  The volatile nature of wind power generation creates challenges in achieving
secure power grid operations. It is, therefore, necessary to make accurate wind
power prediction and its uncertainty quantification. Wind power forecasting
usually depends on wind speed prediction and the wind-to-power conversion
process. However, most current wind power prediction models only consider
portions of the uncertainty. This paper develops an integrative framework for
predicting wind power density, considering uncertainties arising from both wind
speed prediction and the wind-to-power conversion process. Specifically, we
model wind speed using the inhomogeneous Geometric Brownian Motion and convert
the wind speed prediction density into the wind power density in a closed-form.
The resulting wind power density allows quantifying prediction uncertainties
through prediction intervals. To forecast the power output, we minimize the
expected prediction cost with (unequal) penalties on the overestimation and
underestimation. We show the predictive power of the proposed approach using
data from multiple operating wind farms located at different sites.
