Starting and speed control of induction motors

Why it matters

An induction motor switched straight onto the supply draws five to eight times its full-load current, which dips the plant voltage and stresses the machine and coupling. Choosing a starter (DOL, star–delta, autotransformer, soft starter, rotor resistance) and a speed-control method (pole changing, voltage, V/f drive, rotor resistance) is a routine design and maintenance decision, and variable-frequency drives on pumps and fans are one of the biggest energy savers in industry.

Key ideas

Why starting current is high. At standstill s = 1, so the rotor branch resistance R2'/s is small and the motor looks like a transformer with a short-circuited secondary. Starting current Isc is typically 5–8 times full-load current, at a poor power factor. Starting torque, however, is only about 1–2 times full-load torque.

Starting torque relation. Since T ∝ I2²·R2/s, at s = 1 and at full-load slip sfl: Tst/Tfl = (Ist/Ifl)²·sfl. Any method that reduces the phase voltage by a factor x reduces starting current per phase by x and starting torque by x².

Starting methods for cage motors

• Direct-on-line (DOL): full voltage; simplest; used for small motors (a few kW) where the supply can tolerate the current.
• Stator resistance or reactor: series impedance drops the voltage; wasteful, rarely used now.
• Autotransformer starter: tapping x (e.g. 0.5–0.8) on the motor side. Motor current falls by x, but the line current falls by x² (autotransformer action), as does the torque. Best torque per ampere drawn from the line.
• Star–delta starter: for motors designed to run in delta. Started in star, each phase gets V/√3, so phase current and torque both fall to 1/3 of the DOL value, and so does the line current. Equivalent to an autotransformer with x = 1/√3. Cheap; the torque reduction is fixed.
• Soft starter: back-to-back thyristors ramp the voltage; smooth, adjustable current limit, but torque still falls as V².

Slip-ring (wound-rotor) motors are started with external rotor resistance. This lowers the starting current and raises the starting torque (up to Tmax when R2' = X), then the resistance is cut out in steps. Used for cranes, hoists and mill drives with heavy starting loads.

Speed control. N = Ns·(1 − s) = (120·f/P)·(1 − s), so speed can be changed by P, f or s.

• Pole changing: separate windings or a consequent-pole (Dahlander) winding give two or more fixed speeds (e.g. 1500/750 rpm). Cage rotor only, because a cage automatically adapts to any pole number.
• Stator voltage control: reducing V lowers torque (∝ V²) so slip rises. Narrow range, poor efficiency (high slip means high rotor loss); suitable only for fan-type loads.
• Frequency control (V/f): a variable-frequency drive (rectifier + PWM inverter) changes Ns smoothly. V is varied in proportion to f to keep the air-gap flux (∝ V/f) constant: lowering f at full V would saturate the core. Below base frequency this gives constant maximum torque; above base frequency V stays at rated and flux weakens — constant-power region. With constant V/f and low slip, the slip speed at a given torque is roughly constant, so the speed–torque lines shift parallel to each other.
• Rotor resistance (slip-ring motors): at a given torque in the low-slip region s ∝ R2, so speed falls as resistance is added. Simple but the slip power s·Pag is wasted in the resistors.
• Slip-power recovery (static Kramer / Scherbius drives) returns the rotor slip power to the supply through converters instead of burning it.
• Cascade connection of two motors gives additional speeds 120·f/(P1 ± P2).

Formulas

• Tst / Tfl = (Ist / Ifl)² · sfl — starting-to-full-load torque ratio (DOL values for Ist).
• Reduced voltage x·V: I_motor = x·Isc ; Tst = x²·Tst,DOL.
• Autotransformer starter: I_line = x²·Isc.
• Star–delta: I_line = Isc,DOL / 3 ; Tst = Tst,DOL / 3.
• Ns = 120·f / P ; N = Ns·(1 − s) — speed (rpm).
• V / f = constant — keeps air-gap flux constant below base speed.
• Low-slip region at constant torque: s ∝ R2 (rotor resistance control); s ∝ 1/V² (voltage control).
• N_cascade = 120·f / (P1 ± P2) — cascaded motor speeds (rpm).

Worked examples

Example 1 (standard): comparing starters. Given: a delta-connected cage motor has DOL starting current 6 times full-load current and full-load slip 4 %.

1. DOL: Tst/Tfl = (Ist/Ifl)²·sfl = 6² × 0.04 = 1.44; line current 6·Ifl.
2. Star–delta: phase voltage 1/√3, so Tst = 1.44/3 = 0.48 Tfl; line current = 6/3 = 2 Ifl.
3. Autotransformer with 70 % tapping (x = 0.7): motor current 0.7 × 6 = 4.2 Ifl; line current = 0.7² × 6 = 2.94 Ifl; Tst = 0.49 × 1.44 = 0.71 Tfl.
4. Star–delta draws less line current but gives too little torque if the load needs more than about half its full-load torque at standstill; the autotransformer gives more torque per line ampere.

Example 2 (GATE level): V/f control and rotor resistance. Given: a 4-pole, 50 Hz, 400 V motor runs at 1440 rpm at rated load torque. (a) A V/f drive reduces the supply to 30 Hz and 240 V; load torque unchanged.

1. Slip speed at rated torque: 1500 − 1440 = 60 rpm. With constant V/f and low slip, slip speed at a given torque stays the same.
2. New synchronous speed: Ns = 120 × 30/4 = 900 rpm.
3. New speed = 900 − 60 = 840 rpm. (b) Instead, the motor is a slip-ring motor whose rotor-circuit resistance is doubled (50 Hz, 400 V, same torque).
4. At constant torque in the low-slip region s ∝ R2, so s = 2 × 0.04 = 0.08.
5. Speed = 1500 × (1 − 0.08) = 1380 rpm; rotor copper loss doubles to 8 % of air-gap power.

Common mistakes

• Saying star–delta reduces line current to 1/√3; it reduces it to 1/3 (phase current falls by √3 and the delta-to-star change removes another √3).
• Forgetting that line current with an autotransformer starter falls as x², not x.
• Lowering frequency at constant voltage — flux rises and the core saturates.
• Using pole changing on a wound rotor; its winding has a fixed pole number.
• Believing rotor resistance control is efficient; the slip power is lost as heat.
• Assuming starting torque equals full-load torque times the current ratio; torque scales with current squared times slip.

For GATE IN

Expect starting-torque and line-current comparisons (DOL, star–delta, autotransformer), speed after a frequency or rotor-resistance change, and MCQs on V/f control, pole changing and which method suits which rotor. VFD and soft-starter operation links to power electronics and to process-control actuators.

Quick check

1. DOL Ist = 5 Ifl, sfl = 0.05. Find Tst/Tfl.
2. What fraction of DOL line current does a star–delta starter draw?
3. Why must voltage be reduced along with frequency?
4. Which speed-control method suits only cage rotors?

Answers: 1. 25 × 0.05 = 1.25. 2. One third. 3. To keep V/f, and hence flux, constant so the core does not saturate. 4. Pole changing.