170708-1442 EDT
Sahib:
In post #85 I explained it.
Just eliminate your VFD's DC to AC conversion and put your resistive load on the DC filter bank, and assume the ripple is small. Further assume that between the AC line and the filter capacitors we only have diodes. Also assume single phase input for simplicity. This makes the whole circuit simple.
Power in the resistor is Vdc*Idc. Idc must equal Iac ave (full wave recdtified) at the input side of the diodes. Assume the AC source voltage is a sine wave, then Vac rms = 0.707 * Vdc, or Vdc = 1.414*Vac rms.
Note: at the resistor that Vdc = Vrms measured across the resistor, and that Idc = Irms thru the resistor. Both Vdc and Idc are constant values because the capacitor ripple is low. If you place both a DC meter and an AC electrodynamometer meter across a DC voltage source both read the same value.
If the AC current into the diode rectifier was a sine wave (which it is not), then Iac rms would have to equal
Vdc*Idc = 1.414*Vac rms*Idc
Idc = Iac ave
Iac rms = (0.707/0.636)*Iac ave = 1.112*Idc
Vdc*Idc = 1.414*Vac rms*Iac rms/1.112
Vdc*Idc = 1.272*Vac rms*Iac rms (power in has to equal power out in a lossless system which we will assume is true for the diodes and capacitor)
But the AC current is nothing like a sine wave, it is more peaked and thus its RMS value is greater.
Average charge flow on both sides of the rectifier has to be the same, but RMS currents don't have to be the same. Where does the RMS current go --- somewhere in the mathematical world.
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