Q7Electric Drives

In an induction motor, slip s is defined as the fractional difference between the synchronous speed Ns (set by supply frequency and pole count) and the actual rotor speed N: s = (Ns-N)/Ns. When the rotor is not rotating at synchronous speed (s≠0), the relative motion between the rotating stator magnetic field and the rotor conductors induces an EMF in the rotor circuit at the slip frequency fr=s×f (where f is the supply frequency), and this induced rotor EMF, in turn, drives a rotor current through the rotor circuit's own impedance.

Relationship between slip and rotor current: the rotor circuit, referred to a per-phase equivalent representation, has a rotor EMF at standstill E2 (when s=1) that scales directly with slip at any other operating point (the actual induced rotor EMF at slip s is s×E2), while the rotor leakage reactance also scales with slip (since reactance depends on frequency, and rotor frequency is s×f, giving rotor reactance at slip s as s×X2, where X2 is the standstill rotor reactance) — the rotor resistance R2, however, remains unchanged by slip (a pure resistance is frequency-independent). The resulting rotor current is therefore:

Behavior at low slip (near synchronous speed, light load): when s is small, the term sX2 is generally much smaller than R2 (since X2 is a fixed reference value and s is small), so the denominator is approximately just R2, giving I2 ≈ sE2/R2 — rotor current increases approximately linearly (directly proportional) with slip in this low-slip region, which is also the region where developed torque increases approximately linearly with slip (since torque is directly related to the product of rotor current and the in-phase/torque-producing component of rotor flux), explaining why the induction motor's torque-speed curve is nearly linear in the normal operating region near synchronous speed.

Behavior at high slip (near standstill, heavy overload): as slip continues to increase substantially (approaching and exceeding the slip at which maximum/breakdown torque occurs, smax=R2/X2), the sX2 term in the denominator becomes increasingly significant relative to R2, causing the rate of increase of rotor current (and torque) with further slip increase to slow down and eventually reverse — rotor current continues to increase toward standstill (s=1), but torque itself passes through a maximum (breakdown torque) at s=R2/X2 and then decreases as slip increases further toward 1, since the rotor circuit's increasing reactive impedance at high slip causes an increasing phase lag between rotor current and rotor flux, reducing the effective torque-producing (in-phase) component of the current even as its total magnitude continues to rise.

Effect on Motor Performance Under Varying Loads

Under normal (light to moderate) load conditions, operating in the nearly-linear, low-slip region of the torque-slip curve, an increase in mechanical load torque causes the motor to settle at a slightly higher slip (slightly lower speed), with rotor current increasing roughly proportionally to accommodate the additional torque demand — this gives the induction motor good, nearly constant-speed performance across its normal operating load range, similar in character to the separately-excited DC motor's speed-load behavior discussed elsewhere in this paper, though the induction motor's speed variation with load is somewhat larger in relative terms (typical full-load slip for standard induction motors is in the range of 2-5%).

Under severe overload conditions (load torque approaching or exceeding the motor's breakdown torque), the motor's operating point moves past the maximum-torque slip point, at which point any further load torque increase can no longer be met by a corresponding torque increase from the motor — the motor instead rapidly decelerates (stalls), with slip increasing sharply toward 1 (standstill) while rotor (and stator) current continues rising toward its locked-rotor value, a condition that must be avoided in practice (through appropriate motor sizing relative to expected maximum load torque, and through protective overcurrent/thermal protection devices) since sustained stall operation causes rapid, potentially damaging overheating of both stator and rotor windings due to the very high current drawn at low/zero speed with correspondingly poor cooling (since induction motor cooling typically depends on shaft-mounted fan airflow proportional to rotor speed).