Power system voltage small-disturbance stability studies based on the power flow equation

This study first studies power system small-disturbance stability at the operating point where the power flow (PF) equation encounters a saddle-node bifurcation. The authors demonstrate that the linearised model of the differential-algebraic equation (DAE) that describes the power system dynamics will have a zero eigenvalue at the equilibrium precisely when the PF Jacobian is singular. Note that the PF equation and DAE models are general ones. This clarifies a point in previous contributions on this relationship. Numerical results for two power system examples are used to demonstrate the theory, and finally the extension of the theory is discussed for the limit-induced bifurcation associated with the PF equation when some generators reach their reactive power limits.