Wind fractional modeling by spectral analysis

Abstract

This paper deals with wind turbulence modeling by using spectral analysis, in order to have a real-time wind simulator for dynamic models of parabolic tracking antennas. Indeed, such a realistic wind speed is needed to make dynamic models more complete and to design robust controls. The wind speed can be decomposed into two components: a long-term one representing the wind mean speed and a short-term one corresponding to the wind turbulence. Fast wind turbulence is a stochastic process and is difficult to model in time domain. For this reason, the models presented in this paper are based on the wind spectral characteristics. The most used Von Karman model well approximates the power spectral density of the wind turbulence. However, this model lacks precision in middle range frequency. Indeed, the Von Karman model was originially designed for aircrafts, and consequently for high altitudes and moving systems. In our case, tracking antennas are used under different conditions: low altitude and slow moving systems. Therefore, there is a need in more precisely modeling wind turbulence under these specific conditions. As Von Karman’s model expression uses fractional calculus, other models with the same range of parameter number are proposed to better approximate the wind power spectral density by using Cole-Cole and Havriliak-Negami fractional models. The proposed fractional models will enable generating realistic random wind speed turbulence from a random white noise input.