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

5 Scopus citations


Power grids are evolving towards 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 paper, 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 non-identical initial conditions are validated in the experimental setup. Empirical observations further illustrate robust operation during unbalanced conditions.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalIEEE Transactions on Power Electronics
StatePublished - Dec 1 2022
Externally publishedYes

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.


  • Couplings
  • Delta connection
  • Inverters
  • Load modeling
  • Low-pass filters
  • Oscillators
  • Pulse width modulation
  • Voltage control
  • droop control
  • grid-forming inverters
  • phase balancing


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