Electrical – how to calculate rms voltage value of PWM motor

Summary:

• RMS powers can be added.
  So - RMS Volts^2 can be added.

• Offset = Vdc = sqrt( Vrms_total_signal^2 - Vrms_ac_only^2)

  = sqrt (5.452^2 - 5.175^2) = 1.716 volt

(Voltages above are mean RMS voltages from supplied table. )

Calculating AC only RMS from Vpk-pk would give

• Vrms_AC = (Vpk-pk)/2 x 1/sqrt(2) = Vpk-pk/2.sqrt(2)

  = 14.68/2/1.4142 = 5.190 V RMS.

The RMS voltage displayed is 5.175V mean suggesting that
the signal is not quite a pure sinewave
and/or that the measurement system is not 100.000% accurate (of course).

5.19 / 5.175 = 1.0029 or about 0.3% higher.

"RMS powers" add directly.
ie Power total = Power_ACV + Power_DC
Power is proportional to V^2 so
(Vrms_AC+DC)^2 = (Vrms_AC)^2 + (Vrms_DC)^2

as Vrms_DC = Vdc

Vrms_combined^2 = Vrms_AC^2 + Vdc^2

or Vdc^2 = Vrms_combined^2 - Vrnms_ac^2

So Voffset = Vdc = (Vrms_combined^2 - Vrma_ac^2)^ 0.5

Here
Vrms_ac = 5.175V average (from table)
Vrms_combined = 5.452 mean
So
Voffset = sqrt( 5.453^2 - 5.175^2) = 1.716 Volt.

Any help would be appreciated

You can measure phase-neutral voltage and if the supply and load are balanced then you can infer line voltage by: -

line volts = phase volts\$\times\sqrt3\$

This should be one of the easier measurements yet you say you can calculate "real power, reactive power and apparent with ease". This does make me think that you have used one of these measurements, and the RMS measurement of current and back-calculated phase/line voltage and that's when you are seeing a discrepency.

If this is so then I suspect your current measurement may be at fault either through incorrect use of a current transformer or some ratio being incorrect. Or, it could be the \$\sqrt3\$ thing mentioned above.

If you need any further help with this you should consider detailing how you make the other measurements and why you believe voltage to be incorrectly calculated/measured.