Question

A four-pole, 460 V, 25 hp, 60 Hz induction motor connected in (Y), has the following impedances in ohm per phase referred to the stator circuit:

R1=0.641ohms, R2=0.332ohms, X1=1.106ohms, X2=0.464ohms, Xm=26.3ohms
Total rotational losses are 1 100 W and are assumed to be constant. Losses in the core are grouped with losses per rotation. For rotor slippage of 2.2% at rated voltage and frequency, find the following motor quantities:
a) Speed,
b) Stator current,
c) Power factor,
d) Pd and Pout.
(e) Td and T(Load),
(f) Efficiency

Answer 1

The speed of the motor is 1761.6 RPM. The stator current is 312.3 A. The power factor is 0.566 or 56.6%

Step-by-step explanation:

The speed of the motor can be calculated using the formula:

Speed = (1 - Slip) × Synchronous speed

Given that the rotor slip is 2.2%, the synchronous speed is 120 × (60/4) = 1800 RPM, so the actual speed of the motor is:

Speed = (1 - 0.022) × 1800 RPM = 1761.6 RPM

The stator current can be calculated using the formula:

Stator current = Stator voltage / (Stator resistance + Stator impedance)

Given that the stator voltage is 460 V and the stator resistance and impedance are given as R1 = 0.641 ohms, R2 = 0.332 ohms, X1 = 1.106 ohms, X2 = 0.464 ohms, and Xm = 26.3 ohms, we can calculate the stator current:

Stator current = 460 V / (0.641 ohms + 1.106 ohms) = 312.3 A

The power factor (PF) can be calculated using the formula:

PF = Pout / Pd

Given that the total rotational losses are 1100 W, the power dissipated in the core per rotation must be Loss per rotation = Total rotational losses / Rotational speed = 1100 W / 1761.6 RPM = 0.623 W/RPM. The power dissipated in the rotor is given by:

Pd = (Stator current)^2 × R2 + (Rotor current)^2 × R2 + (Stator current × R2) × (Rotor current / Stator current)

Substituting the given values, we can calculate the power dissipated in the rotor:

Pd = (312.3 A)^2 × 0.332 ohms + (312.3 A × 0.332 ohms) × (0.022 / 312.3 A) = 35.3 W

The power output (Pout) can be calculated using the formula:

Pout = Pd + Loss per rotation

Substituting the given values, we can calculate the power output:

Pout = 35.3 W + 0.623 W/RPM × 1761.6 RPM = 1139.4 W

The load torque (TL) can be calculated using the formula:

TL = (Pout - Loss per rotation) / (2π × Speed)

Substituting the given values, we can calculate the load torque:

TL = (1139.4 W - 0.623 W/RPM × 1761.6 RPM) / (2π × 1761.6 RPM) = 0.140 Nm

The efficiency can be calculated using the formula:

Efficiency = Pout / (Pd + Loss per rotation)

Substituting the given values, we can calculate the efficiency:

Efficiency = 1139.4 W / (35.3 W + 0.623 W/RPM × 1761.6 RPM) = 0.566 or 56.6%