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Research Papers

Fast Estimation of the Damage Equivalent Load in Blade Geometry Multidisciplinar Optimization

[+] Author and Article Information
Fernando Echeverría Durá

ACCIONA Windpower,
Polígono industrial Barasoain parcela 2,
Barasoain 31395, Navarra, Spain
e-mail: FEcheverria@nordex-online.com

Fermín Mallor Gimenez

ACCIONA Windpower,
Avenida Innovación 3, Sarriguren,
Pamplona 31621, Spain;
Statistics,
UPNA Universidad Pública de Navarra (UPNA),
Sarriguren 31621, Navarra, Spain
e-mail: mallor@unavarra.es

Javier Sanz Corretge

ACCIONA Windpower,
Polígono industrial Barasoain parcela 2,
Barasoain 31395, Navarra, Spain
e-mail: FSanz@nordex-online.com

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING: INCLUDING WIND ENERGY AND BUILDING ENERGY CONSERVATION. Manuscript received September 14, 2016; final manuscript received April 12, 2017; published online May 22, 2017. Assoc. Editor: Yves Gagnon.

J. Sol. Energy Eng 139(4), 041008 (May 22, 2017) (10 pages) Paper No: SOL-16-1407; doi: 10.1115/1.4036636 History: Received September 14, 2016; Revised April 12, 2017

Designing blade geometry as a multidisciplinary optimization presents important challenges due to the increment in the number of design variables and computational cost of calculating the constraints and objective function. Blades have an important impact on loads because they capture the kinetic energy in wind and transfer it to the rest of the wind turbine components. Thus, consideration of the fatigue response is necessary in the optimization problem. However, the calculation of the damage equivalent loads (DELs) implies time-consuming simulations that restrict the number of design variables due to the increment of the search space. This article proposes a frequency domain method to estimate the fatigue response, which produces an advantage in terms of computational cost. The method is based on wind turbine model linearization by means of an aero-elastic code and the subsequent calculation of a frequency response function (FRF), which serves to estimate the response of the wind turbine. The Dirlik method is then applied to infer the damage equivalent loads. This process, which is useful for variables that have a stochastic nature, provides rapid approximate prediction of the fatigue response. An alternative estimation is proposed for loads subjected to an important periodic component. The results show that the method is useful in the initial stages of design.

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Figures

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Fig. 1

Flow chart describing the DEL calculation in the frequency domain

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Fig. 2

PSD Cumulative variance for the pitch rate signals. Three blades' and three seeds' conditions are shown.

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Fig. 3

PSD Cumulative variance for the generator torque signals. Three blades' and three seeds' conditions are shown.

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Fig. 4

Bode diagram (magnitude and phase) of the FRF that relates wind seed and moment My in hub

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Fig. 5

PSD of effective wind seed (Veff). Excitation frequencies 1P, 3P, 6P, 9P, and 12P are presented in vertical lines.

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Fig. 6

Spanwise distributions: (a) chord, (b) twist, and (c) relative thickness of the ten test blades

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Fig. 7

DEL calculated in the frequency domain versus calculated in the time domain. Each point represents the result for one blade geometry (simulations with mean wind seed of 14 m/s). (a) Blade root Mx, (b) blade root My, (c) blade 75% span My, (d) hub Mx, (e) hub My in stationary axes, and (f) tower base My. The lines represent the linear regressions that minimize the least square error. Goodness of fitness R2 is also presented.

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Fig. 8

DEL of stationary hub My with respect to blade. Values from thirty wind seeds and the mean are presented.

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Fig. 9

Time series (a) and PSD (b) of moment Mx in root for two test blade models (id7 and id9)

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Fig. 10

First-order mass function versus DEL in the time domain. Each point represents the results for one blade geometry. The dashed line represents the linear regression that minimizes the least square error. Goodness of fitness R2 is also presented. (a) Blade root Mx, (b) blade root My, (c) blade Mx (75% span), and (d) tower base Mx.

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Fig. 11

Time series of (a) moment Mx in hub and (b) moment My in hub, for test blade models id7 and id9. The signals are divided into six periods of 100 s.

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Fig. 12

DEL of the six periods and the total value for test blade id7 and id9. (a) Results for hub Mx and (b) results for hub My.

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Fig. 13

Spanwise distributions: (a) chord, (b) twist, and (c) relative thickness of solutions from optimization scenario 1 and scenario 2

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Fig. 14

Bending moment My in hub for baseline and solution (14 m/s mean wind seed)

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