Effects of wind speed probabilistic and possibilistic uncertainties on generation system adequacy

A random fuzzy model is proposed to express the probabilistic and possibilistic uncertainties of wind speed simultaneously. In this model, wind speed is represented by a random variable following Weibull distribution, indicating the probabilistic uncertainty. The Weibull distribution parameters of wind speed are fuzzy numbers, meaning the possibilistic uncertainty of wind speed. For estimating distribution parameters, a multi-objective optimisation problem is developed based on cumulative probability and probability distributions of wind speed. The proposed model is then combined with traditional generation system adequacy (GSA) evaluation method to investigate the effect of wind speed uncertainties on GSA. To overcome the difficulty in calculating fuzzy GSA indices, sparse grid is utilised to select collocation points and single-index regression is employed to fit the relationship between adequacy indices and wind speed parameters. This study illustrates the effectiveness of the model from its application to IEEE Modified Reliability Test System. Compared with previous researches, the proposed model is suitable for the case of incomplete data or containing some outliers. It provides more helpful interval information on wind speed and adequacy indices.