An important consideration in wind power integration studies is the role that wind power forecasting will play in simulated high-penetration system operations. As no wind power forecast is perfect, an understanding of the forecast error distributions that are observed in current system operations is important for modeling the forecast errors that can be expected in future scenarios. In this work, we statistically characterize and model the wind power forecast errors from three different operational forecasting systems at multiple timescales. Comparisons are made with two methods that are commonly used in wind integration studies to represent wind power forecasting: the persistence model, and an assumed normal distribution of forecasting errors. A number of model distributions are fit to the operational system forecast errors and the accuracy of the model fits to extreme events is examined in detail.