fault current contribution for zero source impedance? 1

[royclh]

hi, i'd like to ask a question that perhaps sound a bit stupid. i don't know why, i seem to get clogged up easily with this simple and basic stuff.

Assume a lossless transmission system connecting one single generator (on the left) to a load center (on the right). Assume a series capacitor is placed closed to a generator side station. If the Xc is made exactly equal to the source reactance, what is the fault current contribution if a fault occurs after the capacitor? Some people said it's zero but some said it's maximum... I thought it should be maximum.

 

[jghrist]

Maximum. Z = R + jXL - jXC = R

 

[royclh]

if R = and the fault is the ground fault, would the potential seen by generator is zero as the effective/equivalent impedance in between the fault and the generator is zero, Z=0 (as compensated fully by the capacitor)?

 

[royclh]

if R=0

 

[jghrist]

If the reactance is fully compensated for phase faults, it will not be for ground faults because XL1 is not equal to XL0.

Also, if the generator's synchronous reactance is fully compensated, then the subtransient reactance will not be.

You have to define what you mean by "Xc is made exactly equal to the source reactance." Is it the source reactance seen during normal operation, during a 3Ø fault or during a Ø-grd fault?

 

[ijl]

Zero or maximum current? Neither, but something more interesting, if we believe simulations with ATP, see attached picture.

Generator data: Vpp = 1000V, Xd = Xq = 1 0hm, Xd' = Xq' = 0.2 Ohm, Xd" = Xq" = 0.1 Ohm, Rs = 0.01 Ohm. Capacitor Xc = -1. Fault occurs at 1.5 sec, prefault current = 0.

 

[alehman]

Looks like you selected your capacitor and motor reactance to resonate at 50Hz. Is that your system frequency?

Alan
----
"It’s always fun to do the impossible." - Walt Disney

 

[ijl]

alehman,
Yes, Xd + Xc = 0, that was the point of the original question. And at 50 Hz, but that is not essential, I think.

 

[royclh]

sorry, i was away.. thanks for all the comments.

Jghrist, to answer questions:
You have to define what you mean by "Xc is made exactly equal to the source reactance." Is it the source reactance seen during normal operation, during a 3Ø fault or during a Ø-grd fault?

Actually, I'm hoping to find out the effects of the three conditions (normal operation without fault, balanced fault and asymmetrical fault conditions).

Take a look at the circuit attached. If the fault occurs next to a series capacitor and if Xc is made exactly equal to the source reactance, what are the current contributions from AC and AC2 (I1 and I2) during a 3phase fault, phase to ground fault and phase to phase fault conditions?

Many thanks to ijl for the simulation results from ATP. Can anyone explain to me why it is zero at the pre-fault condition and why it resonates during the fault condition? What type of fault has been injected, is it 3 phase, two phase or phase to ground faults?

Hope for your comments, many thanks for all the efforts.

 

[jghrist]

The capacitor Xc is fixed, but the source impedance varies with time. At first, the generator reactance is Xd", then it increases to Xd', then eventually to Xd.

If you want to find the effect on Ø-grd and Ø-Ø faults, model Xc in your sequence networks and calculate the fault current.

The fault current is zero pre-fault because there is no load modeled and there is no fault current pre-fault.

It resonates because Xc = Xd.

The contribution from AC2 will not be affected by the series capacitor.

In practical terms, the generator will trip off line before the reactance reaches the synchronous Xd value, either on overcurrent or overfrequency.

 

[alehman]

ijl,
You seemed to question the ATP output. My point was just that with Xc=Xd, there is a resonance which probably explains the growing current produced by ATP.

Alan
----
"It’s always fun to do the impossible." - Walt Disney

 

[ijl]

..that with Xc=Xd, there is a resonance which probably explains the growing current produced by ATP

Well, no, it seems that the reason is the capacitor as such. See the attached picture. Things get more interesting, when Xc = Xd".

 

[jghrist]

See the attached picture. Things get more interesting, when Xc = Xd".

Let's get a little practical. You show the current reaching 100 x 10^6 A through a 0.1 ohm capacitor. This would result in a voltage across the capacitor of 10,000 kV. The voltage across the generator winding (with Xd" = 0.1 ohm) would also be 10,000 kV. Do you have any generators and capacitors in mind that will withstand this?

 

[ijl]

You are right. I forgot to add the warning "do not try this at home". But even the initial phases of the transient are interesting (before everything disappears in a big explosion), not exactly from a textbook.

 

[alehman]

Also, I think ATP may not be modelling the saturation characteristics of the generator.

Alan
----
"It’s always fun to do the impossible." - Walt Disney

 

[ijl]

ATP can model saturation, but that was not included in the calculations above.