IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v15y2022i9p2998-d797666.html
   My bibliography  Save this article

Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades

Author

Listed:
  • Michael K. McWilliam

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Antariksh C. Dicholkar

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Frederik Zahle

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

  • Taeseong Kim

    (Department of Wind and Energy System, Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark)

Abstract

Post-Optimum Sensitivity Analysis (POSA) extends numerical design optimization to provide additional information on how the design and performance would change if various parameters and constraints were varied. POSA is challenging since it typically requires accurate gradients and gradient-based optimization problems that provide Lagrange multipliers. To overcome this problem, this paper introduces a technique to automatically tune gradients with statistical methods and algorithms to calculate the Lagrange multipliers after an optimization. This allows these methods to be applied to problems with noisy gradients or problems solved with gradient-free optimization algorithms. These methods have been applied to swept wind turbine blades. Swept blades can reduce wind turbine loads by twisting out of the wind when the wind speed increases. The methods have shown that introducing design freedom in the sweep, blade root flap-wise bending moments and blade tip deflection has a weaker influence on the design. Instead, blade root torsion moment and material failure become the driving constraints.

Suggested Citation

  • Michael K. McWilliam & Antariksh C. Dicholkar & Frederik Zahle & Taeseong Kim, 2022. "Post-Optimum Sensitivity Analysis with Automatically Tuned Numerical Gradients Applied to Swept Wind Turbine Blades," Energies, MDPI, vol. 15(9), pages 1-19, April.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:9:p:2998-:d:797666
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/15/9/2998/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/15/9/2998/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Scott, Samuel & Capuzzi, Marco & Langston, David & Bossanyi, Ervin & McCann, Graeme & Weaver, Paul M. & Pirrera, Alberto, 2017. "Effects of aeroelastic tailoring on performance characteristics of wind turbine systems," Renewable Energy, Elsevier, vol. 114(PB), pages 887-903.
    2. E. Castillo & A. J. Conejo & C. Castillo & R. Mínguez & D. Ortigosa, 2006. "Perturbation Approach to Sensitivity Analysis in Mathematical Programming," Journal of Optimization Theory and Applications, Springer, vol. 128(1), pages 49-74, January.
    3. David G. Luenberger & Yinyu Ye, 2016. "Linear and Nonlinear Programming," International Series in Operations Research and Management Science, Springer, edition 4, number 978-3-319-18842-3, September.
    4. Ashuri, T. & Zaaijer, M.B. & Martins, J.R.R.A. & van Bussel, G.J.W. & van Kuik, G.A.M., 2014. "Multidisciplinary design optimization of offshore wind turbines for minimum levelized cost of energy," Renewable Energy, Elsevier, vol. 68(C), pages 893-905.
    5. Larwood, Scott & van Dam, C.P. & Schow, Daniel, 2014. "Design studies of swept wind turbine blades," Renewable Energy, Elsevier, vol. 71(C), pages 563-571.
    6. Castillo, Enrique & Mínguez, Roberto & Castillo, Carmen, 2008. "Sensitivity analysis in optimization and reliability problems," Reliability Engineering and System Safety, Elsevier, vol. 93(12), pages 1788-1800.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mak, Davye & Choeum, Daranith & Choi, Dae-Hyun, 2020. "Sensitivity analysis of volt-VAR optimization to data changes in distribution networks with distributed energy resources," Applied Energy, Elsevier, vol. 261(C).
    2. Reddy, Sohail R., 2021. "A machine learning approach for modeling irregular regions with multiple owners in wind farm layout design," Energy, Elsevier, vol. 220(C).
    3. Ikeda, Teruaki & Tanaka, Hiroto & Yoshimura, Ryosuke & Noda, Ryusuke & Fujii, Takeo & Liu, Hao, 2018. "A robust biomimetic blade design for micro wind turbines," Renewable Energy, Elsevier, vol. 125(C), pages 155-165.
    4. Sandra S. Y. Tan & Antonios Varvitsiotis & Vincent Y. F. Tan, 2021. "Analysis of Optimization Algorithms via Sum-of-Squares," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 56-81, July.
    5. Castillo, Enrique & Menéndez, José María & Sánchez-Cambronero, Santos, 2008. "Predicting traffic flow using Bayesian networks," Transportation Research Part B: Methodological, Elsevier, vol. 42(5), pages 482-509, June.
    6. Gonzalez Silva, Jean & Ferrari, Riccardo & van Wingerden, Jan-Willem, 2023. "Wind farm control for wake-loss compensation, thrust balancing and load-limiting of turbines," Renewable Energy, Elsevier, vol. 203(C), pages 421-433.
    7. repec:hal:wpspec:info:hdl:2441/4lhe3u3c38ojohjlcbfaupcjr is not listed on IDEAS
    8. Hao, Wenrui & Lu, Zhenzhou & Wei, Pengfei, 2013. "Uncertainty importance measure for models with correlated normal variables," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 48-58.
    9. Vasnev, Andrey L., 2010. "Sensitivity of GLS estimators in random effects models," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1252-1262, May.
    10. Hedlund, Jonas, 2017. "Bayesian persuasion by a privately informed sender," Journal of Economic Theory, Elsevier, vol. 167(C), pages 229-268.
    11. José Luis Torres-Madroñero & Joham Alvarez-Montoya & Daniel Restrepo-Montoya & Jorge Mario Tamayo-Avendaño & César Nieto-Londoño & Julián Sierra-Pérez, 2020. "Technological and Operational Aspects That Limit Small Wind Turbines Performance," Energies, MDPI, vol. 13(22), pages 1-39, November.
    12. Sessarego, Matias & Feng, Ju & Ramos-García, Néstor & Horcas, Sergio González, 2020. "Design optimization of a curved wind turbine blade using neural networks and an aero-elastic vortex method under turbulent inflow," Renewable Energy, Elsevier, vol. 146(C), pages 1524-1535.
    13. Dimitris Drikakis & Talib Dbouk, 2022. "The Role of Computational Science in Wind and Solar Energy: A Critical Review," Energies, MDPI, vol. 15(24), pages 1-20, December.
    14. Gürkan, G. & Ozdemir, O. & Smeers, Y., 2013. "Generation Capacity Investments in Electricity Markets : Perfect Competition," Discussion Paper 2013-045, Tilburg University, Center for Economic Research.
    15. Miriam L. A. Gemaque & Jerson R. P. Vaz & Osvaldo R. Saavedra, 2022. "Optimization of Hydrokinetic Swept Blades," Sustainability, MDPI, vol. 14(21), pages 1-13, October.
    16. Ozan Gözcü & Taeseong Kim & David Robert Verelst & Michael K. McWilliam, 2022. "Swept Blade Dynamic Investigations for a 100 kW Small Wind Turbine," Energies, MDPI, vol. 15(9), pages 1-22, April.
    17. van Dijk, Mike T. & van Wingerden, Jan-Willem & Ashuri, Turaj & Li, Yaoyu, 2017. "Wind farm multi-objective wake redirection for optimizing power production and loads," Energy, Elsevier, vol. 121(C), pages 561-569.
    18. Hailun Xie & Lars Johanning, 2023. "A Hierarchical Met-Ocean Data Selection Model for Fast O&M Simulation in Offshore Renewable Energy Systems," Energies, MDPI, vol. 16(3), pages 1-20, February.
    19. Enrique Castillo & Roberto Mínguez & Antonio Conejo & Beatriz Pérez & Oscar Fontenla, 2013. "Estimating the parameters of a fatigue model using Benders’ decomposition," Annals of Operations Research, Springer, vol. 210(1), pages 309-331, November.
    20. Hasui, Kohei & Kobayashi, Teruyoshi & Sugo, Tomohiro, 2021. "Optimal irreversible monetary policy," European Economic Review, Elsevier, vol. 134(C).
    21. Sedaghat, Ahmad & Hassanzadeh, Arash & Jamali, Jamaloddin & Mostafaeipour, Ali & Chen, Wei-Hsin, 2017. "Determination of rated wind speed for maximum annual energy production of variable speed wind turbines," Applied Energy, Elsevier, vol. 205(C), pages 781-789.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:15:y:2022:i:9:p:2998-:d:797666. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.