The short-term operation of the power system is suffering several changes due to the massive integration of more environmentally friendly generation resources into the energy matrix of the countries. This paper aimed to apply an integrated stochastic unit commitment formulation for the short-term operation of the Colombian electric power system. The proposed formulation can determine, in real-time, the unit commitment, the economic dispatch, and the reserve allocation in the available generation units; this formulation was tested with different levels of renewable energy penetration. In any case, hydraulic generation allows the balance of power by its response times. This formulation is evaluated with a combinatorial analysis of 5 uncertainty sets in a 12-bus system inspired by the Colombian electric power system, which was used as a test bench. To evaluate the scalability of the optimization model, the formulation was implemented on a 118 IEEE bus system by reducing the number of scenarios. The results led to a possible real-time stochastic operation of the Colombian power system. The scenario reduction method reduces the computational burden, improving the time from 4870.48 to 173.7 seconds with a relative error of 2.11\%. However, applying 243 scenarios allows us to observe particular reserve distributions. Finally, in the 12-bus system, a sensitivity analysis is performed by modifying the injected renewable energy from 0 MW to 200 MW peak, finding an increase in the execution times in cases higher than 100 MW peak.