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The application of equilibrium optimizer for solving modern economic load dispatch problem considering renewable energies and multiple-fuel thermal units

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

Received: 25 Feb 2023; Revised: 16 Apr 2023; Accepted: 26 Apr 2023; Available online: 1 May 2023; Published: 15 May 2023.
Editor(s): H Hadiyanto
Open Access Copyright (c) 2023 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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This study presents a modern version of the economic load dispatch (MELD) problem with the contribution of renewable energies and conventional energy, including wind, solar and thermal power plants. In the study, reduction of electricity generation cost is the first priority, while the use of multiple fuels in the thermal power plant is considered in addition to the consideration of all constraints of power plants. Two meta-heuristic algorithms, one conventional and one recently published, including Particle swarm optimization (PSO) and Equilibrium optimizer (EO), are applied to determine the optimal solutions for MELD. A power system with ten thermal power plants using multiple fossil fuels, one wind power plant, and three solar power plants is utilized to evaluate the performance of both PSO and EO. Unlike other previous studies, this paper considers the MELD problem with the change of load demands over one day with 24 periods as a real power system. In addition, the power generated by both wind and solar power plants varies at each period. The results obtained by applying the two algorithms indicate that EO is completely superior to PSO, and the solutions found by EO can satisfy all constraints. Particularly in Case 1 with different load demand values, EO achieves better total electricity production cost (TEGC) than PSO by 0.75%, 0.87%, 0.13%, and 0.45% for the loads of 2400 MW, 2500 MW, 2600 MW and 2700 MW. Moreover, EO also provides a faster response capability over PSO through the four subcases although EO and PSO are run by the same selection of control parameters. In Case 2, the high efficiency provided by EO is still maintained, though the scale of the considered problem has been substantially enlarged. Specifically, EO can save $51.2 compared to PSO for the minimum TEGC. The savings cost is equal to 0.33% for the whole schedule of 24 hours. With these results, EO is acknowledged as a favourable search method for dealing with the MELD problem. Besides, this study also points out the difference in performance between a modern meta-heuristic algorithm (EO) and the classical one (PSO). The modern metaheuristic algorithm with special structure is highly valuable for complicated problem as MELD.
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Keywords: Economic load dispatch; Particle swarm optimization; Equilibrium optimizer; multiple fuels; thermal generator; renewable energies.

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  1. Al-Betar, M.A., Awadallah, M.A. & Krishan, M.M. (2020). A non-convex economic load dispatch problem with valve loading effect using a hybrid grey wolf optimizer. Neural Computing and Applications, 32 (16), 12127–12154.
  2. Alsumait, J.S., Sykulski, J.K. & Al-Othman, A.K. (2010). A hybrid GA–PS–SQP method to solve power system valve-point economic dispatch problems. Applied Energy, 87 (5), 1773–1781.
  3. Amjady, N. & Nasiri-Rad, H. (2010). Solution of nonconvex and nonsmooth economic dispatch by a new Adaptive Real Coded Genetic Algorithm. Expert Systems with Applications, 37 (7), 5239–5245.
  4. Augusteen, W.A., Geetha, S. and Rengaraj, R. (2016). Economic dispatch incorporation solar energy using particle swarm optimization. Paper presented at 2016 3rd International Conference on Electrical Energy Systems (ICEES). 2016. pp. 67–73.
  5. Balamurugan, R. & Subramanian, 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 (3), 543–550
  6. Basu, M. (2008). Dynamic economic emission dispatch using nondominated sorting genetic algorithm-II. International Journal of Electrical Power & Energy Systems, 30(2), 140–149.
  7. Chang, X., Xu, Y., Sun, H., Khan, I. (2021). A distributed robust optimization approach for the economic dispatch of flexible resources. International Journal of Electrical Power & Energy Systems, 124, 106360.
  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.
  9. Chen, P.-H. & Chang, H.-C. (1995) Large-scale economic dispatch by genetic algorithm. IEEE Transactions on Power Systems, 10 (4), 1919–1926.
  10. Chopra, N., Brar, Y.S. & Dhillon, J.S. (2021). An improved particle swarm optimization using simplex-based deterministic approach for economic-emission power dispatch problem. Electrical Engineering, 103(3), 1347–1365.
  11. Coelho, Ld.S. & Mariani, V.C. (2006) Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Transactions on Power Systems, 21(2), 989–996.
  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), 30–39.
  13. 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 Metaheuristic Algorithm Li, Y. (ed.). Mathematical Problems in Engineering, 2021, 1015367.
  14. Faramarzi, A., Heidarinejad, M., Stephens, B., & Mirjalili, S. (2020). Equilibrium optimizer: A novel optimization algorithm. Knowledge-Based Systems, 191, 105190.
  15. Fu, C., Zhang, S. & Chao, K.-H. (2020). Energy Management of a Power System for Economic Load Dispatch Using the Artificial Intelligent Algorithm. Electronics, 9(1).
  16. Ghasemi, M., Akbari, E., Zand, M., Hadipour, M., Ghavidel, S., & Li, L. (2019) An Efficient Modified HPSO-TVAC-Based Dynamic Economic Dispatch of Generating Units. Electric Power Components and Systems, 47 (19–20), 1826–1840.
  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.
  18. Hien, C.T., Ha, P.T., Phan-Van, T. H., & Pham, T. M. (2021). Multi-Period Economic Load Dispatch with Wind Power Using a Novel Metaheuristic. GMSARN International Journal, 16 (2022), 165–173
  19. Hlalele, T.G., Zhang, J., Naidoo, R. M., & Bansal, R. C. (2021). Multi-objective economic dispatch with residential demand response programme under renewable obligation. Energy, 218, 119473.
  20. 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.
  21. Kennedy, J. & Eberhart, R. (1995) “Particle swarm optimization.” In Proceedings of ICNN’95 - International Conference on Neural Networks. 1995. pp. 1942–1948 vol.4.
  22. 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.
  23. Kim, J. & Kim, K.-K.K. (2020). Dynamic programming for scalable just-in-time economic dispatch with non-convex constraints and anytime participation. International Journal of Electrical Power & Energy Systems, 123, 106217.
  24. Kumar, M. and Dhillon, J.S. (2018). Hybrid artificial algae algorithm for economic load dispatch. Applied Soft Computing, 71: 89–109.
  25. Kheiter, A., Souag, S., Chaouch, A., Boukortt, A., Bekkouche, B., & Guezgouz, M. (2022). Energy Management Strategy based on marine predators algorithm for grid-connected microgrid. International Journal of Renewable Energy Development, 11(3), 751–765.
  26. Kaur, S., Brar, Y.S. and Dhillon, J.S. (2021). Short-term hydro-thermal-wind-solar power scheduling: A case study of kanyakumari region of India. International Journal of Renewable Energy Development, 10(3), 635–651.
  27. Khamharnphol, R. Kamdar, I., Waewsak, J., Chaichan, W., Khunpetch, S., Chiwamongkhonkarn, S., & Gagnon, Y. (2022). Microgrid Hybrid Solar/Wind/diesel and Battery Energy Storage Power Generation System: Application to Koh Samui, Southern Thailand. International Journal of Renewable Energy Development, 12(2), 216–226.
  28. Li, X., Wang, W., Wang, H., Wu, J., Fan, X., & Xu, Q. (2020). Dynamic environmental economic dispatch of hybrid renewable energy systems based on tradable green certificates. Energy, 193, 116699.
  29. Nguyen, T. T., Vu, Q. N., Duong, M. Q., & Le, V. D. (2018). Modified differential evolution algorithm: A novel approach to optimize the operation of hydrothermal power systems while considering the different constraints and valve point loading effects. Energies, 11(3), 540.
  30. Nguyen, T. T., Vo, D. N., Tran, H. V., & Le, V. D. (2019). Optimal dispatch of reactive power using modified stochastic fractal search algorithm. Complexity, 2019, Article ID 4670820, 28 pages.
  31. Nguyen, T. T., Nguyen, T. T., Duong, L. T., & Truong, V. A. (2021). An effective method to solve the problem of electric distribution network reconfiguration considering distributed generations for energy loss reduction. Neural Computing and Applications, 33, 1625-1641.
  32. Noman, N. & Iba, H. (2008). Differential evolution for economic load dispatch problems. Electric Power Systems Research, 78 (8), 1322–1331.
  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.
  34. 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.
  35. Park, Y.M., Won, J.R. & Park, J.B. (1998). A new approach to economic load dispatch based on improved evolutionary programming. Engineering Intelligent Systems for Electrical Engineering and Communications, 6 (2), 103–110
  36. Parouha, R.P. & Das, K.N. (2018). Economic load dispatch using memory based differential evolution. International Journal of Bio-Inspired Computation, 11 (3), 159–170.
  37. Pham, L.H., Dinh, B.H. & Nguyen, T.T. (2022). Optimal power flow for an integrated wind-solar-hydro-thermal power system considering uncertainty of wind speed and solar radiation. Neural Computing and Applications, 34 (13), 10655–10689.
  38. Phan, V.-D., Duong, M.Q., Doan, M. M., & Nguyen, T. T. (2021). Optimal Distributed Photovoltaic Units Placement in Radial Distribution System Considering Harmonic Distortion Limitation. International Journal on Electrical Engineering & Informatics, 13 (2).
  39. 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.
  40. Shen, X., Zou, D., Duan, N., & Zhang, Q. (2019). An efficient fitness-based differential evolution algorithm and a constraint handling technique for dynamic economic emission dispatch. Energy, 186, 115801.
  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.
  42. Vaisakh, K. & Reddy, A.S. (2013). MSFLA/GHS/SFLA-GHS/SDE algorithms for economic dispatch problem considering multiple fuels and valve point loadings. Applied Soft Computing, 13 (11), 4281–4291.
  43. Xiang, Y., Wu, G., Shen, X., Ma, Y., Gou, J., Xu, W., & Liu, J. (2021). Low-carbon economic dispatch of electricity-gas systems. Energy, 226, 120267.
  44. Xin-gang, Z., Ze-qi, Z., Yi-min, X., & Jin, M. (2020). Economic-environmental dispatch of microgrid based on improved quantum particle swarm optimization. Energy, 195, 117014.
  45. Xiong, G. & Shi, D. (2018). Hybrid biogeography-based optimization with brain storm optimization for non-convex dynamic economic dispatch with valve-point effects. Energy, 157, 424–435.
  46. Zare, M., Narimani, M. R., Malekpour, M., Azizipanah-Abarghooee, R., & Terzija, V. (2021). Reserve constrained dynamic economic dispatch in multi-area power systems: An improved fireworks algorithm. International Journal of Electrical Power & Energy Systems, 126, 106579.
  47. Zhang, H., Liang, S., Ou, M., & Wei, M. (2021). An asynchronous distributed gradient algorithm for economic dispatch over stochastic networks. International Journal of Electrical Power & Energy Systems, 124, 106240.
  48. Zhang, H., Yue, D., Xie, X., Dou, C., & Sun, F. (2017). Gradient decent based multi-objective cultural differential evolution for short-term hydrothermal optimal scheduling of economic emission with integrating wind power and photovoltaic power. Energy, 122, 748–766.

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