The breadth factor for 3rd harmonic emf of a 3-phase, 4-pole, synchronous machine having 36 stator slots is

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ESE Electrical 2016 Paper 2: Official Paper
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  1. 0.47
  2. 0.53
  3. 0.67
  4. 0.73

Answer (Detailed Solution Below)

Option 3 : 0.67
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The breadth factor or a distribution factor is given by

\({k_d} = \frac{{\sin n \cdot \frac{{m\beta }}{2}}}{{m \cdot \sin \frac{{n\beta }}{2}}}\)          (for nth harmonics)

m = no. of slots per pole per phase

β = slots angle

Calculation:

3 – phase, 4 – pole synchronous machine.

No. of slots = 36 (stator slots)

\(m = \frac{{36}}{{3\; \times \;4}} = 3\)

\(\beta = \frac{{180^\circ }}{{slots\;per\;pole}}\)

\(\beta = \frac{{180^\circ }}{{36/4}} = 20^\circ \)

So, \({k_d} = \frac{{\sin \frac{{\left( 3 \right)\left( 3 \right)\; \times \;20^\circ }}{2}}}{{3\sin \frac{{3\; \times \;20}}{2}}}\)

\(\Rightarrow {k_d} = \frac{{\sin 90^\circ }}{{3\sin 30^\circ }} = \frac{2}{3}\)

⇒ kd = 0.67

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