Heuristic Guided Lagrangian Relaxation and Augmented Lagrange Hopfield Network for Unit Commitment

This paper proposes a heuristic guided Lagrangian relaxation and augmented Lagrange Hopfield network (HLA) for unit commitment (UC) with ramp rate constraints. HLA is a combination of Lagrangian relaxation (LR) and augmented Lagrange Hopfield network (ALHN) guided by heuristic search based algorithms. The proposed HLA method solve UC problem in three stages. In the first stage, LR is use to solve unit scheduling satisfying load demand and spinning reserve constraints neglecting minimum up and down time constraints. In the second stage, heuristic search based algorithms are applied to refine the obtained unit schedule including primary unit de-commitment, unit substitution, minimum up and down time repairing, and de-commitment of excessive units. In the last stage, ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrange relaxation is applied to solve constrained economic dispatch (ED) problem and a repairing strategy for ramp rate constraint violations is used if a feasible solution is not found. The proposed HLA is tested on systems ranging from 17 to 110 units and compared to other methods. Test results indicate that the total production costs obtained by HLA are much less than those of other methods in a fast manner. Therefore, HLA is favorable for large-scale UC implementation.