A 3-∅ SRIM with star connected rotor is having standstill impedance of (0.4 + j 4)Ω and 400V is the peak induced emf across the slip rings. At max torque, what is the rotor current per phase in Amperes? [write the answer upto two decimal points]Correct answer is '28.87'. Can you explain this answer?

Question

Answer

Given:

3-∅ SRIM

Star connected rotor

Standstill impedance = (0.4 + j4)Ω

Peak induced emf = 400V

To find:

Rotor current per phase at max torque in Amperes

Solution:

Step 1: Calculation of maximum torque

Maximum torque occurs at the point where the slip is equal to the standstill slip, i.e., s = 1. From the equivalent circuit of an induction motor, we have:

Max torque = [(3V_φ²) / (2ω_s)] * [(R₂/²) / (R₂/² + (X₂ + X_m)²)]

where,

V_φ = phase voltage

ω_s = synchronous speed

R₂ = rotor resistance per phase

X₂ = rotor reactance per phase

X_m = magnetizing reactance per phase

Calculation:

ω_s = (120f) / p = (120 * 50) / 2 = 3000π rad/s

R₂ = standstill impedance = 0.4Ω

X₂ + X_m = standstill impedance = 4Ω

X₂ = (4 - 0.4)Ω = 3.6Ω

V_φ = (1 / √3) * 400V = 230.94V

Max torque = [(3 * 230.94²) / (2 * 3000π)] * [(0.4/²) / (0.4/² + (3.6 + 4)²)] = 67.6 Nm

Step 2: Calculation of rotor current per phase

At maximum torque, the rotor current per phase is given by:

I₂ = (s * V_φ) / X₂

where,

s = slip at max torque

Calculation:

At maximum torque, s = 1

I₂ = (1 * 230.94V) / 3.

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