# Three phase power derivations

Discussion in 'General Electronics Chat' started by vwdevotee, Sep 7, 2009.

1. ### vwdevotee Thread Starter New Member

Jul 19, 2009
8
0
Hi all. I've been looking at three phase stuff, and can't seem to find a good treatment of the derivations. Basically I want to see where the root 3 that shows up in it comes from. Also, I'd like to play with the math to see what higher order phase systems look like. Can anyone point me to a good derivation website?

Peace!

2. ### mik3 Senior Member

Feb 4, 2008
4,846
70
Represent the line and phase voltages of a star load on a phasor diagram. Then find one line voltage using the phase voltages and a bit of trigonometry.

3. ### kkazem Active Member

Jul 23, 2009
160
31
As Mik3 said, you need to use a phasor diagram and it's fairly obvious that for a balanced 3-phase system, that phase-1 has a 0 degree phasor at lets say 1VRMS for all 3 phases. To balance, take 360 degrees divided by 3phases and you get 120 degrees per phase or the following for our 1V example:
1) Phase-A: 1VRMS, 0 degrees
2) Phase-B: 1VRMS, 120 degrees
3) Phase-C: 1VRMS, 240 degrees
Instead of me explaining anymore, do a google search on the following search term: 3 phase power calculations. You will get several good sites with explanations of the root 3 factor, but it's basically there if you convert between wye and delta for voltagte or current. If you use wye and connect the loads across line to neutral, then the power is just V phase * I phase * 3. So, you don't always have a root 3 factor.

Regards,
Kamran Kazem
kkazem