IEEE Open Access Journal of Power and Energy (Jan 2021)

Generalized Formulation of Steady-State Equivalent Circuit Models of Grid-Forming Inverters

  • Vinicius C. Cunha,
  • Taehyung Kim,
  • Nicholas Barry,
  • Piyapath Siratarnsophon,
  • Surya Santoso,
  • Walmir Freitas,
  • Deepak Ramasubramanian,
  • Roger C. Dugan

DOI
https://doi.org/10.1109/OAJPE.2021.3108680
Journal volume & issue
Vol. 8
pp. 352 – 364

Abstract

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This work proposes positive- and negative-sequence equivalent circuits of grid-forming inverters for steady-state analysis. The proposed models are especially attractive for performing long-duration voltage regulation analysis and short-circuit studies involving grid-forming inverters. Our proposed equivalent circuit models are based on the inverter’s voltage and current control loops in the $\alpha \beta $ and dq frames. For this reason, they operate according to prescribed control functions and specified impedances (i.e., filter impedance, current limiter block, virtual admittance block, and PI/PR controller block). The equivalent circuit model accuracy is validated by comparing system steady-state voltage and current responses obtained by detailed time-domain models in PSCAD/EMTDC to those by the equivalent circuit models implemented in steady-state load flow program (e.g., OpenDSS). Two distinct control structures implemented in the $\alpha \beta $ and dq frames are used for the validation. Single line-to-ground and line-to-line-to-ground faults are simulated in a small islanded microgrid as well as the IEEE 34-node test feeder. Fault impedances varying from 0 to 5 ohms are simulated. We show that the equivalent models precisely replicate the steady-state response of the detailed time-domain models.

Keywords