Macromodel of Spatial Smoothing in Wind Farms

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Departing from aerodynamics (micromodel), the macromodel begins with the power output of a single wind turbine generator (WTG). The <formula formulatype="inline"><tex>$N$</tex></formula> units of WTGs in a wind farm are characterized by the time delays it takes wind, at average velocity, to traverse the distances separating them. Predictions from simulations are in agreement with recorded wind farm data. Smoothing of high-frequency power components is by a factor close to <formula formulatype="inline"><tex>$N^{-1/2}$</tex></formula>. Smoothing of low-frequency harmonic power components is small because the wind farm is limited in size. A theory, based on Fourier analysis, is presented to explain how the macromodel simultaneously copes with: 1) the high-frequency components of wind velocity (which have poor correlation) even for short distances and 2) the low-frequency components (which have some correlation). </para>