Wind Energy

182 F. Böttcher et al.
32.1.2 Additional Noise
So far we assumed a purely deterministic response of the power. On the one
side there might be dynamical noise (D (2) �= 0) on the other side measurement
noise might be present. In the latter case it is no longer the pure state vector
q that is observed but q with a superimposed uncertainty:
yi(t) =qi(t)+σiΓi(t). (32.8)
In this case the evaluation of the coefficients from the conditional moments
according to (32.5) has to be modified [5]:
M (n)
i (y,τ)=d (n)
i (y,τ)+γ (n)
i (y,τ,σ). (32.9)
This means that without measurement noise (provided the temporal resolution
is good enough) the coefficients are simply given by the slope of the conditional
moments as a function of τ. In presence of measurement noise the relation
is more complicated. For an Ornstein–Uhlenbeck process the modified slope
d (n) and the τ-independent term γ (n) can be calculated analytically. For more
complex processes they have to be determined numerically.
32.2 Conclusions and Outlook
We presented a new approach to reconstruct the “real” power curve independent
of location specific parameters such as the turbulence intensity. So
far the analysis is based on a simplified (numerical) wind turbine model but
which can easily be extended to more complex systems.
For instance (1) the wind speed can also be modeled by non-Ornstein–
Uhlenbeck processes (D (2) = f(u)) or non-Langevin processes (in order to
get a more realistic spectrum). Additionally (2) the effects of other noise
sources can be taken into account according to the approach sketched in (32.9)
and finally (3) one might use more wind turbine specific response functions
κ = κ(u, ˙u).
A first application to real wind turbine systems has been presented by
Anahua et al. [6].
References
1. Rosen A., Sheinman Y. (1994) J. Wind Eng. Ind. Aerodyn. 51:287–302
2. Langreder W., Hohlen H., Kaiser K. (2002) Proceedings of Global Windpower
Conference, published by EWEA as CD-Rom
3. The symbol (...)ij indicates that first the square root of the diagonalized matrix
D (2) has to be taken; successively a back transformation gives the ij-coefficients.
4. Rauh A., Peinke J. (2003) J. Wind Eng. Ind. Aerodyn. 92:159–183
5. Boettcher F. (2005) PhD-thesis, University of Oldenburg
6. Anahua E. et al.(2004) Proceedings of EWEC conference, published on CD-Rom