Energies
In this paper, a Hopfield Lagrange network (HLN) method is applied to solve the optimal load dispatch (OLD) problem under the concern of the competitive electric market. The duty of the HLN is to determine optimal active power output of thermal generating units in the aim of maximizing the benefit of electricity generation from all available units. In addition, the performance of the HLN is also tested by using five different functions consisting of the logistic, hyperbolic tangent, Gompertz, error, and Gudermanian functions for updating outputs of continuous neurons. The five functions are tested on two systems with three units and 10 units considering two revenue models in which the first model considers payment for power delivered and the second model concerns payment for reserve allocated. In order to evaluate the real effectiveness and robustness of the HLN, comparisons with other methods such as particle swarm optimization (PSO), the cuckoo search algorithm (CSA) and differential evolution (DE) are also implemented on the same systems. High benefits and fast execution time from the HLN lead to a conclusion that the HLN should be applied for solving the OLD problem in a competitive electric market. Among the five applied functions, error function is considered to be the most effective one because it can support the HLN to find the highest benefit and reach the fastest convergence with the smallest number of iterations. Thus, it is suggested that error function should be used for updating outputs for continuous neurons of the HLN.
