**2. Wind speed variability**

Overall wind variability consists of different fluctuating terms with different periods, depend‐ ing on the sources. For instance, fluctuating term can be caused by day-night effects (e.g., the effects of sea breeze), because there are "quick" fluctuations in some minute periods.

Figure 2 shows a typical power curve of a variable speed wind turbine generator. In general, the operating wind speed is divided into different regions. In Region 1 and Region 2 (low to rated wind speed), a wind turbine is operated in variable speed at a constant pitch angle (typically 0o ). The output power of the generator is low to rated power. The operation is op‐ timum because the turbine is operated at the maximum performance coefficient Cp. When wind speed varies, the output power varies as the cube of wind speed variations. Once wind reaches its rated speed, the rotational speed also reaches the rated speed. This rotational speed must be limited by the pitch control to keep the rotor speed from a runaway condition and to limit the mechanical stresses of the wind turbine structure (tower, blades, and gear‐ box). The output power is limited to its rated value.

Thus, wind power output varies only when wind speeds are below rated value. Below rated wind speed, the rate of change of the output power ( *dP dt* ) is either positive or negative, de‐ pending on the direction of wind speed change. Above rated wind speeds, any fluctuations will be capped at rated by the pitch action, or *dP dt* =0.

**Figure 2.** Power curve of a typical wind turbine generator

Additionally, many wind power plants are co-located in the same region where wind resour‐ ces are excellent; thus, the spatial diversity among wind power plants contributes to a smooth‐ er output power of the region than the output power of an individual wind power plant.

**Figure 1.** Real and reactive power output of a wind power plant; (a) Single turbine representation (b) Sixteen turbines

Figure 1(a) shows the fluctuation in the output power when the wind power plant is repre‐ sented by a single turbine. Figure 1(b) illustrates the real and reactive power output when the wind power plant is represented by sixteen turbines. With greater wind diversity, as shown in Figure 1(b), the power fluctuation is smoother than that with less wind turbine

Overall wind variability consists of different fluctuating terms with different periods, depend‐ ing on the sources. For instance, fluctuating term can be caused by day-night effects (e.g., the

Figure 2 shows a typical power curve of a variable speed wind turbine generator. In general, the operating wind speed is divided into different regions. In Region 1 and Region 2 (low to rated wind speed), a wind turbine is operated in variable speed at a constant pitch angle

timum because the turbine is operated at the maximum performance coefficient Cp. When wind speed varies, the output power varies as the cube of wind speed variations. Once wind reaches its rated speed, the rotational speed also reaches the rated speed. This rotational speed must be limited by the pitch control to keep the rotor speed from a runaway condition and to limit the mechanical stresses of the wind turbine structure (tower, blades, and gear‐

Thus, wind power output varies only when wind speeds are below rated value. Below rated

). The output power of the generator is low to rated power. The operation is op‐

*dt* ) is either positive or negative, de‐

effects of sea breeze), because there are "quick" fluctuations in some minute periods.

representation

286 Advances in Wind Power

(typically 0o

representation, as shown in Figure 1(a) [1].

box). The output power is limited to its rated value.

wind speed, the rate of change of the output power ( *dP*

**2. Wind speed variability**

If the power controller is not properly designed, wind fluctuations may excite the mechani‐ cal resonance of the structure or gearbox, which may lead to mechanical failures of the wind turbine [2]–[3].

Spectral tools are often used to analyze wind speed variability because they make it possible to study different frequency fluctuation terms. The most popular one used for this purpose is the Power Spectral Density (PSD).

The PSD of a function is defined by the Fourier transform of its autocorrelation. PSD is therefore expressed in frequency domain. Its physical meaning is related to fluctuating ki‐ netic energy on a certain frequency.

Van der Hoven [4] analyzed the PSD of horizontal wind speed, based mainly on measure‐ ments done at Brookhaven National Laboratory. Figure 3 shows such spectra, with two main peaks and a spectral gap between them. The first peak occurred at a period of around four days and was caused by migratory pressure systems of a synoptic weather map scale. The second peak occurred at a period of 1 minute because of a mechanical and/or convective type of turbulence. Van der Hoven's observations also showed some relation between the spectral gap shape and surface roughness under some circumstances. Additional analysis shows more complex spectra, especially over the ocean or in smooth terrains [5]–[9]; where there is an important contribution of mesoscale fluctuations combined with various phe‐ nomena such as convective longitudinal rolls [11] or cumulus clouds [12] that may contain considerable spectral density in the frequency range. At some other places, the gap was veri‐ fied by experimental data [4], [13]–[14].

**Figure 3.** Spectrum estimated by Van der Hoven [4]

PSD spectrum is usually calculated by using short segments of data with similar atmospher‐ ic characteristics. The reduction or removal of the spectral gap introduces some difficulties on the analysis because microscale and macroscale are no longer separated. This limits the findings of particular atmospheric regimes lasting long enough to calculate a meaningful spectrum. Thus, some researchers are considering the use of more complex spectral tools based on time and frequency domain. For instance, the Hilbert-Huang transform has been used for analyzing wind fluctuations over the North Sea [8].

Wind speed variability is important with regard to power system management. An example of the significance of these power fluctuations is in Energinet.dk (the Danish Transmission System Operator). According to [15], Energinet.dk has observed that power fluctuations from the 160-MW offshore wind power plant at Horns Rev in West Denmark introduce sev‐ eral challenges to reliable operation of the local power system. The power fluctuations also contribute to deviations from the planned power exchange with the Central European Pow‐ er System. Moreover, it was observed that the timescale of the power fluctuations was from tens of minutes to several hours.

Figure 4 shows the relation between time and geographical scales and the impacts affecting power system operation. Depending on the level of the wind power penetration, power fluc‐ tuations due to wind speed variability may influence the frequency regulation; transmission and distribution efficiency, and load flow; or even efficiency of the thermal and hydro pow‐ er plants connected to the same grid.

**Figure 4.** Time and geographical scales of power system issues [16]

Van der Hoven [4] analyzed the PSD of horizontal wind speed, based mainly on measure‐ ments done at Brookhaven National Laboratory. Figure 3 shows such spectra, with two main peaks and a spectral gap between them. The first peak occurred at a period of around four days and was caused by migratory pressure systems of a synoptic weather map scale. The second peak occurred at a period of 1 minute because of a mechanical and/or convective type of turbulence. Van der Hoven's observations also showed some relation between the spectral gap shape and surface roughness under some circumstances. Additional analysis shows more complex spectra, especially over the ocean or in smooth terrains [5]–[9]; where there is an important contribution of mesoscale fluctuations combined with various phe‐ nomena such as convective longitudinal rolls [11] or cumulus clouds [12] that may contain considerable spectral density in the frequency range. At some other places, the gap was veri‐

PSD spectrum is usually calculated by using short segments of data with similar atmospher‐ ic characteristics. The reduction or removal of the spectral gap introduces some difficulties on the analysis because microscale and macroscale are no longer separated. This limits the findings of particular atmospheric regimes lasting long enough to calculate a meaningful spectrum. Thus, some researchers are considering the use of more complex spectral tools based on time and frequency domain. For instance, the Hilbert-Huang transform has been

Wind speed variability is important with regard to power system management. An example of the significance of these power fluctuations is in Energinet.dk (the Danish Transmission System Operator). According to [15], Energinet.dk has observed that power fluctuations from the 160-MW offshore wind power plant at Horns Rev in West Denmark introduce sev‐ eral challenges to reliable operation of the local power system. The power fluctuations also contribute to deviations from the planned power exchange with the Central European Pow‐ er System. Moreover, it was observed that the timescale of the power fluctuations was from

fied by experimental data [4], [13]–[14].

288 Advances in Wind Power

**Figure 3.** Spectrum estimated by Van der Hoven [4]

tens of minutes to several hours.

used for analyzing wind fluctuations over the North Sea [8].
