A 3-phase full converter feeds power to an R load of 10 Ω. For a firing angle delay of 30° the load takes 5 kW. An inductor of large value is also connected to the load to make the current ripple free. Find the value of per phase input voltage.

To find the per-phase input voltage (V_s) for a 3-phase full converter feeding power to a resistive load with a firing angle delay of ( alpha = 30^circ ), we can use the following formulas.

1. The output power (P) in a resistive load can be calculated using the formula:

[

P = frac{3}{pi} V_m I_{o} cos(alpha)

]

where:

– ( V_m ) is the peak phase voltage,

– ( I_o ) is the average output current,

– ( alpha ) is the firing angle.

2. The average output current (I_o) can be calculated from the power and the load resistance (R):

[

I_o = frac{P}{V_{o}} = frac{P}{R I_{o}}

]

where ( V_{o} = I_o cdot R ).

3. We already know the values:

– ( P = 5000 , W )

– ( R = 10 , Omega )

– ( alpha = 30^circ )

– ( cos(30^circ) = frac{sqrt{3}}{2} )

4. First, we can find the average output current (I_o):

[

I_o = frac{