Sub-synchronous interactions caused by the PLL in the grid-connected PMSG for the wind power generation

A phase locked loop (PLL) functions to connect a grid-connected permanent magnet synchronous generator (PMSG) for wind power generation to a power system. This paper investigates the sub-synchronous interactions (SSIs) caused by a PLL. A closed-loop interconnected model for the power system with the PMSG is established, wherein, the PLL and the rest of power system are modelled as two open-loop subsystems. Analysis in the paper indicates that when an open-loop complex pole of the PLL subsystem is close to an open-loop sub-synchronous oscillation (SSO) mode of the rest of power system, this open-loop modal resonance may cause strong SSIs between the PLL and power system. It is very likely that the strong SSIs may degrade the damping of power system SSOs. Hence, the mechanism that the grid connection of the PMSG may cause the SSO instability of the power system is revealed from the perspective of open-loop modal resonance introduced by the PLL. In the paper, a method of open-loop modal analysis is proposed to identify the instability risk of open-loop modal resonance brought about by the PLL. Study cases are presented in the paper to demonstrate and evaluate the analysis and conclusions.