1. A 3 phase 6 pole star connected alternator revolves at 1000 rpm. The stator has 90 slots and 8 conductors per slot. The flux per pole 0.05wb. Calculate the voltage generated by the machine if the winding factor 0.96.?

Question

Answer

Problem Statement

A 3 phase 6 pole star connected alternator revolves at 1000 rpm. The stator has 90 slots and 8 conductors per slot. The flux per pole 0.05wb. Calculate the voltage generated by the machine if the winding factor 0.96.

Solution

Given parameters:

Number of phases (𝑝) = 3

Number of poles (𝑝𝑜𝑙𝑒𝑠) = 6

Speed of the alternator (𝑁) = 1000 rpm

Number of slots (𝑛) = 90

Number of conductors per slot (𝑞) = 8

Flux per pole (𝜙) = 0.05 Wb

Winding factor (𝑘𝑤) = 0.96

Step 1: Calculate the synchronous speed of the alternator

The synchronous speed of the alternator (𝑁𝑠) can be calculated using the following formula:

𝑁𝑠 = (120 × 𝑓) / 𝑝

where 𝑓 is the frequency of the current and is assumed to be 50 Hz.

Substituting the values in the above formula, we get:

𝑁𝑠 = (120 × 50) / 6 = 1000 rpm

Step 2: Calculate the number of conductors in the stator winding

The number of conductors in the stator winding (𝑁𝑐) can be calculated using the following formula:

𝑁𝑐 = 𝑛 × 𝑞

Substituting the values in the above formula, we get:

𝑁𝑐 = 90 × 8 = 720

Step 3: Calculate the emf generated in one phase

The emf generated in one phase (𝐸𝑃) can be calculated using the following formula:

𝐸𝑃 = (4.44 × 𝑓 × 𝑁𝑠 × 𝜙 × 𝑘𝑤) / 𝑁𝑐

Substituting the values in the above formula, we get:

𝐸𝑃 = (4.44 × 50 × 1000 × 0.05 × 0.96) / 720 = 29.9 V

Step 4: Calculate the line voltage

The line voltage (𝑉𝐿) can be calculated using the following formula:

𝑉𝐿 = √3 × 𝐸𝑃

Substituting the value of

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