3 winding transformer impedance

[wroggent]

I don't know much about three winding transformers and I need some help figuring out what impedance value I should use. A look at our data base says that the impedance of the transformer is 11.28% (I'd expect two values, one for each low side winding, but there is not). Below is a snip from the test report for the transformer, you will find 11.28% given as the impedance for "138kV to 13.09/13.09". I'm not sure what that means or if it is the correct value to use.

There are four impedance values that appear on this report and I'm not sure what they all are. There's 11.28 @ 24MVA, 10.2 @ 12MVA, 10.15 @ 12MVA and 35.2 at 24MVA.

Defining
Z12= impedance measured from winding 1, with 2 shorted and 3 open
Z13 = impedance measured from winding 1, with 3 shorted and 2 open
Z23 = impedance measured from winding 2, with 3 shorted and 1 open

and

Z1, Z2, and Z3 are the series impedances for the windings

where

Z12 = Z1 + Z2
Z13 = Z1 + Z3
Z23 = Z2 + Z3

and

Z1 = 1/2*(Z12+Z13-Z23)
Z2 = 1/2*(Z12+Z23-Z13)
Z3 = 1/2*(Z13+Z23-Z12)

Arbitrarily assigning 10.2 and 10.15 to either of the low voltage windings I'm guessing that:

Z12=10.2
Z13=10.5
Z23=17.6 (35.2*12MVA/24MVA)

So

Z1 = 1.375
Z2 = 8.825
Z3 = 8.775

And I'm guessing 11.28% is supposed to be (Z1 + Z2//Z3)*24MVA/12MVA? Or (1.375 + 8.825*8.775/(8.825+8.775))*2 = 11.56%

But I really have no idea. I am trying to find an impedance value I can lump with the upstream 138kV network impedance to serve as my source model.

 

[cuky2000]

See in the information below can help

 

[7anoter4]

In my opinion 35.2% it is not an existing impedance but it is the sum of ZH,ZX,and ZY in order to show the guarantee is close to ANSI admitted tolerance of 10% [the guarantee it is 9.555%]

 

[prc]

This is a transformer with axially split LV windings. Test report is giving three impedances H-L1 = 10.2 % (12 MVA base) H-L2 = 10.15 % and H-L1+L2 (ie both LVs loaded) = 11.28% on 24 MVA base. 35.2 % is the impedance between L1 to L2 on 24 MVA base. Noting H to x and y impedance is bit misleading. What the engineer wanted to convey is L1-L2 impedance, when measured is actually impedance L1 to H plus impedance H toL2. That is how power is transferred when you measure L1-L2 impedance.

Your calculation is to be corrected - Z12=10.2% Z13=10.15% (not 10.5 %) Z23 =17.6 % all on 12 MVA base. Usually Z12 and Z13 should be exactly same. Then you will find Z1 is almost zero and calculation as done by you will give a value of 10.2 ( on 24 MVA base) for H-L1+L2. But actual value measured is 11.28 % and that is correct. Normally this value will be 15 % more than the calculation as done by you because L1 and L2 are on the same magnetic circuit and when both L1 and L2 are loaded, there will be magnetic linkage between them and that adds the extra 15 %.

 

[7anoter4]

In my opinion 11.78,10.20 and 10.15 are the final impedances per winding [ZH,ZX,ZY) and not ZH_X ,ZH_Y and ZX_Y.

 

[prc]

During testing only Z H-L1 or ZH-L2 can be measured and not ZH or ZL1. Test reports give only the measured values.

 

[wroggent]

prc, so would you use the 11.28% value if you had connected the low voltage windings in parallel rather than just simply 10.2//10.15? And when not in parallel use either 10.2 or 10.15 depending on which winding you're using? (excluding X to Y)

 

[7anoter4]

First, I don't think this is a test result. What is 10% guaranteed tolerance. From what? In my opinion compared with calculated and a priori declared.
How close is the o.p. presented data to the way presented by cuky2000 ?.
Let's say ZX=10.2% [initial declared],it will be guaranteed 11.96% [ZX=11.96%≈12%]
If 11.28% it is ZH referred to 24 MVA but 13.09 kV and if ZX=11.96%[≈12%] it is referred to 12 MVA and 13.09 kV and if we translate the last for 24 MVA then we get ZH_X=ZH+ZX= 11.28%+11.96%*24/12=35.2% [all referred to 24MVA but 13.09 kV].

 

[prc]

wroggent, Yes you are right. But remember 11.28 % is on 24 MVA base and other two impedances are on 12 MVA base. The point I wanted to bring out was as per paralleling theory, under combined load, impedance should have been 10.2 % (24 MVA base),but actually it is 11.28 % , nearly 15 % more. This type of three winding transformers have another interesting characteristic. As we saw ZH is almost zero ie no impedance drop in H circuit ie when LV1 is fully loaded, LV2 terminal voltage under no-load will not be affected by the load regulation in HV-LV1 circuit. This is a requirement under certain applications eg Station start up transformers in thermal power stations.
Actually in this construction, HV is also made up of two equal parts (connected in parallel) placed vertically one above the other facing LV1 & LV2 windings, those too placed vertically one above the other. In reality it is two numbers 12 MVA transformers placed vertically one above the other but in the same magnetic circuit(core limb). When we measure LV1-LV2 impedance, power is transferred first to HV1 and then to LV2 through HV2 connected in parallel to HV1. So LV1-LV2 impedance is two impedances in series ie HV-LV1 & HV-LV2. As per this, LV1-LV2 impedance should be 10.2+10.15= 20.35 %.But actual measured is only 35.2/2 = 17.6 % (on 12 MVA base- approx. 85 % of 20.35 %) Here during the two current transfers to get LV1-LV2, 15 % of impedance is lost in the transaction! Experienced transformer designers know these thumb rules very well.
7anoter4,Experience tells me what is shown is an old transformer test report page(before the days of computers)of legendary US manufacturers (GE, Westinghouse, Allis Chalmers, Waukesha etc) Wroggent can correct me. Test reports always give guaranteed values against measured values for the client to easily check what he is getting is, as he ordered but within 10 % tolerance allowed by National standards.
Last a personal disclosure: self involved in design and engineering of similar three winding transformers for the past half century!

 

[7anoter4]

Thank you, prc.

 

[wroggent]

The report is dated 1974.

Thanks prc.