Stochastic wind speed modelling for estimation of expected wind power output

Increased wind energy penetration causes problems to the operation and system balancing of electric power systems. This in turn leads to the need for more detailed wind power modelling. The modelling and management of wind power involves two stages, neither of which is analytically tractable. In particular, the first stage involves stochastic variations in wind speed; wind speed typically presents noisy short-term variations, plus cyclicality over periods of 24 h and longer. The second stage refers to stochastic variations of the resulting wind power output, a non-linear function of wind speed. This paper proposes and tests an Ornstein-Uhlenbeck Geometric Brownian Motion model in continuous time to represent the wind speed, while including its longer-term daily cycle. It also illustrates a partial differential equation model of the wind speed and of the resulting wind power output, aiming at computing both their statistics. The proposed stochastic model has the potential to be used for various applications where wind speed or wind power are stochastic inputs, such as the optimal valuation of energy storage or system balancing. We verify by statistical tests that the results from the proposed model for the wind speed and the wind power match those from the empirical data of a wind farm located in Spain.