Multivariable control design for grid-forming inverters with decoupled active and reactive power loops

Dayan B. Rathnayake, Behrooz Bahrani

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)


Grid-forming inverters (GFMIs) are recognized as a

prominent driver toward achieving renewable energy-rich power

grids. Unlike grid-following inverters (GFLIs), which are controlled

as current sources,GFMIs are controlled as voltage sources.

In GFMIs, dynamic control of the magnitude (Vc) and angle (θ)

of the point of common coupling (PCC) voltage is used to achieve

active (P) and reactive (Q) power transfer across a line. However,

independent control of P and Q via Vc and θ becomes challenging

due to the coupling between P and Q loops. The coupling

becomes severe as the resistance-to-reactance ratio of the grid

impedance and the power angle between the GFMI and the grid

voltages are increased. This article proposes a novel multivariable

controller to completely decouple P and Q loops in GFMIs. The

proposed multivariable controller could be designed based on

the prevalent control structures for GFMIs such as droop controller,

swing equation-based virtual synchronous generator (VSG)

controller, zero steady-state error reactive power controller, and

fixed steady-state error reactive power controller. The additional

cross-channel decoupling controllers in the proposed multivariable

controller provide superior decoupling action over the existing

decoupling methods, such as the virtual inductor-basedmethod.An

H∞-based method is adopted to tune the proposed multivariable

controller parameters, where the straightforward formulation of

the desired closed-loop dynamics based on the open-loop system

is clearly shown. The decoupling performance of the controller

is experimentally validated extensively. The experimental results

show that the proposed controller results in superior performance

over the prevalent decoupling methods, such as the virtual-inductor

decoupling method.

Original languageEnglish
Pages (from-to)1635-1649
Number of pages15
JournalIEEE Transactions on Power Electronics
Issue number2
Publication statusPublished - Feb 2023


  • Couplings
  • Frequency synchronization
  • grid-forming inverter
  • Impedance
  • Inverters
  • loop shaping
  • power decoupling control
  • Reactive power
  • Steady-state
  • virtual synchronous generator (VSG) control
  • Voltage control

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