Line to line fault analysis and equations. Doubt

[Misqua]

Can I ask this? It's eating away at my head. In my books and notes the line to line fault using symmetrical components, the fault is taken on phase b and c. The current and voltage at the fault is expressed as
[a]=0. = -[c].
[V]- [V][c] = [Z][f]; [Z][f] is the fsult impedance.
Symmetrical components of the fault come out to be [a2]=-[a1] and [a0]=0.
(From power system engg- nagrath, kothari)
I wanter to practice and so took the fault as a-b fault. Now, the transformation matrix for comversion from phase components to symmetrical components as it is- there won't be exact answers. I should have thought of that.
But as it is I can't derive the formula for line to line fault if I am taking something other than b-c.
Aren't the formulae supposed to be universal? Or have I commmitted some technical faux pas? Please help?
I will upload my equations and the henceforth mess if possible.

 

[WHiPCPL]

Hello

I'm a little confused by your writing.

If you have setup the system to have a fault between b-c, then your parameters are:
I[a] = 0
I = - I[c]
V - V[c] = IZ[f]

If you take a fault between a-b, then your system parameters change:
I[a] = - I
I[c] = 0
V[a] - V = I[a]Z[f]

The result should be the same regardless of which reference you take as long as your parameters are correct. I have done the proof myself, but only for a fault between b-c.

If you need more help then don't hesitate to ask



Short circuits, protection, arc flash assessment. That's what I know best

 

[wroggent]

I think the problem is in using the A phase sequence components. With the A phase sequence components, you have Ia = I0 + I1 + I2. If I1 = -I2 and I0 = 0 then Ia must be 0.

I think to do the derivation correctly the sequence component definition you use must match the the phase that has 0 current. In other words in the A-B fault scenario Ic = 0 and so use the C phase sequence components, i.e. A = [1 a^2 a; 1 a a^2; 1 1 1] and [Ia Ib Ic]^T=[A]*[I0 I1 I2]^T
I haven't worked this out myself so take this as a suggestion rather than an answer.