Optimal load-flow solution by reduced-gradient method

An optimisation method employing the reduced-gradient technique for determining the economical voltage level and megawatt loadings of generating units in a power system is presented. The method is applied to find the operating conditions for minimum fuel cost or for minimum transmission loss. The solution is based on the calculation of the gradients of either of these objective functions with respect to the control variables, which are the phases and voltages of the generator busbars plus the voltage excluding slack of the slack busbar, by using the Jacobian matrix at each iterative step. The operating constraints, such as active and reactive loadings and allowable limits of the voltage magnitudes of the generating busbars including slack, are considered, and an algorithm is developed to obtain a fast convergence. Finally, the capability of the method in dealing with other constraints and control variables is discussed.