A Stochastic Differential Equation Based Wind Speed Forecasting Model

Abstract

Stochastic differential equation (SDE) based approaches have demonstrated an improved capability in predicting temporal wind speed patterns that have statistical properties which are very similar to those observed in reality. However, no standard approach for deriving such models exist. One difficulty in arriving at a unified framework is the presence of a seemingly wide variation in the temporal statistical properties that one observes from location to location. In this work, we propose an SDE model for short term wind speed pattern predictions for Kokkilai, an area that is located in the North-Eastern coastal region of Sri Lanka. Here, we propose a systematic approach for modelling short term temporal wind speed variations, using a 1-dimensional stationary stochastic differential equation along with an approximated marginal distribution for the long term empirical wind speed distribution and the corresponding autocorrelation function. The model parameters were estimated to fit the empirical wind speed distribution of wind speed data that has been recorded at the wind measurement center of Kokkilai, from February 2015 to February 2016. The normal Gaussian distribution turned out to be the best fitted marginal distribution, in terms of maximum likelihood, for long term wind speed data. Then, an Ornstein-Uhlenbeck based SDE was obtained using the parameters of the fitted normal Gaussian distribution and the empirical autocorrelation function. Subsequently, considering special features such as cyclic behavior and certain trends of the empirical autocorrelation function, a set of new parameters were introduced to the drift and diffusion terms of the SDE. The obtained model was capable of generating a short-term wind speed forecasting trajectories that fall within an acceptable confidence level.