q., Phan, V. D., Nguyen, T. T., & Nguyen, H. N. (2019). A high-performance stochastic fractal search algorithm for optimal generation dispatch problem. Energies, 12(9), 1796. https://doi.org/10.3390/en12091796
  35. Pradhan, M., Roy, P. K., & Pal, T. (2016). Grey wolf optimization applied to economic load dispatch problems. International Journal of Electrical Power & Energy Systems, 83, 325-334. https://doi.org/10.1016/j.ijepes.2016.04.034
  36. Reddy, S. S., & Bijwe, P. R. (2015). Real time economic dispatch considering renewable energy resources. Renewable Energy, 83, 1215-1226. https://doi.org/10.1016/j.renene.2015.06.011
  37. Said, M., Houssein, E. H., Deb, S., Ghoniem, R. M., & Elsayed, A. G. (2022). Economic load dispatch problem based on search and rescue optimization algorithm. IEEE Access, 10, 47109-47123. https://doi.org/10.1109/ACCESS.2022.3168653
  38. Salim, M.S.M., & Abdullah, M. (2022). Optimal Economic and Emission Dispatch of Photovoltaic Integrated Power System Using Firefly Algorithm. International Journal of Integrated Engineering, 14(1), 50-62. https://doi.org/10.30880/ijie.2022.14.03.006
  39. Shea, R. P., & Ramgolam, Y. K. (2019). Applied levelized cost of electricity for energy technologies in a small island developing state: A case study in Mauritius. Renewable energy, 132, 1415-1424. https://doi.org/10.1016/j.renene.2018.09.021,
  40. Sumanl, M., Sakthivel, V. P., & Sathya, P. D. (2020). Squirrel search optimizer: nature inspired metaheuristic strategy for solving disparate economic dispatch problems. International Journal of Intelligent Engineering and Systems, 13(5), 111-121. https://doi.org/10.22266/ijies2020.1031.11
  41. Suresh, V., Sreejith, S., Sudabattula, S. K., & Kamboj, V. K. (2019). Demand response-integrated economic dispatch incorporating renewable energy sources using ameliorated dragonfly algorithm. Electrical Engineering, 101(2), 421-442. https://doi.org/10.1007/s00202-019-00792-y
  42. Tang, N. A., & Cuong, N. M. D. (2023). Solving the Green Economic Load Dispatch by Applying the Novel Meta-heuristic Algorithm. Journal of Computing Theories and Applications, 1(2), 129-139. https://doi.org/10.33633/jcta.v1i2.9389
  43. The SPP data – Global solar atlas (GAS). https://globalsolaratlas.info/map?s=11.550392,109.028377,10&pv=ground,180,11,100000
  44. Vo, D. N., Schegner, P., & Ongsakul, W. (2013). Cuckoo search algorithm for non‐convex economic dispatch. IET Generation, Transmission & Distribution, 7(6), 645-654. https://doi.org/10.1049/iet-gtd.2012.0617
  45. Wang, Q., Wang, J., & Guan, Y. (2013). Price-based unit commitment with wind power utilization constraints. IEEE Transactions on Power Systems, 28(3), 2718-2726. https://doi.org/10.1109/TPWRS.2012.2231968
  46. Wang, X., Chu, S. C., Snášel, V., Shehadeh, H. A., & Pan, J. S. (2023). Five phases algorithm: A novel meta-heuristic algorithm and its application on economic load dispatch problem. Journal of Internet Technology, 24(4), 837-848
  47. Wu, L. H., Wang, Y. N., Yuan, X. F., & Zhou, S. W. (2010). Environmental/economic power dispatch problem using multi-objective differential evolution algorithm. Electric Power Systems Research, 80(9), 1171-1181. https://doi.org/10.1016/j.epsr.2010.03.010
  48. Xiong, G., & Shi, D. (2018). Hybrid biogeography-based optimization with brainstorm optimization for non-convex dynamic economic dispatch with valve-point effects. Energy, 157, 424-435. https://doi.org/10.1016/j.energy.2018.05.180
  49. Yang, S., & Fu, Y. (2025). Interconnectedness among supply chain disruptions, energy crisis, and oil market volatility on economic resilience. Energy Economics, 108290. https://doi.org/10.1016/j.eneco.2025.108290
  50. Zhang, J., Zhang, J., Zhang, F., Chi, M., & Wan, L. (2021). An improved symbiosis particle swarm optimization for solving economic load dispatch problem. Journal of Electrical and Computer Engineering, 2021, 8869477. https://doi.org/10.1155/2021/8869477
  51. Zhang, M., Wang, B., & Wei, J. (2024). The Robust Optimization of Low-Carbon Economic Dispatching for Regional Integrated Energy Systems Considering Wind and Solar Uncertainty. Electronics, 13(17), 3480. https://doi.org/10.3390/electronics13173480
  52. Zhao, W., Wang, L., Zhang, Z., Fan, H., Zhang, J., Mirjalili, S., Khodadadi, N., & Cao, Q. (2024). Electric eel foraging optimization: A new bio-inspired optimizer for engineering applications. Expert Systems with Applications, 238(F), 122200. https://doi.org/10.1016/j.eswa.2023.122200
  53. Zhao, Z. Y., Chen, Y. L., & Chang, R. D. (2016). How to stimulate renewable energy power generation effectively?–China's incentive approaches and lessons. Renewable Energy, 92, 147-156. https://doi.org/10.1016/j.renene.2016.02.001

Last update:

No citation recorded.

Last update: 2025-05-24 21:59:47

No citation recorded.