Convex Hull Model for a Single-Unit Commitment Problem with Pumped Hydro Storage Unit

Ming Qu, Tao Ding, Yuge Sun, Chenggang Mu, Kai Pan, Mohammad Shahidehpour

Research output: Journal article publicationJournal articleAcademic researchpeer-review


The single-unit commitment (1UC) aims at maximizing the payoff within a time series of given electricity prices. 1UC is subject to generation constraints, which is formulated as a mixed-integer programming (MIP) optimization problem. To reduce the computational complexity of PSU-1UC, this paper constructs the convex hull of PSU-1UC. Focusing on the possible combinations of generating and pumping time intervals, we first establish a dynamic program (DP) model which is solved in polynomial time. Second, a set of public variables were defined to describe the coupling relationship between different consecutive time intervals. Then, we reformulate the DP model into a linear programming (LP) model in a higher-dimensional space, which provides the convex hull formulation of PSU-1UC. Finally, we theoretically prove that the optimal solutions of the proposed convex hull model and the original MIP are the same. The exponential time complexity of PSU-1UC is reduced to polynomial time complexity, which will speed up the PSU self-scheduling/bidding problems and the decomposed algorithm for large-scale hydrothermal UC problems. Numerical experiments demonstrate the effectiveness and efficiency of the proposed model for PSU-1UC.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalIEEE Transactions on Power Systems
Publication statusAccepted/In press - 2022


  • Convex Hull
  • Lagrangian Relaxation
  • Pumped Hydro Storage Units
  • Single Unit Commitment

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Convex Hull Model for a Single-Unit Commitment Problem with Pumped Hydro Storage Unit'. Together they form a unique fingerprint.

Cite this