Spontaneous Phase Balancing in Delta-Connected Single-Phase Droop-Controlled Inverters

Minghui Lu, Sairaj Dhople, Donny Zimmanck, Brian Johnson

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


Power grids are evolving toward a highly distributed architecture with power-electronics circuits interfacing a majority of generation, storage, and loads. To ensure stability as synchronous machines are retired, grid-forming (GFM) inverters will be needed across the board. In this article, we investigate whether systems built with interconnected single-phase droop-controlled GFM inverters are capable of self organizing into balanced three-phase systems. We model, analyze, and build a system comprised of three delta-connected droop-controlled single-phase inverters connected across loads. After deriving a model of the angle dynamics for this system, we show that its stable equilibria coincide with balanced conditions, where each phase is offset by 1/3 of an ac cycle. Furthermore, we observe that the desirable equilibrium with balanced phase offsets is robust against voltage and load imbalances. This demonstrates the feasibility of assembling three-phase systems using fleets of decentralized single-phase GFM inverters. The analytical developments are substantiated experimentally on a system of three delta-connected single-phase inverters. Spontaneous emergence of phase balancing from startup with nonidentical initial conditions are validated in the experimental setup. Empirical observations further illustrate robust operation during unbalanced conditions.

Original languageEnglish (US)
Pages (from-to)14115-14125
Number of pages11
JournalIEEE Transactions on Power Electronics
Issue number12
StatePublished - Dec 1 2022

Bibliographical note

Funding Information:
This work was supported by the U.S. Department of Energy's Office of Energy Efficiency and Renewable Energy (EERE) under Solar Energy Technologies Office (SETO) Agreement EE0009025.

Publisher Copyright:
© 1986-2012 IEEE.


  • Delta connection
  • droop control
  • grid-forming (GFM) inverters
  • phase balancing


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