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

Your Answer

In order to provide an answer to this question, you must Login

I am flagging this question because...

10 inform moderator flags remaining

I am deleting this question because...

I am flagging this answer because...

10 inform moderator flags remaining

Flagging a Post

You have already flagged this post. Clicking "Remove Flag" below will remove your flag, thus reducing the count by one as well.

I am deleting this answer because...

Frame Leakage Protection

While not as popular as it once was, frame leakage protection does still have some use in some circumstances.  In essence frame leakage is an earth fault...

How to measure power supply quality

If your are ever called out to troubleshoot something on your electrical system, one of the first things consider is the supply voltage. You want to ensure...

Variable Frequency Drive

Variable frequency drives are widely used to control the speed of ac motors.  This note looks at the mechanisms which enable drive units to control the...

Why use catalogues

I'm a fan of using manufacturers catalogues. There are two main reasons for this. Firstly, if your involved in the purchase of equipment, you will likely...

IEC 60287 Current Capacity of Cables - Rated Current

In the previous note we looked at the approach taken by the standard to the sizing of cables and illustrated this with an example.  We then looked at one...

Introduction to Lighting

When looking at the design of a lighting scheme it is useful to have an understanding on the nature of light itself and some of the basic theory associated...

Load Flow Study – how they work

A load flow study is the analysis of an electrical network carried out by an electrical engineer. The purpose is to understand how power flows around...

RLC Circuit, Resistor Power Loss - some Modelica experiments

Modelica is an open source (free) software language for modelling complex systems. Having never used it before, I thought I would download a development...

Why a Sine Wave?

I received this question by email a few weeks. First thoughts was that it is a product of the mathematics of rotating a straight conductor in a magnetic...

Low Voltage Circuit Breakers

Circuit breakers are switching devices whose primary function is to isolate parts of an electrical distribution system in the even of abnormal conditions...

Our website uses cookies so that we can provide a better experience.
To learn more about what cookies are and how to manage them visit