Fractal dimension of wind speed time series

• Published in: Applied energy Vol. 93; pp. 742 - 749
• Main Authors: Chang, Tian-Pau, Ko, Hong-Hsi, Liu, Feng-Jiao, Chen, Pai-Hsun, Chang, Ying-Pin, Liang, Ying-Hsin, Jang, Horng-Yuan, Lin, Tsung-Chi, Chen, Yi-Hwa
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.05.2012; Elsevier
• Subjects: algorithms; Applied sciences; chaos theory; climatic factors; dimensions; Energy; energy conversion; Exact sciences and technology; Fluctuation; Fractal analysis; Fractal dimension; fractal dimensions; Fractals; Mathematical analysis; Mathematical models; monsoon season; Probability density function; Seasons; time series analysis; Weibull function; Wind fluctuation; Wind power generation; Wind speed; wind turbines; Probability density function; Weibull function; Fractal dimension; Wind speed; Wind fluctuation
• ISSN: 0306-2619; 1872-9118
• DOI: 10.1016/j.apenergy.2011.08.014

► Fractal dimension of wind speeds in Taiwan is studied considering climate factors. ► Relevant algorithms for the calculation of fractal dimension are presented graphically. ► Fractal dimension reveals negative correlation with mean wind speed. ► Fractal dimension is not lower even wind distribution is well described by Weibull pdf. The fluctuation of wind speed within a specific time period affects a lot the energy conversion rate of wind turbine. In this paper, the concept of fractal dimension in chaos theory is applied to investigate wind speed characterizations; numerical algorithms for the calculation of the fractal dimension are presented graphically. Wind data selected is observed at three wind farms experiencing different climatic conditions from 2006 to 2008 in Taiwan, where wind speed distribution can be properly classified to high wind season from October to March and low wind season from April to September. The variations of fractal dimensions among different wind farms are analyzed from the viewpoint of climatic conditions. The results show that the wind speeds studied are characterized by medium to high values of fractal dimension; the annual dimension values lie between 1.61 and 1.66. Because of monsoon factor, the fluctuation of wind speed during high wind months is not as significant as that during low wind months; the value of fractal dimension reveals negative correlation with that of mean wind speed, irrespective of wind farm considered. For a location where the wind distribution is well described by Weibull function, its fractal dimension is not necessarily lower. These findings are useful to wind analysis.