A three-phase full converter charges a battery from a three-phase supply of 230 V. The battery emf is 200 V. Find the value of the firing angle if the battery terminal voltage is 210 V.

To determine the firing angle (alpha) for a three-phase full converter given the battery emf, supply voltage, and desired terminal voltage, we can use the following formula for the average output voltage (V_dc) of the three-phase full converter:

[

V_{dc} = frac{3 sqrt{2}}{pi} V_s cos(alpha)

]

Where:

– (V_{dc}) is the average output voltage across the battery,

– (V_s) is the line-to-line rms supply voltage,

– (alpha) is the firing angle.

1. We need to first convert the line-to-line voltage (230 V) to the phase voltage ((V_s)):

– The line-to-neutral (phase) voltage (V_p = frac{V_s}{sqrt{3}} = frac{230}{sqrt{3}} approx 132.79 V).

2. Since the average output voltage must equal the desired terminal voltage of the battery (V_dc = 210 V), we can set up the equation as follows:

[

210 = frac{3 sqrt{2}}{pi} (230) cos(alpha)

]

3. Rearranging the equation gives us:

[

cos(alpha) = frac{210 pi}{3 sqrt{2} times 230}

]

4. Simplifying the right side:

[