Electronic – AC-AC Converter 3 phase, Line to line voltage calculation

acpower electronicsrms

I’m working one some assignment like this circuit (AC-AC converter 3 phase, 89 degree firing period). I've done this on PSIM software with 110 Volts 3 phase voltage source.

AC-AC Converter 3 phase, 89 degree firing periode

I've been told to analyze the line to line voltage. The waveform and the value looks like this
enter image description here

My question is, can somebody tell me what is the equation to solve the line to line voltage value?
I've been googling around and found nothing related to this particular circuit.

Best Answer

Start by minimizing the problem to firstly this: -

enter image description here

Then, because the negative half cycle is a mirror image of the positive half cycle, it will have the same RMS value, thus we end up with only needing to analyse this section to get RMS: -

enter image description here

Then it breaks down into 4 sections that you need to find the square of the RMS for each: -

enter image description here

So, find those individual squares then multiply each by their time duration and the final RMS value of your waveform is this: -

$$\sqrt{\dfrac{d_1V_1^2 + d_2V_2^2 + d_3V_3^2 + d_4V_4^2}{d_1+d_2+d_3+d_4}}$$

Related Topic