This paper describes a load dispatch method which minimizes power cost, i.e. [fuel cost]/[electric output], for a power system with thermal plants and energy storage facilities. The proposed method employs fractional programming to convert a minimization problem with fractional objective function to a series of quadratic minimization problem, and semi-definite programming to solve converted problems. The method provides the optimum time-dependent power output/input and storage level of energy storage facilities as well as time-dependent power output of thermal plants.
The method has been applied to a power system with 5 thermal plants, 2 energy storage facilities of various performances and 5 load demands. The optimum load scheme of 4 time mesh points is obtained for the thermal plants and energy storage facilities. The fractional programming successfully converges the optimal scheme through a few iterations. The semi-definite programming deals with a variable matrix of 164 dimensions, and 185 inequality constraints.