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Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
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A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain the Pareto-optimal relationship between power and loads, through the use of KKT-multipliers, leaving an optimization problem that can be solved at each radial station independently. Combining it with a simple cost function it is possible to analytically solve for the optimal Power-per-Cost with given inputs for the aerodynamics and the cost-function.
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https://doi.org/10.5194/wes-2020-99
https://doi.org/10.5194/wes-2020-99

  06 Oct 2020

06 Oct 2020

Review status: this preprint is currently under review for the journal WES.

A Method for Preliminary Rotor Design – Part 2: Wind Turbine Rotor Optimization with Radial Independence

Kenneth Loenbaek1,2, Christian Bak2, and Michael McWilliam2 Kenneth Loenbaek et al.
  • 1Suzlon Blade Science Center, Brendstrupgaardsvej 13, 8210 Aarhus, Denmark
  • 2Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark

Abstract. A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain an optimal relationship between the global power- (CP) and load-coefficient (CT, CFM) through the use of KKT-multipliers, leaving an optimization problem that can be solved at each radial station independently. It allows to solve load constraint power and Annual-Energy-Production (AEP) optimization problems where the optimization variables are only the KKT-multipliers (scalars), one for each of the constraint. For the paper two constraints, namely the thrust and blade-root-flap-moment is used, leading to two optimization variables.

Applying the optimization methodology to maximize power (P) or Annual-Energy-Production (AEP) for a given thrust and blade-root-flap-moment, but without a cost-function, leads to the same overall result with the global optimum being unbounded in terms of rotor radius (R~) with a global optimum being at R~ → ∞. The increase in power and AEP is in this case ΔP = 50 % and ΔAEP = 70 %, with a baseline being the Betz-optimum rotor.

With a simple cost function and with the same setup of the problem a Power-per-Cost (PpC) optimization resulted in a Power-per-Cost increase of ΔPpC = 4.2 % with a radius increase of ΔR = 7.9 % as well as a power increase of ΔP = 9.1 %. This was obtained while keeping the same flap-moment and reaching a lower thrust of ΔT = −3.8 %. The equivalent for AEP-per-Cost (AEPpC) optimization leads to an increased cost efficiency of ΔAEPpC = 2.9 % with a radius increase of a ΔR = 17 % and an AEP increase of ΔAEP = 13 %, again with the same, maximum flap-moment, while the maximum thrust is −9.0 % lower than the baseline.

Kenneth Loenbaek et al.

 
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Status: final response (author comments only)
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Kenneth Loenbaek et al.

Kenneth Loenbaek et al.

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Short summary
A novel wind turbine rotor optimization methodology is presented. Using an assumption of radial independence it is possible to obtain the Pareto-optimal relationship between power and loads, through the use of KKT-multipliers, leaving an optimization problem that can be solved at each radial station independently. Combining it with a simple cost function it is possible to analytically solve for the optimal Power-per-Cost with given inputs for the aerodynamics and the cost-function.
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