We propose a power-based unit commitment formulation with capacity and intra-hour ramp reserves for dealing with intra-hour wind power variability and uncertainty. Although the formulation has an hourly resolution, the intra-hour ramp requirements capture wind power ramp excursions with a time duration below one hour, and thus allows the formulation to consider intra-hourly wind variability and uncertainty. This increases the security of the formulation compared to using hourly ramp reserves and allows more efficient scheduling of units with high ramp rates. We test the formulation with different durations for the intra-hour reserves, and using both hourly and intra-hourly ramp reserves, to find the best reserve formulation. The formulations are evaluated using a 5-min economic dispatch, which simulates the real-time operation of the system, for hundreds of out-of-sample realizations of wind power production. The proposed formulations are then compared to two hourly stochastic formulations and a stochastic formulation with 5-min time resolution. The proposed formulations outperform the stochastic formulations in terms of security, showing that they provide a scheduling which is more robust against intra-hour wind power variations. The proposed formulations also outperform the hourly stochastic formulations in terms of total costs, giving a better trade-off between scheduling costs and security.