Abstract In this paper, a mixed integer quadratically constrained program to solve the unit commitment problem is presented. It is the most complete model found in the literature until now and it can be used to solve real-life, large-scale power systems. The model considers thermal conventional plants, independent power producers, interruptible loads, and a simplified representation of combined cycle plants and hybrid combined cycle plants using the aggregated model. The objective function includes variable generation costs and fixed start-up costs. Important constraints like spinning reserve, power flows in tie-lines, and quadratic fuel consumption constraints are included, among others. Also, the status of every single unit is considered; if the unit is available, if the unit can be committed, and if the unit can be dispatched. The model is implemented in Intel (R) Fortran 11.0 and solved using the commercial optimization software IBM CPLEX 12.1. To prove the usefulness of the formulation, a real life power system is solved for a twenty-four hour planning horizon based on the nodal representation of the Mexican Power System.