# single phase current vs three phase current - transformer



## 170B (Nov 20, 2014)

consider a 100kVA transformer -

Connected phase to phase on 12kv (2 phases of the 3 phase distribution system) it draws 8.3 Amps (each phase) 100*1000/12000=8.3A

Connected to one phase and neutral at 6.9 kV a 100kVA draws 14.4 amps (1.73 time more) 100*1000/6930=14.4A

In simple terms, why is the 1.73 in there? I know somethings not right there. What's missing?


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## Kovz (Nov 20, 2014)

The 12kV voltage is the *V*line-line. The 6.9kV voltage is the *V*line-neutral. In wye connected systems, *V*line-neutral=*V*line-line/sqrt3 (also known as 1.73).

What are you confused about? The answer to the second equation that takes into account 1.73 is because it is connected line-neutral so the 12kv is divided by 1.73 = 6.9kv.

When comparing the two equations, remember, in the second equation less voltage = more current. Where as in the first equation, you have more voltage = less current.


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## J-Dubbs (Nov 20, 2014)

First off, I'm not sure your calculations are right. Remember the formula to find the kVA rating of a 3-Phase transformer is:

kVA = (Line Current * Line kV * 1.73)

By this formula, a 100 kVA, 3-Phase Transformer will draw 4.82 A on its 12 kV side, not 8.3 A.

I'm also assuming you're talking about a Wye-connected transformer since you bring up Line-to-Line and Line-to-Neutral Voltages. Correct me if I'm wrong in this assumption.

Now that we have that cleared up, the answer to your question... when its connected single-phase, where does the 1.73 come from? The answer comes from the same kVA rating formula for a single-phase transformer, which is:

kVA = (Current * kV )

Notice what's NOT there? That's right, the 1.73 factor. This is because when they are connected single-phase, voltage ratios are taken winding-to-winding instead of line-to-line. Even if you have a three phase connection on one side and three individual single-phase transformers on the secondary, the ratio is taken winding-to-winding.

So for each single-phase secondary connection of 6.9 kV on a 100 kVA transformer, your current is now 14.4 A. Notice that this is actually 3 times as much as the same three secondary windings connected in a 3-Phase wye configuration. This is why generally it is more efficient to use a 3 phase connection instead of single phase if possible.

Hope that helps.


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## 170B (Nov 20, 2014)

I guess it's actually 2 single phase 100kVA transformers, on a 12kV 3 phase system.

Case 1 - 12kV high side connected phase to phase.

Case 2 - 6.9kV high side connected phase to neutral

At full load, what are the primary amps seen by the supply system in each case? If they are different, why?

Thanks


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## BamaBino (Nov 21, 2014)

Can we get a diagram of the circuit in the program?


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## 170B (Nov 21, 2014)

Find I1, I2

These two configurations have to pull the same power from the 3 phase line(s) but the 1 phase vs 2 phase is not clear and there is probably a 1.73 that's not being accounted for.


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