Computation of Critical Values of Parameters in Power Systems Using Trajectory Sensitivities

It has been known in the literature that system sensitivity increases sharply as the trajectory approaches the boundary of the region of attraction (ROA) while the trajectory does not exhibit such a sharp behavior. The relationship between sensitivity and stability of a nonlinear dynamic system such as the power system is investigated in this paper. In this context the role of the principal singular surface (PSS) also becomes significant. The principal singular surface is defined as a set of points enclosing the origin and where the Jacobian of the system evaluated at these points is singular. As the trajectory evolves, the Jacobian of the flow becomes singular at a point on the PSS and a sharp increase in trajectory sensitivity is observed. The mode of instability (MOI) can thus be defined very early during a faulted trajectory in most cases. A technique is also proposed using the norm of trajectory sensitivity vector at two points and then extrapolating it to estimate the critical parameter of interest which may be clearing time, mechanical power, etc.