Enhanced merit order and augmented Lagrange Hopfield network for hydrothermal scheduling

This paper proposes an enhanced merit order (EMO) and augmented Lagrange Hopfield network (ALHN) for solving hydrothermal scheduling (HTS) problem with pumped-storage units. EMO is a merit order enhanced by heuristic search based algorithms and the ALHN is a continuous Hopfield network with its energy function based on augmented Lagrangian function. EMO is efficient in unit scheduling, whereas ALHN can properly handle generation ramp rate limits, and time coupling constraints such as limited fuel, water discharge for hydro units, and water balance for pumped-storage units. The proposed method solves HTS problem by optimizing step by step of sub-problems in four phases. In the first phase, EMO is applied to solve only thermal unit commitment satisfying power balance, spinning reserve, limited fuel, and minimum up and down time constraints. In the second phase, the enhanced ALHN is used to solve economic dispatch (ED) and commit hydro units based on the obtained unit schedule from the first phase. In the third phase, the enhanced ALHN is applied to handle transmission constraint. In the last phase, the enhanced ALHN is used to commit pumped-storage units and solve final constrained ED. In each phase, heuristic search based algorithms are applied to repair the constraint violations and refine the obtained solution. The proposed EMO–ALHN is tested on a hydrothermal system with 17 thermal, 2 hydro, and 2 pumped-storage hydro units with a scheduling time horizon of 24 h. Test results indicate that the proposed method obtains less costs and faster computational times than those from augmented Hopfield neural network (AHN) and hybrid enhanced Lagrangian relaxation and quadratic programming (Hybrid LRQP) for two test cases.