Grey parameter estimation method for extreme value distribution of short-term wind speed data

Abstract

Accurate parameter estimation of extreme wind speed distribution is of great importance for the safe utilization and assessment of wind resources. This paper emphatically establishes a novel grey generalized extreme value method for parameter estimation of annual wind speed extremum distribution (AWSED). Considering the uncertainty and frequency characteristics of the parent wind speed, the generalized extreme value distribution (GEVD) is selected as the probability distribution, and the Weibull distribution is utilized as the first-order accumulation generating operator. Then, the GEVD differential equation is derived, and it is transformed into the grey GEVD model using the differential information principle. The least squares method is used to estimate the grey GEVD model parameters, and then a novel estimation method is proposed through grey parameters. A hybrid particle swarm optimization algorithm is used to optimize distribution parameters. The novel method is stable under different sample sizes according to Monte Carlo comparison simulation results, and the suitability for the novel method is confirmed by instance analysis in Wujiaba, Yunnan Province. The new method performs with high accuracy in various indicators, the hypothesis test results are above 95%, and the statistical errors such as MAPE and Wasserstein distance yield the lowest, which are 3.33% and 0.2556, respectively.

Keywords

• probability distribution of wind speed
• generalized extreme value distribution
• parameter estimation
• grey model
• monte carlo simulation