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 Post subject: Calculation of I.E for Main Switchboard connected to Diesel Generator
PostPosted: Fri Apr 25, 2014 12:29 am 

Joined: Fri Apr 25, 2014 12:20 am
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Location: Singapore
Dear Friends,

Referred to IEEE 1584 in annex D of NFPA 70E-2012

As i am making calculation on a 440V Main Switchboard connected to a diesel generator. The only technical specification i can locate about Z% is the following:
7% direct-axis subtransient reactance
14% direct axis transient reactance
159% direct axis synchronous reactance
9% quadrature axis subtransient reactance
74% quadrature axis synchronous reactance
8% negative sequence reactance
1% zero sequence reactance
Which would i be referring to when using the formula D.2(a)?

Also, it was mentioned in AnnexD.5.2 calculation that it only applies for (20 in. on each side, open on one end). Would you be able to clarify from where does the 20inch measurement starts and end?

Looking forward for clarification!


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PostPosted: Fri Apr 25, 2014 5:37 am 
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The subtransient reactance, X"d, is the reactance of the stator at the instant a short circuit occurs and lasts only a few cycles.
The transient reactance, X'd, is the reactance after the first few cycles and last up to 1/2 sec or longer
The synchronous reactance, Xd, is the steady state current flow.

The formula in D.2(a) is for the short circuit at the terminals of a transformer. For a generator the formula is, I" = e"g/X"d. This assumes the internal e is the same as the terminal e (voltage) among others but should be a good approximation. Sometimes in the generator data sheet, the short circuit current will be given.

I'm sure more knowledgeable people will chime in with further details as I writing this on the fly and probably missed some details.

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Barry Donovan, P.E.
www.workplacesafetysolutions.com


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PostPosted: Wed Apr 30, 2014 12:04 am 

Joined: Fri Apr 25, 2014 12:20 am
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Location: Singapore
Hi Barry,

Would you be able to refer me to a documentation with calculation for generator? For the formula,I" = e"g/X"d , what does e"g stands for?

I" would be short-circuit ampere and X"d would be the subtransient reactance as you've mentioned.

Thanks!


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PostPosted: Wed Apr 30, 2014 1:37 am 
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Joined: Fri Jan 03, 2014 6:57 am
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Location: the Netherlands
[font=Calibri]R=U/I >>>> I=U/R >>complex>> I=U/Z since Z is total impedance and generator is mostly reactance you can get away with changing Z into X ( Xd X’d or X’’d). E is same as the voltage the g stands for generator I thinks. Barry does mention E is the voltage.[/font]

It’s a pretty common formula since its basically R=U/I but you can find it for instance in the IEC61363 on page 35 formula 3 and 4.

EDIT--------------------------------------------------------------------------------------------------------------------------------------------------

Just noticed me and Barry made the same mistake, we were looking at formula[D.2(a)] (page 70E-63)and not at formula[D.5.2(a)] (page 70E-66).I found it weird I couldn’t find anything on 20 inches for the first formula :P .

Let me start with saying I do not like to use formulas from the annex since its informative only, I use the IEEE1584 and this formula is not in the IEEE1584.

I don’t know who came to this formula but I think I can explain where the 20 inches come from. The 20 inches is the distance of arcing point to the walls of the enclosure. Why 20? Well maybe it is a common size (I do not have the experience to confirm this). What I do know is that it was probably 20 inches at the test setup and this formula was derived from the results of those tests.

If you have the NFPA70E AND the IEEE1584 why would you use annex D and not the IEEE1584?


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PostPosted: Thu May 01, 2014 7:57 pm 

Joined: Fri Apr 25, 2014 12:20 am
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Location: Singapore
Hi Luc!

Thanks for looking through. Sad to say, with limited resources at hand, i only have NFPA-70E and not IEEE1584, thus i am heavily dependent on the Annex D for calculations.

The formula in [D.2(a)] is I"={[MVA Base x 10^6]/[1.732 x V]} x {100/%Z} which i gathered from Barry's reply that its only for transfomer. (Which i mistakenly tried to use it to calculate it for a Generator) :)

Thus, if i understood Barry and you correctly, assuming i have a generator of the following specifications:

450V output voltage
7% impedance %Z
100,000VA

I should be doing: I"=[100,000VA/450V] x 0.07 ?


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PostPosted: Thu May 01, 2014 11:20 pm 
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I am sad to say that they did not teach me the per unit system at school, so I’m having to figure that out as well as I go.

I have a question though: your asking about a formula for a transformer in your initial post, but you have a generator connected to a main switch board with no transformer in between right?

You should read this: [url='http://www2.schneider-electric.com/documents/technical-publications/en/shared/electrical-engineering/electrical-know-how/low-voltage-minus-1kv/ect158.pdf'][size=3]http://www2.schneider-electric.com/documents/technical-publications/en/shared/electrical-engineering/electrical-know-how/low-voltage-minus-1kv/ect158.pdf[/url]Its a document about short circuit calculations by Schneider Electric, very useful.

Just let us know if you are not able to figure it out after reading this.


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PostPosted: Tue May 06, 2014 7:04 pm 

Joined: Fri Apr 25, 2014 12:20 am
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Location: Singapore
Hi Luc,

In my earlier post, i mistook the formula for Transformer and attempted to use it for a Generator. What i wish to calculate is a Generator connected to a main switch board with no transformer in between. You are right.

I appreciate the document! It has been very informative. But i am sure i did not understand the whole of it, though i did try.

The standardized Isc Calculation: Isc = Un / [sqrt3 x Summation of Z]

I know the Un (Nominal Voltage) is 450V, but am not sure the Z refers to the summation of which Z. Could you advise?

Then looking at the 2 Calculation of Isc by the impedance method, does Zsc = X"d? Or which "series reactances" do i need to add together?

I thank you for your patience and advise thus far, as i do not have an electrical background, i'm trying to get this as i go on. You guys are my only hope in getting through this calculation!


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PostPosted: Tue May 06, 2014 11:08 pm 
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As wdb mentioned in his post the impedance consists of a few parts: subtransient reactance X’’d, transient reactance X’d ,synchronous reactance Xd and the aperiodic component. They contribute to the total short circuit current. This is also explained with a visual on page 9 off the document I gave you to the link. Note that with the formula on page 10 you calculate the upper dotted line of a, b, c and e AND NOT THE GREEN LINE. So the max short circuit current can be calculated on t=T/2.


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PostPosted: Wed May 07, 2014 8:30 am 
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Just to be clear if you don't have an electrical background...we are really looking at time series data so we should be working with either differential equations (not worth the effort) or LaPlace domain which does differential equations in simpler math. However we can go one step further if we assume that we are working with purely periodic functions such as a 60 Hz sine wave. In this case we can get rid of all the complicated calculus if we convert everything into a vector, also known as a phasor. The "real" number represents the current/voltage/resistance that is in phase and the imaginary part represents 90 degree out of phase current/voltage/resistance. It just so happens that inductors and capacitorrs work 90 degrees out of phase. The out-of-phase component is called a reactance. And when we combine both into a complex number, it is a reactance. Sometimes the actual vector matters and sometimes only the magnitude matters.

In the real world, everything is a mixture of real and imaginary values. For example, a capacitor is nothing more than two conductors separated by an insulator. So the entire power system is insulated from the Earth and this entire system forms a large capacitor that becomes a consideration whenever we have a short circuit to ground. And electricity doesn't just travel in straight lines down the wire. It has eddy currents that cause every wire to have a slight amount of self-inductance.

Further, some effects are temporary. For instance when the power system becomes grounded, the system capacitance pushes short circuit current into the system and appears as a transient. When a motor or generator is suddenly disconnected from the power system the magnetic field collapses and drains into the system. These impedances only appear for a short period of time but they definitely create additional short circuit current that can be quite large. To avoid doing calculus we represent these as transient and subtransient impedances.


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