Tight and Compact MILP Formulation of Start-Up and Shut-Down Ramping in Unit Commitment

Germán Morales-España, Jesus M. Latorre, Andres Ramos

Research output: Contribution to journalArticleScientificpeer-review

177 Citations (Scopus)


This paper presents a mixed-integer linear programming (MILP) formulation of start-up (SU) and shut-down (SD) power trajectories of thermal units. Multiple SU power-trajectories and costs are modeled according to how long the unit has been offline. The proposed formulation significantly reduces the computational burden in comparison with others commonly found in the literature. This is because the formulation is 1) tighter, i.e., the relaxed solution is nearer to the optimal integer solution; and 2) more compact, i.e., it needs fewer constraints, variables and nonzero elements in the constraint matrix. For illustration, the self-unit commitment problem faced by a thermal unit is employed. We provide computational results comparing the proposed formulation with others found in the literature.

Original languageEnglish
Pages (from-to)1288-1296
Number of pages9
JournalIEEE Transactions on Power Systems
Issue number2
Publication statusPublished - 29 Nov 2012


  • Mixed-integer linear programming
  • Start-up and shut-down ramps
  • Thermal units
  • Unit commitment


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