1 Mathematical Statistics, Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Informatics and Mathematical Modeling, Technical University of Denmark3 Department of Electrical Engineering, Technical University of Denmark
Wind power generation is a nonlinear and bounded variable, partly owing to the power curve that converts wind to electric power, and partly owing to the very stochastic nature of wind itself. Predictive densities of wind power generation should account for that effect. Such densities are clearly not expected to be Gaussian, with higher order moments being directly related to their expectation and potentially to some external signal. It is proposed here to model such predictive densities with discretecontinuous mixtures of generalized logit-normal distributions and of probability masses at the bounds. In this framework, a transformation is employed so that transformed data can be modeled with censored Normal variables. Two types of models are proposed: a simple autoregressive model and a more advanced conditional parametric autoregressive model, for which wind direction is the variable conditioning the wind power dynamics. In both cases, the model parameters are adaptively and recursively estimated, time-adaptativity being the result of exponential forgetting of past observations. The probabilistic forecasting methodology is applied at the Horns Rev wind farm in Denmark, for 10-minute ahead probabilistic forecasting of wind power generation. Probabilistic forecasts generated from the proposed methodology clearly have higher skill than those obtained from a classical Gaussian assumption about wind power predictive densities. Corresponding point forecasts also exhibit significantly lower error criteria.
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Technical University of Denmark, DTU Informatics, Building 321, 2010