DFRT, starting methods and capacitor start-run motor

Double field revolving theory (DFRT)

A single-phase winding produces a pulsating field $B = B_m\cos\omega t$ along a fixed axis, not a rotating one. DFRT states that this pulsating field can be split into two fields of half amplitude ($B_m/2$ each) rotating at synchronous speed in opposite directions:

$$B_m \cos\omega t\,\cos\theta = \frac{B_m}{2}\cos(\theta - \omega t) + \frac{B_m}{2}\cos(\theta + \omega t)$$

• The forward field (FF) gives torque $T_f$ in its direction, the backward field (BF) gives $T_b$ in the opposite direction.
• At standstill both slips are 1, so $T_f = T_b$ and net torque is zero: the motor is not self-starting.
• If the rotor is pushed in either direction, the slip w.r.t. that field becomes small, $T_f > T_b$, and the motor keeps running in that direction.

 T  |   Tf
    |  /\
    | /  \___      net T = Tf - Tb
  --+------------------------------> speed
 -n |\___   /           +n
    |    \ /
    |     \/  Tb

Starting methods

1. Split-phase (resistance start) motor
2. Capacitor-start induction-run motor
3. Capacitor-start capacitor-run (two-value capacitor) motor
4. Permanent split capacitor (PSC) motor
5. Shaded-pole motor

All of them create a second field displaced in space and time so that a rotating field exists at start.

Capacitor-start capacitor-run (CSCR) motor

Construction: a main winding and an auxiliary winding displaced by $90^\circ$ electrical. The auxiliary circuit has two capacitors in parallel: a large electrolytic starting capacitor $C_s$ in series with a centrifugal switch, and a small oil-type running capacitor $C_r$ that stays in circuit.

  o------+-----------+
         |           |
       Main      Auxiliary
         |           |
         |       +---+---+
  V      |       |       |
         |      C_s     C_r
         |       |       |
         |      CS       |
         |       +---+---+
  o------+-----------+

Operation:

• At start $C_s + C_r$ make $I_a$ lead $I_m$ by nearly $90^\circ$, giving high starting torque ($T_{st} \propto I_m I_a \sin\alpha$).
• At about 75% of synchronous speed the centrifugal switch removes $C_s$.
• $C_r$ keeps the motor running as a nearly balanced two-phase motor.

Advantages: high starting torque, high power factor and efficiency, quiet operation. Used in compressors, refrigerators and air-conditioners.