# Three Phase Y-Connection Line Voltage ?

Discussion in 'Homework Help' started by Xufyan, May 17, 2011.

1. ### Xufyan Thread Starter Member

Aug 3, 2010
114
0
Hello,

for 3-Phase Y-Connection the Line Voltage is,

VL=$\sqrt{3}$xVp

This can be proved using this equation,

Vab = Van + Vnb , looking at this circuit, how this equation is derived ?

2. ### jegues Well-Known Member

Sep 13, 2010
735
43
$V_{ab} = V_{a} - V_{b}$

$\text{Because, } V_{a} = V_{m} \angle 0^{o} \text{ and } V_{b} = V_{m} \angle -120^{o}, \text{ we have,}$

$V_{ab} = V_{m} - V_{m}(-1.5 - j0.866)$

$= V_{m}(1.5 - j0.866)$

$V_{ab} = \sqrt{3}V_{m} \angle 30^{o}$

Similarly,

$V_{bc} = \sqrt{3}V_{m} \angle -90^{o}$

$V_{ca} = \sqrt{3}V_{m} \angle -210^{o}$

Thus the line-to-line voltage is √(3) times the phase voltage and is displace 30° in phase.

If you are asking where the equation,

Vab = Va-Vb comes from,

see the figure attached.

• ###### l2l.JPG
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Last edited: May 17, 2011
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3. ### Xufyan Thread Starter Member

Aug 3, 2010
114
0
the attached figure solved my problem

thanks alot