Augmented Lagrangian approach to hydro-thermal scheduling

This paper presents an augmented Lagrangian approach to hydro-thermal scheduling. It adds to the standard Lagrangian function a quadratic penalty function which associates generation-load balance, spinning reserve and emission constraints. This makes better commitment solutions that may exist in a dual gap very likely reachable by adjusting penalty and Lagrangian multipliers parameters. Advantage of this approach over Lagrangian relaxation and augmented Lagrangian with only the generation-load balance constraint penalized is discussed. An IEEE test system is used for illustration. Our results show that the augmented Lagrangian with all coupling constraints penalized can provide better scheduling results as it can detect in-between-hours shutdown of some units, earlier shutdown, and/or later startup of some other units.