Hybrid Robust/Stochastic Unit Commitment With Iterative Partitions of the Continuous Uncertainty Set

Patrick Gögler, Magdalena Dorfner, Thomas Hamacher

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


As an attempt to reduce reliance on fossil fuels to satisfy electricity demand, the penetration of renewable sources like wind or solar power has experienced rapid growth in recent years. Due to their intermittent nature, the exact contribution of renewable sources to electricity supply is at least partly unknown. In order to be able to accommodate this uncertainty in real-time, sufficient capacities in the form of thermal and hydro power plants must be available. On that account, power system operators solve the so-called unit commitment problem after bidding in the day-ahead market closes to derive schedules for their power plants which can ensure system reliability at low costs. In literature, two approaches have mainly been studied in this context: Robust and stochastic unit commitment. Being a worst-case formulation, robust unit commitment puts its focus on reliability. A common drawback of this approach is that it tends to deliver over-conservative schedules. Stochastic unit commitment on the other hand creates more cost-effective schedules by preparing for the expected case, but either fails to guarantee system reliability or puts a high workload on the CPU. The limitations of known formulations have sparked interest in so-called hybrid approaches, which aim at combining the ideas of robust and stochastic unit commitment in a favorable way. This paper reports a novel hybrid approach to solve the unit commitment under uncertainty, which yields both robust and cost-efficient schedules. The new method respects the continuous nature of uncertainties and is thus in particular favorable for applications in power systems with high penetration of volatile renewable sources. By merging the ideas of robust and stochastic unit commitment, the proposed hybrid formulation minimizes the expected worst-case dispatch costs. Our method relies on partitioning the continuous range of the uncertainties into subsets. By means of the number of partitions, the solution can be adjusted between the conservative robust and the cost-efficient stochastic unit commitment in a user-friendly manner. A Benders decomposition algorithm is derived to solve the hybrid unit commitment efficiently. Finally, a case study confirms the superior performance of the proposed method.

Original languageEnglish
Article number71
JournalFrontiers in Energy Research
StatePublished - 20 Jul 2018


  • Benders decomposition
  • continuous uncertainty
  • robust optimization
  • stochastic programming
  • unit commitment


Dive into the research topics of 'Hybrid Robust/Stochastic Unit Commitment With Iterative Partitions of the Continuous Uncertainty Set'. Together they form a unique fingerprint.

Cite this