Multistage robust optimization for the day-ahead scheduling of hybrid thermal-hydro-wind-solar systems

Zhiming Zhong, Neng Fan, Lei Wu

Research output: Contribution to journalArticlepeer-review


The integration of large-scale uncertain and uncontrollable wind and solar power generation has brought new challenges to the operations of modern power systems. In a power system with abundant water resources, hydroelectric generation with high operational flexibility is a powerful tool to promote a higher penetration of wind and solar power generation. In this paper, we study the day-ahead scheduling of a thermal-hydro-wind-solar power system. The uncertainties of renewable energy generation, including uncertain natural water inflow and wind/solar power output, are taken into consideration. We explore how the operational flexibility of hydroelectric generation and the coordination of thermal-hydro power can be utilized to hedge against uncertain wind/solar power under a multistage robust optimization (MRO) framework. To address the computational issue, mixed decision rules are employed to reformulate the original MRO model with a multi-level structure into a bi-level one. Column-and-constraint generation (C &CG) algorithm is extended into the MRO case to solve the bi-level model. The proposed optimization approach is tested in three real-world cases. The computational results demonstrate the capability of hydroelectric generation to promote the accommodation of uncertain wind and solar power.

Original languageEnglish (US)
JournalJournal of Global Optimization
StateAccepted/In press - 2023


  • Day-ahead scheduling
  • Hybrid power system
  • Multistage robust optimization
  • Renewable energy

ASJC Scopus subject areas

  • Business, Management and Accounting (miscellaneous)
  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics


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