Single-phase motor conceptualized as single common stator winding, but two rotors revolving in opposite directions.

Equivalent circuit based on double-field revolving theory

Without Core Loss

The stator impedance: \(Z_1 = R_1 + j X_1\)

Each rotor impedance: \(r_2 + jx_2\)

\(r_2\) (rotor resistance), \(x_2\) (standstill reactance), and \(x_m\) (magnetising reactance) are half the actual values w.r.t stator (as referred to stator)

Iron loss neglected so exciting branch has only \(x_m\)

Full values by capital letters and half-values by small letters

Impedance of forward running motor with \(s_f =s\) \[Z_f = \dfrac{jx_m\left(\dfrac{r_2}{s}+jx_2\right)}{\dfrac{r_2}{s}+j\left(x_m+x_2\right)}\]

Impedance of backward running motor with \(s_b =(2-s)\) \[Z_b = \dfrac{jx_m\left(\dfrac{r_2}{2-s}+jx_2\right)}{\dfrac{r_2}{2-s}+j\left(x_m+x_2\right)}\]

Under standstill condition, \(V_f = V_b\)

Under running condition, \(V_f\) almost \(90-95\%\) of \(V\)

Power developed by the rotor : \[P_g = \left(\dfrac{1-s}{s}\right) \cdot I_2^2R_2\]

If \(N\) is the rotor r.p.s, then torque is \[T_g = \dfrac{1}{2\pi N} \left(\dfrac{1-s}{s}\right) \cdot I_2^2R_2\]

Since \(N=N_s\left(1-s\right)\), then \[T_g = \dfrac{1}{2\pi N_s} \dfrac{I_2^2R_2}{s} = k \cdot \dfrac{I_2^2R_2}{s}\]

Therefore, forward and backward torques are: \[T_f = K \cdot \dfrac{I_2^2R_2}{s} \qquad T_b = -K \cdot \dfrac{I_2^2R_2}{(2-s)}\]

Total torque \(T=T_f+T_b\)

Forward torque in synchronous watts: \[T_f = I_3^2\cdot r_2/s\]

Backward torque : \[T_b = I_5^2 \cdot r_2/(2-s)\]

Total torque: \[T = T_f - T_b\]

core loss represented by \(r_c\) connected in parallel with \(x_m\)

Running condition: \(V_f >> V_b\)

Most of the iron-loss take place in forward motor \(I_w = P_i/V_f\)

Advantages:

smaller in size and lighter in weight

cheaper in cost

highly efficient

requires less maintenance

have a longer life

can be designed in a variety of sizes

Limitations

For a given frame size and temperature, its output is only 50% of the three-phase induction motor

Not self-started

Have a lower power factor

Efficiency is lower

Do not have a starting torque

For the same power output, these motors are more expensive than three-phase induction motors.