This paper proposes a residue based open-loop modal analysis method to detect low frequency modal resonance(LFMR)

including asymmetric low frequency modal attraction(ALFMA) and asymmetric low frequency modal repulsion(ALFMR)

of permanent magnetic synchronous generator based wind farms(PMSG-WFs) penetrated power systems. The formation of ALFMA and ALFMR caused by two open-loop low frequency oscillation(LFO) modes moving close and apart is analyzed in detail. Via predicting the trajectories of closed-loop LFO modes based on calculation of residue of open-loop LFO modes

both ALFMA and ALFMR can be detected. The proposed method can select LFO modes which move to the right half complex plane as control parameters vary. Simulation studies are carried out on a three-machine power system and a four-machine 11-bus power system to verify the properties of the proposed method.