Economic Dispatch with Emission and Transmission Constraints by Augmented Lagrange Hopfield Network

This paper proposes an augmented Lagrange Hopfield network (ALHN) for solving economic dispatch (ED) problem with ramp rate, emission and transmission constraints. The proposed ALHN method is the continuous Hopfield neural network with its energy function based on augmented Lagrangian function. In ALHN, the energy function is augmented by Hopfield terms from Hopfield neural network and penalty factors from augmented Lagrangian function to damp out oscillation of the Hopfield network during its convergence. Consequently, ALHN can overcome the drawbacks of the conventional Hopfield network due to its simplicity, better optimal solution and faster computing time. The proposed method has been tested on large-scale systems up to 1,200 units and the New England 39-bus system and the obtained results are compared to other methods available in the literature. The test results have shown that the proposed method is more favorable than the others for less total costs and faster computational times.