Wind turbulence modeling for real-time simulation

Abstract

This paper proposes a method to design a real-time wind turbulence simulator. The objective of such a simulator is to make dynamical models more accurate in order to develop more robust controls, especially in the case of mechanical systems operating outdoors such as tracking antennas. The models used to generate a random wind speed are based on the wind spectral characteristics rather than time domain ones. Indeed, turbulence is a stochastic and non-stationary process corresponding to the short-term component of wind and therefore is difficult to model in time domain. Wind spectral characteristics are described by the power spectral density whose approximation is used in the real-time simulator to reproduce wind behavior. The von Kármán model is the most commonly used model to approximate the power spectral density of wind turbulence. However, this model was originally designed for aircraft, and therefore for high altitudes and moving systems. In our case, tracking antennas are used under different conditions: low altitude and slow moving systems. This makes the von Kármán model less precise in middle and high range frequency. Consequently, there is a need in more accurately 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 Davidson-Cole fractional models. The idea is to use shaping filters issued from these more precise fractional models to generate realistic random wind speed turbulence from a random white noise input. These filters are approximated by rational functions and their parameters are tuned in the same way as those of the von Kármán model with the same inputs (mean speed, standard deviation and length scale). If a rational model is sought, a very high number of parameters (more than six times) is needed to have the same precision as our proposed fractional Cole-Cole model which has only four parameters. Finally, an accurate turbulence wind speed generator is proposed.