How to limit DC offset to 20% with a time delay?

"Lets say you wanted to add a time delay to the relay in order to allow the DC Component to decay before interrupting the fault.
How would you calculate it by hand?
%dc = 100e(-t/45)"

asked 3/7/2012

6 Answers

If you looking for a 20% decay; 20% on 100 = 80. Putting this in your equation would gives 80=100e(-t/45), which you need to solve by taking the natural log of both sides and finding t. Also think 45 should be 0.045.

If I have misunderstood your question, please let me know.

The time constant of 45 ms is recommended by the standards as typical. If you know the X/R ratio you can get a more accurate estimate from time constant = (X/R)/2πf
answered 3/8/2012 Steven McFadyen 246
Steven McFadyen
thank you for the quick response and you answered the question, but i'm a little confused on when the standard gives you standard time constants. But your saying that at your fault location if the X/R ratio is greater than 17 than you would use the X/R to calculate the new time constant? Is that Correct?
If i wanted to add a time delay for before the circuit breaker would trip, would it be added with the contact parting time (t/.045) numerator.
answered 3/8/2012 Mjomah 6
Here is a link to a Siemens page which tries to explain this (pretty much in line with what your saying):

This is the standard the beakers are tested to, but in reality you may have a quicker (or slower) decay. By using actual system X/R, I think you will get a better solution to your problem.

Without knowing your problem, isn't the dc decay taken into consideration in the performance of your circuit breaker. Do you really need an external delay for this. If your problem is such that you do need this delay, my first thought would be to not include any contact parting time.
answered 3/9/2012 Steven McFadyen 246
Steven McFadyen
please excuse my ignorance, but to make sure i understand can you provide an example? Let's say for instance the a power system study was conducted and the X/R ratio at the bus was 26 (hypothetically). Let's assume that the Circuit breaker had a DC% capability of 20%. How would you show you added time delay in order for the Circuit breaker to allow enough time for the DC component to decay? (If you can show a calculation)
It's not an actual problem, but I am aware that IEC accounts for the DC component.
answered 3/13/2012 Mjomah 6
Mjomah I don’ think there is any ignorance. You question is investigative and forcing me to think a bit.

From your description, the time constant would be (1/2*pi*f)(X/R); at 50 Hz this would be 82.8 mS.

For the dc component, I=Ipeak*e^(-t/timeConstant); so to get to 20% we have (I’ll do this in stages):

20=100*e^(t/0.0828) -> 0.2=e^(-t/0.0828)
-> ln(0.2)=-t/0.0828 -> -1.6094=-t/0.0828
-> t=133.3 mS

If you see any problems with the above, please post and we can keep working through this till we have a good answer.

As a note, the peak dc current on which the breaker 20% is decided is likely higher than the actual fault peak current you will be seeing. If 133.3mS is too long, by modifying the method above to use both these figures, you could theoretically derive a shorter time.
answered 3/14/2012 Steven McFadyen 246
Steven McFadyen
Thank you Steven.
answered 3/15/2012 Mjomah 6

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