Wind Energy

31
Characterisation of the Power Curve for Wind
Turbines by Stochastic Modelling
E. Anahua, S. Barth and J. Peinke
Summary. We investigate how the power curve of a wind turbine is affected by
turbulent wind fields. The electrical power output can be separated into two parts
namely the relaxation part which describes the dynamic response of the wind turbine
on sudden changes in wind velocity and a noise part. We have shown that those two
parts describe the power-curve properly if they are calculated from stationary wind
measurements. This analysis is very usefull to describe power curve characteristic
for situation with increased turbulent intensities and it can be easily applied to
measured data.
31.1 Introduction
Let us start with the definition of the power curve which is a nonlinear function
of wind velocity
L(u) ∝ u 3 .
A standard procedure (IEC 61400-12) to characterise the energy production
of a wind electro converter (WEC) is to measure average values of elect. power
output and longitudinal wind velocity at the hub hight simultaneously. From
those measurements a power curve is obtained by: 〈u〉 →〈L(u)〉 as shown
in Fig. 31.1 (the brackets denote the ensemble averages). This procedure is
limited due to (1) nonlinearity of the power curve and (2) relaxation time
which describes the dynamic response of the WEC on sudden changes of
wind velocity. Such effects lead to the following inequality: L(〈u〉) �= 〈L(u)〉.
To include those effects into the stationary power curve one could use a Taylor
expansion of second-order which is expressed by
〈L(u)〉 = L(〈u〉)+ 1 ∂
2
2
∂u 2 L(〈u〉)σ2 u ,
where σ 2 u is the variance of the wind velocity. Obviously this method is only
appropiate for the case of symmetric and weak (quasi-laminar) fluctuations