A 3-phase, 4 pole, 55 hp squirrel cage induction motor has the following result from the no load test: supply frequency = 50 Hz, line voltage = 2 kV, line current = 4.5 A and input power = 1600 W. Assuming an average DC resistance per stator phase being 2.8 Ω, determine the no load rotational loss.

Explanation:

Calculation of No Load Rotational Loss:

To determine the no load rotational loss of the given motor, we need to analyze the results provided in the no-load test and calculate the power losses. The no-load rotational loss primarily consists of friction, windage, and core losses.

Given Data:

• Supply frequency (f) = 50 Hz
• Line voltage (V_L) = 2 kV = 2000 V
• Line current (I_L) = 4.5 A
• Input power (P_in) = 1600 W
• Stator phase DC resistance (R_s) = 2.8 Ω

Step-by-Step Calculation:

1. Convert Line Voltage to Phase Voltage:

The motor is a three-phase system, and the relationship between line voltage and phase voltage for a star connection is:

V_ph = V_L / √3

Substituting the values:

V_ph = 2000 / √3 = 1154.7 V

2. Calculate Phase Current:

For a three-phase system, the line current is equal to the phase current in a star connection:

I_ph = I_L = 4.5 A

3. Determine Stator Copper Loss:

The stator copper loss is the power loss due to the resistance of the stator winding. It is calculated using:

P_Cu = 3 × I_ph² × R_s

Substituting the values:

P_Cu = 3 × (4.5)² × 2.8

P_Cu = 3 × 20.25 × 2.8 = 170.1 W

4. Calculate No Load Rotational Loss:

The no-load input power is the total power supplied to the motor under no-load conditions. This power is used to overcome the rotational losses and stator copper losses. The rotational loss can be determined by subtracting the stator copper loss from the input power:

P_rotational = P_in - P_Cu

Substituting the values:

P_rotational = 1600 - 170.1 = 1429.9 W

Conclusion:

The no load rotational loss is 1429.9 W, which corresponds to Option 1.

Important Information

To further analyze the other options, let's evaluate their values:

Option 2: 1562.2 W - This value is incorrect because it does not account for the proper calculation of stator copper loss. It seems to be an overestimation.

Option 3: 1829.9 W - This option is incorrect as it assumes higher losses than actually calculated, indicating a significant deviation from the correct procedure.

Option 4: 1494.16 W - While closer to the correct answer, this option is still incorrect due to a slight overestimation of losses, possibly from rounding errors or incorrect assumptions.

Conclusion:

By accurately calculating the stator copper loss and subtracting it from the input power, the correct value of no load rotational loss is determined to be 1429.9 W, as explained above. This corresponds to Option 1, reaffirming its correctness based on the given data and proper analysis.