Fitting the Variations from the Wind Speed to the Active Power of a Wind Powered Generator by a Low-Pass Filter

A smart electrical grid must accommodate all kinds of green renewable energy, especially the wind power. The mapping from a wind speed to the active power of a mechanical wind powered generator is a key fundamental technique for the wind power accommodation. To find explicit analytical functions from a wind speed to the active power, according to the law of rotation of a rigid body in rotational motion in physics, the function from wind speed variations to active power variations can be approximately reduced to a first-order low-pass filter. This analytical function is verified by three time series, i.e., the wind speed, blade rotation and active power with 10s sampling period. The variational components of wind speed and active power are decomposed by the 7 points smoothing filter, a linear Gaussian filtering and the biorthogonal 6.8 wavelet (bior6.8). The standard deviations ratio of active power variations to wind speed variations is very close to the magnitude frequency response of a first-order low-pass filter. The cross wavelet transform and wavelet coherence between time series of wind speed and active power also confirm the filter function. The numerical simulations show that a first-order low-pass filter can approximately represent the function from wind speed variations to active power variations.