3 phase power and cable calcs.

[richardindorset]

Just wanted to confirm my understanding here.


Ignoring power factor for the moment, I know that the formula used to get current from total power is total power/(root 3 x phase voltage)

This is the phase current, so we use this for each line cable and fuse, of which there'll be 3.

The root 3 part confused me a bit, as it seems to give a voltage of 692.8, but as the line voltage is 230v, the phase voltage is root 3 times, or 400v.

Another way to look at it is total power/line voltage. Gives total current. So phase current will be one third.

So a 9kw heater, 400v 3 phase will have a total current of 9000/230 = 39.19A spread across 3 phases so each line cable carries one third or 13.04A.

9000/(root 3 * 400) gives the line current too. 9000/692.8 = 12.99A

 

[fixitflav]

The root 3 part confused me a bit, as it seems to give a voltage of 692.8,

Not with you there. It's 692.8 after multiplying phase voltage (400) by root 3. Line current is still total power/(root 3 x phase voltage).
Also root 3 x phase voltage = (root 3)^2 x line voltage = 3 x line voltage = 690 (or 692.8 depending how you round it).

 

[plugwash]

The root 3 part confused me a bit,

If we think of the load as three resistors connected in a delta configuration, the division by sqrt(3) can be seen as an amalgamation of three factors.

* The load being split into 3 parts. (divide by 3)
* Two of those three parts being connected to each phase (multiply by 2).
* The currents in the two parts connected to each phase being out of phase and thus partially cancelling (multiply by cos 30° = sqrt(3) / 2 )

As you point out, if you think of the load as three resistors in a star connection, you get the same overall result (the slight differences in your numeric value being caused by the fact that 230*sqrt(3) is not exactly 400).