Modeling wind speed time series by Chebyshev polynomial expansion method

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 $0.015$; 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 $0.15$.

KEYWORDS:

• Non-Gaussian wind speed time series
• translation model
• Fourier series
• Chebyshev polynomial

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Qing Xiao

Qing Xiao received the Ph.D degree  from Hunan University of Science and Technology in 2020. He is currently with School of Information and Electrical Engineering, Hunan University of Science and Technology.  His research interests include statistical modeling in power systems, probabilistic power flow computation and probabilistic optimal power flow computation.