Three Phase Voltage Calculations

Thread Starter


Joined Jul 30, 2005

In a 4-wire, three phase unbalanced voltage system, where the following voltages are known :

RN, YN and BN,

where R, Y and B are the three phases and N is the neutral point.

How can we calculate the RMS voltage between RY, YB and BR ?

Please note that the voltages are not balanced or else the following formula could be used :

RY = R*1.732 and so on...

I have searched so many sites but could not find it, so a little help here, would be highly appreciated.

Thanks all,


Joined May 16, 2005
We use trigonometry and the Pythagorean theorem.

√3 is used for balanced loads because 3 =0.75 + 2.25 = ( √3 / 2)^2 + (1+.5)^2

The sine of 60 degrees is half of √3 (about .866) and the cosine of 60 degrees is exactly .5

RY = sqrt( (YN*.866)^2 + (RN+YN*.5)^2 ) = sqrt( (RN*.866)^2 + (YN+RN*.5)^2 )