This chapter presents some data examples to illustrate a stochastic model that can be used to estimate the smoothing effect of the spatial diversity of the wind across a wind farm on the total generated power. The models developed in this chapter are based in the personal experience gained designing and installing multipurpose data loggers for wind turbines, and wind farms, and analyzing their time series.
Due to turbulence, vibration and control issues, the power injected in the grid has a stochastic nature. There are many specific characteristics that impact notably the power fluctuations between the first tower frequency (usually some tenths of Hertzs) and the grid frequency. The realistic reproduction of power fluctuations needs a comprehensive model of each turbine, which is usually confidential and private. Thus, it is easier to measure the fluctuations in a site and estimate the behaviour in other wind farms.
Variations during the continuous operation of turbines are experimentally characterized for timescales in the range of minutes to fractions of seconds. A stochastic model is derived in the frequency domain to link the overall behaviour of a large number of wind turbines from the operation of a single turbine. Some experimental measurements in the joint time-frequency domain are presented to test the mathematical model of the fluctuations. The admittance of the wind farm is defined as the ratio of the oscillations from a wind farm to the fluctuations from a single turbine, representative of the operation of the turbines in the farm. The partial cancellation of power fluctuations in a wind farm are estimated from the ratio of the farm fluctuation relative to the fluctuation of one representative turbine.
Provided the Gaussian approximation is accurate enough, the wind farm power variability is fully characterized by its auto spectrum and many interesting properties can be estimated applying the outstanding properties of Gaussian processes (the mean power fluctuation shape during a period, the distribution of power variation in a time period, the most extreme power variation expected during a short period, etc.).
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