A comparison of Gumbel and Weibull statistical models to estimate wind speed for wind power generation

Wind energy is becoming more common, especially as costs are falling. In Australia´s National Electricity Market, the total available generation is managed by the Australian Energy Market Operator (AEMO). One of its tasks is to forecast the availability of generation twenty four months into the future, to ensure that the predicted customer load requirements are met. A challenge, however, is to accurately forecast the contribution of wind energy to the market on this time frame. Since the energy of wind is a function of its speed, it is common to use climate data to estimate the wind speed into the future using statistical distributions. In this analysis measurements on power generation from a South Australian wind farm and on wind speed from a weather station were compared. Statistical techniques were applied to monthly data samples. The power generated from a wind turbine is generally highest at the tail end of the wind speed distribution. Thus, the accuracy of two distributions to model wind speed, the Weibull and the Gumbel, was investigated to see which gave better fits. The Gumbel distribution was found to estimate wind speed more accurately than the Weibull model, not only at the tail end of the distribution, but also at lower levels.