Small-Signal Modelling and Stability Assessment of Phase-Locked Loops in Weak Grids

This paper proposes a low-complexity small signal model for a 3-leg converter connected to a balanced three-phase, three-wire weak grid and synchronised to this grid using a PLL implemented in a synchronous rotating d-q axis. A thorough analysis of the system stability as a function of the PLL bandwidth and the short circuit ratio (SCR) of the grid is performed based on a linearised model. By using the proposed model, an improved design process is proposed for the commonly used dq-PLL that accounts for the potential stability issues which may occur in weak grids. Using the proposed approach, it is possible to optimise the PLL design to find the fastest PLL that can operate stably considering the SCR of the grid. In addition, the proposed model is very simple, resulting in a straightforward design tool that could also be used for online stability monitoring. The method is validated through simulations and experimental results from a 5kW laboratory system.