  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, under the
assumption that the grid is characterized by relatively high
short-circuit-ratio (SCR) and inertia. In particular we derive, using passivity
arguments, generalization of the conventional synchronous reference frame (SRF)
and arctangent (ATAN) PLL, which are the standard solutions in power
applications. The analysis is further extended to the case of connection of the
VSC 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.
