Passivity-based design and analysis of phase-locked loops

We consider a grid-connected voltage source converter (VSC) and address the problem of estimating the grid angle and frequency-information that is essential for an appropriate operation of the converter. We design phase-locked loop (PLL) algorithms with guaranteed stability properties, assuming that the grid is characterized by relatively high short-circuit-ratio and inertia. In particular we derive, using passivity arguments, generalization of the conventional synchronous reference frame and arctangent PLL, which are the standard solutions in power applications. The analysis is further extended to the case of interconnection to a low-inertia grid, ensuring robustness of the algorithms in case of frequency variations. The results are validated on a benchmark including the grid, the VSC and related controllers.