The locked rotor current in a 3-phase, st ar connected 15

The locked rotor current in a 3-phase, st ar connected 15 kW, 4-pole, 230 V, 50 Hz induction motor at rated conditions is 50 A. Neglecting losses and magnetizing current, the approximate locked rotor line current drawn when the motor is connected to a 236 V, 57 Hz supply is

For the rotor at blocked position, slip, s = 1.
As magnetizing current is negligible, therefore

I_BR =	V_BR
	√(r₁ + r₂)² + (x₁ + x₂)²

=	V_BR
	√R² × x²

R = r₁ + r₂ , x = x₁ + x₂ and, P_BR = I_BR² .R

⇒	15 × 10³	= R
	3 × 50²

⇒ R = 2 Ω

then , 50 =	230 / √3
	√R² × x²

=	230 / √3
	√4 + x²

⇒ x = 1.74 Ω . at f = 50 Hz
At f = 57 Hz, x '

= 1.74 ×	57	= 1.98 Ω
	50

hence, at f = 57 Hz, V_BR = 236 V,

I' =	236 / √3
	√R² + x'²

I' =	236 / √3	≅ 46 Amp.
	√2² + 1.98²