Characterization of power system small disturbance stability with models incorporating voltage variation

The small disturbance (SD) stability of a power system is studied with the model including generator swing equations, the real and reactive power flow equations. The effects of voltage variation and reactive power constraints are thus explicitly represented in the model. It is shown that the necessary and sufficient condition for an operating point to be SD stable is that the reduced matrix from the power flow Jacobian is positive definite. A sufficient condition is that the power flow Jacobian itself is positive definite. The result is compared to the one obtained from the constant voltage model and the latter is shown to be more optimistic. Also derived are conditions for steady-state security regions to be SD stable.