## % impedance of 3 phase 15 KVA transformer - normal values

## % impedance of 3 phase 15 KVA transformer - normal values

(OP)

480 V Delta / 400 V Wye, 60 Hz, 15 KVA 3-phase transformer.

The OEM says %impedance will be about 1.375.

Is this normal value for such transformers?

The OEM says %impedance will be about 1.375.

Is this normal value for such transformers?

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

I’ll see your silver lining and raise you two black clouds. - Protection Operations

## RE: % impedance of 3 phase 15 KVA transformer - normal values

So,

* if there is no problem for the transformer designer and

* if there is no problem with the secondary switchboard fault rating,

there is no issue with the indicated low value %Z, I think.

## RE: % impedance of 3 phase 15 KVA transformer - normal values

One more question. The transformer is going for an off-shore rig with 60 Hz supply. The transformer is being made and tested at 50 Hz with 400 V, 50 Hz primary voltage for open circuit test and 5.5 V, 50 Hz primary voltage for short circuit test => %impedance of 5.5x100/400V = 1.375.

Will the %impedance go up by 60/50 at 60 Hz due to proportional increase in inductive impedance? (though the V/Hz is constant)

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

The inductive reactance will increase in the ratio of 6/5.

There will be a slight increase in the effective resistance due to increased skin effect, but probably less than the PU increase in inductive reactance.

I tasked a class of students with verifying the nameplate %imp of some 2 KVA transformers.

The students found noticeable differences in the measured %imp between room temperature tests and tests on transformers at operating temperature.

Considering that the predominance of inductive reactance and the quadrature relationship between inductive reactance and resistance, I suggest that the 1.375 figure is usable but not 100& accurate.

I suggest that the difference due to skin effect will be less than the difference in actual impedance between a hot day and a cold day.

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

Agreed the winding resistance increase due to frequency increase will be negligible.

On further thought, while the inductive impedance will rise at 60 Hz proportionately, since the voltage is also being raised to 480 V, the net effect on %imp will be zero. Am I correct?

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

The inductive component of the %imp will remain the same. The resistive component of the %imp will drop by about 5/6.

With an X/R ratio of 8:1 I estimate an error of 0.235% if you ignore the resistance.

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

The transformer impedance (read inductive reactance) is increasing by 1.2 times whereas, the base impedance increases by square of 1.2. Hence, %impedance will be lower by a factor of 1.2.

## RE: % impedance of 3 phase 15 KVA transformer - normal values

2) YEs. Your estimate is correct.

% X= k x If/V where I = rated current V= applied terminal voltage F= frequency.

Please see Annexure B of C57.12.90-2015 for corrections when 60 Hz transformer is tested at 50HZ.

You got 5.5 V on 480 V winding to get rated flow in shorted 400 V winding. Then % impedance at 60 Hz= (5.5/480)x1.2= 1.375

## RE: % impedance of 3 phase 15 KVA transformer - normal values

The rated Amps and the test Amps remain the same.

The inductive reactance increases by a factor of 1.2.

The rated voltage increases by a factor of 1.2.

At the higher impedance the test voltage to force rated current through a short circuit is 1.2 times higer.

%imp is test Volts/rated Volts, which becomes test Volts x 1.2/rated Volts x 1.2

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

Bill, isn't prc saying the same thing?

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

## RE: % impedance of 3 phase 15 KVA transformer - normal values

I agree with RRaghunath's latest post, and I now understand the basis for his earlier comment. The increase in KVA capacity is inherent in the increase in voltage whether the nameplate rating is increased or not. The maximum allowable current remains the same. If you are basing your maximum allowable current on nameplate ratings, then you will use the nameplate rated voltage of 400 Volts.

The 15 KVA transformer becomes an 18 KVA transformer at 60 Hz.

When calculating loading, it may be best to use current rather than KVA or kW for loading. You may then calculate the transformer loading to the nameplate current without regard to frequency, or base KVA adjustments.

Edison123, prc, RRaghunath, I know that you all understand this, but other readers may appreciate some additiona explanation.

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

Percentage or per unit impedance= impedance in ohms/base impedance ; base impedance= (Rated kV)

^{2}/MVA2) When you try to use a 50 HZ designed transformer on 60 Hz system, there will be no increase in voltage or KVA. The flux density in the core will decrease by 1.2 and % impedance will go up by approx 1.2.

3) When you use a 60 Hz designed transformer on 50 Hz, then also voltage or current will not be an issue. The core flux density will go to saturation if the designed flux density at 60 Hz is not 20 % below the saturation flux density. Hence you can say a 50 Hz transformer can be used at 60 Hz, but the reverse may not be feasible.

4) Here edison's issue is - he made a transformer for 60 HZ, but testing at 50 Hz. He wants to extrapolate % impedance for 60 Hz operation from 50 Hz measured data. A caution note- in such small transformers impedance may go up by 1.3 instead of 1.2. But in large units (10 MVA and above) 1.2 is correct.

5) Hope waross and Raghu will agree with me. It is not clear to me how KVA or kV will go up with frequency.

## RE: % impedance of 3 phase 15 KVA transformer - normal values

Limit #2, Maximum voltage: The maximum voltage is limited more by by saturation than by insulation, and saturation is directly related to frequency.

Single phase example:

Hence maximum safe KVA ="Amps" times "Test frequency (F1) voltage times (test frequency/frequency of interest (F2)).

Or Maximum KVA = I x E x(F2/F1)

Or

KVA at 50 Hz = 22 Amps x 400 Volts/1000 = 8.8 KVA (50Hz/50Hz) = 1

KVA at 60 Hz = 22 Amps x 480 Volts/1000 = 10.56 KVA (60Hz/50Hz) = 1.2

8.8 KVA x 1.2 = 10.56 KVA

400 Volts x 1.2 = 480 Volts.

I have done similar calculations many times, in both directions for motor horsepower and occasionally for control circuit transformers, when imported 50Hz equipment was being converted for 60 Hz operation.

Impedance voltage by the test definition is the percent of rated voltage required to drive full load current through a short circuit secondary.

The target current is 22 Amps for both frequencies.

For 5%Imp, the voltage required at 50 Hz will be 5% of 400 Volts.

For 5%Imp, the voltage required at 60 Hz will be 5% of 480 Volts.

The only time you need to involve KVA in impedance PU calculations, when the rated full load current is not readily available. In that instance you will use rated KVA and rrated voltage to calculate rated Amperes.

You may need to know the KVA for loading calculations,but you have no further need of KVA for %imp voltage calculations or conversions.

Motor calculations, on the other hand, are generally to determine HP at a different frequency. HP is roughly analogous to KVA, and we are not interested in the %imp values, which in any case, change with motor loading.

The same formula is used, but the formula is transcribed to find a different unknown variable.

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

The voltage applied to transformer- fixed, nothing to do with frequency. Then the condition is fixed by the following transformer formula:

V/N = 4.44xfxBmx A where V/N =volts per turn; F=frequency Hz; Bm= maximum flux density in core T; A= effective area of core in square meter.

Since all other parameters are fixed, the only variable in formula is flux density in the core. So when you connect a 60 HZ designed transformer to 50 Hz supply, core flux density will go up by 1.2,but primary and secondary voltages will remain the same. If the B selected for 60 Hz is high ( more than 1.4 T), then you have to reduce supply voltage to avoid core saturation.( your example for that situation) But then purpose of transformer is defeated.

But if you use a 50 Hz designed unit in 60 Hz, above concerns are not required as flux density will come down with higher frequency.

## RE: % impedance of 3 phase 15 KVA transformer - normal values

Your statement is not valid when considering frequency changes of actual equipment in the real world.

The current is fixed due to heating. The safe voltage varies with the frequency.

If you energize a 480 Volt, 60 Hz transformer with 50 Hz, you have converted it to 50 Hz and it becomes a 400 Volt transformer.

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

In this particular case, since V/f is maintained constant - 480/400 V at 60/50 Hz, the flux density does not change, right? But the KVA will change up or down with V.

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

2) During the short circuit test ( impedance and copper loss) you apply the necessary voltage to get rated current in the shorted secondary. During 60 Hz you will require 1.2 times more voltage to get rated secondary current.

3) In real life when you shift a 60Hz transformer to 50 Hz with the same primary voltage, only the flux density will change( sine V/N is constant). But then flux density can get saturated if the designed B is > 1,4 T. In such cases, you have to reduce primary voltage by 1.2. Then of course you can say you will get only reduced kVA. Otherwise, you will get the same kVA in both 50 & 60 Hz.

## RE: % impedance of 3 phase 15 KVA transformer - normal values

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

@400 V, 50 Hz - 2.46/1.78/1.68 A & 333/332/332 V output

@480 V, 50 Hz - 5.32/4.04/3.70 A & 400/399/398 V output

confirming the core saturation at higher V/Hz.

Muthu

www.edison.co.in

## RE: % impedance of 3 phase 15 KVA transformer - normal values

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Ohm's lawNot just a good idea;

It's the LAW!## RE: % impedance of 3 phase 15 KVA transformer - normal values

2) I believe you are supplying a 15 KVA 480 V 60 HZ unit. Designed for 60 Hz but testing at 50 Hz. You propose to extrapolate test results for 60 Hz from 50 Hz measued values. I had done that many times. Earlier days, these conversion factors were not stanbdardised. Thanks to Ramsis Girgis of ABB, St.Louis, these were studied in detail during 2000-2001 and IEEE incorporated these recommendations in latest revision of the standard. You can get more details from below:

a)R. S. Girgis, B. Beaster, and E. G. teNyenhuis, “Proposed standards for frequency conversion factors of transformer performance parameters,” in Proc. IEEE Power Eng. Soc. Transm. Dist. Conf. Expo., vol. 1, Oct. 28–Nov. 2, 2001, pp. 153–158.

b)Ramsis Girgis, and Ed te Nyenhuis, 50 Hz to 60 Hz Conversion factors for transformer performance factors, Presentation at IEEE/PAS Spring 2002 Meeting

c)IEEE Std C57.12.90-2015; IEEE Standard Test Code for Liquid-Immersed Distribution, Power, and Regulating Transformer- Annexure B- 50/60-Hz frequency conversion of measured performance parameters.

d)K R M Nair, Power & Distribution Transformers, Practical Design Guide, Section 30.7, Pages 408-411, CRC Press, 2021

3) Regarding kVA at different frequencies- When a 60 Hz transformer is used in 50 Hz, voltages are reduced by 1.2 to avoid core saturation. Thnen your kVA will be reduced by 1.2 as mentioned by waross. ( when you use a 50 Hz unit in 60 Hz this limitation is not there as B will be coming down at higher frequency) But this is not a must. If your designed B is below 1.4 T, you can use without reducing voltages and the rated kVa will remain the same at both frequencies.