Extreme ray feasibility cuts for unit commitment with uncertainty

Chao Li, Muhong Zhang, Kory Hedman

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The unit commitment problem with uncertainty is considered one of the most challenging power system scheduling problems. Different stochastic models have been proposed to solve the problem, but such approaches have yet to be applied in industry practice because of computational challenges. In practice, the problem is formulated as a deterministic model with reserve requirements to hedge against uncertainty. However, simply requiring a certain level of reserves cannot ensure power system reliability as the procured reserves may be nondispatchable because of transmission limitations. In this paper, we derive a set of feasibility cuts (constraints) for managing the unit commitment problem with uncertainty. These cuts eliminate unreliable scheduling solutions and reallocate reserves in the power system; they are induced by the extreme rays of a polyhedral dual cone. This paper shows that, with the proposed reformulation, the extreme rays of the dual cone can be characterized by combinatorial selections of transmission lines (arcs) and buses (nodes) of the power system. As a result, the cuts can then be characterized using engineering insights. The unit commitment problem with uncertainty is formulated as a deterministic model with the identified extreme ray feasibility cuts. Test results show that, with the proposed extreme ray feasibility cuts, the problem can be solved more efficiently, and the resulting scheduling decision is also more reliable.

Original languageEnglish (US)
Pages (from-to)1037-1055
Number of pages19
JournalINFORMS Journal on Computing
Issue number3
StatePublished - Jun 2021


  • Benders decomposition
  • Mixed integer programming
  • Polyhedral study
  • Stochastic programming
  • Unit commitment

ASJC Scopus subject areas

  • Software
  • Information Systems
  • Computer Science Applications
  • Management Science and Operations Research


Dive into the research topics of 'Extreme ray feasibility cuts for unit commitment with uncertainty'. Together they form a unique fingerprint.

Cite this