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# Transformer Impedance Data2

## Transformer Impedance Data

(OP)
Here is one of the downsides of deregulation. I'm a steam guy that needs to provide data to our Independant System Operator on GSU Transformers. There used to be a whole department of knowledgeable electrical engineers across the hall, but with FERC 888 and 889, we can't talk.

Here is my problem. I need to provide impedance data (R and X) at 100 MVA Base for GSUs ranging fron 5MVA to 700MVA. I have the test reports so I can get the following:

Nameplate Voltage, H & X
Test MVA
% impedance

I think that is all I need to get nominal resistance and reactance, but I could be wrong. If that data is sufficient could someone show me the formulas needed?

### RE: Transformer Impedance Data

For the usual case, you have every thing you need

%R = 100*(Load Loss)/(MVA of test)
note: the test MVA will usually be the base or OA rating of the transformer.

%X = sqrt(%Z**2 - %R**2)

The values of %R and %Z are on the transformer's base MVA.  To convert multiple by the 100 MVA and divide by the transformer's base MVA.

Example

20 MVA transformer
Impedance 10.24%

%R = 100*(75.8 kW)/20,000 kVA = 0.379%
%X = sqrt(10.24*10.24 - 0.379*0.379) = 10.23%

Change to 100 MVA base

%R (on 100 MVA base) = 0.379*100/20 = 1.895%
%X (on 100 MVA base) = 10.23*100/20 = 51.15%

If the transformer's not on its rated tap or does not match the system's nominal voltage, additional adjustments must be made.  I would suggest talking to one of those EEs over lunch to verify you have what you need.

### RE: Transformer Impedance Data

Call % impedance: %Z
Call % resistance: %R
Call % reactance: %X
Call transformer MVA: TMVA
Call base MVA: BMVA
Call per unit resistance at base MVA: R
Call per unit reactance at base MVA: X

%R=100*LL/(TMVA*1000000)
%X=sqrt(%Z^2-%R^2)

R=(%R/100)*BMVA/TMVA

Likewise for X.

### RE: Transformer Impedance Data

(OP)
jnims and stevenal thanks. You have saved me alot of time and effort.

Jack

### RE: Transformer Impedance Data

You're welcome. Guess jnims hit the submit button before I did. Just a followup on the difference of our answers. Jnims gave a final answer in percent. Convention is to express transformer impedances in percent, but system impedances in per unit. Divide the percent answer by 100 to get per unit.

Jnims, how do you adjust for the off rated tap situation?

### RE: Transformer Impedance Data

Suggestion: To avoid any ambiguity, the voltage base should be stated and used appropriately. See IEEE Std 141-1993 Section 4.7.1 Step 1: Convert all element impedances to per-unit on a common base, on page 161.

### RE: Transformer Impedance Data

jbartos is correct that all elements must be on a common MVA and kV base.  Selecting the kV base may require a little more knowledge of the entire system and not just a specific substation.  When the voltage of the transformer and the system base voltage does not match you must multiple the impedances found above by (transformer kV/system kV)**2.  As far as impedance changes versus NL taps, I don't generally try to account for this.  For the normal concentric two-winding transformer with the HV winding center-tapped, the impedance will decrease as the more turns are added to the HV winding (amps-turn imbalance along the length of the windings improves). For example, here are the results from several certified test reports

Taps           Impedance
169400:13090        12.26
161700:13090        12.27
154000:13090        12.51

141900:11000         7.58
135300:11000         7.59
128700:11000         7.85

However, this is not alway true.  I can easily find units where this is not true.  I would use the best data available (from the nameplate or test report) then correct it to the system base voltage.

### RE: Transformer Impedance Data

jnims - great posts so far, just a note re the voltage question in your last one.
In system studies, we usually define a base MVA, but not a base kV.  All voltages are stated in per unit of the particular voltage level - a transformer on the nominal tap will have 1.0 pu voltage on both sides and will have the same per unit impedance at both voltage levels.
Impedances are rationalized to the base MVA by the relationship Z (pu) = Z(Ohms)/Z(base Ohms), where Z(base Ohms) = (kV^2)/MVA(base).  This puts all voltage levels on a common basis for simplified analysis.
If the nominal voltage level varies from 1.0 pu, say because of tapchanger position, then the impedance at that voltage level must be adjusted accordingly.

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