This study deals with a new formulation for the direct current corrective optimal power flow. The formulation is based on the outage of generators and/or branches modelled as fictitious injections of active power. By including that fictitious injections in the optimisation problem, the injections are adjusted to the post-contingency state as a consequence of the corrective actions carried out to bring the system back to its normal state. So, when the analysis of contingencies is performed, the classical topological analysis and the subsequent analyses are avoided with this approach. This new formulation uses the sensitivity matrix between branch power flows and powers injected in a power system. An important feature of this matrix is to remain constant during the contingency analysis performed for the generation-load scenario (base case) of each period of time to be analysed. The approach proposed is illustrated in the IEEE-RTS of 24 buses. The results obtained in this distribution network demonstrate that the proposed methodology can assess the impact of contingencies with an acceptable accuracy and a short computation time.