Symmetrical Components Example Problem

[trchambe]

Hello,

I'm trying to teach myself a little about symmetrical components, and am in the middle of a problem. To any who has a copy of the Westinghouse Transmission and Distribution Reference Book (or would like a pdf

http://www.scribd.com/doc/7010747/E...stribution-Reference-Book-of-We-Sting-House),

please refer to the example problem at the end of Chapter 2: Symmetrical Components (From previous posts it seems many out there have this book).

"It should be remembered that unit I_0 is one ampere in each of the three line conductors with three amperes returning to ground; unit Ig is 3/2 amperes in each of the two ground wires with three amperes returning in the ground; unit I'0 is one ampere in each of the three line conductors with three amperes returning in the ground; and unit I'g is three amperes in the ground wire with three amperes returning to ground"

Where did those numbers come from?

Also, in order to determine the zero-sequence self reactance in the presence of all zero-sequence circuits, E0/I0 = 2.05 ohms/mile, E'0/I'0 = 2.25 ohms/mile, and E'0/I0 = 0.87 ohms per mile from the 110kV self, 66kV self, and mutual impedances, respectively. I don't understand how these numbers were found.

If anyone has worked through this problem before or has any immediate thoughts as to the solution, I'd appreciate the help.

 

[magoo2]

The first part is pretty straightforward. When you have a single line to ground fault, the fault current is Ia. This results in a series connection of the sequence networks. Because of this, I1 = I2 = I0.

Solving for Ia, you get Ia = I1 + I2 + I0 or Ia = 3 * I0, a result that is common to most relay engineers. This gives you the 3:1 ratio that the Westinghouse authors (Hobson and Whitehead) mentions.

Because you have 2 ground wires, each ground wire carries half of the fault current (Ia/2) or 3/2 * I0.