Abstract
Wind energy is one of the fastest-growing energy sources due to its cleanness, sustainability, and cost-effectiveness. In the past, wind turbine design studies focused primarily on a sub-system or single-discipline design and analysis, including control, structural, aerodynamic, and electro-mechanical studies, for example. More recent studies formulated wind turbine design problems using multidisciplinary design optimization (MDO) strategies, with either static or dynamic system models, providing the potential for identifying system-level optimal designs. On the other hand, efforts have also been made to increase the reliability and robustness of wind turbines by accounting for various sources of uncertainty explicitly in the design process. In the presented study, the MDO formulation of wind turbine design problem has been extended to include both control system co-design and reliability considerations in an integrated manner. As a result, the optimal wind turbine design that has an optimal control solution and is robust to uncertainties can be obtained at an early design stage, which would benefit the controller design and maintenance design at latter phases. In this paper, the design of a horizontal axis wind turbine (HAWT) supported by a tubular tower is considered and formulated as a multi-objective control co-design problem with design parameter uncertainties and stochastic wind load. A physics-based multidisciplinary dynamic model of tubular-tower-supported pitch-controlled HAWT that captures the main design conflicts under extreme wind is provided and implemented, along with the necessary modifications to make nested control co-design comply with modern reliability-based design optimization structures, forming a new class of reliability-based co-design (RBCD) problems. In particular, we provide detailed discussions about RBCD problem formulations and implementation strategies, and with the HAWT design problem, we demonstrate the results and computational costs with integrated double-loop, single-loop, as well as decoupled methods.
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Acknowledgements
This research is partially supported by National Science Foundation through Faculty Early Career Development (CAREER) awards CMMI-1813111 and the Engineering Research Center for Power Optimization of Electro-Thermal Systems (POETS) with cooperative agreement EEC-1449548.
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This manuscript is self-contained, in that it contains all necessary theory and data to reproduce the results, including the preliminaries, i.e., the wind turbine design specifications and the theory on reliability-based co-design methodology. The design problem formulation and all parameters for the examples are provided and described in detail. Lastly, the source codes for the implementation of the wind turbine design study can be provided upon requests from interested readers.
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Appendices
Appendices
Appendix 1: NREL 5MW wind turbine blade parameters
This appendix provides the NREL 5MW wind turbine blade parameters (Jager and Andreas 1996). Additionally, the listed airfoils are corresponding to the lift and drag coefficients extended to \([-180^\circ , 180^\circ ]\), based on the DOWEC blades (Kooijman et al. 2003; Lindenburg 2002) (Table 9).
Appendix 2: HAWT deterministic co-design state and control trajectories
Appendix 2 provides state and control trajectories of the optimum design obtained from the HAWT deterministic co-design formulation.
Appendix 3: HAWT reliability-based co-design with DLP state and control trajectories
Appendix 3 provides state and control trajectories of the optimum design obtained from the HAWT reliability-based co-design with the DLP formulation.
Appendix 4: HAWT reliability-based co-design with SLP state and control trajectories
Appendix 4 provides state and control trajectories of the optimum design obtained from the HAWT reliability-based co-design with the SLP formulation.
Appendix 5: HAWT reliability-based co-design with SORA state and control trajectories
Appendix 5 provides state and control trajectories of the optimum design obtained from the HAWT reliability-based co-design with the SORA formulation.
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Cui, T., Allison, J.T. & Wang, P. Reliability-based control co-design of horizontal axis wind turbines. Struct Multidisc Optim 64, 3653–3679 (2021). https://doi.org/10.1007/s00158-021-03046-3
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DOI: https://doi.org/10.1007/s00158-021-03046-3