A Matrix Inversion-Based Algorithm for Economic Scheduling of Power Outputs of Thermal Units in an Electric Power System Without Losses

The economic load scheduling of thermal generating units in a power system is aimed at optimally allocating a stipulated load demand from the load dispatch center, among the several generating units in operation, in a power plant, with the objective of minimizing the overall cost of the generation, while satisfying all the equality (load-generation balance) and inequality (limits on the generating units) constraints of the plant. In the power system parlance, this is famously called as the economic load dispatch without losses, and generally considered cost curves for the thermal units are quadratic approximations. There are several algorithms in use, all of them being iterative in nature, like the λ-iteration technique. This paper presents a matrix formulation of the same problem, that yields a matrix-based non-iterative, direct solution, with a matrix inversion. This technique is elegant and gives quick and accurate results. It is direct for the cases of schedule without violation of limits and requires minimal adjustments for cases of violating the limits. Few examples are considered, to demonstrate the effectiveness of the technique implemented in MATLAB® R2019a, and the results are presented.