Modeling of start-up and shut-down power trajectories of thermal units

This paper presents a detailed formulation to model the power trajectories followed by a thermal unit during the start-up and shut-down processes, as well as the ramping limitations when increasing or decreasing power. This model is formulated using mixed-integer linear constraints, thereby overcoming some drawbacks of those approaches based on heuristics, dynamic programming or Lagrangian relaxation. The formulation presented can be used in different scheduling problems arising in centralized and deregulated frameworks. The self-scheduling problem faced by a thermal generator in a pool-based electric energy market is used to illustrate the proposed model. Finally, a realistic case study is analyzed to show the computational behavior of the proposed model.