3 phase Fault Currents 3

[xxx23]

Hi,

I've recently carried out short circuit analysis for the initial symmetrical 3 phase short circuit current for embedded generation.[ I"k = Cmax . Vn / (1.732 . Zk) according to IEC 60909].

Looking a some grid application forms, they require the initial short circuit current I"k as well as the short circuit current for a given times Ik(t) i.e.

Ik(t=0 sec,)
Ik(t=10ms)
Ik(t=50ms,)
Ik(t=100ms) etc....

Can anyone provide some information on how to calculate the short circuit current for the given times Ik(t) or any literature/books that may have the relevant information.

Thanks in Advance.

 

[dpc]

I don't know much about IEC terminology, but I think you will need the generator time constants and the system X/R ratio.

Do a web search for "Generator Decrement Curve". The fault current out of a generator is not constant - it decays over time. This is determined by the generator time constants and also the excitation system.

Any power system analysis text (Stevenson, Anderson, etc) has at least some discussion on this.

 

[ijl]

It seems that you have a near-to-generator short circuit. If you are interested in the AC-component only, you can use the (well known?) equation for the current as function of time, see for example

http://www.iea.lth.se/eks/L7.pdf

, or the book of Nasser Tleis. (The book contains a thorough discussion of the current as function of time.) Or you can let the computer do the job, see

http://pp.kpnet.fi/ijl

.

But if you need the breaking current, that is, the sum of the AC- and DC-components, then the IEC-standard should be used. It gives (complicated instructions for the calculation of the breaking current at different times. The calculation method is also described in several books, see the books of Kasikci or Schlabbach, for example.

 

[odlanor]

You have to to read Factors for the calculation of short-circuit currents in a short circuit book based on IEC standard.

book: Short-circuit currents - J. Schlabbach

search: gigapedia.com/ libray Nu

 

[veritas]

xxx23

Some terminology correction:

The actual fault current waveform is based on the analysis of an RL circuit with no pre-fault current.

The instantaneous current is given by:

i(t) = idc(t) + iac(t) - note this is an instantaneous value

The symmetrical value of i(t) at t = 0 is the initial symmetrical fault current, Ik" (rms value). Due to AC decay (from rotating plant) the symmetrical current decays to a steady state value called Ik (rms). Thus one does not calculate Ik at different time values as you have stated above. Note that Ik" is a theoretical rms value (cannot be measured) whilst Ik is an actual rms value (can be physically measured). Exception is when there is no AC decay and then Ik" = Ik.

The instantaneous/(theoretical)rms current can be calculated at various points of the transient waveform.

i(0)or I(0)
i(0.01) or I(0.01)
i(0.05) or I(0.05)
i(0.1) or I(0.1)

As a first pass you can calculate the above by hand or using Excel IF you know what Ik and the X/R is using the following formula:

i(t) = 1.414*Ik*[sin(w*t+90)-e^(-t/T)]


where T = X/(w*R)

Of course you need to use the same voltage factors (usually 1.1p.u.) to calculate Ik as you would have done doing the full IEC 60909 analysis.

The above can be used if you have an analysis package that only determine the steady state fault currents.

Please note that the above does not consider AC decay (only DC decay) so may not be much use in your case but could be helpful to get ballpark figures.

The formula for considering AC as well as DC decay is to cumbersome to write out here with the limited text abilities. The others posts will undoubtedly be more useful in this regard.

Regards.

 

[ijl]

veritas,
Can you check the equation for i(t). A printing error or two, perhaps?

 

[veritas]

The formula I have stated is not the general form of the equation but the form of the equation where maximum offset is assumed.

In the attachment, I have stated equation 2 and not equation 1 which is the general form.

If this does not answer your question, then do let know if there is an actual typo.

Regards.

 

[ijl]

Maybe
Ik", not Ik
In addition, I would prefer -pi/2 (not +90) and +exp(-t/T), to be consistent with the normal usage (positive DC).

 

[veritas]

ijl

Yes, you are correct. It should be Ik" and not Ik unless of course there is no AC decay in which case the two are always the same. Thanks for that.

With regards to +ve or _ve DC I guess it depends on the convention you're familiar with. I've come across a derivation of the fault current equation using calculus and the fault current is all in terms of cosines rather than sine resulting in the first peak being positive rather than negative. I tend to work with both.

Regards.