Transformer Impedance and Full Load kVA 1

[recs]

I understand that the transformer nameplate impedance (Z%) is related to the nominal kVA.

I also understand that this impedance will change if we consider the full-load kVA of the transformer.

The result is that the short-circuit current delivered by the transformer is the same no matter which kVA is chosen (nominal kVA or full-load kVA).

I would like to be sure of this and I have not found any IEEE publication or paper explaining this fact in detail.

Does anybody now about an IEEE or another reputable institution that has a technical paper demonstrating this fact?

Thanks.

 

[dpc]

The transformer impedance is a physical constant determined by the construction of the transformer and the material used. It basically does not change. The percent impedance (or impedance voltage) is expressed as percentage (or per unit) referenced to some base MVA. For an ANSI-rated transformer, the %Z is expressed in terms of the lowest transformer kVA rating (generally, but not always), the self-cooled rating. The base MVA of the percent impedance should be stated on the nameplate. For IEC-rated transformers, I believe the %Z is stated in terms of the highest forced cooled rating of the transformer. Again, this should be indicated on the nameplate.

Just like any per unit calculation, you can use any base MVA that you want as long as you properly convert the per unit values. Regardless of the base MVA used to express the transformer percent impedance, the short circuit current does not change, because the transformer itself has not changed. Review the IEEE Red Book if you still have doubts.

 

[recs]

DPC:

Thanks for your prompt answer.

Actually, the Z% impedance does change when the full-load kVA is used instead of the nominal kVA. If it would not change, the short-circuit delivered by the transformer would be greater when using the full-load kVA instead of the nominal kVA.

The Z% is the ratio of the voltage at the primary (when the secondary windings have been short-circuited and reached FLA at the primary) to the nominal primary voltage. The FLA for the full-load kVA is greater than the FLA for the nominal kVA. Therefore we need to raise the voltage higher in the primary of the short-circuited transformer to obtain higher FLA at the primary.

Therefore, the Z% (which is the ratio of Vp/Vnominal) is greater that the Z% for the nominal kVA.

This increase in the value of the Z% compensates the increase of the value of the full-load kVA and the result for the short-circuit delivered by the transformer is the same.

If have read many articles stating this very fact. But none have been from a reliable and well known source. If you come across such a publication, I would appreciate if you can share it with me.

Thanks

 

[dpc]

You need to read my previous post again. You are confusing actual ohmic impedance with %Z. Transformer ohmic impedance does NOT change. The %Z does change if you change the MVA base used to calculate the %Z. The impedance voltage measurement is simply a technique used to measure transformer impedance. It is generally expressed in percent AT SOME BASE MVA, but can easily be converted to ohms referred to one winding or the other. Or converted to another base MVA.

 

[waross]

The transformer impedance is a physical constant determined by the construction of the transformer and the material used. It basically does not change.

Looks OK to me.


Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[DRWeig]

If have read many articles stating this very fact. But none have been from a reliable and well known source. If you come across such a publication, I would appreciate if you can share it with me.

Review the IEEE Red Book if you still have doubts.

'nuff said.

Best to you,

Goober Dave

Haven't see the forum policies? Do so now: Forum Policies

 

[recs]

DPC:

Your are right, I should have read your response more carefully.

The whole discussion that I started with my first post, was not about the "actual ohmic impedance", but the Z%. Please review my first post. But now that you mentioned this "actual ohmic impedance", I realized that I have less knowledge in this subject that I thought. Here is why.

The Z% (in a specific power base, normally the nominal kVA) is used to calculate the short-circuit current when using the PU method or in software packages like SKM. Not the "actual ohmic impedance".

Knowing this Z% (per cent) you can convert this impedance in Per Unit on the selected base power and then covert it to the "calculated ohmic value" at the primary of secondary voltage using the per unit calculations.

Lets assume that Z%1 is referred to the nominal kVA and Z%2 is referred to the full- load kVA.

Now we can obtain the "calculated ohmic value" of each one of these percent impedances (Z%1 and Z%2)using the PU calculations as you stated in your response. Since Z%1 and Z%2 were different at the start, their "calculated ohmic values" will also be different.

The short-circuit calculations should be based on the Z% values (if you use the PU method) or the calculated ohmic values of the Z% (if using the ohmic method).

Here is where I am confused. I kind of agree with you that the "actual ohmic impedance" you mentioned in your response should not change depending on the base kVA chosen because the transformer construction remains the same. But the "calculated ohmic value" of the Z% do change depending the base kVA. The question therefore is:

Are the "calculated ohmic values" (obtained from the PU calculations starting from the Z% impedance) the same as the "actual ohmic impedance" you referred in your response?

If it is, something is wrong. They can't change and not change at the same time.

If it is not, what is the difference between the "actual ohmic impedance" and the "calculated ohmic impedances" based on the Z%?

Does the manufacturer publish this "actual ohmic impedance"? It does publish the Z%.

I know I am missing the magic link to put these two concepts together. Therefore, if you have a reputable reference (like and IEEE publication) that zooms in this problem specifically, I would appreciate if you or any other engineer following this thread can send it to me.

Thanks

 

[waross]

Percent impedance is a percentage of a specified base. It is measured in percent.
The "actual ohmic impedance" is a value measured in Ohms. This impedance value does not change. (Well, not much. More about that later.)
In the NEMA world the norm is to express this based on the ONAN rating of the transformer.
Now if the transformer MVA rating is increased by the addition of cooling fans, (ONAF) the rated current will be proportionately greater. It will now take a higher primary voltage to drive this new, rerated, higher current through a short circuit.

An anecdote concerning a possible change in the Ohmic value of the impedance.
I prepared a shop project to measure the impedance and then calculate the %Imp. and compare it with the nameplate value. I foolishly neglected to run through the worksheet in the shop myself. The transformers may have been 2 KVA 120/240:240/480 Volt units but memory fades.
All the measurements were off enough that most of the students queried the large error between the measured values and the nameplate values. All the calculated values were reasonably close to each other but noticeably lower than the nameplate information.
I made fast return to the text books.
Impedance tests on transformers are done with the transformer at full load temperature. The resistance and impedance values will be low on cold transformers.
These transformers had a high enough resistance in relation to the inductive reactance that the students immediately realized that the error was more than acceptable.
I kept using that work sheet.
1> It got the students attention and they were more motivated to listen to an answer to their own question than to a lecture.
2> Some classes were great. Some had one or two slackers. If a student reported accurate results, I had reason to suspect that he was "Cooking" the experiment.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[dpc]

I'd suggest reviewing Chapter 2 in J. Lewis Blackburn's Protective Relaying book. He has a straightforward discussion of per unit calculations and transformer impedances. I think if you get comfortable with per unit base conversions, this issue will be easier to understand. Other good references would be Analysis of Faulted Power Systems by Paul Anderson and A Practical Guide to Short Circuit Calculations by Conrad St. Pierre. I suspect there are also some good tutorials on per unit calculations available on-line as well.

 

[rcw retired EE]

IEEE C57.112.10 defines % impedance voltage but doesn't really define %Z, even though they are equal.
"The percent impedance voltage at the self-cooled rating as measured on the rated voltage connection shall be as listed in Table 3..."

Note the "self-cooled" rating. The impedance voltage from the factory test is stamped on the nameplate and referred to as %Z by all of us. A good engineer always notes the MVA rating or base the %Z refers to. "Z=9% at 90 MVA rating."

For example, a 90/120/150 MVA, ONAN/ONAF1/ONAF2 transformer will have a %Z of 9% at 90 MVA, 12 % at 120 MVA and 15% at 150 MVA. Connect the transformer to an infinte bus and short circuit the other side and it will deliver 90 MVA/9%= 1000 MVA to the short circuit. Note that the short circuit level will not change if someone wants to use the 15% @ 150 MVA rating. The ohmic impedance doesn't change.
The short circuit MVA is still 1000 MVA = 150 MVA/15%

Assume 345 kV voltage and 90 MVA.
Base amps = 90/(345x1.732)=150.6A. Base ohms = 345 x 345/90= 1322.5 ohms
Transformer ohmic impedance at 90 MVA = 9% x 1322.5 = 119 ohms.
Short circuit current from infinite bus = 345 kv/(119ohms x 1.732) = 1,674 A
MVA short circuit = 1674 x 345kV x 1.732= 1000 MVA, same as before.

Assume 345 kv voltage and 150 MVA base. %Z=15
Base amps = 150/(345x 1.732)= 251 amps. Bse Ohms = 345x345/150 = 793.5 ohms
Transformer ohmic impedance on 345 kv side = 15% x 793.5 = 119 ohms.

You are over thinking this.

 

[racobb]

You have gotten several reputable references right here. You just need to heed the advice as you are not grasping the basics with this. These guys are correct....and to quote DRWeig.....'nuff said. Otherwise, you really need to hit the books!

Alan

 

[recs]

RC Wilson:

You are a good teacher and communicator. Thanks for your step by step explanation .... I got it!!!!!! I am slow but not totally retarded.

Thanks all for your patient comments and responses.

For some stupid reason, (all mistakes are) I though that the "calculated ohmic value" derived from the Z% using the PU formulas, was going to change if the Z% change. I stand corrected. It stays the same.

It was not that I did not know the PU formulas or theory, it was just a pre-conceived idea that needed to be eradicated.

Thanks to all again.