Articles | Volume 9, issue 4
https://doi.org/10.5194/wes-9-841-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/wes-9-841-2024
© Author(s) 2024. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Control-oriented modelling of wind direction variability
Wind and Marine Energy Systems and Structures, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, United Kingdom
Adam Stock
Institute of Mechanical, Processes and Energy Engineering, School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, United Kingdom
Edward Hart
Wind Energy and Control Centre, Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, United Kingdom
Related authors
No articles found.
Edward Hart
Wind Energ. Sci., 10, 1821–1827, https://doi.org/10.5194/wes-10-1821-2025, https://doi.org/10.5194/wes-10-1821-2025, 2025
Short summary
Short summary
A parametric model for the wind direction rose is presented, with testing on real offshore wind farm data indicating that the model performs well. The presented model provides opportunities for standardisation and enables more systematic analyses of wind direction distribution impacts and sensitivities.
Julian Quick, Edward Hart, Marcus Binder Nilsen, Rasmus Sode Lund, Jaime Liew, Piinshin Huang, Pierre-Elouan Rethore, Jonathan Keller, Wooyong Song, and Yi Guo
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-63, https://doi.org/10.5194/wes-2025-63, 2025
Revised manuscript under review for WES
Short summary
Short summary
Wind turbine main bearings often fail prematurely, creating costly maintenance challenges. This study examined how wake effects – where upstream turbines create disturbed airflow that impacts downstream turbines – affect bearing lifespans. Using computer simulations, we found that wake effects reduce bearing life by 16% on average. The direction of wake impact matters significantly due to interactions between wind forces and gravity, informing better wind turbine and farm farm design strategies.
Piotr Fojcik, Edward Hart, and Emil Hedevang
Wind Energ. Sci. Discuss., https://doi.org/10.5194/wes-2025-17, https://doi.org/10.5194/wes-2025-17, 2025
Revised manuscript accepted for WES
Short summary
Short summary
Increasing the efficiency of wind farms can be achieved via reducing the impact of wakes: flow regions with lower wind speed occurring downwind from turbines. This work describes training and validation of a novel method for estimation of the wake effects impacting a turbine. The results show that for most tested wind conditions, the developed model is capable of robust detection of wake presence, and accurate characterisation of its properties. Further validation and improvements are planned.
Edward Hart, Elisha de Mello, and Rob Dwyer-Joyce
Wind Energ. Sci., 7, 1533–1550, https://doi.org/10.5194/wes-7-1533-2022, https://doi.org/10.5194/wes-7-1533-2022, 2022
Short summary
Short summary
This paper is the second in a two-part study on lubrication in wind turbine main bearings. Investigations are conducted concerning lubrication in the double-row spherical roller main bearing of a 1.5 MW wind turbine. This includes effects relating to temperature, starvation, grease-thickener interactions and possible non-steady EHL effects. Results predict that the modelled main bearing would be expected to operate under mixed lubrication conditions for a non-negligible proportion of its life.
Edward Hart, Adam Stock, George Elderfield, Robin Elliott, James Brasseur, Jonathan Keller, Yi Guo, and Wooyong Song
Wind Energ. Sci., 7, 1209–1226, https://doi.org/10.5194/wes-7-1209-2022, https://doi.org/10.5194/wes-7-1209-2022, 2022
Short summary
Short summary
We consider characteristics and drivers of loads experienced by wind turbine main bearings using simplified models of hub and main-bearing configurations. Influences of deterministic wind characteristics are investigated for 5, 7.5, and 10 MW turbine models. Load response to gusts and wind direction changes are also considered. Cubic load scaling is observed, veer is identified as an important driver of load fluctuations, and strong links between control and main-bearing load response are shown.
Edward Hart, Elisha de Mello, and Rob Dwyer-Joyce
Wind Energ. Sci., 7, 1021–1042, https://doi.org/10.5194/wes-7-1021-2022, https://doi.org/10.5194/wes-7-1021-2022, 2022
Short summary
Short summary
This work provides an accessible introduction to elastohydrodynamic lubrication theory as a precursor to analysis of lubrication in a wind turbine main bearing. Fundamental concepts, derivations and formulas are presented, followed by the more advanced topics of starvation, non-steady effects, surface roughness interactions and grease lubrication.
Amir R. Nejad, Jonathan Keller, Yi Guo, Shawn Sheng, Henk Polinder, Simon Watson, Jianning Dong, Zian Qin, Amir Ebrahimi, Ralf Schelenz, Francisco Gutiérrez Guzmán, Daniel Cornel, Reza Golafshan, Georg Jacobs, Bart Blockmans, Jelle Bosmans, Bert Pluymers, James Carroll, Sofia Koukoura, Edward Hart, Alasdair McDonald, Anand Natarajan, Jone Torsvik, Farid K. Moghadam, Pieter-Jan Daems, Timothy Verstraeten, Cédric Peeters, and Jan Helsen
Wind Energ. Sci., 7, 387–411, https://doi.org/10.5194/wes-7-387-2022, https://doi.org/10.5194/wes-7-387-2022, 2022
Short summary
Short summary
This paper presents the state-of-the-art technologies and development trends of wind turbine drivetrains – the energy conversion systems transferring the kinetic energy of the wind to electrical energy – in different stages of their life cycle: design, manufacturing, installation, operation, lifetime extension, decommissioning and recycling. The main aim of this article is to review the drivetrain technology development as well as to identify future challenges and research gaps.
James Stirling, Edward Hart, and Abbas Kazemi Amiri
Wind Energ. Sci., 6, 15–31, https://doi.org/10.5194/wes-6-15-2021, https://doi.org/10.5194/wes-6-15-2021, 2021
Short summary
Short summary
This paper considers the modelling of wind turbine main bearings using analytical models. The validity of simplified analytical representations is explored by comparing main-bearing force reactions with those obtained from higher-fidelity 3D finite-element models. Results indicate that good agreement can be achieved between the analytical and 3D models in the case of both non-moment-reacting (such as for a spherical roller bearing) and moment-reacting (such as a tapered roller bearing) set-ups.
Cited articles
Andrade, J. R. and Bessa, R. J.: Improving renewable energy forecasting with a grid of numerical weather predictions, IEEE T. Sustain. Energ., 8, 1571–1580, https://doi.org/10.1109/TSTE.2017.2694340, 2017. a
Annoni, J., Bay, C., Taylor, T., Pao, L., Fleming, P., and Johnson, K.: Efficient optimization of large wind farms for real-time control, in: 2018 Annual American Control Conference (ACC), Milwaukee, 27–29 June 2018, 6200–6205, IEEE, https://doi.org/10.23919/ACC.2018.8430751, 2018a. a
Annoni, J., Fleming, P., Scholbrock, A., Roadman, J., Dana, S., Adcock, C., Porte-Agel, F., Raach, S., Haizmann, F., and Schlipf, D.: Analysis of control-oriented wake modeling tools using lidar field results, Wind Energ. Sci., 3, 819–831, https://doi.org/10.5194/wes-3-819-2018, 2018b. a
Annoni, J., Dall'Anese, E., Hong, M., and Bay, C. J.: Efficient distributed optimization of wind farms using proximal primal-dual algorithms, 2019 American Control Conference, Philadelphia, USA, 10–12 July 2019, 4173–4178, IEEE, https://doi.org/10.23919/ACC.2019.8814655, 2019b. a
Bao, L., Gneiting, T., Grimit, E. P., Guttorp, P., and Raftery, A. E.: Bias correction and Bayesian model averaging for ensemble forecasts of surface wind direction, Mon. Weather Rev., 138, 1811–1821, https://doi.org/10.1175/2009MWR3138.1, 2010. a
Barthelmie, R. J., Wang, H., Doubrawa, P., and Pryor, S.: Best Practice for Measuring Wind Speeds and Turbulence Offshore through In-Situ and Remote Sensing Technologies, Technical report, Cornell University, Upson Hall, NY, USA, https://doi.org/10.7298/X4QV3JGF, 2016. a
Bay, C. J., Annoni, J., Taylor, T., Pao, L., and Johnson, K.: Active power control for wind farms using distributed model predictive control and nearest neighbor communication, in: 2018 Annual American Control Conference (ACC), Atlanta, Georgia, USA, 8–10 June 2022, 682–687, IEEE, https://doi.org/10.23919/ACC.2018.8431764, 2018. a
Bernardoni, F., Ciri, U., Rotea, M., and Leonardi, S.: Real-time identification of clusters of turbines, J. Phys. Conf. Ser., 1618, 022032, https://doi.org/10.1088/1742-6596/1618/2/022032, 2020. a
Bernardoni, F., Ciri, U., Rotea, M. A., and Leonardi, S.: Identification of turbine clusters during time varying wind direction, in: 2022 American Control Conference (ACC), Atlanta, Georgia, USA, 8–10 June 2022, 4236–4241, IEEE, https://doi.org/10.23919/ACC53348.2022.9867223, 2022. a, b
Bivona, S., Bonanno, G., Burlon, R., Gurrera, D., and Leone, C.: Stochastic models for wind speed forecasting, Energy conversion and management, 52, 1157–1165, https://doi.org/10.1016/j.enconman.2010.09.010, 2011. a
Boersma, S.: Towards closed-loop dynamical wind farm control: model development and control applications, PhD thesis, Delft University of Technology, https://doi.org/10.4233/uuid:48572080-bc51-4ffe-9ba5-676ee9ab5fcc, 2019. a, b
Boersma, S., Doekemeijer, B. M., Gebraad, P. M., Fleming, P. A., Annoni, J., Scholbrock, A. K., Frederik, J. A., and van Wingerden, J.-W.: A tutorial on control-oriented modeling and control of wind farms, in: 2017 American control conference (ACC), 1–18, IEEE, https://doi.org/10.23919/ACC.2017.7962923, 2017. a, b
Bossanyi, E.: Combining induction control and wake steering for wind farm energy and fatigue loads optimisation, J. Phys. Conf. Ser., 1037, 032011, https://doi.org/10.1088/1742-6596/1037/3/032011, 2018. a, b
Bossanyi, E. and Ruisi, R.: Axial induction controller field test at Sedini wind farm, Wind Energ. Sci., 6, 389–408, https://doi.org/10.5194/wes-6-389-2021, 2021. a
Breedt, H. J., Craig, K. J., and Jothiprakasam, V. D.: Monin-Obukhov similarity theory and its application to wind flow modelling over complex terrain, J. Wind Eng. Ind. Aerod., 182, 308–321, https://doi.org/10.1016/j.jweia.2018.09.026, 2018. a
Calaf, M., Meneveau, C., and Meyers, J.: Large eddy simulation study of fully developed wind-turbine array boundary layers, Phys. Fluids, 22, 015110, https://doi.org/10.1063/1.3291077, 2010. a
Campagnolo, F., Weber, R., Schreiber, J., and Bottasso, C. L.: Wind tunnel testing of wake steering with dynamic wind direction changes, Wind Energ. Sci., 5, 1273–1295, https://doi.org/10.5194/wes-5-1273-2020, 2020. a
Cardaun, M., Roscher, B., Schelenz, R., and Jacobs, G.: Analysis of wind-turbine main bearing loads due to constant yaw misalignments over a 20 years timespan, Energies, 12, 1768, https://doi.org/10.3390/en12091768, 2019. a
Carvalho, D., Rocha, A., Gómez-Gesteira, M., and Santos, C.: A sensitivity study of the WRF model in wind simulation for an area of high wind energy, Environ. Modell. Softw., 33, 23–34, https://doi.org/10.1016/j.envsoft.2012.01.019, 2012. a, b
Chan, P. and Hon, K.: Performance of super high resolution numerical weather prediction model in forecasting terrain-disrupted airflow at the Hong Kong International Airport: case studies, Meteorol. Appl., 23, 101–114, https://doi.org/10.1002/met.1534, 2016. a
Chatterjee, T., Cherukuru, N. W., Peet, Y. T., and Calhoun, R. J.: Large eddy simulation with realistic geophysical inflow of Alpha Ventus wind farm: a comparison with LIDAR field experiments, J. Phys. Conf. Ser., 1037, 072056, https://doi.org/10.1088/1742-6596/1037/7/072056, 2018. a, b, c, d
Chen, W., Liu, H., Lin, Y., Li, W., Sun, Y., and Zhang, D.: LSTM-NN yaw control of wind turbines based on upstream wind information, Energies, 13, 1482, https://doi.org/10.3390/en13061482, 2020. a, b, c
Chen, W., Qian, G., Qi, W., Luo, G., Zhao, L., and Yuan, X.: Layout Method of Met Mast Based on Macro Zoning and Micro Quantitative Siting in a Wind Farm, Processes, 10, 1708, https://doi.org/10.3390/pr10091708, 2022. a
Chitsazan, M. A., Fadali, M. S., and Trzynadlowski, A. M.: Wind speed and wind direction forecasting using echo state network with nonlinear functions, Renew. Energ., 131, 879–889, https://doi.org/10.1016/j.renene.2018.07.060, 2019. a
Coleman, J. and Law, K.: Meteorology, Elsevier, https://doi.org/10.1016/B978-0-12-409548-9.09492-6, 2015. a, b, c
Cortina, G., Sharma, V., and Calaf, M.: Investigation of the incoming wind vector for improved wind turbine yaw-adjustment under different atmospheric and wind farm conditions, Renew. Energ., 101, 376–386, https://doi.org/10.1016/j.renene.2016.08.011, 2017. a
Cremers, J. and Klugkist, I.: One direction? A tutorial for circular data analysis using R with examples in cognitive psychology, Front. Psychol., 9, 2040, https://doi.org/10.3389/fpsyg.2018.02040, 2018. a
Damiani, R., Dana, S., Annoni, J., Fleming, P., Roadman, J., van Dam, J., and Dykes, K.: Assessment of wind turbine component loads under yaw-offset conditions, Wind Energ. Sci., 3, 173–189, https://doi.org/10.5194/wes-3-173-2018, 2018. a, b, c
Davies, B. M. and Thomson, D. J.: Comparisons of some parametrizations of wind direction variability with observations, Atmos. Environ., 33, 4909–4917, https://doi.org/10.1016/S1352-2310(99)00287-3, 1999. a, b, c, d
Doekemeijer, B. M., Boersma, S., Pao, L. Y., Knudsen, T., and van Wingerden, J.-W.: Online model calibration for a simplified LES model in pursuit of real-time closed-loop wind farm control, Wind Energ. Sci., 3, 749–765, https://doi.org/10.5194/wes-3-749-2018, 2018. a
Dong, L., Lio, W. H., and Simley, E.: On turbulence models and lidar measurements for wind turbine control, Wind Energ. Sci., 6, 1491–1500, https://doi.org/10.5194/wes-6-1491-2021, 2021. a
Draper, M., Guggeri, A., López, B., Díaz, A., Campagnolo, F., and Usera, G.: A Large Eddy Simulation framework to assess wind farm power maximization strategies: Validation of maximization by yawing, J. Phys. Conf. Ser., 1037, 072051, https://doi.org/10.1088/1742-6596/1037/7/072051, 2018. a
Draxl, C., Allaerts, D., Quon, E., and Churchfield, M.: Coupling mesoscale budget components to large-eddy simulations for wind-energy applications, Bound.-Lay. Meteorol., 179, 73–98, https://doi.org/10.1007/s10546-020-00584-z, 2021. a, b
Eecen, P., Wagenaar, J., Stefanatos, N., Pedersen, T. F., Wagner, R., and Hansen, K. S.: UPWIND 1A2 Metrology, Final Report, https://orbit.dtu.dk/en/publications/upwind-1a2-metrology-final-report (last access: 26 August 2022), 2011. a
El-Fouly, T. H., El-Saadany, E. F., and Salama, M. M.: One day ahead prediction of wind speed and direction, IEEE T. Energy Conver., 23, 191–201, https://doi.org/10.1109/TEC.2007.905069, 2008. a
Energy, S. G. R.: Onshore product portfolio, Brochure, https://www.siemensgamesa.com/en-int/-/media/siemensgamesa/downloads/en/products-and-services/onshore/brochures/siemens-gamesa-onshore-product-portfolio-en.pdf (last access: 16 September 2022), 2022. a
Erdem, E. and Shi, J.: ARMA based approaches for forecasting the tuple of wind speed and direction, Appl. Energ., 88, 1405–1414, https://doi.org/10.1016/j.apenergy.2010.10.031, 2011. a
Etling, D.: On plume meandering under stable stratification, Atmos. Environ. A-Gen., 24, 1979–1985, https://doi.org/10.1016/0960-1686(90)90232-C, 1990. a
Farret, F. A., Pfitscher, L. L., and Bernardon, D. P.: Sensorless active yaw control for wind turbines, in: IECON'01. 27th Annual Conference of the IEEE Industrial Electronics Society (Cat. No. 37243), vol. 2, Denver, Colorado, USA, 29 November–2 December, 1370–1375, IEEE, https://doi.org/10.1109/IECON.2001.975981, 2001. a
Farrugia, P. S. and Micallef, A.: Vectorial statistics for the standard deviation of wind direction, Meteorol. Atmos. Phys., 129, 495–506, https://doi.org/10.1007/s00703-016-0483-8, 2017. a
Farrugia, P. S., Borg, J. L., and Micallef, A.: On the algorithms used to compute the standard deviation of wind direction, J. Appl. Meteorol. Clim., 48, 2144–2151, https://doi.org/10.1175/2009JAMC2050.1, 2009. a, b
Feijóo, A. and Villanueva, D.: Contributions to wind farm power estimation considering wind direction-dependent wake effects, Wind Energy, 20, 221–231, https://doi.org/10.1002/we.2002, 2017. a
Fisher, N. and Lee, A.: Time series analysis of circular data, J. R. Stat. Soc. B, 56, 327–339, https://doi.org/10.1111/j.2517-6161.1994.tb01981.x, 1994. a
Fisher, N. I.: Statistical analysis of circular data, Cambridge University Press, https://doi.org/10.1017/CBO9780511564345, 1995. a
Fleming, P., Gebraad, P. M., Lee, S., van Wingerden, J.-W., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P., and Moriarty, P.: Simulation comparison of wake mitigation control strategies for a two-turbine case, Wind Energy, 18, 2135–2143, https://doi.org/10.1002/we.1810, 2015. a
Fleming, P., Churchfield, M., Scholbrock, A., Clifton, A., Schreck, S., Johnson, K., Wright, A., Gebraad, P., Annoni, J., Naughton, B., Berg, J., Herges, T., White, J., Mikkelsen, T., Sjöholm, M., and Angelou, N.: Detailed field test of yaw-based wake steering, J. Phys. Conf. Ser., 753, 052003, https://doi.org/10.1088/1742-6596/753/5/052003, 2016. a
Fleming, P., Annoni, J., Shah, J. J., Wang, L., Ananthan, S., Zhang, Z., Hutchings, K., Wang, P., Chen, W., and Chen, L.: Field test of wake steering at an offshore wind farm, Wind Energ. Sci., 2, 229–239, https://doi.org/10.5194/wes-2-229-2017, 2017. a
Fleming, P., King, J., Dykes, K., Simley, E., Roadman, J., Scholbrock, A., Murphy, P., Lundquist, J. K., Moriarty, P., Fleming, K., van Dam, J., Bay, C., Mudafort, R., Lopez, H., Skopek, J., Scott, M., Ryan, B., Guernsey, C., and Brake, D.: Initial results from a field campaign of wake steering applied at a commercial wind farm – Part 1, Wind Energ. Sci., 4, 273–285, https://doi.org/10.5194/wes-4-273-2019, 2019. a, b
Fleming, P. A., Gebraad, P. M., Lee, S., van Wingerden, J.-W., Johnson, K., Churchfield, M., Michalakes, J., Spalart, P., and Moriarty, P.: Evaluating techniques for redirecting turbine wakes using SOWFA, Renew. Energ., 70, 211–218, https://doi.org/10.1016/j.renene.2014.02.015, 2014a. a
Fleming, P. A., Scholbrock, A., Jehu, A., Davoust, S., Osler, E., Wright, A. D., and Clifton, A.: Field-test results using a nacelle-mounted lidar for improving wind turbine power capture by reducing yaw misalignment, J. Phys. Conf. Ser., 524, 012002, https://doi.org/10.1088/1742-6596/524/1/012002, 2014b. a, b
Gebraad, P. M., Teeuwisse, F., van Wingerden, J.-W., Fleming, P. A., Ruben, S. D., Marden, J. R., and Pao, L. Y.: A data-driven model for wind plant power optimization by yaw control, in: 2014 American Control Conference, Portland, Oregon, USA, 4–6 June 2014, 3128–3134, IEEE, https://doi.org/10.1109/ACC.2014.6859118, 2014. a
Gebraad, P. M., Teeuwisse, F., Van Wingerden, J., Fleming, P. A., Ruben, S., Marden, J., and Pao, L.: Wind plant power optimization through yaw control using a parametric model for wake effects – a CFD simulation study, Wind Energy, 19, 95–114, https://doi.org/10.1002/we.1822, 2016. a, b
Goit, J. P., Munters, W., and Meyers, J.: Optimal coordinated control of power extraction in LES of a wind farm with entrance effects, Energies, 9, 29, https://doi.org/10.3390/en9010029, 2016. a
Hanna, S.: Lateral dispersion in light-wind stable conditions, Il Nuovo Cimento C, 13, 889–894, https://doi.org/10.1007/BF02514777, 1990. a, b
Hans, A. P. and Jhon, A.: Atmospheric turbulence, models and methods for engineering applications, Willy, New York, ISBN 0471057142, 1984. a
Hart, E., Stock, A., Elderfield, G., Elliott, R., Brasseur, J., Keller, J., Guo, Y., and Song, W.: Impacts of wind field characteristics and non-steady deterministic wind events on time-varying main-bearing loads, Wind Energ. Sci., 7, 1209–1226, https://doi.org/10.5194/wes-7-1209-2022, 2022. a
Hau, E.: Wind turbines: fundamentals, technologies, application, economics, Springer Science & Business Media, https://doi.org/10.1007/978-3-642-27151-9, 2013. a
Haupt, S., Berg, L., Anderson, A., Brown, B., Churchfield, M., Draxl, C., Ennis, B., Feng, Y., Kosovic, B., Kotamarthi, V., Linn, R., Mirocha, J., Moriarty, P., Muñoz-Esparza, D., Rai, K., and Shaw, W.: First year report of the a2e mesoscale to microscale coupling project, Pacific Northwest National Laboratory, Tech. Report PNNL-25108, https://doi.org/10.13140/RG.2.2.21572.01927, 2015. a
Haupt, S., Berg, L., Churchfield, M., Kosovic, B., Mirocha, J., and Shaw, W.: Mesoscale to microscale coupling for wind energy applications: Addressing the challenges, J. Phys. Conf. Ser., 1452, 012076, https://doi.org/10.1088/1742-6596/1452/1/012076, 2020. a, b, c
Haupt, S. E., Kotamarthi, R., Feng, Y., Mirocha, J. D., Koo, E., Linn, R., Kosovic, B., Brown, B., Anderson, A., Churchfield, M. J., Draxl, C., Quon, E., Shaw, W. J., Berg, L. K., Rai, R. K., and Ennis, B. L.: Second year report of the atmosphere to electrons mesoscale to microscale coupling project: Nonstationary modeling techniques and assessment, Tech. rep., Pacific Northwest National Lab.(PNNL), Richland, WA (United States), https://doi.org/10.2172/1573811, 2017. a, b, c, d
Haupt, S. E., Kosovic, B., Shaw, W., Berg, L. K., Churchfield, M., Cline, J., Draxl, C., Ennis, B., Koo, E., Kotamarthi, R., Mazzaro, L., Mirocha, J., Moriarty, P., Muñoz-Esparza, D., Quon, E., Rai, R. K., Robinson, M., and Sever, G.: On bridging a modeling scale gap: Mesoscale to microscale coupling for wind energy, B. Am. Meteorol. Soc., 100, 2533–2550, https://doi.org/10.1175/BAMS-D-18-0033.1, 2019. a, b
Heck, K. S., Johlas, H. M., and Howland, M. F.: Modelling the induction, thrust and power of a yaw-misaligned actuator disk, J. Fluid Mech., 959, A9, https://doi.org/10.1017/jfm.2023.129, 2023. a, b
Hirata, Y., Mandic, D. P., Suzuki, H., and Aihara, K.: Wind direction modelling using multiple observation points, Philos. T. R. Soc. A, 366, 591–607, https://doi.org/10.1098/rsta.2007.2112, 2008. a, b
Houck, D. R.: Review of wake management techniques for wind turbines, Wind Energy, 25, 195–220, https://doi.org/10.1002/we.2668, 2022. a
Howland, M. F.: Wind farm yaw control set-point optimization under model parameter uncertainty, J. Renew. Sustain. Ener., 13, 043303, https://doi.org/10.1063/5.0051071, 2021. a
Howland, M. F., Lele, S. K., and Dabiri, J. O.: Wind farm power optimization through wake steering, P. Natl. Acad. Sci. USA, 116, 14495–14500, https://doi.org/10.1073/pnas.1903680116, 2019. a
Howland, M. F., González, C. M., Martínez, J. J. P., Quesada, J. B., Larranaga, F. P., Yadav, N. K., Chawla, J. S., and Dabiri, J. O.: Influence of atmospheric conditions on the power production of utility-scale wind turbines in yaw misalignment, J. Renew. Sustain. Ener., 12, 063307, https://doi.org/10.1063/5.0023746, 2020. a, b, c, d, e
Howland, M. F., Ghate, A. S., Quesada, J. B., Pena Martínez, J. J., Zhong, W., Larrañaga, F. P., Lele, S. K., and Dabiri, J. O.: Optimal closed-loop wake steering – Part 2: Diurnal cycle atmospheric boundary layer conditions, Wind Energ. Sci., 7, 345–365, https://doi.org/10.5194/wes-7-345-2022, 2022a. a, b, c
Howland, M. F., Quesada, J. B., Martínez, J. J. P., Larrañaga, F. P., Yadav, N., Chawla, J. S., Sivaram, V., and Dabiri, J. O.: Collective wind farm operation based on a predictive model increases utility-scale energy production, Nature Energy, 7, 818–827, https://doi.org/10.1038/s41560-022-01085-8, 2022b. a
Jammalamadaka, S. R. and SenGupta, A.: Topics in circular statistics, vol. 5, World Scientific, https://doi.org/10.1142/4031, 2001. a, b
Jiménez, P. A. and Dudhia, J.: On the ability of the WRF model to reproduce the surface wind direction over complex terrain, J. Appl. Meteorol. Clim., 52, 1610–1617, https://doi.org/10.1175/JAMC-D-12-0266.1, 2013. a, b, c
Joffre, S. M. and Laurila, T.: Standard deviations of wind speed and direction from observations over a smooth surface, J. Appl. Meteorol. Clim., 27, 550–561, https://doi.org/10.1175/1520-0450(1988)027<0550:SDOWSA>2.0.CO;2, 1988. a, b, c
Karakasis, N., Mesemanolis, A., Nalmpantis, T., and Mademlis, C.: Active yaw control in a horizontal axis wind system without requiring wind direction measurement, IET Renew. Power Gen., 10, 1441–1449, https://doi.org/10.1049/iet-rpg.2016.0005, 2016. a, b
Karami, F., Zhang, Y., Rotea, M. A., Bernardoni, F., and Leonardi, S.: Real-time Wind Direction Estimation using Machine Learning on Operational Wind Farm Data, in: 2021 60th IEEE Conference on Decision and Control (CDC), Virtual conference, 13–15 December 2021, 2456–2461, IEEE, https://doi.org/10.1109/CDC45484.2021.9683613, 2021. a
Kau, W., Lee, H., and Kao, S.: A statistical model for wind prediction at a mountain and valley station near Anderson Creek, California, J. Appl. Meteorol., 21, 18–21, 1982. a
Kheirabadi, A. C. and Nagamune, R.: A quantitative review of wind farm control with the objective of wind farm power maximization, J. Wind Eng. Ind. Aerod., 192, 45–73, https://doi.org/10.1016/j.jweia.2019.06.015, 2019. a
Kheirabadi, A. C. and Nagamune, R.: A low-fidelity dynamic wind farm model for simulating time-varying wind conditions and floating platform motion, Ocean Eng., 234, 109313, https://doi.org/10.1016/j.oceaneng.2021.109313, 2021. a
Kim, J. H.: Forecasting autoregressive time series with bias-corrected parameter estimators, Int. J. Forecasting, 19, 493–502, https://doi.org/10.1016/S0169-2070(02)00062-6, 2003. a
Kim, M. and Dalhoff, P.: Yaw Systems for wind turbines–Overview of concepts, current challenges and design methods, J. Phys. Conf. Ser., 524, 012086, https://doi.org/10.1088/1742-6596/524/1/012086, 2014. a
Kooijman, H., Lindenburg, C., Winkelaar, D., and Van der Hooft, E.: DOWEC 6 MW Pre-Design: Aero-elastic modeling of the DOWEC 6 MW pre-design in PHATAS, DOWEC Dutch Offshore Wind Energy Converter 1997–2003 Public Reports, https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=b331d7f80401ca1058058f4d130c3246843a1989 (last access: 10 August 2022), 2003. a
Kragh, K. and Fleming, P.: Rotor speed dependent yaw control of wind turbines based on empirical data, in: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, Tennessee, USA, 9–12 January 2012, p. 1018, https://doi.org/10.2514/6.2012-1018, 2012. a, b, c, d
Kragh, K., Hansen, M., and Mikkelsen, T.: Improving yaw alignment using spinner based LIDAR, in: 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Orlando, Florida, USA, 4–7 January 2011, p. 264, https://doi.org/10.2514/6.2011-264, 2011. a
Kragh, K. A. and Hansen, M. H.: Load alleviation of wind turbines by yaw misalignment, Wind Energy, 17, 971–982, https://doi.org/10.1002/we.1612, 2014. a, b
Kragh, K. A. and Hansen, M. H.: Potential of power gain with improved yaw alignment, Wind Energy, 18, 979–989, https://doi.org/10.1002/we.1739, 2015. a
Kragh, K. A., Hansen, M. H., and Mikkelsen, T.: Precision and shortcomings of yaw error estimation using spinner-based light detection and ranging, Wind Energy, 16, 353–366, https://doi.org/10.1002/we.1492, 2013b. a, b
Kristensen, L., Jensen, N. O., and Petersen, E. L.: Lateral dispersion of pollutants in a very stable atmosphere – the effect of meandering, Atmos. Environ., 15, 837–844, https://doi.org/10.1016/0004-6981(81)90288-2, 1981. a
Krogstad, P.-Å. and Adaramola, M. S.: Performance and near wake measurements of a model horizontal axis wind turbine, Wind Energy, 15, 743–756, https://doi.org/10.1002/we.502, 2012. a, b
Larsen, G. C., Larsen, T. J., and Chougule, A.: Medium fidelity modelling of loads in wind farms under non-neutral ABL stability conditions – a full-scale validation study, J. Phys. Conf. Ser., 854, 012026, https://doi.org/10.1088/1742-6596/854/1/012026, 2017. a
Li, J.-Q. J., Yang, X. I., and Kunz, R. F.: Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier–Stokes of stratified wakes, Phys. Fluids, 34, 115125, https://doi.org/10.1063/5.0127487, 2022. a
Mahrt, L.: Mesoscale wind direction shifts in the stable boundary-layer, Tellus A, 60, 700–705, https://doi.org/10.1111/j.1600-0870.2008.00324.x, 2008. a
Mahrt, L.: Surface wind direction variability, J. Appl. Meteorol. Clim., 50, 144–152, https://doi.org/10.1175/2010JAMC2560.1, 2011. a, b, c, d
Mann, J.: Wind field simulation, Probabilist. Eng. Mech., 13, 269–282, https://doi.org/10.1016/S0266-8920(97)00036-2, 1998. a
Mardia, K. V., Jupp, P. E., and Mardia, K.: Directional statistics, vol. 2, Wiley Online Library, https://doi.org/10.1002/9780470316979, 2000. a
Medici, D.: Experimental studies of wind turbine wakes: power optimisation and meandering, PhD thesis, KTH, https://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-598 (last access: 9 March 2022), 2005. a
Mikkelsen, T., Hansen, K. H., Angelou, N., Sjöholm, M., Harris, M., Hadley, P., Scullion, R., Ellis, G., and Vives, G.: Lidar wind speed measurements from a rotating spinner, in: European Wind Energy Conference and Exhibition, https://backend.orbit.dtu.dk/ws/portalfiles/portal/4553836/Mikkelsen_EWEC_2010.pdf (last access: 23 August 2022), 2010. a, b
Mikkelsen, T., Angelou, N., Hansen, K., Sjöholm, M., Harris, M., Slinger, C., Hadley, P., Scullion, R., Ellis, G., and Vives, G.: A spinner-integrated wind lidar for enhanced wind turbine control, Wind Energy, 16, 625–643, https://doi.org/10.1002/we.1564, 2013. a
Mirocha, J., Kosović, B., and Kirkil, G.: Resolved turbulence characteristics in large-eddy simulations nested within mesoscale simulations using the Weather Research and Forecasting Model, Mon. Weather Rev., 142, 806–831, https://doi.org/10.1175/MWR-D-13-00064.1, 2014. a
Muñoz-Esparza, D. and Kosović, B.: Generation of inflow turbulence in large-eddy simulations of nonneutral atmospheric boundary layers with the cell perturbation method, Mon. Weather Rev., 146, 1889–1909, https://doi.org/10.1175/MWR-D-18-0077.1, 2018. a
Muñoz-Esparza, D., Kosović, B., Mirocha, J., and van Beeck, J.: Bridging the transition from mesoscale to microscale turbulence in numerical weather prediction models, Bound.-Lay. Meteorol., 153, 409–440, https://doi.org/10.1007/s10546-014-9956-9, 2014. a
Ouyang, T., Kusiak, A., and He, Y.: Predictive model of yaw error in a wind turbine, Energy, 123, 119–130, https://doi.org/10.1016/j.energy.2017.01.150, 2017. a
Pao, L. Y. and Johnson, K. E.: A tutorial on the dynamics and control of wind turbines and wind farms, in: 2009 American Control Conference, St. Louis, Missouri, USA, 10–12 June 2009, 2076–2089, IEEE, https://doi.org/10.1109/ACC.2009.5160195, 2009. a
Pedersen, T. F., Gottschall, J., Kristoffersen, J. R., and Dahlberg, J.-Å.: Yawing and performance of an offshore wind farm, in: EWEA Annual Event 2011, European Wind Energy Association (EWEA), https://orbit.dtu.dk/en/publications/yawing-and-performance-of-an-offshore-wind-farm (last access: 23 August 2022), 2011. a, b
Peña, A. and Hahmann, A. N.: Atmospheric stability and turbulence fluxes at Horns Rev – An intercomparison of sonic, bulk and WRF model data, Wind Energy, 15, 717–731, https://doi.org/10.1002/we.500, 2012. a
Porté-Agel, F., Wu, Y.-T., and Chen, C.-H.: A numerical study of the effects of wind direction on turbine wakes and power losses in a large wind farm, Energies, 6, 5297–5313, https://doi.org/10.3390/en6105297, 2013. a
Porté-Agel, F., Bastankhah, M., and Shamsoddin, S.: Wind-turbine and wind-farm flows: a review, Bound.-Lay. Meteorol., 174, 1–59, https://doi.org/10.1007/s10546-019-00473-0, 2020. a
Quick, J., Annoni, J., King, R., Dykes, K., Fleming, P., and Ning, A.: Optimization under uncertainty for wake steering strategies, J. Phys. Conf. Ser., 854, 012036, https://doi.org/10.1088/1742-6596/854/1/012036, 2017. a
Quick, J., King, J., King, R. N., Hamlington, P. E., and Dykes, K.: Wake steering optimization under uncertainty, Wind Energ. Sci., 5, 413–426, https://doi.org/10.5194/wes-5-413-2020, 2020. a, b, c
Rasmussen, C. E.: Gaussian processes in machine learning, in: Summer school on machine learning, Springer, 63–71, https://doi.org/10.1007/978-3-540-28650-9_4, 2003. a
Sanz Rodrigo, J., Chávez Arroyo, R. A., Moriarty, P., Churchfield, M., Kosović, B., Réthoré, P.-E., Hansen, K. S., Hahmann, A., Mirocha, J. D., and Rife, D.: Mesoscale to microscale wind farm flow modeling and evaluation, Wires: Energy Environ., 6, e214, https://doi.org/10.1002/wene.214, 2017. a
Schalkwijk, J., Jonker, H. J., Siebesma, A. P., and Bosveld, F. C.: A year-long large-eddy simulation of the weather over Cabauw: An overview, Mon. Weather Rev., 143, 828–844, https://doi.org/10.1175/MWR-D-14-00293.1, 2015. a
Schepers, J., Boorsma, K., and Munduate, X.: Final Results from Mexnext-I: Analysis of detailed aerodynamic measurements on a 4.5 m diameter rotor placed in the large German Dutch Wind Tunnel DNW, J. Phys. Conf. Ser., 555, 012089, https://doi.org/10.1088/1742-6596/555/1/012089, 2014. a
Scholbrock, A., Fleming, P., Schlipf, D., Wright, A., Johnson, K., and Wang, N.: Lidar-enhanced wind turbine control: Past, present, and future, in: 2016 American Control Conference (ACC), Boston, Massachusetts, USA, 6–8 July 2016, 1399–1406, IEEE, https://doi.org/10.1109/ACC.2016.7525113, 2016. a
Schreiber, J., Nanos, E., Campagnolo, F., and Bottasso, C. L.: Verification and calibration of a reduced order wind farm model by wind tunnel experiments, J. Phys. Conf. Ser., 854, 012041, https://doi.org/10.1088/1742-6596/854/1/012041, 2017. a
Schreiber, J., Bottasso, C. L., Salbert, B., and Campagnolo, F.: Improving wind farm flow models by learning from operational data, Wind Energ. Sci., 5, 647–673, https://doi.org/10.5194/wes-5-647-2020, 2020. a
Shapiro, C. R., Starke, G. M., Meneveau, C., and Gayme, D. F.: A wake modeling paradigm for wind farm design and control, Energies, 12, 2956, https://doi.org/10.3390/en12152956, 2019. a
Simley, E., Pao, L. Y., Frehlich, R., Jonkman, B., and Kelley, N.: Analysis of light detection and ranging wind speed measurements for wind turbine control, Wind Energy, 17, 413–433, https://doi.org/10.1002/we.1584, 2014. a
Simley, E., Fleming, P., and King, J.: Field validation of wake steering control with wind direction variability, J. Phys. Conf. Ser., 1452, 012012, https://doi.org/10.1088/1742-6596/1452/1/012012, 2020b. a
Simley, E., Fleming, P., King, J., and Sinner, M.: Wake steering wind farm control with preview wind direction information, Tech. rep., National Renewable Energy Lab. (NREL), Golden, CO (United States), https://doi.org/10.23919/ACC50511.2021.9483008, 2021. a
Sinner, M., Pao, L. Y., and King, J.: Estimation of large-scale wind field characteristics using supervisory control and data acquisition measurements, in: 2020 American Control Conference (ACC), Denver, Colorado, USA, 1–3 July 2020, 2357–2362, IEEE, https://doi.org/10.23919/ACC45564.2020.9147859, 2020. a
Smith, B., Link, H., Randall, G., and McCoy, T.: Applicability of nacelle anemometer measurements for use in turbine power performance tests, Tech. rep., National Renewable Energy Lab., Golden, CO (US), https://www.nrel.gov/docs/fy02osti/32494.pdf (last access: 18 May 2023), 2002. a
Song, D., Yang, J., Liu, Y., Su, M., Liu, A., and Joo, Y. H.: Wind direction prediction for yaw control of wind turbines, International Journal of Control, Automation and Systems, 15, 1720–1728, https://doi.org/10.1007/s12555-017-0289-6, 2017. a, b
Song, D., Yang, J., Fan, X., Liu, Y., Liu, A., Chen, G., and Joo, Y. H.: Maximum power extraction for wind turbines through a novel yaw control solution using predicted wind directions, Energ. Convers. Manage., 157, 587–599, https://doi.org/10.1016/j.enconman.2017.12.019, 2018. a, b
Spencer, M., Stol, K., and Cater, J.: Predictive yaw control of a 5 MW wind turbine model, in: 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, Tennessee, USA, 9–12 January 2012, p. 1020, https://doi.org/10.2514/6.2012-1020, 2013. a, b, c
Starke, G. M., Stanfel, P., Meneveau, C., Gayme, D. F., and King, J.: Network based estimation of wind farm power and velocity data under changing wind direction, in: 2021 American Control Conference (ACC), virtual conference, 25–28 May 2021, 1803–1810, IEEE, https://doi.org/10.23919/ACC50511.2021.9483060, 2021. a, b, c, d
Storey, R., Cater, J., and Norris, S.: Large eddy simulation of turbine loading and performance in a wind farm, Renew. Energ., 95, 31–42, https://doi.org/10.1016/j.renene.2016.03.067, 2016. a, b
Stull, R. B.: An introduction to boundary layer meteorology, vol. 13, Springer Science & Business Media, https://doi.org/10.1007/978-94-009-3027-8, 1988. a, b
Su, Z., Wang, J., Lu, H., and Zhao, G.: A new hybrid model optimized by an intelligent optimization algorithm for wind speed forecasting, Energ. Convers. Manage., 85, 443–452, https://doi.org/10.1016/j.enconman.2014.05.058, 2014. a
Talbot, C., Bou-Zeid, E., and Smith, J.: Nested mesoscale large-eddy simulations with WRF: Performance in real test cases, J. Hydrometeorol., 13, 1421–1441, https://doi.org/10.1175/JHM-D-11-048.1, 2012. a, b
Tsioumas, E., Karakasis, N., Jabbour, N., and Mademlis, C.: Indirect estimation of the Yaw-Angle misalignment in a horizontal axis wind turbine, in: 2017 IEEE 11th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), Tinos, Greece, 29 August–1 September 2017, 45–51, IEEE, https://doi.org/10.1109/DEMPED.2017.8062332, 2017. a
Van Der Hoek, D., Sinner, M., Simley, E., Pao, L., and van Wingerden, J.-W.: Estimation of the Ambient Wind Field From Wind Turbine Measurements Using Gaussian Process Regression, in: 2021 American Control Conference (ACC), virtual conference, 25–28 May 2021, 558–563, IEEE, https://doi.org/10.23919/ACC50511.2021.9483088, 2021. a, b, c, d, e, f, g, h, i
Veers, P. S.: Three-dimensional wind simulation, Tech. rep., Sandia National Labs., Albuquerque, NM (USA), https://www.osti.gov/biblio/6633902 (last access: 19 May 2023), 1988. a
Vincent, C., Giebel, G., Pinson, P., and Madsen, H.: Resolving nonstationary spectral information in wind speed time series using the Hilbert–Huang transform, J. Appl. Meteorol. Clim., 49, 253–267, https://doi.org/10.1175/2009JAMC2058.1, 2010. a
Wu, Y.-T. and Porté-Agel, F.: Large-eddy simulation of wind-turbine wakes: evaluation of turbine parametrisations, Bound.-Lay. Meteorol., 138, 345–366, https://doi.org/10.1007/s10546-010-9569-x, 2011. a
Xin, W., Yanping, L., and Wei, T.: Modified hill climbing method for active yaw control in wind turbine, in: Proceedings of the 31st Chinese Control Conference, Nanchang, China, 3–5 June 2019, 6677–6680, IEEE, Electronic ISBN 978-988-15638-1-1, Print ISBN 978-1-4673-2581-3, https://doi.org/10.1016/j.enconman.2017.12.019, 2012. a
Yamartino, R. J.: A comparison of several “single-pass” estimators of the standard deviation of wind direction, J. Appl. Meteorol. Clim., 23, 1362–1366, https://doi.org/10.1175/1520-0450(1984)023<1362:ACOSPE>2.0.CO;2, 1984. a
Yassin, K., Helms, A., Moreno, D., Kassem, H., Höning, L., and Lukassen, L. J.: Applying a random time mapping to Mann-modeled turbulence for the generation of intermittent wind fields, Wind Energ. Sci., 8, 1133–1152, https://doi.org/10.5194/wes-8-1133-2023, 2023. a
Zahle, F. and Sørensen, N. N.: Characterization of the unsteady flow in the nacelle region of a modern wind turbine, Wind Energy, 14, 271–283, https://doi.org/10.1002/we.418, 2011. a, b
Zalkind, D. S. and Pao, L. Y.: The fatigue loading effects of yaw control for wind plants, in: 2016 American Control Conference (ACC), Boston, MA, USA, 6–8 July, 537–542, IEEE, https://doi.org/10.1109/ACC.2016.7524969, 2016. a, b
Short summary
This review presents the current understanding of wind direction variability in the context of control-oriented modelling of wind turbines and wind farms in a manner suitable to a wide audience. Motivation comes from the significant and commonly seen yaw error of horizontal axis wind turbines, which carries substantial negative impacts on annual energy production and the levellised cost of wind energy. Gaps in the literature are identified, and the critical challenges in this area are discussed.
This review presents the current understanding of wind direction variability in the context of...
Altmetrics
Final-revised paper
Preprint