On discrete-time models for grid-connected converters with L- and LCL-filter in synchronous reference frame

The objective of this paper is to develop discrete-time models for grid-connected converters in synchronous reference frame. As the current controllers are generally implemented in microprocessors, some problems that arise in the discrete-time domain are addressed. The time delay of the digital implementation is modeled and its effect on the synchronous transformation is discussed in this paper. Additionally, in the synchronous reference frame, the coupling between the axes must be considered, resulting in a multi-input, multi-output (MIMO) model.