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Recent works have shown that phase-locked loop (PLL) synchronized wind turbines (WTs) suffer stability issues when integrated into weak grids. However, most of the current studies are limited to a single machine case, the interactions among the WTs are usually overlooked. This paper studies the stability of multiple doubly-fed induction generators (DFIGs) that are connected in parallel to a weak AC grid. A state space model of a two-DFIG system is firstly presented. Subsequently, eigenvalue sensitivity analysis shows that instability can occur at low short-circuit ratio (SCR) or heavy loading conditions. Meanwhile, participation factor analysis implies that the unstable mode is primarily induced by the interactions between the PLLs of the two WTs. Further, to make out how the PLLs interact to cause instability, a reduced-order model is proposed for analysis simplicity, and an explanation in terms of transfer function residue is given for illustration. Detailed model-based time domain simulations are conducted to validate the analyses’ results.

Grid-Synchronization Stability Analysis for Multi DFIGs Connected in Parallel to Weak AC Grids