Wind speed variability study based on the Hurst coefficient and fractal dimensional analysis

Abstract

AbstractThis paper presents a study of a wind speed time series from La Venta, Oaxaca, Mexico. The time series consists of anemometric measurements taken by the Federal Electricity Commission of Mexico throughout a little over 6 years. The study was conducted to calculate the Hurst correlation coefficient using: box counting, rescaled range, power spectrum, detrended fluctuation analysis, and multifractal detrended fluctuation analysis techniques. The main objective of this research is to know the correlation among wind speed data to obtain a better description of real conditions of the time series, which is not always available, and to define the structure of its behavior. In this way, more suitable wind speed prediction models can be achieved. Results obtained from techniques above were used to generate fractals time series for a typical month, using the Hurst coefficient and a self‐affine trace generator, which produces fractals time series whose probability distribution is always normal. These time series were compared against time series generated by using random numbers with Gaussian behavior and the characteristics of a typical month. Fractals time series highlight in the qualitative part regarding the modeling of wind speed variability and the descriptive statistics (average, standard deviation, and coefficient of variation), which is similar to the real series. Discordance tests were applied to the datasets to detect deviated values, and so ensure the normal behavior of the samples. These tests showed the existence of different populations with normal behavior in the samples that had bimodal characteristics. By separating the samples, it was possible to apply the self‐affine trace generator to each population found, to generate the fractal time series. An additional objective was to find the level of change in the structure of the original series concerning its statistical and fractal characteristics at different window widths of the time series (daily, monthly, seasonal, and annual) to identify either a specific tendency or dynamic behavior. The results showed a wind speed time series with a negative correlation (antipersistent), a high degree of scale invariance (homothetic), and a fractal dimension very close to 2, thus indicating that the time series is more irregular than a random process.