Invariant manifolds and start-up dynamics of induction machines

Time-scale properties are investigated for several induction machines with sizes ranging from 3 to 6000 hp. Whereas third-order models neglecting stator transients are relatively accurate, first-order models should not be used for machines of sizes greater than 250 hp unless higher-order corrections are used. Exact invariant manifolds are derived in the case of zero stator resistance and constant or ramping input voltages. Off-manifold variables are used to account properly for the neglected dynamics in studies where such effects can be preponderant. This was illustrated by simulating the dynamic startup of an induction machine with a negligible resistance and by showing the detrimental effects of the braking torque. Using a ramping input voltage effectively reduces this braking torque and allows a smooth acceleration towards rated speed. This shows the significance of starting as close as possible to the invariant manifold corresponding to the stator variables