Asymmetrical Component of Fault Current 3

[charz]

On reading the literature of asymmetrical fault current, I'm unable to grasp the concept completely. I have the following questions,
1) Why does the DC component occur?
2) Why is the maximum asymmetry when the fault occurs at the 0 time crossing on the voltage wave form?
3) Does the maximum asymmetry occurs at voltage zero irrespective of the load is resistive, inductive or capacitive?
4) Why does the Idc component have negative sign?

 

[davidbeach]

Without the DC component there would have to be an instantaneous change in current through the reactance of the system.

 

[dpc]

1. See David's response. If you remember your differential equations class, the dc offset is the transient part of the solution. The symmetrical current is the steady state.
2. See David's response. Current must lag the voltage per the system X/R ratio. Nearly 90 degrees. Look at the other extreme. If fault occurs at peak voltage and current zero, the current is already lagging by 90 deg and there will be essentially no dc offset current.
3. If load is 100% R, there is no dc offset.
4. This is not always true.

 

[davidbeach]

What's load got to do with it? ;-)

The dc offset is produced by the reactive component of the source impedance. That's why generators, with extremely high X/R, can become essentially 100% offset and go multiple cycles without a zero crossing. Load on the other side of a bolted 3LG fault ceases to exist.

 

[dpc]

Poor choice of words on my part. I should have said "system impedance".

 

[charz]

Thanks DPC and davidbeach,
The fault has a very low PF. When the Voltage is at its peak, in order to maintain the lagging effect, the current would not shoot up, while the voltage is at zero, the current has to shoot up to maintain the lagging. The DC component occur as result of maintaining the lagging effect. Is my understanding right?

On the other hand I read that at voltage zero, the Inrush of the capacitor is minimum. Yes without voltage there couldn't be any current but how do I understand this with the leading effect of capacitors?

 

[cuky2000]

Question 1: Why does the DC component occur? Response 1: DC component occur because it’s required to maintain the principle of energy conservation at the instant after and the pre-fault. A dc off-set current appear with opposite polarity to compensate for the jump of AC current at the fault inception. Therefore, the flux linking the circuit stored energy remains constant during this transient period.
Additional discussion on this topic could be found at

https://relaytraining.com/what-is-dc-offset-ask-chris/

Question 2: Why is the maximum asymmetry when the fault occurs at the 0 time crossing on the voltage wave form?. Response 2: “At time zero (t=0), the dc component of fault current is exactly equal in magnitude to the value of the ac fault current component but opposite in sign. (See graph below for t-0) This condition must exist due to the fact that the initial current in the circuit is zero and the fact that current cannot change instantaneously”. For reference, see IEEE Std 551.

Question 3: Does the maximum asymmetry occurs at voltage zero irrespective of the load is resistive, inductive or capacitive? Response 3: No, the maximum asymmetry current at V=0 only occur for inductive circuit. See figures below: For X/R=2, I_max occur at V≠ 0; For Inductive load, X/R =∞ , I_max occur at V=0

Question 4: Why does the I_dc component have negative sign? Response 4: No necessary the I_dc component is negative. For a three phase fault, see the graph below with I_dc components negative and positive as well.

 

[prc]

Thank you Cuky for the lucid explanation.