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

Abstract

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 <inline-formula> <tex-math notation= LaTeX >$\\alpha \\beta $ </tex-math></inline-formula> and <italic>dq</italic> frames. For this reason, they operate according to prescribed control functions and specified impedances (<italic>i.e.</italic>, 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 (<italic>e.g.</italic>, OpenDSS). Two distinct control structures implemented in the <inline-formula> <tex-math notation= LaTeX >$\\alpha \\beta $ </tex-math></inline-formula> and <italic>dq</italic> 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.