Enhanced augmented Lagrange Hopfield network for economic dispatch with piecewise quadratic cost functions

This paper proposes a simple enhanced augmented Hopfield Lagrange neural network (EALH) for solving economic dispatch (ED) problem with piecewise quadratic cost functions. The EALH is an augmented Lagrange Hopfield neural network (ALH), which is a combination of continuous Hopfield neural network and augmented Lagrangian relaxation function as its energy function, enhanced by a heuristic search algorithm for determination of fuel type. The proposed EALH solve the problem in two phases. In the first phase, a heuristic algorithm based on average production cost of generating units is used to determine the most suitable fuel type of units satisfying load demand. In the last phase, the ALH is applied to solve economic dispatch to find optimal solution with the fuel types selected. The proposed method is tested on two test systems with various load demands and compared to hierarchical approach based on the numerical method (HNUM), Hopfield neural network (HNN), adaptive Hopfield neural network (AHNN), enhanced Lagrangian artificial neural network (ELANN), improved evolutionary programming (IEP), modified particle swarm optimization (MPSO), and hybrid real coded genetic algorithm (HRCGA). The results have shown that the proposed method is efficient and fast for the ED problems with multiple fuel types represented by quadratic cost functions. Keywords— Augmented Lagrange Hopfield neural network, economic dispatch, piecewise quadratic cost function.