Power curves for wind turbines - Wind Power Generation and Wind Turbine Design - page 608

Figure 10 : Drift fi eld D (1) ( P ; u ) (arrows), Langevin power curve (crosses) and
IEC power curve (background line) for a multi-MW wind turbine.
The intensity of the drift fi eld is proportional to the length of the
arrows. The power output is normalized by its rated value P r . This fi gure
represents the same wind turbine as Fig. 4.

Indeed, a striking limitation of the IEC method lies in the way it discretizes the
domain { u , P }. As detailed in the Section 2.3, the IEC method averages all data in
speed bins of size d u = 0.5 m/s. The domain is discretized only for the wind speed,
resulting in a unique point every 0.5 m/s for the IEC power curve. The IEC power
curve is one-dimensional, it is the line P IEC ( u ) (as represented in Fig. 9).
The dynamical method, however, discretizes the domain { u , P } on both wind
speed and power output. The resulting power curve, derived from the drift fi eld
D (1) ( P ; u ), is a two-dimensional quantity. As shown in Fig. 10, each point in the
domain displays a vector indicating how fast (length of the vectors) and in which
direction the system wants to evolve.
Obviously in low power but high wind regions, the vectors point upwards to
higher power values. Correspondingly, high power but low wind regions vectors
point downwards to smaller power values. This is shown in Fig. 10.
This mathematical framework is necessary to observe the dynamics of a wind
turbine. This point is crucial to characterize power performance. Thanks to the
dynamical method, multi-stable behaviors can be observed, and a greater insight
can be reached. This is easily seen in Fig. 10, where multiple fi xed points appear
in several speed bins. Multi-stable behavior appears in the slow region ( u ≈ u cutin =

4 m/s) and in the fast region ( u u r = 13 m/s), where complex dynamics take place.

In the slow region, the turbine transits between the rest and the partial load modes.

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