To delve into the mechanism behind wideband oscillation instability in voltage source converter based high voltage direct current(VSC-HVDC)transmission system and swiftly assess system stability with precision,a modeling method and a stability criterion based on z-domain impedance are proposed.Firstly,employing precise dis-cretization techniques,a z-domain impedance model is established for voltage-source converters considering phase-locked loops(PLLs),inner-current loop,and voltage feedforward control,along with a z-domain impedance model for AC grids in a global coordinate system.Subsequently,a criterion for generalized forbidden zone is proposed us-ing Gershgorin circle theorem to analyze the impact of phase-locked loops and line impedances on system stability.Finally,simulation analysis is conducted on the VSC-HVDC system to demonstrate the effectiveness of the proposed generalized impedance criterion.