Envelope-based Modeling for Single-Phase Grid-Following and Forming Converters

The study of the interaction with the grid, including synchronization, controller design and stability assessment for 1 phi grid-following (GFL) and grid-forming (GFM) power converters requires an efficient modeling tool to design universal grid-connected converters considering the different grid scenarios. From the initial time-periodic system, approximated linear time-invariant (LTI) models are obtained through dynamic phasors, linearization of variables represented in a virtual synchronous rotating reference frame (RRF) or linearization in the frequency domain, i.e. harmonic linearization. The accuracy and complexity of the obtained model depend on the method used. This work proposes to use the well-known envelope modeling approach used for resonant converters but requiring the time periodic input to generate its related phase synchronization for the model. The result is a simple and accurate LTI model of 1 phi GFL/GFM power converter for such stability studies. The proposed 1 phi modeling approach is valid for any application with phase locked loop (PLL) synchronization. Simulation results validating de proposal are provided.