Modeling wind speed time series by Chebyshev polynomial expansion method

Abstract

ABSTRACT This paper sets out to simulate non-Gaussian wind speed time series. Given a set of historical wind speed observations, if the cumulative distribution function is not explicitly known, a probability distribution based on Fourier series is developed to recover the analytical expression of the cumulative distribution function. The marginal transformation is then applied to map wind speed observations to the standard normal space, where the autocorrelation function is represented by a weighted sum of Chebyshev polynomials. Finally, an explicit formula is derived to generate samples of wind speed time series. Testing on three sets of historical wind speed observations, it shows that the proposed method can well match the cumulative distribution function and autocorrelation function of wind speed time series, the absolute errors between the fitted cumulative distribution function and empirical cumulative distribution function are less than ; the autocorrelation function of generated wind speed time series is in a good agreement with that of historical wind speed observations, the differences are less than .