Induction & Synchronous Machines Notes

Last reviewed 16 Sept 2026 · 8 min read

Three-phase induction motor

The most widely used industrial motor — simple, rugged, cheap, low maintenance (pumps, fans, compressors, conveyors, mixers, cranes).

Rotating magnetic field

A balanced three-phase supply to a three-phase stator winding produces a magnetic field of constant magnitude rotating at synchronous speed:

N_{s} = \frac{120 f}{P}

Reversing any two supply phases reverses the direction of rotation.

Poles (50 Hz)	2	4	6	8	10	12
$N_{s}$ (rpm)	3000	1500	1000	750	600	500

Construction

Part	Details
Stator	Laminated core with slots carrying a three-phase winding
Squirrel cage rotor	Copper/aluminium bars short-circuited by end rings — simple, robust, cheap; no external rotor resistance possible; moderate starting torque
Slip-ring (wound) rotor	Three-phase rotor winding connected through slip rings and brushes to external resistances — high starting torque, lower starting current, speed control; more maintenance
Air gap	Kept small to reduce magnetising current (improves pf)

Principle

The rotating field cuts rotor conductors → EMF and current induced in the rotor → force on the rotor conductors → rotor rotates in the direction of the field but at a speed less than $N_{s}$ (if it reached $N_{s}$ , there would be no relative motion, no induced current and no torque). Hence also called an asynchronous motor.

Slip

FormulaSlip and rotor quantities

s = \frac{N _{s} - N}{N _{s}}, N = N_{s} (1 - s)

Typical full-load slip: about 2–6% (small motors higher)
Rotor frequency $f_{r} = s f$
Rotor EMF per phase (running) $E_{2 r} = s E_{2}$ ; rotor reactance $X_{2 r} = s X_{2}$
At standstill (starting) $s = 1$ ; at synchronous speed $s = 0$

Torque

FormulaTorque equation

T \propto \frac{s E _{2}^{2} R _{2}}{R _{2}^{2} + ( s X _{2} ) ^{2}}

Maximum torque occurs when $R_{2} = s X_{2}$ → slip at maximum torque $s_{m} = R_{2} / X_{2}$
$T_{ma x} \propto \frac{E _{2}^{2}}{2 X _{2}}$ — independent of rotor resistance
Starting torque ( $s = 1$ ): $T_{s t} \propto \frac{E _{2}^{2} R _{2}}{R _{2}^{2} + X _{2}^{2}}$ — maximum at starting when $R_{2} = X_{2}$
Torque ∝ (supply voltage)²

Torque–slip characteristic:

Low slip region (normal operation): $T \propto s$ — approximately linear (stable).
High slip region: $T \propto 1/ s$ (unstable).
Adding rotor resistance (slip-ring motors) increases starting torque without changing maximum torque (the peak shifts to higher slip).

Power flow

FormulaPower stages

Stator input → (stator copper + iron losses) → air-gap (rotor input) power $P_{2}$

Rotor copper loss = s P_{2}, Gross mechanical power = (1 - s) P_{2}

P_{2} : P_{c u 2} : P_{m} = 1 : s : (1 - s)

Net output = gross mechanical power − friction and windage losses. Rotor efficiency ≈ $(1 - s)$ .

Starting methods

Direct starting draws a large current (commonly 5–8 times full-load current) at low power factor.

Method	Principle	Starting current / torque
Direct-on-line (DOL)	Full voltage	Highest current; for small motors
Star–delta starter	Stator connected in star at start (phase voltage $V_{L} / 3$ ), then delta for running	Line current and torque reduced to 1/3 of DOL values
Autotransformer starter	Reduced voltage via autotransformer tapping $x$	Line current and torque ∝ $x^{2}$
Stator resistance/reactance	Series impedance drops voltage	Torque reduced more than current
Rotor resistance starter (slip-ring motors only)	External resistance in rotor	Reduces current and increases starting torque
Soft starters / VFDs	Power electronic control	Smooth starting

Speed control

Variable frequency drives (VFD) — varying supply frequency (with V/f constant) — most common today, energy saving for pumps and fans.
Pole changing (multi-speed motors), rotor resistance (slip-ring, inefficient), supply voltage control, slip energy recovery.

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