Invariant set design of decentralized control for islanded microgrids under plug-and-play operation

Ehab Bayoumi*, Hisham M. Soliman, Mohammed Albadi, Mostafa Soliman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This article presents a new invariant-set design for voltage regulation of islanded microgrids (MGs) composed of several distributed generators (DGs). The advantages of the proposed control are: (1) the control structure is decentralized, and (2) it tracks the reference inputs quickly and maintains robust stability against the MG's load changes and plug- and-play operation. To achieve these objectives, the global system is decomposed into several subsystems. Each DG subsystem is modeled as a linear time-invariant system with norm-bounded uncertainty representing load changes. For a specific subsystem, the effect of the rest of subsystems is represented as a disturbance. The effect of the disturbance on the subsystem is reduced by minimizing the volume of its invariant ellipsoid (approximating and bounding its invariant set). The changes in the disturbance is modeled by the norm-bounded form. The controller design is based on a derived sufficient condition in the form of nonlinear matrix inequality (solved iteratively by fixing a positive scalar as a convex linear matrix inequality, LMI, optimization problem). To evaluate the effectiveness of the proposed control strategy, different time-domain simulations are conducted using MATLAB/SimPowerSystems Toolbox. Simulations demonstrate that the suggested controller provides excellent performance in terms of voltage tracking under load changes and MG's plug-and-play operation.

Original languageEnglish
Article number106678
JournalInternational Journal of Electrical Power and Energy Systems
Publication statusPublished - Jun 2021


  • Invariant sets
  • Islanded microgrids
  • Linear matrix inequality
  • Robust stability

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


Dive into the research topics of 'Invariant set design of decentralized control for islanded microgrids under plug-and-play operation'. Together they form a unique fingerprint.

Cite this