skip to main content

Determining solutions to new economic load dispatch problems by war strategy optimization algorithm

1Department of Power Delivery, Ho Chi Minh City University of Technology (HCMUT), 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City,, Viet Nam

2Vietnam National University Ho Chi Minh City, Linh Trung Ward, Thu Duc City, Ho Chi Minh City,, Viet Nam

3Power System Optimization Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam

Received: 5 Sep 2024; Revised: 29 Oct 2024; Accepted: 25 Nov 2024; Available online: 18 Dec 2024; Published: 1 Jan 2025.
Editor(s): Grigorios Kyriakopoulos
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
The paper applies three cutting-edge algorithms - War Strategy Optimization Algorithm (WSO), Egret Swarm Optimization Algorithm (ESOA), and  Black Widow Optimization Algorithm (BWOA) - as potential tools to determining the optimal generation power of power plants in both the Economic Load Dispatch problem (ELD) and the New ELD problem (NELD), which incorporates renewable energy resources into the traditional power system. These algorithms underwent rigorous evaluation using various test systems with complex constraints, a multi-fuel objective function, and 24-hour load demands. In System 1, at various load levels, WSO method achieves a lower total minimum cost compared to BWOA and ESOA. Specifically, WSO outperforms BWOA and ESOA by $0.68 and $2.79 for a load of 2400 MW, by $0.49 and $4.41 for a load of 2500 MW, by $0.79 and $4.83 for a load of 2600 MW, and by $0.54 and $4.53 for a load of 2700 MW. In System 2, WSO method is less cost in a day than ESOA by $ 80.92 and BWOA by $ 46.73, corresponding to 0.39% and 0.23%, respectively. Additionally, WSO excels in response capability, providing a quicker reaction time than BWOA and ESOA across all four subcases while maintaining the same control parameters. Moreover, WSO demonstrated comparable or superior results and improved search capabilities compared to previous methods. The comparison of these results underscored WSO's effectiveness in addressing these challenges and its potential for resolving broader engineering issues beyond ELD. Ultimately, the study aimed to offer valuable insights into the role of renewable energy resources in the traditional power system, particularly in cost savings.
Fulltext View|Download
Keywords: Economic load dispatch; War Strategy Optimization; Egret Swarm Optimization Algorithm; Black Widow Optimization Algorithm

Article Metrics:

  1. Alharbi, A. G., Fathy, A., Rezk, H., Abdelkareem, M. A., & Olabi, A. G. (2023). An efficient war strategy optimization reconfiguration method for improving the PV array generated power. Energy, 283, 129129. https://doi.org/10.1016/j.energy.2023.129129
  2. Amjady, N., & Nasiri-Rad, H. (2009). Nonconvex Economic Dispatch With AC Constraints by a New Real Coded Genetic Algorithm. IEEE Transactions on Power Systems, 24(3), 1489–1502. https://doi.org/10.1109/TPWRS.2009.2022998
  3. Arul, R., Velusami, S., & Ravi, G. (2013). Chaotic firefly algorithm to solve economic load dispatch problems. 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE), 458–464. https://doi.org/10.1109/ICGCE.2013.6823480
  4. Ayyarao, T. S. L. V, L V, S. K., Sasapu, P., & Padi, H. S. (2023). Optimal Load Frequency Control of Renewable Integrated Multi-Area Power System using War Strategy Optimization Algorithm. 2023 First International Conference on Cyber Physical Systems, Power Electronics and Electric Vehicles (ICPEEV), 1–5. https://doi.org/10.1109/ICPEEV58650.2023.10391921
  5. Ayyarao, Tummala. S. L. V., & Kumar, P. P. (2022). Parameter estimation of solar models with a new proposed war strategy optimization algorithm. International Journal of Energy Research, 46(6), 7215–7238. https://doi.org/10.1002/er.7629
  6. Ayyarao, Tummala. S. L. V., Ramakrishna, N. S. S., Elavarasan, R. M., Polumahanthi, N., Rambabu, M., Saini, G., Khan, B., & Alatas, B. (2022). War Strategy Optimization Algorithm: A New Effective Metaheuristic Algorithm for Global Optimization. IEEE Access, 10, 25073–25105. https://doi.org/10.1109/ACCESS.2022.3153493
  7. Balamurugan, R. , & S. S. (2007). Self-adaptive differential evolution based power economic dispatch of generators with valve-point effects and multiple fuel options. International Journal of Electrical and Computer Engineering, 1(1), 543–550
  8. Baskar, S., Subbaraj, P., & Rao, M. V. C. (2003). Hybrid real coded genetic algorithm solution to economic dispatch problem. Computers & Electrical Engineering, 29(3), 407–419. https://doi.org/10.1016/S0045-7906(01)00039-8
  9. Basu, M. (2019). Squirrel search algorithm for multi-region combined heat and power economic dispatch incorporating renewable energy sources. Energy, 182, 296–305. https://doi.org/10.1016/j.energy.2019.06.087
  10. Chen, Z., Francis, A., Li, S., Liao, B., Xiao, D., Ha, T., Li, J., Ding, L., & Cao, X. (2022). Egret Swarm Optimization Algorithm: An Evolutionary Computation Approach for Model Free Optimization. Biomimetics, 7(4), 144. https://doi.org/10.3390/biomimetics7040144
  11. Deb, S., Houssein, E. H., Said, M., & Abdelminaam, D. S. (2021). Performance of Turbulent Flow of Water Optimization on Economic Load Dispatch Problem. IEEE Access, 9, 77882–77893. https://doi.org/10.1109/ACCESS.2021.3083531
  12. Dieu, V. N., Ongsakul, W., & Polprasert, J. (2013). The augmented Lagrange Hopfield network for economic dispatch with multiple fuel options. Mathematical and Computer Modelling, 57(1–2), 30–39. https://doi.org/10.1016/j.mcm.2011.03.041
  13. Dinh, B. H., Pham, T. Van, Nguyen, T. T., Sava, G. N., & Duong, M. Q. (2020). An Effective Method for Minimizing Electric Generation Costs of Thermal Systems with Complex Constraints and Large Scale. Applied Sciences, 10(10), 3507. https://doi.org/10.3390/app10103507
  14. Ellahi, M., & Abbas, G. (2020). A Hybrid Metaheuristic Approach for the Solution of Renewables-Incorporated Economic Dispatch Problems. IEEE Access, 8, 127608–127621. https://doi.org/10.1109/ACCESS.2020.3008570
  15. 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.2009.02.007
  16. Gehad Ismail Sayed, & Aboul Ella Hassanein. (2023). Air Pollutants Classification Using Optimized Neural Network Based on War Strategy Optimization Algorithm. Automatic Control and Computer Sciences, 57(6), 600–607. https://doi.org/10.3103/S0146411623060081
  17. Huu Pham, L., Hoang Dinh, B., Trung Nguyen, T., & Phan, V.-D. (2021). Optimal operation of wind-hydrothermal systems considering certainty and uncertainty of wind. Alexandria Engineering Journal, 60(6), 5431–5461. https://doi.org/10.1016/j.aej.2021.04.025
  18. Ismaeel, A. A. K., Houssein, E. H., Khafaga, D. S., Abdullah Aldakheel, E., AbdElrazek, A. S., & Said, M. (2023). Performance of Osprey Optimization Algorithm for Solving Economic Load Dispatch Problem. Mathematics, 11(19), 4107. https://doi.org/10.3390/math11194107
  19. Jeyakumar, D. N., Jayabarathi, T., & Raghunathan, T. (2006). Particle swarm optimization for various types of economic dispatch problems. International Journal of Electrical Power & Energy Systems, 28(1), 36–42. https://doi.org/10.1016/j.ijepes.2005.09.004
  20. 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
  21. Kien, L. C., Nguyen, T. T., Hien, C. T., & Duong, M. Q. (2019). A Novel Social Spider Optimization Algorithm for Large-Scale Economic Load Dispatch Problem. Energies, 12(6), 1075. https://doi.org/10.3390/en12061075
  22. Lai, C. S., Jia, Y., Xu, Z., Lai, L. L., Li, X., Cao, J., & McCulloch, M. D. (2017). Levelized cost of electricity for photovoltaic/biogas power plant hybrid system with electrical energy storage degradation costs. Energy Conversion and Management, 153, 34–47. https://doi.org/10.1016/j.enconman.2017.09.076
  23. Lee, S. C., & Kim, Y. H. (2002). An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints. Electric Power Systems Research, 60(3), 167–177. https://doi.org/10.1016/S0378-7796(01)00181-X
  24. Li, M., Hou, J., Niu, Y., & Liu, J. (2016). Economic dispatch of wind-thermal power system by using aggregated output characteristics of virtual power plants. 2016 12th IEEE International Conference on Control and Automation (ICCA), 830–835. https://doi.org/10.1109/ICCA.2016.7505381
  25. Liang, H., Liu, Y., Shen, Y., Li, F., & Man, Y. (2018). A Hybrid Bat Algorithm for Economic Dispatch With Random Wind Power. IEEE Transactions on Power Systems, 33(5), 5052–5061. https://doi.org/10.1109/TPWRS.2018.2812711
  26. Losada-Puente, L. et al. (2023) ‘Cross-Case Analysis of the Energy Communities in Spain, Italy, and Greece: Progress, Barriers, and the Road Ahead’, Sustainability, 15(18), p. 14016. https://doi.org/10.3390/su151814016
  27. Martín-Ortega, J.L. et al. (2024) ‘Enhancing Transparency of Climate Efforts: MITICA’s Integrated Approach to Greenhouse Gas Mitigation’, Sustainability, 16(10), p. 4219. https://doi.org/10.3390/su16104219
  28. 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, 1–23. https://doi.org/10.1155/2018/7267593
  29. Nguyen, T. T., Vo, D. N., Dinhhoang, B., & Pham, L. H. (2016). Modified Cuckoo Search Algorithm for Solving Nonconvex Economic Load Dispatch Problems. Advances in Electrical and Electronic Engineering, 14(3). https://doi.org/10.15598/aeee.v14i3.1633
  30. Nguyen, T. T., Vo, D. N., Vu Quynh, N., & Van Dai, L. (2018). Modified Cuckoo Search Algorithm: A Novel Method to Minimize the Fuel Cost. Energies, 11(6), 1328. https://doi.org/10.3390/en11061328
  31. Niknam, T., Mojarrad, H. D., & Meymand, H. Z. (2011). Non-smooth economic dispatch computation by fuzzy and self adaptive particle swarm optimization. Applied Soft Computing, 11(2), 2805–2817. https://doi.org/10.1016/j.asoc.2010.11.010
  32. Noman, N., & Iba, H. (2008). Differential evolution for economic load dispatch problems. Electric Power Systems Research, 78(8), 1322–1331. https://doi.org/10.1016/j.epsr.2007.11.007
  33. Papadogiannaki, S. et al. (2023) ‘Evaluating the Impact of COVID-19 on the Carbon Footprint of Two Research Projects: A Comparative Analysis’, Atmosphere, 14(9), p. 1365. https://doi.org/10.3390/atmos14091365
  34. Park, J. H., Kim, Y. S., Eom, I. K., & Lee, K. Y. (1993). Economic load dispatch for piecewise quadratic cost function using Hopfield neural network. IEEE Transactions on Power Systems, 8(3), 1030–1038. https://doi.org/10.1109/59.260897
  35. Park, J.-B., Lee, K.-S., Shin, J.-R., & Lee, K. Y. (2005). A Particle Swarm Optimization for Economic Dispatch With Nonsmooth Cost Functions. IEEE Transactions on Power Systems, 20(1), 34–42. https://doi.org/10.1109/TPWRS.2004.831275
  36. Peña-Delgado, A. F., Peraza-Vázquez, H., Almazán-Covarrubias, J. H., Torres Cruz, N., García-Vite, P. M., Morales-Cepeda, A. B., & Ramirez-Arredondo, J. M. (2020). A Novel Bio-Inspired Algorithm Applied to Selective Harmonic Elimination in a Three-Phase Eleven-Level Inverter. Mathematical Problems in Engineering, 2020, 1–10. https://doi.org/10.1155/2020/8856040
  37. Pham, L. H., An, N. H., & Tam, D. T. (2018). Modified Flower Pollination Algorithm for Solving Economic Dispatch Problem (pp. 934–942). https://doi.org/10.1007/978-3-319-69814-4_90
  38. Pham, L. H., Ho, T. H., Nguyen, T. T., & Vo, D. N. (2017). Modified Bat Algorithm for Combined Economic and Emission Dispatch Problem (pp. 589–597). https://doi.org/10.1007/978-3-319-50904-4_62
  39. Pham, L. H., Nguyen, T. T., Vo, D. N., & Tran, C. D. (2016). Adaptive Cuckoo Search Algorithm based Method for Economic Load Dispatch with Multiple Fuel Options and Valve Point Effect. International Journal of Hybrid Information Technology, 9(1), 41–50. https://doi.org/10.14257/ijhit.2016.9.1.05
  40. Progiou, A., Liora, N., Sebos, I., Chatzimichail, C.,, Melas, D. (2023) Measures and Policies for Reducing PM Exceedances through the Use of Air Quality Modeling: The Case of Thessaloniki, Greece, Sustainability, 15(2), p. 930. https://doi.org/10.3390/su15020930
  41. Reddy, S. S. (2017). Optimal scheduling of thermal-wind-solar power system with storage. Renewable Energy, 101, 1357–1368. https://doi.org/10.1016/j.renene.2016.10.022
  42. Sebos, I., Progiou, A., Kallinikos, L., Eleni, P., Katsavou, I., Mangouta, K. and Ziomas, I (2016) Mitigation and Adaptation Policies Related to Climate Change in Greece. In: Grammelis, P. (eds) Energy, Transportation and Global Warming. Green Energy and Technology. Springer, Cham, pp. 35–49. https://doi.org/10.1007/978-3-319-30127-3_4
  43. Shou, S., Luo, H., Zhang, R., Ji, T., Liu, Q., & Su, L. (2023). Optimal Configuration of Voltage Sag Monitoring Points Considering Branch Current based on War Strategy Optimization Algorithm. Journal of Physics: Conference Series, 2659(1), 012009. https://doi.org/10.1088/1742-6596/2659/1/012009
  44. Thang, N. T. (2011). Solving Economic Dispatch Problem with Piecewise Quadratic Cost Functions Using Lagrange Multiplier Theory. In International Conference on Computer Technology and Development, 3rd (ICCTD 2011) (pp. 359–363). ASME Press. https://doi.org/10.1115/1.859919.paper62
  45. Tsepi, E., Sebos, I. and Kyriakopoulos, G.L. (2024) ‘Decomposition Analysis of CO2 Emissions in Greece from 1996 to 2020’, Strategic Planning for Energy and the Environment, pp. 517–544. https://doi.org/10.13052/spee1048-5236.4332
  46. Vo, D. N., & Ongsakul, W. (2012). Economic dispatch with multiple fuel types by enhanced augmented Lagrange Hopfield network. Applied Energy, 91(1), 281–289. https://doi.org/10.1016/j.apenergy.2011.09.025
  47. Yassine, C. and Sebos, I. (2024) ‘Quantifying COVID-19′s impact on GHG emission reduction in Oman’s transportation sector: A bottom-up analysis of pre-pandemic years (2015–2019) and the pandemic year (2020)’, Case Studies on Transport Policy, 16, p. 101204. https://doi.org/10.1016/j.cstp.2024.101204

Last update:

No citation recorded.

Last update: 2025-02-08 05:55:30

No citation recorded.