Equivalent modeling of wind energy conversion considering overall effect of pitch angle controllers in wind farm

The correct electric power fluctuation process of a wind farm is essential for the operation and studying of the power grid integrated with wind power. A complete wind energy conversion model, that should take both the spatial effects and the overall effect of all the pitch angle controllers into account, is required to convert the wind fluctuation into the electric power fluctuation. Although some equivalent models have been proposed in previous studies, there is no simple solution for equivalently modeling the non-synchronous actions of the pitch angle controllers in individual wind turbine generators. This study found the relationship between the overall effect of all the pitch angle controllers and the spatial effects of the wind farm and presented a theoretical derivation of the frequency-domain equivalent modeling method. The proposed modeling method is the simplest way to obtain the equivalent model of the complete wind energy conversion process of a wind farm with consideration of all the spatial effects and the overall effects of all the pitch angle controllers. The only input signal of the proposed equivalent model is the speed of the wind before entering the wind farm, which is called the “original incoming wind speed” and the only output signal is the total power of the wind farm. In this proposed equivalent modeling method, a discrete transfer function for representing both the wind energy conversion process, and all the spatial effects of a wind farm, can be obtained, first through a wind process below the rated wind speed. Second, a compensation factor for calculating a “compensation wind speed” of the original incoming wind can be obtained through a wind process that partly exceeds the rated wind speed. Using this compensation wind speed, a compensation power with negative values can be obtained to represent the total reduced power caused by the pitch angle controllers in individual wind turbine generators. A frequency-domain equivalent model has been identified and validated by field measurements of an actual wind farm. The normalized root-mean-squared error of the model is less than 8% over the entire wind process, and the maximum error of the power ramp rate in 10 min is less than 5 MW. Finally, an example is provided to demonstrate the online use of the proposed model to convert the forecasted wind speed into output power of a wind farm in ultra-short-term wind power forecast.