Handbook's Fault Diagrams -> Equations

[jd5191]

Is there an intuitive way to derive equations from the Handbook's Fault Diagrams (Pg 66) without memorizing them. Particularly for the Line-to-Line Fault and Double Line-to-Ground Fault?

e.g for L-L faults, that Ia2 = (Ea)/(jX1+jX2)

 

[akyip]

The best way for me to remember the sequence network diagrams are:

Single line to ground: all 3 sequence networks in series

Ia1 = Ia2 = Ia0 = Vg / (Z1 + Z2 + Zp)

Ia = Ia1 + Ia2 + Ia0 = 3Ia1

Line to line fault: positive and negative sequence networks in series. Zero sequence is not included (because ground or neutral is not involved).

Ia1 = Vg / (Z1 + Z2)

Ia1 and Ia2 are in opposite directions, so:

Ia1 = -Ia2, Ia2 = -Ia1, Ia0 = 0

Ia = Ia1 + Ia2 + Ia0 = Ia1 + -Ia1 + 0 = 0

Double line to ground fault: all sequence networks are in parallel.

Ia1 = Vg / (Z1 + (Z2 || Z0)

 

[akyip]

Here's a line-to-line conceptual diagram (Phase B to Phase C example) I drew up to try to help you.

I learned this from Zach Stone's Electrical PE Review.

If the line-to-line fault is Phase A to Phase B, use Ic1 and Ic2 in the sequence network circuit diagram.

If the line-to-line fault is Phase C to Phase A, use Ib1 and Ib2 in the sequence network circuit diagram.

I'll try to draw one up for double-line-to-ground fault later after my dinner.

 

[Zach Stone P.E.]

Is there an intuitive way to derive equations from the Handbook's Fault Diagrams (Pg 66) without memorizing them. Particularly for the Line-to-Line Fault and Double Line-to-Ground Fault?

e.g for L-L faults, that Ia2 = (Ea)/(jX1+jX2)

Just about everything can be derived from KCL, KVL, and Ohm's law. Is there anything in particular you are having trouble deriving? 

Here's a line-to-line conceptual diagram (Phase B to Phase C example) I drew up to try to help you.

I learned this from Zach Stone's Electrical PE Review.

If the line-to-line fault is Phase A to Phase B, use Ic1 and Ic2 in the sequence network circuit diagram.

If the line-to-line fault is Phase C to Phase A, use Ib1 and Ib2 in the sequence network circuit diagram.

I'll try to draw one up for double-line-to-ground fault later after my dinner.

View attachment 19741

Nicely done @akyip!

 

[jd5191]

Thanks @akyip and @Zach Stone, P.E. for the advice. I spent some time watching videos of double-line to ground fault and line-line faults to get me more comfortable with the formula derivations. I'll just continue practicing this topic more before the exam and hopefully that'll help.