Weibull-based Wind Cost Modeling in Dynamic Optimal Power Flow with Carbon Tax Considerations
Received: 28 March 2025 | Revised: 21 April 2025 | Accepted: 4 May 2025 | Online: 4 June 2025
Corresponding author: Adi Soeprijanto
Abstract
In the transition toward sustainable energy, economic optimization of power systems remains a critical challenge, particularly due to the variability of renewable energy sources, such as wind. By addressing the limitations of earlier research, which frequently make the assumption that wind speed is fixed, this article aims to determine a more realistic estimation of the Levelized Cost of Energy (LCOE) for wind power. In order to accomplish this, a Dynamic Optimal Power Flow (DOPF) framework is proposed, which incorporates carbon tax compensation and wind power cost modeling using a probabilistic Weibull distribution as its basis that represents wind speed variability. This approach leads to a more natural and representative estimation of annual wind energy production compared to conventional deterministic models. The DOPF problem is applied to a modified IEEE 30-bus system with integrated wind farms and is solved using the Improved Whale Optimization Algorithm (IWOA). According to the simulation results, the proposed Weibull-based LCOE formulation more accurately captures wind conditions in the real world. In comparison to the traditional LCOE approach, the introduced model lowers the overall generation cost by about 10,500 $/day under a carbon tax scenario of 50 $/MWh. This illustrates how enacting a carbon tax improves wind energy's economic competitiveness while simultaneously promoting emissions reduction. This study offers a fresh and thorough modeling framework that better captures wind energy costs in practical settings, assisting in the implementation of low-carbon policies and the development of optimal dispatch plans.
Keywords:
dynamic optimal power flow, Weibull, levelized cost of energy, wind energy, improved whale optimization algorithmDownloads
References
Y. J. Chen, N. Chindarkar, and Y. Xiao, "Effect of reliable electricity on health facilities, health information, and child and maternal health services utilization: evidence from rural Gujarat, India," Journal of Health, Population and Nutrition, vol. 38, no. 1, Feb. 2019, Art. no. 7. DOI: https://doi.org/10.1186/s41043-019-0164-6
P. Kwakwa, "Disaggregated Energy Consumption and Economic Growth in Ghana, " International Journal of Energy Economics and Policy, vol. 2, pp. 34–40, Jan. 2011.
A. A. Rafindadi, "Econometric Prediction on the Effects of Financial Development and Trade Openness on the German Energy Consumption: A Startling Revelation from the Data Set," International Journal of Energy Economics and Policy, vol. 5, no. 1, pp. 182–196, Dec. 2014.
M. R. Alam, M. St-Hilaire, and T. Kunz, "Peer-to-peer energy trading among smart homes," Applied Energy, vol. 238, pp. 1434–1443, Mar. 2019. DOI: https://doi.org/10.1016/j.apenergy.2019.01.091
H. S. Salama and I. Vokony, "Voltage and Frequency Control of Balanced/Unbalanced Distribution System Using the SMES System in the Presence of Wind Energy," Electricity, vol. 2, no. 2, pp. 205–224, Jun. 2021. DOI: https://doi.org/10.3390/electricity2020013
A. M. Ilyas, A. Suyuti, I. C. Gunadin, and S. M. Said, "Optimal Power Flow Model Integrated Electric Power System with Wind Power Generation - Case Study: Electricity System South Sulawesi-Indonesia," International Journal of Intelligent Engineering and Systems, vol. 15, no. 4, pp. 415–425, 2022. DOI: https://doi.org/10.22266/ijies2022.0831.37
M. Basu, "Dynamic optimal power flow for isolated microgrid incorporating renewable energy sources," Energy, vol. 264, Feb. 2023, Art. no. 126065. DOI: https://doi.org/10.1016/j.energy.2022.126065
H. R. E. H. Bouchekara, M. A. Abido, A. E. Chaib, and R. Mehasni, "Optimal power flow using the league championship algorithm: A case study of the Algerian power system," Energy Conversion and Management, vol. 87, pp. 58–70, Nov. 2014. DOI: https://doi.org/10.1016/j.enconman.2014.06.088
S. Gill, I. Kockar, and G. W. Ault, "Dynamic Optimal Power Flow for Active Distribution Networks," IEEE Transactions on Power Systems, vol. 29, no. 1, pp. 121–131, Jan. 2014. DOI: https://doi.org/10.1109/TPWRS.2013.2279263
P. Chen, X. Xiao, and X. Wang, "Dynamic optimal power flow model incorporating interval uncertainty applied to distribution network, " IET Generation, Transmission & Distribution, vol. 12, no. 12, pp. 2926–2936, 2018. DOI: https://doi.org/10.1049/iet-gtd.2017.1874
B. Thomas, X. Costoya, M. deCastro, G. Iglesias, and M. Gómez-Gesteira, "Levelized cost of energy for various floating offshore wind farm designs in the areas covered by the Spanish maritime spatial planning," Applied Energy, vol. 381, Mar. 2025, Art. no. 125165. DOI: https://doi.org/10.1016/j.apenergy.2024.125165
H. Klinge Jacobsen, P. Hevia-Koch, and C. Wolter, "Nearshore and offshore wind development: Costs and competitive advantage exemplified by nearshore wind in Denmark," Energy for Sustainable Development, vol. 50, pp. 91–100, Jun. 2019. DOI: https://doi.org/10.1016/j.esd.2019.03.006
J. P. Arenas-López and M. Badaoui, "The levelized cost of energy in the presence of uncertainty on the offshore wind speed," Heliyon, vol. 11, no. 2, Jan. 2025, Art. no. e41818. DOI: https://doi.org/10.1016/j.heliyon.2025.e41818
Y. Kassem, H. Camur, and A. A. S. Mosbah, "Feasibility Analysis of the Wind Energy Potential in Libya using the RETScreen Expert," Engineering, Technology & Applied Science Research, vol. 13, no. 4, pp. 11277–11289, Aug. 2023. DOI: https://doi.org/10.48084/etasr.6007
T. L. Duong and T. T. Nguyen, "Application of Sunflower Optimization Algorithm for Solving the Security Constrained Optimal Power Flow Problem," Engineering, Technology & Applied Science Research, vol. 10, no. 3, pp. 5700–5705, Jun. 2020. DOI: https://doi.org/10.48084/etasr.3511
K. Widarsono, A. Soeprijanto, and R. S. Wibowo, "Improved Whale Optimization Algorithm for Dynamic Optimal Power Flow with Renewable Energy Penetration," Engineering, Technology & Applied Science Research, vol. 15, no. 1, pp. 20379–20387, Feb. 2025. DOI: https://doi.org/10.48084/etasr.9662
J. Black, N. Hashimzade, and G. D. Myles, A Dictionary of Economics, 5th ed. Oxford, UK, England: Oxford University Press, 2017. DOI: https://doi.org/10.1093/acref/9780198759430.001.0001
A. Martinez and G. Iglesias, "Mapping of the levelised cost of energy for floating offshore wind in the European Atlantic," Renewable and Sustainable Energy Reviews, vol. 154, Feb. 2022, Art. no. 111889. DOI: https://doi.org/10.1016/j.rser.2021.111889
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