Numerical Computation of Parameter-Space Stability/Instability Partitions for Induction Motor Stalling

Abstract

Abstract: Electrical power distribution networks are susceptible to Fault Induced Delayed Voltage Recovery (FIDVR). Such events are usually initiated by faults at substations and lead to sustained low voltages throughout the distribution grid. The mechanism underpinning this phenomenon is known to be the stalling of induction motors in residential air conditioners. It is useful to be able to partition parameter space into parameters that induce motor stalling versus those for which the motors recover for a particular fault. Novel algorithms are presented for numerically computing the border that separates such parameter-space partitions, and for finding the point on the border that is closest to a given point in parameter space. These algorithms are justified by theoretical results which exploit the presence of a special equilibrium point on the state-space stability boundary, called the controlling unstable equilibrium point. The key idea is to vary parameters in order to drive the trajectory to spend a fixed amount of time inside a ball centered at the controlling unstable equilibrium point, and then to maximize the amount of time inside that ball. The algorithms are applied to a modified version of the IEEE 37-bus test feeder.