Abstract
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 1-D axial momentum theory, the captured power P̃ 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 (DDLCs), e.g., limits on the permissible root-bending moment or tip deflection, may be generalized into a form that also depends on CT and R. The developed model is based on simple relations and makes explorations of overall parameters possible in the early stage of the rotor design process. Using these relationships to maximize P̃ 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 constraint may achieve 1.9 % extra power capture P̃ compared to the baseline (Betz limit) rotor. This method is extended to the optimization of rotors with respect to annual energy production (AEP), in which the thrust characteristics CT(V) need to be determined together with R. This results in a much higher relative potential for improvement 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 to 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.
Highlights
From the inception of the wind energy industry, it has been a clear trend that rotor sizes have been increasing
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
This follows a trend occurring in recent years in which there is a belief that wind turbine optimization should include a more holistic approach, with concepts like multidisciplinary design analysis and optimization (MDAO) and systems engineering (Bottasso et al, 2012; Zahle et al, 2015; Fleming et al, 2016; and Perez-Moreno et al, 2016), where all of the parts of the turbine design that affect the cost should be taken into account along with the overall objective
Summary
From the inception of the wind energy industry, it has been a clear trend that rotor sizes have been increasing. They found the same results as the previous two investigations; the LIR can improve AEP, but when they consider the CoE they find that the LIR is not cost effective, meaning that the additional cost of extending the blade is not compensated by the increase in power This conclusion is opposed to the conclusion made by Buck and Garvey (2015b) who set out to minimize the ratio between capital expenditures (CapEx) and AEP. Simple analytical models, based on 1-D aerodynamic momentum theory and Euler–Bernoulli beam theory, are introduced to establish the first-order relationship between these responses This provides a useful framework for the initial rotor design, especially when high-level design parameters such as the rotor radius need to be fixed or there is a need to understand how load/structural responses will change with rotor size.
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