Tight MIP formulations of the power-based unit commitment problem

Abstract

This paper provides the convex hull description for the basic operation of slow-and quick-start units in power-based unit commitment (UC) problems. The basic operating constraints that are modeled for both types of units are (1) generation limits and (2) minimum up and down times. Apart from this, the startup and shutdown processes are also modeled, using (3) startup and shutdown power trajectories for slow-start units, and (4) startup and shutdown capabilities for quick-start units. In the conventional UC problem, power schedules are used to represent the staircase energy schedule; however, this simplification leads to infeasible energy delivery, as stated in the literature. To overcome this drawback, this paper provides a power-based UC formulation drawing a clear distinction between power and energy. The proposed constraints can be used as the core of any power-based UC formulation, thus tightening the final mixed-integer programming UC problem. We provide evidence that dramatic improvements in computational time are obtained by solving different case studies, for self-UC and network-constrained UC problems.

Column generation for the discrete UC problem with min-stop ramping constraints

“…Many works deal with additional dynamic constraints on thermal production. Arroyo and Carrion (2006); Morales-España et al (2015) and Gentile et al (2017) provided efficient MILP formulation to model start-up and shut-down trajectories when a thermal production is in the domain [0, P min u ]. Silbernagl et al (2016) and Brandenberg et al (2017) provided efficient models to compute start-up costs and curves.…”

Parallel matheuristics for the discrete unit commitment problem with min‐stop ramping constraints

“…If such constraints were included in the model of Arroyo and Carrion (), recent work in Morales‐España et al. () and Gentile et al. () provided tight MIP formulations, with the possibility to differentiate slow‐start and quick‐start (warm‐start) units.…”

Power-Capacity and Ramp-Capability Reserves for Wind Integration in Power-Based UC

“…In short, (11) ensures that the system provides the power and ramp requirements for the wind nominal case; (12) and (13) guarantee that enough up and down power-capacity reserves are scheduled, respectively; similarly, (14) and (15) ensure enough up and down ramp-capability reserves, respectively. …”

“…The core of the proposed MIP formulation is built upon the convex-hull and the tight-and-compact formulations presented in [8] and [11], respectively, thus taking advantage of their mathematical properties. These formulations improve the convergence speed by reducing the search space (tightness) and at the same time increasing the searching speed with which solvers explore that reduced space (compactness).…”