Single phase induction motor

Single-phase induction motors power most household and small commercial equipment in Nepal — ceiling and table fans, water pumps, refrigerators, washing machines and small workshop tools — because homes receive single-phase 230 V supply. Their main problem is that a single winding cannot produce a rotating field, so they are not self-starting. This topic explains why, how split-phase, capacitor and shaded-pole motors solve the starting problem, their characteristics and applications, and how their speed is controlled.

Key concepts

• Why not self-starting: a single-phase winding produces a pulsating field, not a rotating one. By the double-revolving field theory, the pulsating field equals two fields of half amplitude rotating in opposite directions at synchronous speed. At standstill their torques are equal and opposite → zero net torque. Once spun in either direction, the forward torque dominates and the motor keeps running in that direction.
• Cross-field theory is an alternative explanation; both lead to the same result.
• Construction: like a 3-phase squirrel-cage motor, but the stator has a main (running) winding plus an auxiliary (starting) winding displaced 90° electrical in space; rotor is a squirrel cage. A centrifugal switch disconnects the auxiliary winding at about 70–80% of synchronous speed in some types.
• Starting principle: currents in the two windings must be out of time phase so the combination produces an (elliptical) rotating field.

Type	How phase difference is made	Starting torque	Typical uses
Resistance split-phase	Aux winding of high R / low X (thin wire); phase shift ≈ 25–30°	Moderate (≈1.5× FL)	Fans, blowers, washing machines, small grinders
Capacitor-start	Capacitor (electrolytic) in series with aux; ≈ 80–90° shift; switch removes it	High (3–4.5× FL)	Compressors, pumps, refrigerators, air conditioners
Permanent split capacitor (PSC)	Paper/oil capacitor stays in circuit	Low–moderate; quiet, good pf	Ceiling fans, blowers, AC fans
Capacitor-start capacitor-run	Large start capacitor + smaller run capacitor	High; best running pf and efficiency	Larger compressors, pumps
Shaded-pole	Copper shading ring on part of each pole delays the flux	Very low (≈0.5× FL); low efficiency	Table fans, hair dryers, exhaust fans, record players, small timers

• Shaded-pole motor: salient poles split by a slot; the smaller part carries a short-circuited copper ring. Induced current in the ring makes the flux in the shaded part lag, so the field shifts from the unshaded to the shaded part — rotor turns in that direction. Direction cannot be reversed electrically (fixed by the ring location). Simple, cheap, robust, but efficiency only about 5–35%.
• Reversing: in split-phase and capacitor motors, reverse the connections of either the main or the auxiliary winding (not both).
• Characteristics: speed nearly constant (slip 3–5%), torque pulsates at twice supply frequency (100 Hz hum), lower efficiency and pf than 3-phase motors of the same size, and larger size per kW.
• Speed control:
  • Voltage control — series resistor/inductor (choke) regulator, auto-transformer, or TRIAC phase-angle regulator (electronic fan regulator). Works well for fan loads where torque falls with speed.
  • Tapped winding — fan regulators selecting different winding sections.
  • Capacitor-switching (step capacitor regulators in some fans).
  • Variable frequency drives for higher-end applications; pole changing for two-speed motors.
• Other single-phase motors (useful for comparison): universal (series) motor — runs on AC/DC, high speed, used in mixers, drills, vacuum cleaners; reluctance and hysteresis synchronous motors for clocks and timers.

High-yield points

• A single-phase winding gives a pulsating field — zero starting torque (double-revolving field theory).
• Starting torque $\propto I_mI_a\sin\alpha$; capacitor-start gives α near 90°.
• Highest starting torque: capacitor-start (and capacitor-start capacitor-run); lowest: shaded-pole.
• Ceiling fans use PSC motors; shaded-pole motors cannot be reversed electrically.
• Centrifugal switch cuts out the auxiliary winding at about 75% of synchronous speed.
• Torque pulsates at twice supply frequency (100 Hz on a 50 Hz supply).

Formulas

Ideal capacitor-start: the auxiliary current should lead the main current by about 90°: $\alpha = \phi_m - \phi_a$ where $\phi_m$ and $\phi_a$ are the impedance angles of main and auxiliary branches; starting torque $T_{st} \propto I_m I_a \sin\alpha$.

Synchronous speed is still $N_s = 120f/P$; a 4-pole fan motor on 50 Hz has $N_s = 1500$ rpm.

Worked example

At standstill the main winding current lags the voltage by 40° and the auxiliary (with capacitor) current leads by 45°. Starting torque is proportional to $I_mI_a\sin\alpha$. Find α and the fraction of the maximum possible torque (for the same currents).

1. $\alpha = 40° - (-45°) = 85°$.
2. $\sin 85° = 0.996$ → 99.6% of the value at 90°, so the capacitor gives near-ideal starting.
3. For a resistance split-phase motor with α = 25°, $\sin25° = 0.42$ — only 42%, which is why its starting torque is lower.

Exam tips

• Single-phase induction motor: not self-starting because the field is pulsating (double-revolving field theory).
• Highest starting torque: capacitor-start (or capacitor-start capacitor-run); lowest: shaded-pole.
• Ceiling fans use PSC motors; table fans and exhaust fans often shaded-pole.
• Shaded-pole direction is fixed; others reverse by swapping one winding's leads.
• Centrifugal switch opens at about 75% speed; a failed-open switch means no start, failed-closed burns the auxiliary winding.

Exam-style questions

From Calmon's question bank, which has 25 questions on this topic.

1. In a capacitor-start capacitor-run motor, compared with the starting capacitor, the running capacitor is:

• A. Smaller in value and of the oil-filled or paper (continuous-duty) type
• B. Connected in series with the main winding
• C. Larger in value and of the electrolytic type
• D. Identical in value

Answer: A. The run capacitor stays in circuit permanently, so it is a smaller, continuously rated (paper/oil or film) capacitor; the large electrolytic start capacitor is switched out.

2. If the run capacitor of a ceiling fan becomes open-circuited, the fan will typically:

• A. Run normally but in reverse
• B. Run at synchronous speed
• C. Hum and not start by itself, but may run if spun by hand
• D. Run at double speed

Answer: C. Without the capacitor only a pulsating field exists, so there is no starting torque; once spun, the motor can continue running like any single-phase induction motor.

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