Robust trajectory-constrained frequency control for microgrids considering model linearization error

Yichen Zhang, Chen Chen, Tianqi Hong, Bai Cui, Zhe Xu, Bo Chen, Feng Qiu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. The simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

Original languageEnglish (US)
Article number120559
JournalApplied Energy
StatePublished - Mar 1 2023


  • Frequency response
  • Interval analysis
  • Microgrids
  • Mixed-integer linear programming
  • Numerical optimal control
  • Reachability
  • Uncertainty quantification
  • Wind turbine generator

ASJC Scopus subject areas

  • Building and Construction
  • Renewable Energy, Sustainability and the Environment
  • Mechanical Engineering
  • General Energy
  • Management, Monitoring, Policy and Law


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