“On the Necessity of Dynamic Inflow”
Authors: Finn Matras and Morten D. Pedersen,Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2024, Vol 45, No 1, pp. 29-39.
Keywords: scaling, eigenvalues, time constants, wind turbine
Abstract: This work explores the importance of dynamic inflow for wind turbines of varying rotor radius and also includes various coplanar multirotor setups. A parametrized model including the rotor and inflow dynamics is formulated. Typical values and ranges for the parameters are estimated using theoretical results and empirical data. The model is analyzed in terms of the kinetic energy and its dynamic responses. By analyzing the ratio of kinetic energy in the rotor vs. induced flow, we obtain a scalar measure for the relative importance of the dynamic inflow. Furthermore, the linearized closed-loop dynamics of a wind turbine around its optimum are examined in terms of the eigenvalues and time constants. This gives insights into the stability and control requirements for wind turbine systems. The results show that dynamic inflow should be included in wind turbine modeling and control of most wind turbines, and can only be ignored for small isolated rotors.
PDF (550 Kb) DOI: 10.4173/mic.2024.1.3
DOI forward links to this article:
[1] Finn Matras, Frida Xiang Nordas Arsandoy and Morten D. Pedersen (2024), doi:10.1109/CoDIT62066.2024.10708188 |
[1] Ashwill, T. (2006). Blade Technology Innovations for Utility-Scale Turbines, 2006.
[2] Bakırcı, M. and Yılmaz, S. (2018). Theoretical and computational investigations of the optimal tip-speed ratio of horizontal-axis wind turbines, Engineering Science and Technology, an International Journal, 2018. 21(6):1128--1142. doi:https://doi.org/10.1016/j.jestch.2018.05.006
[3] Bashetty, S. and Ozcelik, S. (2021). Review on dynamics of offshore floating wind turbine platforms, Energies. 14(19). doi:10.3390/en14196026
[4] Batchelor, G.K. (1967). An introduction to fluid dynamics, Cambridge mathematical library. Cambridge University Press, Cambridge.
[5] Canet, H., Bortolotti, P., and Bottasso, C.L. (2021). On the scaling of wind turbine rotors, Wind Energy Science. 6(3):601--626. doi:10.5194/wes-6-601-2021
[6] Conway, J.T. (1995). Analytical solutions for the actuator disk with variable radial distribution of load, Journal of Fluid Mechanics. 297:327–355. doi:10.1017/S0022112095003120
[7] Crawford, C.A. (2011). The Path From Functional to Detailed Design of a Coning Rotor Wind Turbine Concept, Proceedings of the Canadian Engineering Education Association (CEEA). doi:10.24908/pceea.v0i0.3768
[8] Griffith, D. and Richards, P. (2014). The SNL100-03 Blade: Design Studies with Flatback Airfoils for the Sandia 100-meter Blade, Technical Report SAND2014-18129, 1159116, 537751.
[9] Henriksen, L., Hansen, M., and Poulsen, N. (2012). Beyond the cp-curve in model-based control of wind turbines, European Wind Energy Conference and Exhibition 2012, EWEC 2012. 1:143--152.
[10] Henriksen, L.C., Hansen, M.H., and Poulsen, N.K. (2013). A simplified dynamic inflow model and its effect on the performance of free mean wind speed estimation, Wind Energy. 16(8):1213--1224. doi:https://doi.org/10.1002/we.1548
[11] Hutchinson, M. and Zhao, F. (2023). Global wind report 2023, Technical report. https://gwec.net/wp-content/uploads/2023/03/GWR-2023_interactive.pdf.
[12] Istabreeze. (2023). Blades of wind generators, https://istabreeze.us/wind-generators-accessories/blades-of-wind-generators/, 2023. [Online; accessed 10-October-2.
[13] Johnson, K., Pao, L., Balas, M., and Fingersh, L. (2006). Control of variable-speed wind turbines: standard and adaptive techniques for maximizing energy capture, IEEE Control Systems Magazine. 26(3):70--81. doi:10.1109/MCS.2006.1636311
[14] Jonkman, J., Butterfield, S., Musial, W., and Scott, G. (2009). Definition of a 5MW reference wind turbine for offshore system development, Technical report, National Renewable Energy Laboratory (NREL).
[15] Mancini, S., Boorsma, K., Schepers, G., and Savenije, F. (2023). A comparison of dynamic inflow models for the blade element momentum method, Wind Energy Science. 8(2):193--210. doi:10.5194/wes-8-193-2023
[16] Manwell, J., McGowan, J., and Rogers, A. (2002). Wind Energy Explained, John Wiley & Sons, Ltd, Chichester, UK. doi:10.1002/0470846127
[17] More, A. and Roy, A. (2020). Design and Weight Minimization of Small Wind Turbine Blade for Operation in Low-Wind Areas, In S.Singh and V.Ramadesigan, editors, Advances in Energy Research, Vol. 2, pages 311--322. Springer Singapore, Singapore. Series Title: Springer Proceedings in Energy. doi:10.1007/978-981-15-2662-6_29
[18] Novaes Menezes, E.J., Araujo, A.M., and Bouchonneau da Silva, N.S. (2018). A review on wind turbine control and its associated methods, Journal of Cleaner Production. 174:945--953. doi:https://doi.org/10.1016/j.jclepro.2017.10.297
[19] Odgaaard, P.F., Knudsen, T., Overgaard, A., Steffensen, H., and Jørgensen, M. (2015). Importance of dynamic inflow in model predictive control of wind turbines, IFAC-PapersOnLine. 48(30):90--95. 9th IFAC Symposium on Control of Power and Energy Systems CPES 2015. doi:https://doi.org/10.1016/j.ifacol.2015.12.359
[20] Pao, L.Y. and Johnson, K.E. (2009). A tutorial on the dynamics and control of wind turbines and wind farms, In 2009 American Control Conference. pages 2076--2089. doi:10.1109/ACC.2009.5160195
[21] Papi, F., Jonkman, J., Robertson, A., and Bianchini, A. (2023). Going beyond bem with bem: an insight into dynamic inflow effects on floating wind turbines, Wind Energy Science Discussions. 2023:1--29. doi:10.5194/wes-2023-109
[22] Peters, D.A. (2009). How dynamic inflow survives in the competitive world of rotorcraft aerodynamics, Journal of the American Helicopter Society. 54(1).
[23] Rinker, J. and Dykes, K. (2018). WindPACT Reference Wind Turbines, Technical Report NREL/TP--5000-67667, 1432194.
[24] Tang, C., Pathmanathan, M., Soong, W.L., and Ertugrul, N. (2008). Effects of Inertia on Dynamic Performance of Wind Turbines, Australasian Universities Power Engineering Conference.
[25] Zhang, Y., Cai, X., Lin, S., Wang, Y., and Guo, X. (2022). Cfd simulation of co-planar multi-rotor wind turbine aerodynamic performance based on alm method, Energies. 15(17). doi:10.3390/en15176422
BibTeX:
@article{MIC-2024-1-3,
title={{On the Necessity of Dynamic Inflow}},
author={Matras, Finn and Pedersen, Morten D.},
journal={Modeling, Identification and Control},
volume={45},
number={1},
pages={29--39},
year={2024},
doi={10.4173/mic.2024.1.3},
publisher={Norwegian Society of Automatic Control}
};