Solving economic dispatch problem under valve- point loading effects and generation constrains using a multi-gradient PSO algorithm

Economic dispatch (ED) of power performs an important part in the economic operation of power generating system. The ED problem is considered as a non-linear constrained optimization problem. The problem becomes non- convex and non-smooth when the thermal generating units are subjected to valve-point loading (VPL) effects.One popular optimization technique used to solve the ED problem is global particle swarm optimization with inertia weight (GPSO- w) algorithm. However, under VPL effects constraint, the GPSO- w becomes inefficient. Thus, the multi-gradient PSO (MG-PSO) algorithm is proposed to solve such a complex problem. In this algorithm, two phases, called Exploration and Exploitation, are used. In the Exploration phase, the m particles are called Explorers and undergo multiple episodes. In each episode, the Explorers use a different negative gradient to explore new neighborhood. In the Exploitation phase, the m particles are called Exploiters and they use only one negative gradient that is less than that of the Exploration phase, to exploit the best neighborhood. This diversity in negative gradients provides a balance between global search and local search. The simulations have been carried using 13 TGUs under VPL effects and generation limits. Superior performance of MG-PSO algorithm has been achieved over the GPSO- w algorithm and several competing algorithms in terms of several performance measures.