  The thermal unit commitment (UC) problem often can be formulated as a mixed
integer quadratic programming (MIQP), which is difficult to solve efficiently,
especially for large-scale instances. The tighter characteristic reduces the
search space, therefore, as a natural conse-quence, significantly reduces the
computational burden. In the literature, many tightened formulations for single
units with parts of constraints were reported without presenting how they were
derived. In this paper, a sys-tematic approach is developed to formulate the
tight formulations. The idea is using more new variables in high dimension
space to capture all the states for single units within three periods, and
then, using these state variables systematic derive three-periods locally ideal
expressions for a subset of the constraints in UC. Meanwhile, the linear
dependence relations of those new state variables are leveraged to keep the
compactness of the obtained formulations. Based on this approach, we propose
two tighter models, namely 3P-HD and 3P-HD-Pr. The proposed models and other
four state-of-the-art models were tested on 51 instances, including 42
realistic instances and 9 8-unit-based instances, over a scheduling period of
24 h for systems ranging from 10 to 1080 generating units. The simulation
results show that our proposed MIQP UC formulations are the tightest and can be
solved most efficiently. After using piecewise technique to approxi-mate the
quadratic operational cost function, the six UC MIQP formulations can be
approximated by six corre-sponding mixed-integer linear programming (MILP)
formulations. Our experiments show that the proposed 3P-HD and 3P-HD-Pr MILP
formulations also perform the best in terms of tightness and solution times.
