A rank correlation based translation model for simulating wind speed time series

Abstract

Abstract The translation model is a useful tool for simulating non-Gaussian wind speed time series, it employs marginal transformation to fit the distribution function of wind speed, and deploys a Gaussian process with a specified autocorrelation function (ACF) ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ to match the ACF of wind speed. However, determining ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ requires solving an integral equation, which is not computationally convenient. In this paper, an easy-to-use method is presented for determining ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ . Based on Spearman’s rank correlation coefficient, a rank ACF is proposed to characterize the time-dependent behavior of wind speed time series, whereby ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ can be specified by an analytical formula. In the case that only discrete values of ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ are available, a Laguerre polynomial based model is developed to fit ρ Z ( τ ) ${\rho }_{Z}\left(\tau \right)$ . Furthermore, if the distribution function of wind data is unknown, the kappa distribution is introduced to fit the quantile function of wind speed. Finally, a case study is conducted to check the proposed method, the results indicate that the rank correlation based translation model can yield a satisfactory representation for statistical features of wind speed time series.