Optimisation of economic dispatch through quadratic and linear programming

Abstract
Mathematical programming offers attractive advantages as an optimising technique. Unfortunately, the optimisation of economic dispatch in power systems is a nonlinear problem, and so it is, in principle, beyond the reach of mathematical programming. In the paper, this difficulty is resolved by the derivation of linear constraints through the system sensitivity relations and by the use of a 2nd-order approximation to the power-generation-cost function. Quadratic programming is employed to solve the problem, and, with only one application of the algorithm, the results are comparable to those obtained from gradient techniques. The use of quadratic programming and the change of type of control variables during optimisation obviate the need for penalty functions. The computing times taken by the algorithm when it is applied to test systems are encouragingly short. Security constraints can be easily incorporated, and, if required, the minimum-reactive-power problem can be solved. A solution of the minimum-loss problem with linear programming is also illustrated.

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