The optimisation of power-system operating conditions is formulated as aduallinear programming problem. This suboptimal model allows fast solutions to be obtained dependably by applyingn the revised simplex I.p method to the problem of minimising total generation costs subject to the constraints imposed. These constraints include the network equations, the inequalities restricting generator loading, running-spare capacity and transmission-line loading under normal and outage conditions. The fast speed of solution and low computer-storage requirements result from the reduced mathematical model developed by means of the variable elimination and the computing strategy used. The computational procedure automatically adjusts the size of the problem to be solved according to indications obtained of the likely critical line-outage security constraints, a small number in relation to the prohibitivelylarge number of possible outage constraints. A sample application of the method is given for a 2700MW, 275/132kv system of 23 busbars,30 lines and transformers, supplied by 24 generators. Using ALGOL 60 on the Atlas computer, solutions were obtained in 5's neglecting line-outage security, and 11.5's including security under all possible single-line-outage conditons. For accuracy, comparisons are also made with the network-flow technique and the full nonlinear programming solutions.