Dashboard › Deep Learning › Electrical Machines › Induction machines › Slip and rotor frequency

Slip and rotor frequency

s, f_r = s·f, E_2s = s·E_2 — three numbers that move together across every induction-machine operating region.

Freshman ~8 min

Step 1 — Slip: s = (n_s − n) / n_s

Animation speed 0.55×

s 1.00 f_r 50 Hz E_2s/E₂ 1.00

Reference notes

Use Next → on the narrator above to step through key operating points — from standstill through rated load to synchronous speed — watching how slip and rotor frequency change in lockstep.

Slip and the three derived quantities

Slip is the per-unit difference between synchronous speed and actual rotor speed:

s = (n_s − n) / n_s ⇒ n = (1 − s)·n_s

s = 1: standstill — rotor stationary.
0 < s < 1: motoring, rotor running below synchronous.
s = 0: rotor exactly at synchronous speed (impossible at non-zero load).
s < 0: generating — rotor driven above synchronous; the machine pushes real power into the grid (induction generator).
s > 1: plugging — supply reversed while rotor still spins forward, used for emergency stops.

Rotor EMF frequency

The rotating stator field sweeps past the rotor bars at the relative speed (n_s − n). Convert to electrical frequency:

f_r = s · f

where f is the supply frequency. At standstill (s = 1), the rotor sees the full supply frequency. At rated full load (s ≈ 0.04), the rotor sees only about 2 Hz on a 50 Hz supply. Rotor currents are LF currents, which is why slip-ring rotor harmonics behave very differently from stator currents.

Rotor EMF magnitude

The induced EMF in a stationary rotor (s = 1) is some value E₂, dictated by the rotor turns and the air-gap flux. When the rotor moves, the relative speed drops by factor s, so:

E_2s = s · E₂

The rotor's own leakage reactance also scales with slip:

X_2s = s · X₂

(because reactance is proportional to frequency.) The rotor resistance R₂ is unchanged.

Why these scalings matter

At standstill, both the rotor EMF AND its reactance are at their maximum — that's why starting currents are large and starting torque is hard to control without a starter or VFD.
At running speed, the rotor EMF is small, the rotor reactance is small, but the effective rotor impedance is dominated by R₂/s — exactly what makes the equivalent circuit work (next lesson).
The 2-Hz rotor current at full load is why slip-ring machines exhibit very different acoustic behaviour from stator: the rotor whine is at slip frequency, not at supply frequency.

Operating regions at a glance

Slip	n	Behaviour
s = 1.0	0 rpm	Standstill / starting
s ≈ 0.04	~96 % n_s	Steady running, full load
s → 0	~n_s	No-load (just bearings + friction)
s < 0	> n_s	Induction generator (rotor driven above n_s)
s > 1	Reverse direction	Plugging (emergency stop)

Take-away. Three numbers all move together — slip, rotor frequency, rotor EMF. They're all multiplied by the same factor s relative to their standstill values. Once you've internalised this, the equivalent circuit and the torque-slip curve drop out easily.

Keyboard shortcuts

→ next step · ← previous step
R replay narration · M mute / unmute · F fullscreen