When an electrical power system gets into na emergency state during its real time operation the main objective of the control center is to calculate corrective controls in order to put the system back in the normal region as fast as possible. Almost every time, in such a situation, it ought to be necessary to calculate and implement corrective actions, such as real and reactive constraints, while keeping the load constraints satisfied. This research was developed having as objectives: a) the critical review of many of the algorithms using linear formulations know up to now for calculating corrective controls; b) the elaboration of a mathematical model of this problem; c) the analysis of algebraic aspects of the linear formulations and theirs consequences on the solution; d) the proposition of a more complete and concise formulation. Several methods are presented and applied to a small size system