Analysis of Wind Velocity and the Quantification of Wind Turbulence in Rural and Urban Environments Using the Levy Index and Fractal Dimension

Abstract

This paper is concerned with a quantitative and comparative analysis of wind velocities in urban and rural environments. It is undertaken to provide a route to the classification of wind energy in a rural and urban setting. This is a common problem and the basis of a significant focus of research into wind energy. In this paper, we use a non-Gaussian statistical model to undertake this task, and, through a further modification of the data analysis algorithms used, extend the model to study the effect of wind turbulence, thereby introducing a new metric for this effect that is arguably superior to a more commonly used and qualitatively derived measure known as the Turbulence Intensity. Starting from Einstein’s evolution equation for an elastic scattering process, we consider a stochastic model for the wind velocity that is based on the Generalised Kolmogorov Feller Equation. For a specific ‘memory function’ the Mittag-Leffler function it is shown that, under specified conditions, this model is compatible with a non-Gaussian processes characterised by a Levy distribution that, although previously used in wind velocity analysis, has been introduced phenomenologically. By computing the Levy index for a range of wind velocities in both rural and urban environments using industry standard cup anemometers, wind vanes and compatible data collection conditions (in terms of height and sampling rates), we show that the intuitive notion that the ‘quality’ of wind velocity in an urban environment is poor compared to a rural environment is entirely quantifiable. This quantifies the notion that a rural wind resource is, on average, of higher yield when compared to that of the urban environment in the context of the model used. In this respect, results are provided that are based on five rural and urban locations in Ireland and the UK and illustrate the potential value of the model in the consideration of locating suitable sites for the development of wind farms (irrespective of the demarcation between an urban and rural environment). On this basis, the paper explores an approach whereby the same model is used for evaluating wind turbulence based on the Fractal Dimension using the ‘polar wind speed’ obtained from three-dimensional data sets collected in urban environments.