Refined augmented Lagrange Hopfield network-based Lagrange relaxation for hydrothermal scheduling

This paper proposes a refined augmented Lagrange Hopfield network‐based Lagrange relaxation (ALHN‐LR) for solving short term hydrothermal scheduling (HTS) problem with pumped‐storage hydro units. ALHN‐LR consists of improved Lagrange relaxation (ILR) and augmented Lagrange Hopfield network (ALHN). For solving the HTS problem, the proposed method applies enhanced ILR for finding thermal unit scheduling, ALHN for solving constrained economic dispatch (CED), and heuristic search‐based algorithms in earlier papers for committing hydro and pumped‐storage units, repairing ramp rate, emission, and transmission constraint violations, and refining the obtained result. The proposed ALHN which is a continuous Hopfield network with its energy function based on augmented Lagrangian function can properly handle both equality and inequality constraints in CED problem. The proposed ALHN‐LR is tested on a hydrothermal system with 17 thermal, two hydro and two pumped‐storage units, and the IEEE 24‐bus reliability test system over the 168‐hour schedule time horizon. Test results indicate that the proposed method can obtain less total costs than those from augmented Hopfield network (AHN), hybrid enhanced Lagrangian relaxation and quadratic programming (hybrid LRQP), and augmented Lagrangian relaxation (ALR).