Large-Signal Models of the Park Transformation and Phase-Locked Loop Algorithms

The control of modern grid-connected converters often relies on Park Transform and synchronization algorithms. These are highly nonlinear subsystems integrated into even larger systems that include other nonlinearities. Thus, strictly speaking, large-signal models are required when analysing and designing such systems. However, a limited number of mathematical tools is available to that end. This work proposes a nonlinear time-invariant model for the Park Transformation and the Synchronous Reference Frame Phase-Locked Loop (SRF-PLL), which are based on the Harmonic State-Space (HSS) in a stationary coordinate frame. The HSS modeling technique is reviewed as a basis for nonlinear models of functions based on polynomial nonlinear systems. This serves as an appropriate formal basis for the model of 2-D rotations as means of modeling the SRF-PLL and other similar algorithms. The models are validated through simulations to verify their accuracy when compared to the original Nonlinear Time-Periodic (NLTP) Systems.