Reduced-Order Aggregate Model for Parallel-Connected Single-Phase Inverters

Miguel Rodriguez, Victor Purba, Brian Johnson, Saber Jafarpour, Francesco Bullo, Sairaj Dhople

Research output: Contribution to journalArticlepeer-review

41 Scopus Citations


This paper outlines a reduced-order aggregate dynamical model for parallel-connected single-phase grid-connected inverters. For each inverter, we place no restrictions on the converter topology and merely assume that the ac-side switch-averaged voltage can be controlled via pulsewidth modulation. The ac output of each inverter interfaces through an LCL filter to the grid. The closed-loop system contains a phase locked loop for grid synchronization, and real- and reactive-power control are realized with inner and outer PI current- and power-control loops. We derive a necessary and sufficient set of parametric relationships to ensure that a reduced-order aggregated state-space model for an arbitrary number of such paralleled inverters has the same model order and structure as any single inverter. We also present reduced-order models for the settings where the real- and reactive-power setpoints are different and where the inverters have different power ratings. We anticipate the proposed model being useful in analyzing the dynamics of large collections of parallel-connected inverters with minimal computational complexity. The aggregate model is validated against measurements obtained from a multi-inverter experimental setup consisting of three 750-VA paralleled grid-connected inverters, hence establishing robustness of the analytical result to parametric variations seen in practice.
Original languageAmerican English
Pages (from-to)824-837
Number of pages14
JournalIEEE Transactions on Energy Conversion
Issue number2
StatePublished - 2019

NREL Publication Number

  • NREL/JA-5D00-74568


  • model reduction
  • phase-locked loop
  • single-phase inverter
  • voltage-source inverter


Dive into the research topics of 'Reduced-Order Aggregate Model for Parallel-Connected Single-Phase Inverters'. Together they form a unique fingerprint.

Cite this