This article presents a new nonlinear convex network flow programming model and algorithm for solving the on-line economic power dispatch with N and N−1 security. Based on the load flow equations, a new nonlinear convex network flow model for secure economic power dispatch is set up and then transformed into a quadratic programming model, in which the search direction in the space of the flow variables is to be solved. The concept of maximum basis in a network flow graph was introduced so that the constrained quadratic programming model was changed into an unconstrained quadratic programming model which was then solved by the reduced gradient method. The proposed model and its algorithm were examined numerically with an IEEE 30-bus test system on an ALPHA 400 Model 610 machine. Satisfactory results were obtaine
