Comparison of the Lagrange´s and Particle Swarm Optimisation solutions of an Economic Emission Dispatch problem with transmission constraints

The power demand is increased rapidly and hence the power systems become more complex, so it is necessary to solve the dispatch problem with less computation time. This paper uses the optimization approach (Lagrange´s) and random variables selection approach Particle Swarm Optimisation (PSO) to solve the dispatch problem with transmission constraints and to compare the obtained solution and the time for its calculation. Formulation of a bi-criteria Combined Economic Emission Dispatch (CEED) problem is given. The application of Lagrange´s and PSO methods to the CEED problem is described and the algorithms for calculations are given. The computational time of the Lagrange´s algorithm depends on the selection of the initial values of the Lagrange´s variable (λ), and on the swarms, positions, and velocity selection in PSO algorithm. The IEEE 30 bus system is considered to validate the simulation results in MATLAB environment. It concludes that Lagrange´s algorithm provides better results for CEED problem in comparison to the PSO algorithm.