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On the Aggregated Modelling of Large-Scale Wind Farms for Harmonic Studies

A. Bracale(1), P. Caramia(1), R. Langella(2), P. Varilone(3) and P. Verde(3)

1. Department of Engineering, University of Naples Parthenope, Naples (Italy)

2. Department of Engineering University of Campania Aversa, Italy

3. Dep. of Electrical and Information Engineering & DIAEE
University of Cassino and Lazio Meridionale & La Sapienza Università di Roma, Cassino (Italy)

2026-02-15

In this paper, the aggregated modelling of large-scalewind farms for harmonic studies is considered. The limitations of the harmonic emission assessment based on the IEC 61000-3-6 summation rule are analysed in a probabilistic framework. An iterative probabilistic procedure based on the Quasi Monte Carlo technique is proposed and applied to a simplified electromagnetic transient model of an exemplary wind power plant. Then, detailed results obtained are used to quantify the above mentioned limitations of the summation rule.

Key words: Aggregated Inverter-Based Resources, Harmonics,IEC summation rule, IEEE St. P2800, Power Quality.

[1] IEEE Std. 1547.1-2020 “Conformance Test Procedures for Equipment Interconnecting Distributed Energy Resources
with Electric Power Systems and Associated Interfaces," May 2020.

[2] IEEE Std. 2800-2022, “Interconnection and Interoperability of Inverter-Based Resources (IBRs) Interconnecting with
Associated Transmission Electric Power Systems”, April 2022.

[3] J. Arrillaga and N.R. Watson, “Power System Harmonics” published by Wiley, 2003.

[4] IEEE Harmonics Modeling and Simulation TF, “Characteristics and modeling of harmonic sources - power electronic devices," IEEE Trans. on Power Delivery, vol. 16, no. 4, pp. 791-800, Oct. 2001.

[5] CIGRE TB 766 “Network modelling for harmonic studies”, by JWG C4/B4.38. April 2019.

[6] A. Božiček, J. Kilter, T. Sarnet, I. Papič and B. Blažič, "Harmonic Emissions of Power Electronic Devices Under Different Transmission Network Operating Conditions," in IEEE Transactions on Industry Applications, vol. 54, no. 5, pp. 5216-5226, Sept.-Oct. 2018.

[7] W. Xu, R. Langella, A. Bracale; Y. Sun; K. L. Lian, Y. Wang, “Modeling of Inverter-Based Resources for Power System Harmonics Studies,” in IEEE Transactions on Power Delivery, vol. 40, no. 1, pp. 166-177, Feb. 2025, doi: 10.1109/TPWRD.2024.

[8] Y. Baghzouz et al., "Time-varying harmonics. II. Harmonic summation and propagation," in IEEE Transactions on Power Delivery, vol. 17, no. 1, pp. 279-285, Jan. 2002.

[9] IEC, “Electromagnetic compatibility, limits – assessment of emission limits for the connection of distorting installations to MV, HV and EHV power systems,” Tech. Rep. TR 61000-3-6, 2008.

[10] Xiao, Y.; Yang, X., "Harmonic Summation and Assessment Based on Probability Distribution," IEEE Transactions on Power Delivery, vol.27, no.2, pp.1030,1032, April 2012.

[11] K.L. Koo, Z. Emin, “Comparative evaluation of power quality modelling approaches for offshore wind farms”, 5th IET International Conference on Renewable Power Generation (RPG) 2016, 2016 p. 52 (7).

[12] L. Shuai ,Ł. H. Kocewiak, K. H. Jensen, "Application of Type 4 Wind Turbine Harmonic Model for Wind Power Plant Harmonic Study", Int.WS on Large-Scale Integration of Wind Power into Power Systems, and Transmission Networks for Offshore Wind Farms, Vienna, 2016.

[13] M. Eltouki, T. W. Rasmussen, E. Guest, L. Shuai, Ł. Kocewiak. “Analysis of Harmonic Summation in Wind Power Plants Based on Harmonic Phase Modelling and Measurements”. 17th Wind Integration Workshop. 17 - 19 October 2018. Stockholm, Sweden.

[14] CIGRE TB 672 “Power Quality Aspects of Solar Power”, by JWG C4/C6.29. December 2016.

[15] J. David, D. Robinson and S. Elphick, "Aggregation of multiple inverter-based harmonic sources within a renewable energy generation plant," 2022 20th International Conference on Harmonics & Quality of Power (ICHQP), Naples, Italy, 2022, pp. 1-6.

[16] R. Salles, M. Silva, P. Ribeiro, “Observations on Harmonics Summation in Transmission Systems: Alternative Aggregation Estimation”, International Transactions on Electrical Energy Systems, 2022, 5313417, 13 pages, 2022.

[17] H. Zong, J. Lyu, X. Cai, C. Zhang, M. Molinas, F. Rao, “Accurate aggregated modelling of wind farm systems in modified sequence domain for stability analysis”, Electric Power Systems Research, Volume 175, 2019.

[18] Y. C. Hung, “A review of Monte Carlo and quasi-Monte Carlo sampling techniques,” Wiley Interdisciplinary Reviews: Computational Statistics. John Wiley and Sons Inc, 2023.

[19] IM. Sobol Distribution of points in a cube and approximate evaluation of integrals. U.S.S.R. Comput. Maths. Maqth. Phys. 7, 86-112, 196

[20] A. Bracale, M. Ishaq and R. Langella, " Norton Based Modelling Techniques for Assessing the Harmonic Emissions of Inverter Based Resources," 2024 International Conference on Harmonic & Quality of Power (ICHQP), China, 2024, pp. 1-6.

[21] Bracale, A., Caramia, P., Carpinelli, G., & Falco, P. D. (2020). Day-ahead probabilistic wind power forecasting based on ranking and combining NWPs. International Transactions on Electrical Energy Systems, 30(7).

[22] "IEEE Standard for Harmonic Control in Electric Power Systems," in IEEE Std 519-2022, vol., no., pp.1-31, 5 Aug. 2022

[23] B. Zou and Q. Xiao, "Solving Probabilistic Optimal Power Flow Problem Using Quasi Monte Carlo Method and Ninth-Order Polynomial Normal Transformation," in IEEE Transactions on Power Systems, vol. 29, no. 1, pp. 300-306, Jan. 2014.

[24] A. Bracale, P. Caramia, G.M. Casolino, P. De Falco, I. Hussain, P. Varilone, and P. Verde, “On the global harmonic and supraharmonic emission of an electric vehicle charging station: investigation of aggregation and diversity,” 2023 ICCEP, June 2023, pp. 858-863

[25] A. Bracale et al., "Harmonic and Supra-Harmonic Emissions of Electric Vehicle Chargers: Modeling and Cumulative Impact Indices," in IEEE Open Access Journal of Power and Energy, vol. 11, pp. 690-702, 2024, doi: 10.1109/OAJPE.2024.3521030.