**3. From wind speed variability to regional wind power fluctuations**

As highlighted above, from the point of view of power systems, it is important to analyze wind power fluctuations from tens of minutes to several hours. Therefore, it is important to study the relation between wind speed variability and wind power fluctuations.

Different operating regions give different rates of power fluctuations. The first stage in the conversion of wind power to electrical power is the smoothing and sampling effect pro‐ duced by the size of the wind turbine rotor. In fact, some variations in wind speed at a sin‐ gle point within the rotor swept area are smoothed out when considering the entire blade length. Particularly, uncorrelated oscillations of wind speed are attenuated when consider‐ ing several points within the rotor swept area. To analyze the correlation between such os‐ cillations, spectral coherence is usually considered. Studies have been done of spectral coherence between the horizontal wind speeds within the rotor disk, showing a large smoothing of the (high-frequency) quickest variations [17]. To illustrate these effects, Figure 5 compares wind speed at a single point within the rotor swept area, with an equivalent wind speed over the rotor disk [18].

**Figure 5.** Comparison between wind speed in a single point of the rotor disk and the equivalent wind over the rotor disk

Moreover, the conversion of wind energy into electrical power is not linear. In a typical power curve (Fig. 2), there are wind speed ranges with different impacts on the conversion from wind speed variations to wind power fluctuations. Between cut-in wind speed and nominal wind speed, variability in power tends to amplify wind speed variability because of the "near" cubic dependence between power and wind speed. On the other hand, for wind speeds below cut-in wind speed or between nominal and cut-out wind speed, power fluctuations are smoothed considerably. However, if wind speed crosses cut-out speed or oscillates around it, fluctuations can be significantly increased as power varies from 100% (rated output power) to 0% (when the wind power plant is disconnected above cut out wind speeds). Figure 6 shows two different series of power: the reduction or increasing of varia‐ bility depending on the wind speed range within the wind turbine power curve.

The second stage considers the reduction of the power fluctuations when aggregating sever‐ al wind turbines within a wind power plant and even aggregating wind power plants in a large region. Aggregated power fluctuations are reduced by the diversity of the wind speeds within a large area. Analogously to the effect mentioned above, with regard to the rotor disk effect, spectral coherence can also be studied in wind power plants or even larger regions, analyzing which parts of the power fluctuations are not correlated or even which parts are delayed between wind turbines or power plants [19]–[20]. Studies on spectral co‐ herence in wind power plants or regions can be found in the literature [21]–[23]. Examples of those effects are illustrated in Figure 7 and Figure 8, where power in a single turbine is compared with the aggregated power of a wind power plant and a set of wind power plants, respectively.

**Figure 6.** The figure on the left shows the power generated from a single wind turbine when wind is between cut-in and nominal speed; whereas the figure on the right shows wind speed between nominal and cut-out speed [23]

**Figure 5.** Comparison between wind speed in a single point of the rotor disk and the equivalent wind over the rotor

Moreover, the conversion of wind energy into electrical power is not linear. In a typical power curve (Fig. 2), there are wind speed ranges with different impacts on the conversion from wind speed variations to wind power fluctuations. Between cut-in wind speed and nominal wind speed, variability in power tends to amplify wind speed variability because of the "near" cubic dependence between power and wind speed. On the other hand, for wind speeds below cut-in wind speed or between nominal and cut-out wind speed, power fluctuations are smoothed considerably. However, if wind speed crosses cut-out speed or oscillates around it, fluctuations can be significantly increased as power varies from 100% (rated output power) to 0% (when the wind power plant is disconnected above cut out wind speeds). Figure 6 shows two different series of power: the reduction or increasing of varia‐

bility depending on the wind speed range within the wind turbine power curve.

The second stage considers the reduction of the power fluctuations when aggregating sever‐ al wind turbines within a wind power plant and even aggregating wind power plants in a large region. Aggregated power fluctuations are reduced by the diversity of the wind speeds within a large area. Analogously to the effect mentioned above, with regard to the rotor disk effect, spectral coherence can also be studied in wind power plants or even larger regions, analyzing which parts of the power fluctuations are not correlated or even which parts are delayed between wind turbines or power plants [19]–[20]. Studies on spectral co‐ herence in wind power plants or regions can be found in the literature [21]–[23]. Examples

disk

290 Advances in Wind Power

**Figure 7.** Comparison between a single wind turbine in an offshore wind power plant and the aggregated production of the whole wind power plant

**Figure 8.** Comparison between the power produced by two wind power plants with the aggregation of nine wind power plants (including the previous ones) and the whole of Spanish wind power output

Finally, when aggregation includes different types of wind turbines, with different nominal wind speeds and different cut-out speeds, extreme aggregated fluctuations are also reduced significantly.In short, temporal diversities and spatial diversities reduces the peak-to-peak magnitudes of power fluctuations.

On the other hand, some regions wind power fluctuations are not related wind speed varia‐ bility. Instead, the power fluctuations are caused by technical and operational challenges rather than by meteorological phenomena.Particularly, these include:


Another classification is laid down. Attending to their ramping characteristics, wind power fluctuations events can be classified in:

**•** Wind power die-out. A wind power die-out refers to a persistent drop in wind power.

