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| Titel |
Estimating of a nonlinear power curve for a Wind Turbine Generator |
| VerfasserIn |
R. Calif, F. G. Schmitt |
| Konferenz |
EGU General Assembly 2012
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 14 (2012) |
| Datensatznummer |
250069400
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| Zusammenfassung |
| The output power from a Wind Turbine Generator (WTG) is an intermittent resource, due to
the high variability of the atmospheric wind at all spatial or temporal scales ranging from
large scale variations to very short variations. Generally, a function transfer or a power curve
of WTG is estimated with the IEC standard 61400 - 12 giving a relation of coupling
between the measured wind speed and the output power for the considered WTG.
However, this relation is a statistical representation and not takes into account the
dynamics of the power output, more precisely on small time scales. The goal is
to provide a method to estimate and to model the function transfer of a WTG, in
order to synthesize the output power mimicking the statistical and the dynamical
properties of the real output power. For that, we study the statistics of power curve
in the multifractal framework motivated by the presence of spectral scaling for
the wind speed and the output power data from a WTG. The first step consists to
quantify the power curve or the transfer function of two intermittent stochastic
processes such as the wind speed u(t) and the output power p(t) at all temporal
scales and at all intensities. In this study, firstly, we define the time increment of the
wind speed measurement u′(t) = u(t + Ï) - u(t) and the time increment of the
output power measurement p′(t) = p(t + Ï) - p(t) characterized by mth and nth
order structure functions to estimate the exponent functions ζu′(m) and ζp′(n) that
characterize respectively the multifractal properties of the wind speed fluctuations u′(t)
and the output power fluctuations p′(t) from the WTG. The exponent function
ζ defines the types of scaling behavior of a process: if ζ is linear the statistical
behavior is monoscaling corresponding to a monofractal process. If ζ is nonlinear and
concave, the statistical behavior is multiscaling corresponding to a multifractal process.
The concavity of this function is a characteristic of the intermittency, the more the
curve is concave, the more the process is intermittent [1,2]. Secondly, we apply a
technique given in Seuront & Schmitt 2005 [3], to estimate the power curve of joint
fluctuations < u′(t)mp′(t)n > at all scales and at all intensities, by the function
Su′p′(m,n):
Su′p′(m,n ) = ζu′(m )+ ζp′(n)- r(m,n)
(1)
where r(n,m) is estimated as the slope of the power law of c(n,m) versus Ï in a log-log
plot, that is defined as [3]:
–– -r(m,n)
c(m, n) = < u′m >< p′n > ~ Ï
(2)
the brackets < . > defines the statistical average.
The analysis presented in this work, is performed with simultaneous time series of wind
speed u(t) and output power p(t) for two types of WTGs, loaded from the Database of Wind
Characteristics of the Technical University of Denmark [4]: i) a 300 kW Nordtank wind
turbine located in the North Jutland, on the south bank of the Limfjord, about 36 km west of
Alborg and 8 km north east of Loegstoer, Denmark. The wind speed and the output power are
measured with a sampling rate at 20 Hz during 746 hours. The measurement are
obtained at 31 m above the ground. ii) a 2 MW wind turbine at Tjaereborg, Esbjerg,
Denmark. The wind speed and the output power are measured with a sampling
rate at 25 Hz during 64 hours. The measurement are obtained at 90 m above the
ground.
References
[1]Â Â Â Frisch, U., Turbulence, the legacy of A.N. Kolmogorov, Cambridge
University Press, Cambridge, 1995
[2]Â Â Â Schertzer, D., Lovejoy, S., Schmitt, Chigirinskaya, Y. and Marsan, D.,
Multifractal cascade dynamics and turbulent intermittency, Fractals 5 (3),
427-471, 1997
[3]Â Â Â Seuront, L. and Schmitt, F. G. Multiscaling statistical procedures for the
exploration of biophysical couplings in intermittent turbulence. Part I. Theory,
Deep-Sea Research II 52, 1308-1324, 2005
[4]Â Â Â See http://www.winddata.com/ |
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