Synchronization Stability of 3-phase Grid Connected Inverters in Weak Grids

Abstract

This paper formulates the relation between the Phase-Locked Loop (PLL) dynamics of a grid-connected distributed source and the impedance of the grid. Conventionally the design of the PLL for a grid following inverter is performed independently of the grid impedance. With the advent of micro-grids, these design procedures require modification. Microgrids are characterized by higher grid impedances which severely impact the PLL dynamics. The grid voltage in a microgrid is not a stiff variable and thus cannot be assumed to be independent of its interaction with a distributed source. The PLL dynamics in these cases affect the voltage at the point of common coupling (PCC) and vice-versa. In this paper, the relation between the grid impedance and the PLL parameters is analytically derived using dynamic phasors. A distributed resource connected to the grid via a 3-phase inverter is considered for the analysis. Grid synchronization is achieved using a synchronous reference frame (SRF) PLL. It is shown that under weak grid conditions, the PLL can get de-synchronized if the magnitude of grid impedance or the current levels are higher than the thresholds derived in this paper. Microgrids with higher grid impedance are highly susceptible to such situations. The design of SRF-PLL for grid-connected inverters thus needs to include an estimate of the maximum system ratings and the grid impedance.