Journal of Energy Management and Technology

Journal of Energy Management and Technology

Analyzing the Effect of Wind Speed Correlation at Wind Farms on ED Using Copula Method

Document Type : Original Article

Author
Department of Electrical Engineering, Faculty of Electrical and Computer Engineering, Technical and Vocational University (TVU), Tehran, Iran.
Abstract
Along with increasing the wind power generation share in total generation capacity in power systems, maximum use of wind power generation capacity has been a major challenge for system operators. This is due to wind power generation is inherently uncontrollable and stochastic, and can notably affect the power systems operation. Therefore, the effect of wind power generations and especially their correlation on the power systems operation should be accurately studied and analyzed. Economic Dispatch (ED) is a proper tool to study the effect of wind power generations on the power systems operation.

In this paper, initially, wind speed is modeled and forecasted for a specific time. Then, correlation among wind farm generations is modeled and simulated using Copula method. Finally, the effect of wind power generations and correlation among them on ED quantities is investigated. The simulation results show that wind power generations and correlation among them can notably affect the ED quantities such as operational cost, power units’ generations and reserves, and wind generation curtailment. For instance, the absorbed wind power generation reduces and its curtailment increases. The simulations are implemented on the IEEE 30 buses test system with different load levels and different numbers, capacities and correlation intensities of wind farms installed in it. To solve the optimization problem of ED, the GA-RDPSO is proposed and used. The capability of this algorithm in finding the optimal solution for the ED problem is compared with the well-known optimizing algorithms of GA, PSO, RDPSO.
Keywords
Subjects

[1]     A. Q. Huang, "Renewable energy system research and education at the NSF FREEDM systems center," in 2009 IEEE Power & Energy Society General Meeting, IEEE, pp. 1-6, 2009.
[2]     M. A. Shirazi, S. M. Moezzi, N. Arzaghi, and H. Yousefi, "Solar Energy Development Trends and Climate Impacts on its Performance in Iran: A Comparative Analysis," Results in Engineering, vol. 30, p. 111229, 2026.
[3]     M. A. Allahrabbi Shirazi, A. Goldoust, M. Khatami, E. Abedi, and M. H. Janfeshan, "Modeling and simulation of a solar tracker with bifacial panel: a case study of Tehran city," Journal of Sustainable Energy Systems, vol. 3, no. 3, pp. 271-287, 2024.
[4]     R. S. M. A. Allah, "Idea generation and examination of environmental challenges of floating solar photovoltaic power plants on wetlands and its economic advantage for local communities," Journal of sustainable Energy Systems, vol. 3, no. 1, pp. 39-51, 2024.
[5]     J. F. Manwell, J. G. McGowan, and A. L. Rogers, Wind energy explained: theory, design and application. John Wiley & Sons, 2010.
[7]     L. Han, C. E. Romero, X. Wang, and L. Shi, "Economic dispatch considering the wind power forecast error," IET Generation, Transmission & Distribution, vol. 12, no. 12, pp. 2861-2870, 2018.
[8]     H. Lu, X. Gao, Z. Xu, H. Xiao, Y. Gao, H. Zhang, H. Ma, Y. Zhu, X. Zhu, and Y Wang, "Wind direction prediction combined with wind speed in a wind farm," Energy, vol. 333, p. 137334, 2025.
[9]     H. Liang, Y. Liu, Y. Shen, F. Li, and Y. Man, "A hybrid bat algorithm for economic dispatch with random wind power," IEEE Transactions on Power Systems, vol. 33, no. 5, pp. 5052-5061, 2018.
[10]   A. M. Shaheen, A. R. Ginidi, R. A. El-Sehiemy, and E. E. Elattar, "Optimal economic power and heat dispatch in Cogeneration Systems including wind power," Energy, vol. 225, p. 120263, 2021.
[11]   J. Wu, Y. Liu, X. Chen, C. Wang, and W. Li, "Data-driven adjustable robust Day-ahead economic dispatch strategy considering uncertainties of wind power generation and electric vehicles," International Journal of Electrical Power & Energy Systems, vol. 138, p. 107898, 2022.
[12]   H. Berahmandpour, S. M. Kouhsari, and H. Rastegar, "A new flexibility based probabilistic economic load dispatch solution incorporating wind power," International Journal of Electrical Power & Energy Systems, vol. 135, p. 107546, 2022.
[13]   Y. Zeng, C. Li, and H. Wang, "Scenario-set-based economic dispatch of power system with wind power and energy storage system," IEEE access, vol. 8, pp. 109105-109119, 2020.
[14]   X. Zhang, Z. Han, C. Zhao, and J. Zhong, "Multi‐objective economic dispatch of power system with wind farm considering flexible load response," International Journal of Energy Research, vol. 45, no. 6, pp. 8735-8748, 2021.
[15]   F. A. Gers, J. Schmidhuber, and F. Cummins, "Learning to forget: Continual prediction with LSTM," Neural computation, vol. 12, no. 10, pp. 2451-2471, 2000.
[16]   A. Graves, "Long short-term memory," Supervised sequence labelling with recurrent neural networks, pp. 37-45, 2012, (Book Chapter).
[17]   K. Yadav, P. Soram, S. Bijlwan, B. Goyal, A. Dogra, and D. C. Lepcha, "Dynamic economic load dispatch problem in power system using iterative genetic algorithm," in 2023 5th International Conference on Inventive Research in Computing Applications (ICIRCA), IEEE, pp. 1629-1632, 2023.
[18]   S. Sivanandam and S. Deepa, "Genetic algorithms," in Introduction to genetic algorithms: Springer, pp. 15-37, 2008.
[19]   J. Zhang, J. Zhang, F. Zhang, M. Chi, and L. Wan, "An improved symbiosis particle swarm optimization for solving economic load dispatch problem," Journal of Electrical and Computer Engineering, vol. 2021, no. 1, p. 8869477, 2021.
[20]   F. Marini and B. Walczak, "Particle swarm optimization (PSO). A tutorial," Chemometrics and intelligent laboratory systems, vol. 149, pp. 153-165, 2015.
[21]   J. Sun, V. Palade, X.-J. Wu, W. Fang, and Z. Wang, "Solving the power economic dispatch problem with generator constraints by random drift particle swarm optimization," IEEE Transactions on Industrial Informatics, vol. 10, no. 1, pp. 222-232, 2013.
[22]   A. Patton, "Copula methods for forecasting multivariate time series," Handbook of economic forecasting, vol. 2, pp. 899-960, 2013.
[23]   M. Xie, J. Xiong, S. Ke, and M. Liu, "Two-stage compensation algorithm for dynamic economic dispatching considering copula correlation of multiwind farms generation," IEEE Transactions on Sustainable Energy, vol. 8, no. 2, pp. 763-771, 2016.
[24]   J. Zhang, M. Zhang, H. Liu, and H. Wang, "Bayesian updating for Copula-based joint probability modeling of wind speed, wind direction, and air temperature under parameter uncertainty," Probabilistic Engineering Mechanics, vol. 85, p. 103985, 2026.
[25]   A. B. Kunya, A. S. Abubakar, and S. S. Yusuf, "Review of economic dispatch in multi-area power system: State-of-the-art and future prospective," Electric Power Systems Research, vol. 217, p. 109089, 2023.
[27]   "http://www.mathpower.com." (accessed).
[28]   A. Saifoddin, N. Mirzaei, M. Allahrabbi Shirazi, and H. Yousefi, "Comparative Applications of Supervised and Unsupervised Machine Learning Models in Energy Systems," Journal of Energy Management and Technology, vol. 9, no. 4, pp. 284-290, 2025.
[29]   A. Naziri, A. R. Tahavvor, M. A. Shirazi, and R. Zahedi, "Feasibility study on heat recovery from gas turbine exhaust for absorption chiller operation and efficiency enhancement using neural networks," Thermal Science and Engineering Progress, vol. 67, p. 104210, 2025.
[30]   P. K. Pathak, A. K. Yadav, R. Abbassi, and S. Mirjalili, "Metaheuristics-Driven Smart Grid for Economic Dispatch and Optimal Power Flow Solutions: A Critical Review: PK Pathak et al," Archives of Computational Methods in Engineering, vol. 33, no. 1, pp. 917-961, 2026.
Volume 10, Issue 2
Spring 2026
Pages 144-155

  • Receive Date 22 April 2026
  • Revise Date 06 August 2026
  • Accept Date 15 August 2026