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 allocation of the reserve in the available generation units, this formulation was tested with different levels of renew- able energy penetration, in any case, the hydraulic generation allows the balance of power by its response times. This formulation is evaluated with a combinatorial analysis of 5 sets of uncertainty in a 12-bus system inspired by the Colombian electric power system, which was used as a test bench. In order 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 were shown to lead to a real-time stochastic operation of the Colombian power system is possible, the scenario reduction method is used to reduce the computational burden improving the time from 4870.48 to 173.7 seconds with a relative error of 2.11%, however, the application of 243 scenarios allows 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.