Wind Energy

32
Handling Systems Driven by Different Noise
Sources: Implications for Power Curve
Estimations
F. Böttcher, J. Peinke, D. Kleinhans, and R. Friedrich
Summary. A frequent challenge for wind energy applications is to grasp the impacts
of turbulent wind speeds properly. Here we present a general new approach
to analyze time series – interpreted as a realization of complex dynamical systems –
which are spoiled by the simultaneous presence of dynamical noise and measurement
noise. It is shown that such noise implications can be quantified solely on the basis
of measured times series.
32.1 Power Curve Estimation in a Turbulent
Environment
A fundamental problem in wind energy production is a proper estimation of
the wind turbine-specific power curve, i.e., the functional relation between the
(averaged) wind speed u(t) and the corresponding (averaged) power output
P (t): 〈u(t)〉 →〈P (u(t))〉. On the basis of this relation and the expected annual
wind speed distribution at a specific location the annual energy production
(AEP) is estimated.
The main problem of a proper determination of the power curve (officially
regularized in IEC 61400-12) is its nonlinearity in combination with the turbulent
wind field. It is well known that to characterize a fluctuating nonlinear
quantity higher order moments are generally needed to be considered. In view
of the determination of a proper power curve this means that the association
of an averaged power to an averaged wind speed is not unique but will depend
at least on the intensity of fluctuations. To circumvent this difficulty it was
suggested to expand the power curve into a Taylor series (e.g., [1, 2])
P (u) =Pr(V )+
∂P(V )
∂u
· v + 1 ∂
2
2P (V )
∂u2 · v 2 + O(v 3 ) , (32.1)
where the notation u(t) =V + v(t) (with V := 〈u(t)〉 and 〈v(t)〉 =0)for
the instantaneous wind speed is used. Assuming that the fluctuations v(t) are