Wind resource and site assessment - Wind Power Generation and Wind Turbine Design - page 84

7 Energy yield and losses

7.1 Single wind turbine

The power production varies with the wind speed that strikes the rotor. The wind
speed at hub height is normally used as a reference for the power response of the
wind turbine. Knowing the power curve of a wind turbine P ( u ), the mean power pro-
duction can be estimated using the probability density function of the wind speed at
hub height f ( u ), which is typically expressed as a Weibull distribution (see eqn (3)):

k − 1

⎛

k

⎞

∞ ∞

ku u

⎛⎞ ⎛⎞

∫ ∫

Pf uPuu = () ()d = exp − Puu ()d (14)

⎜⎟ ⎜ ⎜⎟ ⎟

⎝⎠ ⎝⎠

AA A

⎝ ⎠

0 0

This integral cannot be computed analytically and thus has to be solved numer-
ically. For this purpose the power curve is divided into a suffi cient number of lin-
ear sections, typically for 0.5 m/s steps. The power output can now be calculated
by summing up the produced energy for each wind speed bin.
Care has to be taken as the power of the wind is proportional to the air density.
A power curve normally refers to an air density of 1.225 kg/m 3 which corresponds
to a temperature of 15°C at sea level. A higher elevation and/or a warmer site will
lead to a lower air density and thus to a lower energy output.
Special considerations should be given to the fact that a number of site-specifi c
parameters infl uence the power curve and thus the energy yield most signifi cantly
turbulence and wind shear [30].
Another way of stating the annual energy output from a wind turbine is to look
at the capacity factor for the turbine in its particular location. By capacity factor
we mean its actual annual energy output divided by the theoretical maximum out-
put if the machine were running at its rated (maximum) power during all of the
8760 h of the year. The capacity factors may theoretically vary from 0 to 100%, but
in practice they will mostly be around 30-40%.

7.2 Wake and other losses

As mentioned in Section 5.2.2 and shown in Fig. 23 the wake of a wind turbine
is characterised by a velocity defi cit. This will lead to a reduced effi ciency of
any wind turbine operating in its wake. The so-called park loss is dependent on the
thrust curve of the rotor, on the wake decay constant (which in turn is a function
of the ambient turbulence intensity), and the distance between the turbines. High
ambient turbulence intensity will lead to an increased mixing between the wake and
the surrounding undisturbed fl ow. As a consequence the opening angle of the wake
increases, thus resulting in smaller park losses than low turbulence situations.
Two models are commonly used in the industry, the N.O. Jensen model and the
Eddy-Viscosity model of Ainslie [32]. The N.O. Jensen model is a simple, single
wake kinematic model, in terms of an initial velocity defi cit and a wake decay
constant. It is based on the assumption that the wake right behind the wind turbine