Real-time Capable Non-Uniformly Spaced MILP Unit Commitment Formulation for Units with Startup and Shutdown Trajectories

This paper proposes a reformulation of an existing mixed integer linear programming (MILP) tight unit commitment (UC) problem for thermal power units with startup and shutdown trajectories. The presented UC formulation introduces a non-uniformly spaced time horizon, where later sample steps are resolved more coarsely than earlier ones. For equal prediction time horizons, this makes the UC problem significantly smaller than a uniform formulation, while however losing accuracy at later prediction steps. These properties make the proposed formulation perfectly suitable for the use case of model predictive control (MPC), where fast solving times are necessary, but only the near horizon needs to be accurate. The feasibility of that is shown in simplified MPC simulations, where the presented nonuniform UC problem is on average solved 42 times faster than a uniform one, while only incurring 1.14 % higher costs.