Annals of Operations Research

, Volume 274, Issue 1–2, pp 241–265 | Cite as

Fix-and-optimize procedures for solving the long-term unit commitment problem with pumped storages

  • Alexander FranzEmail author
  • Julia Rieck
  • Jürgen Zimmermann
Original Research


In this paper, we consider a long-term unit commitment problem with thermal and renewable energy sources, where system operating costs have to be minimized. The problem is enhanced by adding pumped storages, where water is stored in reservoirs, being turbinated or pumped up if it is beneficial in terms of reducing the operating costs. We present a tight mixed-integer linear programming model with a redefinition of decision variables and a reformulation of constraints, e.g., for the spinning reserve. The model serves as a basis for a new decomposition method, where fix-and-optimize schemes are used. In particular, a time-oriented, a unit-oriented, and a generic fix-and-optimize procedure are presented. A computational performance analysis shows that the mixed-integer linear model is efficient in supporting the solution process for small- and medium-scale instances. Furthermore, the fix-and-optimize procedures are able to tackle even large-scale instances. Particularly, problem instances with real-world energy demands, power plant-specific characteristics, and a one-year planning horizon with hourly time steps are solved to near-optimality in reasonable time.


Unit commitment problem Pumped storages Hydrothermal coordination Volatile residual demand patterns Mixed-integer linear programming model Fix-and-optimize procedure 

JEL Classification

C61 Q41 Q42 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Alexander Franz
    • 1
    Email author
  • Julia Rieck
    • 2
  • Jürgen Zimmermann
    • 1
  1. 1.Operations Research Group, Institute of Management and EconomicsClausthal University of TechnologyClausthal-ZellerfeldGermany
  2. 2.Operations Research Group, Institute of Economics and Computer ScienceUniversity of HildesheimHildesheimGermany

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