AC Motors & Transformers Question

[itln_boysparks]

Hey guys, First time user here. 2nd year electrical apprentice down under! Need help and guidance with a question i've been tasked with here. Don't neccersarily need the answer to the question but any guidance into it would be helpful.
Question is 'You have a three phase induction motor (415V) rated at 240nm. It is connected to An auto tranformer starter that starts at 70% supply voltage. What is the torque developed at start up? Show any working out?

 

[marconi]

Does this help you? I will let you study my scribbles and if they do not make sense come back to me. The key things to know are (1) at locked rotor when the torque is 240Nm at 100% Vs the induction motor is acting as a transformer with an N to 1 turns ratio between stator and rotor and (2) the force F between the stator and rotor is proportional to the product of the stator and rotor currents Is x Ir and (3) the torque T is proportional to the force F and (4) the stator current is Vs/Z where Z is impedance the supply sees looking into the motor .

PS: I ignore magnetization current and transformer core losses.

Forces Between Parallel Conductors – Learn – ScienceFlip - https://www.scienceflip.com.au/subjects/physics/electromagnetism/learn4/#:~:text=When%20two%20wires%20carrying%20a,carry%20currents%20of%20different%20magnitudes.

Equivalent Circuit for an Induction Motor | Electrical4U - https://www.electrical4u.com/equivalent-circuit-for-an-induction-motor/

 

[marconi]

I should have written Es x Is = Er x Ir, and then Es/Er = Ir/Is = N. The equivalent circuit assumes the transformer is perfect with its resistance and reactance and losses as lumped components connected to it externally. This correction does not alter what follows in my analysis.