A 1,1kV, 60Hz, three-phase induction motor runs ar 1200r/min. Calculate the number of poles if the motor is operating

Question

operating at a slip of 33%.

Answer 1

To calculate the number of poles of the motor, we can use the following formulas:

1. Synchronous Speed (Ns) can be calculated using the formula: \[ Ns = \frac{120 \times f}{P} \] where:

   • \(Ns\) = synchronous speed in revolutions per minute (rpm)
   • \(f\) = frequency in hertz (Hz)
   • \(P\) = number of poles

2. Actual Speed (N) and Slip (S) relationship: \[ S = \frac{Ns - N}{Ns} \] Rearranging this, we get: \[ Ns = \frac{N}{1 - S} \]

Given:

• The motor runs at \(N = 1200 , \text{rpm}\)
• The slip \(S = 33% = 0.33\)

Now we can calculate the synchronous speed \(Ns\): \[ Ns = \frac{1200}{1 - 0.33} = \frac{1200}{0.67} \approx 1790.15 , \text{rpm} \]

Now that we have \(Ns\), we can substitute it into the first synchronous speed formula to find the number of poles \(P\): \[ 1790.15 = \frac{120 \times 60}{P} \]

Now, rearranging for \(P\): \[ P = \frac{120 \times 60}{1790.15} \approx \frac{7200}{1790.15} \approx 4.02 \]

Since the number of poles must be a whole number, we round to the nearest whole number, which gives \(P = 4\).

Thus, the number of poles in the motor is 4 poles.