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Power Electronics: power converter Answered

I have been running through example questions for an exam I have coming up; the following picture is a condensed version of half a page of working.

My lecturer gave us the solutions and a few steps between beginning and end to get to the solution so we could work it out. However, as you can see the picture below I got 30.6A whereas she wrote 54.2 down.

The problem is to "Find the maximum values of the average" (done this bit) "and rms thyristor currents for any firing angle, alpha.". The values of R and Vs are in the diagram. Alpha is assumed to be 0 since then the thyristors will conduct for the greatest possible length of time.

I think she may have got to the end then forgotten to square root of Pi before multiplying Vm/2PiR by it. Does anyone agree?

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Well that's what the question says, in which case my answer underneath the downwards arrow would suffice wouldn't it? But she also gave a numerical answer for average and rms current through the thyristor; since it's on for longest when the firing angle alpha is 0 then that would give the max possible average and rms current right? I was trying to work through for when alpha=0, at which point her answer and my answer disagree.

For anyone that finds this later, the correct answer IS 76.6A. When alpha is 0 the output is sinusoidal so you can use V=IR and Vm = Vrms*sqrt(2). This would match up with the answer from integrating had I (and my lecturer) got the integration right. I found the correct expression, plugged in R, Vm and alpha and got 76.6 as expected.