This paper presents a technique that can obtain an optimal solution for the Security-Constrained Economic Dispatch (SCED) problems using the Interior Point Method (IPM) while taking into account of the power flow constraints. The SCED equations are formulated by using only the real power flow equations from the optimal power flow. Then an algorithm is presented that can linearize the SCED equations based on the relationships among generation real power outputs, loads, and transmission losses to obtain the optimal solutions by applying the linear programming (LP) technique. The objective function of the proposed linearization algorithm are formulated based on the fuel cost functions of the power plants. The power balance equations utilize the Incremental Transmission Loss Factor (ITLF) corresponding to the incremental generation outputs and the line constraints equations are linearized based on the Generalized Generation Distribution Factor (GGDF). Finally, the application of the Primal Interior Point Method (PIPM) for solving the optimization problem based on the proposed linearized objective function is presented. The results are compared with the Simplex Method and the promising results ard obtained.