# DC bus inversion to 3 phase AC modified sine wave using IGBTs

I'm working with a variable voltage inverter.

I have 3 phase AC voltage coming in at 480V RMS line to line. It hits a full wave SCR front end, has a DC bus link, and is inverted with IGBTs to created a six step output wave form.

The IGBTs are firing in 180 degree conduction mode and I'm measuring the output waveform with a true RMS meter.

Here's my confusion:

With a full wave SCR front end I'm aware that I should be able to approach Sqrt(2)*line to lone RMS incoming, and I'm seeing that on the DC bus.

But I can't seem to find the equation that dictates how to calculate the conversion from my DC bus voltage to line to line RMS voltage of my six step output wave.

I've found a million different equations about converting from DC to 3 phase AC but none of them seem to match what I'm seeing.

The output waveform line to line voltage in my tests is always right around .816*DC bus voltage. This conversion factor stays accurate from low voltage all the way up to max DC voltage at ~680V DC (480*1.414).

No where in my research have I found where this number comes from. The closest I've come is an equation on the wiki page for RMS voltage

If I divide peak (DC bus) voltage by the sqrt(3/2) I in fact get the conversion factor I was seeing in my tests. But I have no idea where this comes from. And if I'm not mistaken in what I'm seeing this means that with 480VAC RMS in I can get around ~554 VAC RMS out (480*1.414= ~678. 678*.816=~554).

Since we obviously can't just create energy out of no where would this higher voltage come with a reduced current compared with the incoming? Or can someone explain what's going on here and where this Sqrt(3/2) conversion factor comes from please.