Power Fluctuations in a Wind Farm Compared to a Single Turbine

This chapter is focused on the estimation of wind farm power fluctuations from the behaviour of a single turbine during continuous operation (special events such as turbine tripping, grid transients, sudden voltages changes, etc. are not considered). The time scope ranges from seconds to some minutes and the geographic scope is bounded to one or a few nearby wind farms. One of the objectives of this chapter is to explain quantitatively the wind power variability in a farm from the behaviour of a single turbine. For short intervals and inside a wind farm, the model is based on the experience with a logger system designed and installed in four wind farms (Sanz et al., 2000a), the classic theory of Gaussian (normal) stochastic processes, the wind coherence model (Schlez & Infield, 1998), and the general coherence function derived by Riso Institute in Horns Rev wind farm (Martins et al., 2006; Sorensen et al., 2008a). For larger distances and slower variations, the model has been tested with meteorological data from the weather network. The complexities inherent to stochastic processes are partially circumvented presenting some case studies with meaningful graphs and using classical tools of signal processing and time series analysis when possible. The sum of the power from many turbines is a stochastic process that is the outcome of many interactions from different sources. The sum of the power variations from more than four turbines converges approximately to a Gaussian process despite of the process nature (deterministic, stochastic, broadband or narrowband), analogously to the martingale central limit theorem (Hall & Heyde, 1980). The only required condition is the negligible effect of synchronization forces among turbine oscillations. The data logged at some wind farms are smooth and they have good mathematical properties except during special events such as turbine breaker trips or severe weather. This chapter will show that, under some circumstances, the power output of a wind farm can be approximated to a Gaussian process and its auto spectrum density can be estimated from the spectrum of a turbine, wind farm dimensions and wind coherence. The wind farm power variability is fully characterized by its auto spectrum provided the Gaussian approximation is accurate enough. Many interesting properties such as the mean power fluctuation shape during a period, the distribution of power variation in a time period, the more extreme power variation expected during a short period, etc. can be estimated applying the outstanding properties of Gaussian processes according to (Bierbooms, 2008) and (Mur-Amada, 2009).