Gone With the Wind: A Stochastic Model of Wind Energy Crossing Time and Error Distributions

Abstract

This thesis develops several models to analyze and accurately predict for the above and below crossing time distributions and the density of wind errors, which we calculate as the difference between the observed and forecasted wind power. We first consider conventional time series models including ARMA and GARCH, before concluding that these models cannot properly account for the volatility in the distribution of wind errors. We develop the logic of applying generalized linear regression models to predicting wind errors of individual farms at time t dependent on its previous history. The key concept we keep in mind is that error distributions of individual farms may not be completely independent of one other. To account for the possible correlation between farms, we model linear regressions for the error distribution of individual farms on not only its own history, but also the history of all other farms. In the last part of this thesis, we implement a linear aggregate error model, eventually adding a Lasso penalty term, for each farm. The goal is to predict individual error distributions that when summed together in aggregate will behave similarly to the observed aggregate model.