A Small Signal Rotating Frame Model of a Self-synchronizing Single-phase Grid-tied Inverter

A self-synchronizing grid-tied inverter uses the internal dynamic states of the current regulator to estimate the grid voltage for synchronization. The stability analysis of a single-phase grid-tied inverter is complex because of the lack of an orthogonal channel and non-linearities present due to the phase-locked loop (PLL). This paper introduces fictitious orthogonal quantities for a single-phase grid-tied inverter, creating a model in the synchronous reference frame. This approach enables Jacobian linearization to develop a small-signal inverter model. The stability analysis of the small-signal model using Floquet theory then allows for stability boundaries to be determined across a wide range of operating conditions. The model has been validated using detailed switched simulations of a single-phase grid-tied inverter with matching experimental results.