Electronic – RMS value calculation of 3 phase line voltages for power calculations

accircuit analysispowerthree phasevoltage

In my textbook in the power calculations section of the balanced three phase circuits, a part confused me a little bit, it is this part:

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Why are we dividing by \$\sqrt{3}\$ to find RMS values of \$V_{\phi}\$ and \$I_{\phi}\$? As far as I know, we are dealing with sinusoidal sources and in sinusoidal sources, RMS transformation was done by diving to \$\sqrt{2}\$. In the same textbook in the previous chapter, power calculation for sinusoidal sources were shown like this;

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I didn't understand where this \$\sqrt{3}\$ come from in the 3-phase power calculation.

Best Answer

You're not doing an RMS transformation. You're converting L-N (RMS) to L-L (RMS).

You can use either but you have to remember that the phase to phase voltage is \$ \sqrt{3} \$ times the phase to neutral voltage.

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Figure 1. The phasor 3-phase and neutral diagram.

The \$ \sqrt{3} \$ term just comes from the trigonometric relationship between the voltages in Figure 1. (Remember that the \$sin(60) = \frac {\sqrt 3} 2 \$.)