Electricity Generation Cost Optimization Based on Lagrange Function and Local Search
DOI:
https://doi.org/10.33633/jcta.v1i2.9354Keywords:
Renewable energies, Optimal generation dispatch, Lagrange function, Multiple fuels, Wind power, Solar powerAbstract
This paper proposes a method based on the Lagrange optimization function and local search technique for minimizing the total cost of two power systems. The first system comprises ten multiple fuel thermal units (MFTUs) while the second system combines the first system with renewable energies, solar and wind power. The proposed method has advantages over its conventional method without a local search technique, called the conventional Lagrange function-based method (CLM), such as having the same parameters and exploiting other search spaces after getting convergence. The proposed method is more effective than CLM for the first system with the last case of load demand. In addition, the proposed method has better costs than previous algorithms, such as the Hierarchical numerical method (HNUM), Hopfield neural network, Adaptive Hopfield neural networks (AHNN) and modified Lagrange neural network (MLANN). Especially, the proposed method can find smaller costs than them, up to $6.78, corresponding to 1.4% for Case 1, and up to $2.43, corresponding to 0.4% for Case 4. Only the proposed method is tested on the second test system. The simulation results indicate that the method is very efficient for the problem with solar and wind energies and multiple fuel thermal units.References
A. Naresh Kumar and D. Suchitra, “AI based Economic Load Dispatch incorporating wind power penetration,” in Proceedings of the 2011 International Conference on Electrical Engineering and Informatics, Jul. 2011, pp. 1–8. doi: 10.1109/ICEEI.2011.6021520.
Z.-X. Liang and J. D. Glover, “A zoom feature for a dynamic programming solution to economic dispatch including transmission losses,” IEEE Trans. Power Syst., vol. 7, no. 2, pp. 544–550, May 1992, doi: 10.1109/59.141757.
N. Noman and H. Iba, “Differential evolution for economic load dispatch problems,” Electr. Power Syst. Res., vol. 78, no. 8, pp. 1322–1331, Aug. 2008, doi: 10.1016/j.epsr.2007.11.007.
K. P. Wong and Y. W. Wong, “Genetic and genetic/simulated-annealing approaches to economic dispatch,” IEE Proc. - Gener. Transm. Distrib., vol. 141, no. 5, p. 507, 1994, doi: 10.1049/ip-gtd:19941354.
S. C. Lee and Y. H. Kim, “An enhanced Lagrangian neural network for the ELD problems with piecewise quadratic cost functions and nonlinear constraints,” Electr. Power Syst. Res., vol. 60, no. 3, pp. 167–177, Jan. 2002, doi: 10.1016/S0378-7796(01)00181-X.
J.-B. Park, K.-S. Lee, J.-R. Shin, and K. Y. Lee, “A Particle Swarm Optimization for Economic Dispatch With Nonsmooth Cost Functions,” IEEE Trans. Power Syst., vol. 20, no. 1, pp. 34–42, Feb. 2005, doi: 10.1109/TPWRS.2004.831275.
R. Balamurugan and S. Subramanian, “Self-Adaptive Differential Evolution Based Power Economic Dispatch of Generators with Valve-Point Effects and Multiple Fuel Options,” Int. J. Electr. Comput. Eng., vol. 1, pp. 543–550, 2007.
V. N. Dieu and W. Ongsakul, “Economic Dispatch with Multiple Fuel Types by Enhanced Augmented Lagrange Hopfield Network,” in 2008 Joint International Conference on Power System Technology and IEEE Power India Conference, Oct. 2008, pp. 1–8. doi: 10.1109/ICPST.2008.4745336.
N. Noman and H. Iba, “Differential evolution for economic load dispatch problems,” Electr. Power Syst. 2008, 78, 1322–1331. doi: 10.1016/j.epsr.2007.11.007.
M. Said, E. H. Houssein, S. Deb, R. M. Ghoniem and A. G. Elsayed, “Economic Load Dispatch Problem Based on Search and Rescue Optimization Algorithm,” IEEE Access 2022, 10, 47109–47123. doi: 10.1109/ACCESS.2022.3168653.
W. K. Hao, J. S. Wang, X. D. Li, M. Wang, and M. Zhang, “Arithmetic optimization algorithm based on elementary function disturbance for solving economic load dispatch problem in power system,” Appl. Intell. 2022, 52, 11846–11872. doi: 10.1007/s10489-021-03125-4.
B. Dai, F. Wang, and Y. Chang, “Multi-objective economic load dispatch method based on data mining technology for large coal-fired power plants,” Control Eng. Pract. 2022, 121, 105018. doi: 10.1016/j.conengprac.2021.105018.
A. S. Alghamdi, “Greedy Sine-Cosine Non-Hierarchical Grey Wolf Optimizer for Solving Non-Convex Economic Load Dispatch Problems,” Energies 2022, 15, 3904. doi: 10.3390/en15113904.
M. A. Al-Betar, M. A. Awadallah, and S. N. Makhadmeh, I. Abu Doush, R. Abu Zitar, S. Alshathri, M.A. Elaziz, “A hybrid Harris Hawks optimizer for economic load dispatch problems,” Alex. Eng. J. 2023, 64, 365–389. doi: 10.1016/j.aej.2022.09.010.
M. H. Hassan, S. Kamel, A. Eid, L. Nasrat, F. Jurado, and M. F. Elnaggar, “A developed eagle-strategy supply-demand optimizer for solving economic load dispatch problems,” Ain Shams Eng. J. 2023, 14, 32–46. doi:10.1016/j.asej.2022.102083.
T. C. Tai, C. C. Lee, and C. C. Kuo, “A Hybrid Grey Wolf Optimization Algorithm Using Robust Learning Mechanism for Large Scale Economic Load Dispatch with Vale-Point Effect,” Appl. Sci. 2023, 13, 2727. doi: 10.3390/app13042727.
X.-Y. Zhang, W.-K. Hao, J.-S. Wang, J.-H. Zhu, X.-R. Zhao and Y. Zheng, “Manta ray foraging optimization algorithm with mathematical spiral foraging strategies for solving economic load dispatching problems in power systems,” Alex. Eng. J. 2023, 70, 613–640. doi: 10.1016/j.aej.2023.03.017.
C.E. Lin and G.L. Viviani, "Hierarchical economic dispatch for piecewise quadratic cost functions," IEEE Trans. Power Apparatus and Systems, vol. PAS-103, pp. 1170-1175, 1984. doi: 10.1109/TPAS.1984.318445.
J.H. Park, Y.S. Kim, I.K. Eom, and K.Y. Lee, "Economic load dispatch for piecewise quadratic cost function using Hopfield neural network," IEEE Trans. Power Systems, vol. 8, pp. 1030-1038, 1993. doi: 10.1109/59.260897.
K.Y. Lee, A. Sode-Yome, and J.H. Park, "Adaptive Hopfield neural networks for economic load dispatch," IEEE Trans. Power Systems, vol. 13, pp. 519-526, 1998. doi: 10.1109/59.667377.
R. Wang, T. Xu and H. Xu, “Robust multi-objective load dispatch in microgrid involving unstable renewable generation,” Int. J. Electr. Power Energy Syst. 2023, 148, 137–149. doi: 10.1016/j.ijepes.2023.108991.
A. Potfode and S. Bhongade, (2022). “Economic Load Dispatch of Renewable Energy Integrated System Using Jaya? Algorithm,” Journal of Operation and Automation in Power Engineering, 10(1), 1-12. doi: 10.22098/joape.2022.7562.1538.
T. T. Nguyen, H. D. Nguyen, and M. Q. Duong, “Optimal Power Flow Solutions for Power System Considering Electric Market and Renewable Energy,” Appl. Sci., vol. 13, no. 5, p. 3330, Mar. 2023, doi: 10.3390/app13053330.
L. H. Pham, B. H. Dinh, and T. T. Nguyen, “Optimal power flow for an integrated wind-solar-hydro-thermal power system considering uncertainty of wind speed and solar radiation,” Neural Comput. Appl., vol. 34, no. 13, pp. 10655–10689, Jul. 2022, doi: 10.1007/s00521-022-07000-2.
N. T. Thang, “Solving Economic Dispatch Problem with Piecewise Quadratic Cost Functions Using Lagrange Multiplier Theory,” in International Conference on Computer Technology and Development, 3rd (ICCTD 2011), ASME Press, 2011, pp. 359–363. doi: 10.1115/1.859919.paper62.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Nguyen Van Thanh
This work is licensed under a Creative Commons Attribution 4.0 International License.
