We present high resolution wind power statistical models fitted to meteorological data for the island of Ireland. We find that a discrete Burr model efficiently represents the number of consecutive hours of wind power availability. Burr models are also useful to model the complement of the wind power availability events, wind droughts, when wind speed is insufficient to produce wind power. The models developed in this study may be most useful at time resolutions less than 6 hours to capture zero power and short bursts of wind power potential. They could serve as a useful complement to other wind power modelling approaches such as MERRA reanalysis models. Wind power duration models, and their wind drought complements, also provide insights for investors on potential wind power availability at geographic locations.