The increase in complexity of the electrical power systems have risen the interest on real-time operation and control. The built of computarized control centers whose main objective is to supply the loads, with all the operation constratints satisfied at lowest cost, became necessary. Therefore, the development of real-time algorithms for secure and economic operation, as for instance for overload corrective control, turned out to be a consequence. The non-linear injected nodal power equations have been written in polar form in the existing algorithms. In rectangular form in the existing algorithms. In rectangular form, these equations are quadratic and their Taylor series expansion have only the first three terms. Hence, the first order term of the expansion in rectangular form might be more representative of the non-linear equations than the first order term in polar form. This may improve the converge characteristic of the Newton-Raphson method. Moreover, a quadratic equation solution method can be used. In this method, all the three terms of the Taylor series expansion are taken into account. In the dissertation 1st and 2nd orde algorithms in rectangular form for real-time overload corrective control are developed. The best way to deal with constraints on the control variables is pointed out. The algorithms use sensitivity analysis among the many system variables and, searching for the best formulation, the results using several test-systems are compared with each other and with those obtained with the equations in polar form.