Voltage stability evaluation by using extended modal analysis with dynamic internal impedance of synchronous generators

The steady-state analysis of power system voltage stability usually overlooks the dynamic characteristic of internal impedance of synchronous generators, which may cause errors when evaluating the margin of voltage stability. In this paper, the dynamic generator internal impedance (dGII) is calculated based on phasor measurements. Then the dGIIs are incorporated into the modal analysis of the power system to get an extended admittance matrix and the corresponding Jacobian matrix. The eigenvalue of the extended Jacobian matrix offers a relative measure to predict the voltage instability. By considering the dGIIs, the extended modal method is able to estimate the voltage instability more accurately than the conventional one without dGIIs. The effectiveness of the proposed method is verified by the simulation studies on a 4-bus system, a WECC 9-bus system, and an IEEE 14-bus system.