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Wind Energy Science The interactive open-access journal of the European Academy of Wind Energy
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© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 08 Jul 2019

Submitted as: research article | 08 Jul 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Wind Energy Science (WES).

Optimal relationship between power and design driving loads for wind turbine rotors using 1D models

Kenneth Loenbaek1,2, Christian Bak2, Jens I. Madsen1, and Bjarke Dam1 Kenneth Loenbaek et al.
  • 1Suzlon Blade Science Center, Havneparken 1, 7100 Vejle, Denmark
  • 2Technical University of Denmark, Frederiksborgvej 399, 4000 Roskilde, Denmark

Abstract. We investigate the optimal relationship between the aerodynamic power, thrust loading, and size of a wind turbine rotor when its design is constrained by a static aerodynamic load. Based on 1D-axial momentum theory, the captured power P~ for a uniformly loaded rotor can be expressed in terms of the rotor radius R and the rotor thrust coefficient CT. Common types of static Design Driving Load Constraints (DDLC), e.g. limits on permissible root-bending moment or tip deflection, may be generalized into a form that also depends on CT and R. Using these relationships to maximize P~ subject to a DDLC, shows that operating the rotor at the Betz limit (maximum CP) does not lead to the highest power capture. Rather, it is possible to improve performance with a larger rotor radius and lower CT without violating the DDLC. As an example, a rotor design driven by a tip-deflection constraints, may achieve 1.9 % extra power capture P~ compared to the baseline (Betz limit) rotor. The method is extended for optimization of rotors with respect to Annual Energy Production (AEP), where the thrust characteristics CT(V) needs to be determined together with R. This results in much higher relative potential for improvements, since the constraint limit can be met over a larger range of wind speeds. For example, a relative gain in AEP of +5.7 % is possible for a rotor design constrained by tip deflections compared with a rotor designed for optimal CP. The optimal solution for AEP leads to a thrust curve with three distinct operational regimes and so called thrust-clipping.

Kenneth Loenbaek et al.
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Kenneth Loenbaek et al.
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Short summary
From the basic aerodynamic theory of wind turbine rotors it is well know fact that there is a relationship between the loading of the rotor and the power efficiency. It shows that there is a loading that maximizes the power efficiency and it is common to target this maximum when designing rotors. But in this paper it is found that for rotors constrained by a load, the maximum power is found by decreasing the loading and increasing the rotor radius. Max power efficiency is therefore not optimal.
From the basic aerodynamic theory of wind turbine rotors it is well know fact that there is a...