An almost globally stable adaptive phase-locked loop for synchronization of a voltage source converter to a weak grid

In this article, we are interested in the problem of adaptive synchronization of a voltage source converter with a possibly weak grid with unknown angle and frequency. To guarantee a suitable synchronization with the angle of the three-phase grid voltage we design an adaptive observer for such a signal requiring measurements only at the point of common coupling. Then we propose an alternative certainty-equivalent, adaptive phase-locked loop that ensures the angle estimation error goes to zero for almost all initial conditions. Although well-known, for the sake of completeness, we also present a PI controller with feedforward action that ensures the converter currents converge to an arbitrary desired value. Relevance of the theoretical results and their robustness to variation of the grid parameters are thoroughly discussed and validated in the challenging scenario of a converter connected to a grid with low short-circuit-ratio.