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jonald
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Join Date: Sep 2009
Location: Singapore
Posts: 77
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Zero Sequence Impadance

01/25/2010 7:35 PM

Dear Fellow Engineers,

I want to calculate the line to ground fault of a given Transformer 500kVA,3.16kV-.48V,3ph,%z"=5.5 with 250MVAsc Utility. In order to solve this I need positive(x1), negative(x2) and zero sequence impedance(x0).

( x1 )

= xd synchorous reactance

= xd' direct axis transient reactance

= xd" direct axis subtransient reactance

xd" is prefered as it will give highest short circuit

(x2 = (xd"+xq")/2)

subtransient reactance is almost equal to quadrature axis subtransient reactace

hence, it is good assumption that negative sequence is equal to direct axis

subtransient reactace

( xo )

x0 of synchronous machine should be smaller than the positive sequence impedance.

(query)

Is there any formula to get negative sequence impedance(xo) of a rotating machine?

Thank you!
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Electronaut
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Location: Mangalore, India
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Good Answers: 4
#1

Re: Zero Sequence Impadance

01/25/2010 9:45 PM

For a transformer, the positive and negative phase sequence impedance are the equal since thee are no rotating parts in a transformer. A zero phase sequence impedance exists for a transformer only if its neutral is grounded. For a shell type transformer the zero sequence impedance is equal to the positive sequence and for a core type transformer, the zero sequence impedance is equal to 90% of the positive sequence impedance. However, you may neglect this variation in the zero sequence impedance and you may consider that both the impedances are equal.

For a synchronous machine, X1 = Xd or X'd or X"d, X2 = (X"d+X"q)/2. You will have to refer to the machine manual to get the value for zero sequence impedance. I don't think that there is any emperical formula to calculate zero phase sequence impedance.
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Anonymous Poster
#2

Re: Zero Sequence Impadance

01/27/2010 12:29 PM

So can you pls tell me how to get the XD",XD' & XD?Is XD same as percentage impedence.How to apply this to find out the ground fault current.I would be greatful to you.
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jonald
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Location: Singapore
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#4
In reply to #2

Re: Zero Sequence Impadance

01/27/2010 11:32 PM

Xd", Xd' and Xd can be found in manufacturer data sheet.

Ex. 14MW,13.8kV,3ph,.8pf Generator

xd"=14%

xd'=28%

xd=180%

Generator will experience three values of 3ph fault if it does'nt isolated by protective relays.

Iload=14MW/(1.732*13.8kV*.8)=732amps (Load Current)

Ifault 3ph = 732/.14 = 5230amps (sub transient current)

Ifault 3ph = 732/.28 = 2615amps (Transient current)

Ifault 3ph = 732/1.8 = 407amps (sustain current)
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Akihito Shigeno
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#3

Re: Zero Sequence Impadance

01/27/2010 8:09 PM

Dear all,

Xd'', Xd' or Xd are required for near generator fault.

All you have to do for earth fault current calculation is following.

Fault capacity Utility 250MVA

Fault capacity 500kVA Transformer 0.5MVA/0.055*1.1 = 10MVA

1.1 is by transformer impedance tolerance +/-10%.

Fault capacity total 250//10 = 9.62MVA

3 phase Fault current at 480V (I think it is 480 not 48)

9.62MVA / √3 /0.48kV = 11.57 kA

You need a earth fault current, use the following relation.

3phase short circuit current I3p = Ea / Z1

1phase earth fault current Ief = 3Ea / (Z1 + Z2 + Z0) = 3Ea / 2.9Z1 = 1.035 I3p

I assumed Z0 is 90% of Z1.

So, resulting earth fault current is 11.57 x 1.035 = 11.98kA

Regards

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 Akihito Shigeno @ JGC-Indonesia
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jonald
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Location: Singapore
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#5
In reply to #3

Re: Zero Sequence Impadance

01/27/2010 11:38 PM

Yes sir it is 0.48kV secondary voltage. Thank you
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Anonymous Poster
#7
In reply to #3

Re: Zero Sequence Impadance

01/28/2010 12:37 PM

But the 3ph fault current is the most severe in any system,but your calculation shows ground fault current is more than the 3 phase.Pls clarify for me.
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kellytshort
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Join Date: Jan 2010
Posts: 13
#8
In reply to #7

Re: Zero Sequence Impadance

01/28/2010 12:53 PM

Isc SLG can easily be great then the Isc 3p. Got off cat site is a 2500kW 480V Cat Gen set with pu imp. x''d=.1194, x2=.1166 and x0=.0081. that is off the CAT cut sheet and notice the 0 sequence imp. is CRAZY low, so the lower the imp. the higher the Fault current.

Here is some math for you (note I gave pu values) and zbase=.073

Isc SLG=3(E/1.73)/(x''d+x2+x0)

831/(.1194+.1166+.0081) now divide by zbase to get 46kA

Isc 3p=(E/1.73)/x''d

277/.1194... zbase...=31.7kA so

as you can see the ground fault is way higher than the 3p phase fault. In a post yesterday I raised the question...ANSI standards require that the Isc 3p=>Isc SLG for generator applications therefore on generators like this we must install a neutral grounding system to be ANSI compliant. NO Gen manufacters have responded to my emails yet.
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jonald
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Location: Singapore
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#11
In reply to #8

Re: Zero Sequence Impadance

01/28/2010 8:11 PM

Another solution for 2500kW 480V Cat Gen set with pu imp. x''d=.1194, x2=.1166 and x0=.0081:

Formula for 3phase fault = Power Base/(1.732*Voltage*X"*power factor)

Formula for line to ground fault = (3*Power Base)/(1.732*Voltage*X"+X2+X0*power factor)

3phase fault = 2500kW/(1.732*480*.1194*.8)= 31kA symm.

Line to ground fault = (3*2500kW)/(1.732*480*(.1194+.1166+.0081)*.8)= 46.2kA symm
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Anonymous Poster
#12
In reply to #8

Re: Zero Sequence Impadance

02/03/2010 12:57 PM

pls tell me why the multiplicaiotn by 3 has come in ground fault current calculation,Isc SLG=3(E/1.73)/(x''d+x2+x0)?
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jonald
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Location: Singapore
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#13
In reply to #12

Re: Zero Sequence Impadance

02/04/2010 1:43 AM

Iao = (Ia+Ib+Ic)/3 zero sequence component (general formula).

If line1 is grounded then Ia = Ifault(line to ground)

Ib = 0 and Ic = 0 see fig 1.

Iao= (Ifault+0+0)/3

Therefore:

Ifault = 3 x Iao = Line to ground fault

Thats why we multiplied by three.
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Akihito Shigeno
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Location: Jakarta Indonesia
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#10
In reply to #7

Re: Zero Sequence Impadance

01/28/2010 6:52 PM

Dear al,

In directly earthed system, an earth fault current is slightly higher than the 3Ph fault current.

This is what symmetrical components explains us.

Regards

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 Akihito Shigeno @ JGC-Indonesia
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MegaThink
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Join Date: Aug 2011
Posts: 12
#14
In reply to #3

Re: Zero Sequence Impadance

12/01/2011 11:54 AM

sorry, but how did you get 9.62 MVA AND WHY? THANKS
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Akihito Shigeno
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#15
In reply to #14

Re: Zero Sequence Impedance

12/05/2011 12:33 AM

Dear Mega Think,

I used "MVA method" to calculate short circuit capacity.

A Utility 250MVA

B 500kVA Transformer 5.5%, short circuit capacity is 500kVA / 0.055 * 1.1 = 10 MVA

C Total short circuit capacity is:

C = 1/(1/A + 1/B) = 1 / (1/250 MVA + 1/10 MVA) =9.6154 MVA

Regards

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 Akihito Shigeno @ JGC-Indonesia
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jonald
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Location: Singapore
Posts: 77
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#6

Re: Zero Sequence Impadance

01/27/2010 11:41 PM

If there is no formula to calculate the zero sequence impedance of the rotating machine how about measuring this?Can we measure this?Thank you.
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kellytshort
Active Contributor

Join Date: Jan 2010
Posts: 13
#9
In reply to #6

Re: Zero Sequence Impadance

01/28/2010 6:44 PM

Found this on the world wide web for transformer testing

http://www.tirathai-transformer.com/21.htm
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Users who posted comments:

Akihito Shigeno (3); Anonymous Poster (3); Electronaut (1); jonald (5); kellytshort (2); MegaThink (1)

Previous in Forum: Converting Mechanical Pot Control (50 k ohms) to 4-20 mA Signal control   Next in Forum: Substation Transformer Modeling

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