square root of 3

[trainee]

This concept has never been clearly explained to me ...fortunately, I've memorized the formulas during the exams but I want to be able to make heads and tails of it now....of course we're talking about 3 phase systems.

First of all, how come root 3? What's the reasoning behind using sqrt(3)? Can someone clearly explain when root 3 is used, when it isn't?

Thanks

 

[mascott]

Actually, it's Sqrt(3) divided by 2 that shows up everywhere, but the 2 often gets hidden. Basic equilateral triangle geometry. Phasors are separated by 120 degrees. Points comprise an equilateral triangle.

Sin (60) = Sin (120) = 0.866 = Sqrt (3) / 2

2 * Sin (60) = 1.732

(2 * Sin (60))^2 = 3

In all the conversions for 3 phase power, the equilateral triangle always shows up.

Hope this helps!

 

[RIP - VTEnviro]

Looks like less than 120 degrees to me. :dunno:

 

[Wolverine]

That's only a two phasor system.

 

[Art]

envision a Y phasor diagram...

VLL = Y tip to Y tip

VLN = tip to center

draw the line from tip to tip and bisect it....

2 triangles: 90 (from perpendicular intersection), 120/2 (1/2 of the angle between phases), and 180 - 120/2 - 90 = 30

looking at 1 triangle resulting from the bisection we observe that VLL/2 = VLN cos(30)

VLL = (2 x cos(30)) VLN

cos 30 = sqrt(3/4) from unit circle...

therefore: (2 x cos(30)) = 2 x sqrt(3/4) = 2 x sqrt(3) / 2

2's cancel

so (2 x cos(30)) = sqrt(3)

therefore: VLL = sqrt(3) VLN