Emission, reserve and economic load dispatch problem with non-smooth and non-convex cost functions using the hybrid bacterial foraging-Nelder–Mead algorithm

In this paper, a new approach is proposed to solve the economic load dispatch (ELD) problem. Power generation, spinning reserve and emission costs are simultaneously considered in the objective function of the proposed ELD problem. In this condition, if the valve-point effects of thermal units are considered in the proposed emission, reserve and economic load dispatch (ERELD) problem, a non-smooth and non-convex cost function will be obtained. Frequency deviation, minimum frequency limits and other practical constraints are also considered in this problem. For this purpose, ramp rate limit, transmission line losses, maximum emission limit for specific power plants or total power system, prohibited operating zones and frequency constraints are considered in the optimization problem. A hybrid method that combines the bacterial foraging (BF) algorithm with the Nelder–Mead (NM) method (called BF–NM algorithm) is used to solve the problem. In this study, the performance of the proposed BF–NM algorithm is compared with the performance of other classic (non-linear programming) and intelligent algorithms such as particle swarm optimization (PSO) as well as genetic algorithm (GA), differential evolution (DE) and BF algorithms. The simulation results show the advantages of the proposed method for reducing the total cost of the system.