In a pure single phase current (some single phase or three-phase with only two wires without capacitors) both current components are equal. However, the impedance of the motor is not equal (if the motor rotates) as the impedance is higher for low slip: for instance 5% compared to 195%. So the voltages are closer to the symmetry than the currents, except at standstill.

Dear Dr. Alex Van den Bossche 

Thanks a lot for your response, but I should clarify that I am assuming a single phase induction motor with the starting winding open. It means that there is only one single phase stator winding and we are interested in the rotor current components under such a situation. We want to compare the rotor current component with frequency s*f and that with frequency (2-s)*f, s being the (forward) slip and f being the single phase stator supply frequency.

I am looking forward to receiving your answer.

Mohammad, it was formulated for that case.

i(theta) =0.5*Ipeak* (e^jtheta+e^-jtheta) is real, so it is a  single phase current which contains exactly as much forward and reverse component contribution.

R2*(1-s)/s is the back emf in the induction motor model and it is much bigger for one component than the other one, which makes a difference in impedance, also at stator level.

Back emf and rotor current result in synchronous power and divided by 2*pi*f in torque, which has to be corrected for the number of pole pairs. The story above is for steady state, for a starting behavior you need simulations.

Dear Dr. Alex Van den Bossche

Thanks a lot for your response. Please clarify which of the rotor current components are higher? I know that at standstill they have equal amplitudes and also equal frequency (similar to the stator). When the rotor starts to rotate, which rotor current component is dominant? I have read in Fitzgerald's book that the backward component increases and the forward component decreases; but this is in contrast to the oscilloscope of rotor current tabulated in the Generalized theory electric machines book by p.S. Bimbhara.

The manner in which torque components are calculated is clear and the theory is well explained in any electric machinery book devoted to single phase induction motors. I just wanted a comparison of the rotor current components (forward and backward) when the rotor is rotating. I am interested in the steady state values rather than the transient state.

Best regards

Naser

In fact both stator currents are equal, an eaquivalent network with two impedances canb be put in series.

At no-load the direct current makes magnetising current.

The inverse current slips at almost 100Hz. The resverse current sees a higher rotor resistance as the eddy currents for almost 100Hz is much bigger (due to skin-effect) than for a few Hz which is almost DC.

Dear Dr. Alex Van den Bossche

Thanks a lot for your response.

I should notify that we have neglected the skin effect in the standard model of the single phase induction motor. The rotor circuit has two stages namely, the forward and the backward ones. My question is that which of the rotor currents is higher? That flowing in the forward circuit or that flowing in the backward circuit?

At no load the forward rotor current is very low, The forward stator current is mainly magnetising. The reverse component in the rotor is hence related to the magnetising of the stator forward current, as they components are equal at stator level.

The reverse component brakes the motor and will hence result in some slip at no-load.

At standstill, both forward and reverse current are also equal in the rotor, no torque.

Dear Professor Alex Van den Bossche ,

Thanks for your kind response.

But would you please justify using the equivalent circuit of single phase induction motor referred to the stator?