A joint probabilistic analytical model with consideration of wind power and load uncertainties

A joint probabilistic analytical model for modeling wind farm power output and load demand considering uncertainties is proposed in this paper. Compared with traditional numerical solutions, the proposed model can improve computational efficiency remarkably while keeping the accuracy. Firstly, based on a series of typical wind speed distributions whilst considering the wake effect of wind farm, the probabilistic analytical models of wind farm power output via introducing the concept of impulse function in the signal system are proposed. In order to better reflect the effects of wind power and load uncertainties simultaneously, in accordance with the convolution method described in probability theory and combined with the normal probability density function (PDF) of load, a joint probabilistic analytical model for describing the uncertainties of wind farm power output and load is deduced. Finally, the comparisons with numerical simulation method are conducted to demonstrate the effectiveness and validity of the proposed model.