The Development of Synthetic Wind Series Based on Gaussian and Non Gaussian Statistics

The ability to summarise the characteristics of turbulence into classical statistical models has long been a cause of intrigue for the wind energy industry. Currently, in the context of wind energy systems, a representation of turbulence is by a singular numerical value, turbulence intensity (TI), but the question is whether a classical statistic has the ability to accurately quantify the turbulence characteristic in question.

Time series modelling of consecutive wind speed datum's is currently the only way to consider a system response of a turbine with an ever changing input variable. Due to the current data summarisation techniques such as averaging, standard deviation and in some instances frequency based histograms over a prescribed observation window (e.g. 10 minutes) the seriatim nature of the wind speed signal is lost. This leaves the industry in an awkward position. Should investment into an achievable means of recording all data be prioritised, i.e. towards a removal of the concept of data summarisation? This would inevitably increase the volume of data considerably; for instance 1 Hz data compressed to a singular 10 minute datum would increase the data storage capacity by a factor of 600 for a unit of similar accuracy. Alternatively should the wind energy industry continue along a data summarisation path losing any inherent time series information within the observational period and attempt to accommodate the inherent inaccuracies by some other means?

In this paper we propose an alternative solution that could essentially be regarded as a compromised approach. Data is first summarised in terms of Gaussian and non Gaussian statistics over a summary observation period (e.g. 10 minutes). Whereas the former represents the standard TI metric as well as arithmetic mean, the latter concerns a new concept, the Turbulent Fourier Dimension T_Df. T_DF is a non Gaussian statistic based on a crossover of fractal mathematics and noise theory. Following this, these three quantities are then used in a data extraction process to give a synthetic time series that is both statistically representative of the original wind signal, but also capable of approximating the time series inter variability of the wind speed signal within the observation period. A validation comparison utilising 10Hz meteorology located in an urban context is subsequently presented to assess the mathematical accuracy of the data summarisation and artificial synthesisation process. Finally a brief discussion will outline the potential application of this mathematical development in areas such as the transient response rate of a wind turbine in a fluctuating wind stream.