Phase boundary computation for Fault Induced Delayed Voltage Recovery

Distribution networks that supply large numbers of induction motors are vulnerable to Fault Induced Delayed Voltage Recovery. This phenomenon is usually triggered by a transmission fault but results in a delayed recovery of voltages in the distribution feeder, usually taking several seconds for a return to pre-fault conditions, if at all. The general mechanism underlying this delayed recovery arises from the coupled nonlinear dynamics of induction motors stalling. It is important to establish the phase boundary that separates parameters that lead to stalled versus unstalled motor states. This paper develops a novel algorithm, based on shooting methods and Euler homotopy continuation, for obtaining the phase boundaries. It forces a trajectory to spend a fixed amount of time near an unstable equilibrium, and then increases that time until the trajectory approaches the unstable equilibrium point arbitrarily closely. This technique does not require prior knowledge of the unstable equilibrium point. Numerically computed phase boundaries, in terms of induction motor moments of inertia, fault clearing times, and nonhomogeneous networks are presented. The techniques are formulated in generality, and could be applied to compute phase boundaries for a large class of dynamical systems.