# 3 Phase calculations

I have 3-phase utility mains power supply whose phase voltage is 220 V, 50 Hz.

I keep getting confused about various calculations of the 3-phase mains as follows:

1. Formula for the line voltage.
2. Formula for the Average and RMS outputs of 3-phase full bridge rectifier.
3. If I use this output of the bridge rectifier as my DC Link voltage to feed a 3-phase full H-bridge and drive it with 3-phase sinusoidal PWM then what will be Average and RMS voltages of the resulting 3-phase sinusoids?
• Regarding Q3. The average of a sine is zero. – Transistor Dec 27 '18 at 23:19

1. Formula for the line voltage.

$$V_{ph-ph} = \sqrt 3 V_{ph-n}$$

1. Formula for the Average and RMS outputs of 3-phase full bridge rectifier.

$$V_a = \frac {3 \sqrt 3}{\pi}V_m = 1.654 V_m$$

where $$\ V_m \$$ is the peak phase to neutral voltage.

$$V_{rms} = 1.655 V_m$$

which is very close to the average value.

The tutorial paper by Dublin Institute of Technology - Three-phase rectifier looks like it should be of considerable help to you.

1. If I use this output of the bridge rectifier as my DC Link voltage to feed a 3-phase full H-bridge and drive it with 3-phase sinusoidal PWM then what will be Average and RMS voltages of the resulting 3-phase sinusoids?

Average of a sine is zero.

Ignoring losses the maximum phase to phase output voltage is the DC-link voltage. That will be your peak AC so the RMS value of your output voltage will be $$\ \frac {1}{\sqrt 2}V_{DC} \$$. (The RMS value of a sine is $$\ \frac {1}{\sqrt 2}V_{pk} \$$.)

• I tried to work out the above formulas to get DC link voltage which is 600 V for a 3-phase mains whose phase voltage is 200 V.. but i only get approx. 515 V. Why is this difference in the calculations? – scico111 Dec 28 '18 at 9:30
• Add your calculations into your question as an update and we'll have a look. – Transistor Dec 28 '18 at 15:18