## Transformer Impedance Mismatch in 3-Phase Transformer Bank

## Transformer Impedance Mismatch in 3-Phase Transformer Bank

(OP)

Can anyone point me to an IEEE or ANSI standard that addresses the maximum variation in transformer impedance for a three-phase delta connected bank? I cannot seem to find a definitive answer, but rather some generalities (such as + or - 7.5%).

I have a client who recently lost two transformers (due to a secondary bus fault) and is in need of getting two replacement single-phase transformers. The problems are; immediate delivery; and matching the existing 2.0%Z. I have located two transformer with 1.9%Z and 2.1%Z. Will the 1.9%Z unit have to be de-rated due to a 10% difference between the two new units?

I have a client who recently lost two transformers (due to a secondary bus fault) and is in need of getting two replacement single-phase transformers. The problems are; immediate delivery; and matching the existing 2.0%Z. I have located two transformer with 1.9%Z and 2.1%Z. Will the 1.9%Z unit have to be de-rated due to a 10% difference between the two new units?

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

The impedance determines the current under short circuit conditions when the transformer impedance is almost the total impedance of the current path.

During normal operation there are two voltage drops in the transformer. The resistive voltage drop and the reactive voltage drop. You must use vector addition (subtraction) to determine the total voltage drop and the resulting phase angle of the current.

With loads of unity power factor the resistive component is in phase with the applied voltage and predominates. Even though the reactive voltage drop may have a greater magnitude it is acting at 90 degrees which greatly reduces its effect on the total voltage.

With loads of varying power factor you may have to use vector analysis to solve each case.

Transformers from different manufacturers may have equal impedances but slightly different X/R ratios. They may share the current fairly well but you may find that the line current is less than the sum of the transformer currents.

In answer to your question, I have seen 10% quoted as the maximum difference in impedance percentages to parallel transformers but I can't put my hands on the reference just now.

If you load has a good power factor you may find that matching voltage regulation is more important than matching P.U. impedances.

If you must use the units, monitor the current and temperatures of the transformers.

respectfully

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

The bank is actually a Wye-Delta. The general consensus, for a 2%Z transformer is + or - .1%Z on the nameplate or about a 10% variance. I will look again at the GE & ABB manuals I have and see if I've missed something.

Thanks.

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

Using a 1pu load @ 0.95pf (18.2deg), and 2.2% and 2.0% Z xfmrs (10% variance) with X/R = 5 (78.7deg), and reflecting all the impedance onto the wye secondary, I believe the calculation for the secondary voltages is:

1-[(1.0<-18.2)x(0.022<78.7)] = 0.9893<-1.109deg

1-[(1.0<-18.2)x(0.020<78.7)] = 0.9903<-1.007deg

The magnitude ratio is 1.0010, or about 0.1% difference. Seems pretty small. For a three phase system, this might give a set of secondary voltages of:

Va= 0.9893<(-1.109deg)

Vb= 0.9893<(-1.109 - 120deg)

Vc= 0.9903<(-1.007 - 240deg)

I ran this through a Vabc to V012 calculator and found:

V1 = 0.9896<-1.1deg

V2 = 0.0007<-60.6deg

V0 = 0.0007<179.4deg

The negative sequence is about 0.07%. Seems pretty small.

Using the same math for Z xfmr of 10% and 11%, the ratio of Vmagnitude comes to 1.0043, V1 (without manual tap and automatic tap changer effects) would be 0.9543, and V0 and V2 would be 0.0033. Still, well below 1%.

Anyone see any errors in my math?

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

Some time past, it was pointed out to me on this forum that the voltage drop of a transformer under normal loading was determined by the regulation, not the impedance.

Voltage drop under normal loading is less than would be indicated by calculations based on the impedance.

In the case of a load of unity power factor, The internal voltage drop due to resistance will be in phase with the load voltage. The internal voltage drop due to reactance will be at 90 degrees to the resistive voltage drop. These drops are quite small compared to the load voltage so the effect of the reactive voltage drop is quite small.

For a complete solution we must know the X/R ratio of the transformer (or the resistance or the regulation).

Percent impedance is used to determine short circuit currents, where the transformer impedance is the predominant circuit impedance.

Oh, and don't forget the power factor. With less than unity power factor the reactive component of the internal voltage drop becomes more significant.

Impedances are used to match transformers because it may be the only information avalable on the nameplate.

However two transformers may have identical percent impedances but different voltage drops under the same percentage loading.

respectfully

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

"Some time past, it was pointed out to me on this forum that the voltage drop of a transformer under normal loading was determined by the regulation, not the impedance."

Do you happen to remember the thread this was discussed in?

If not, would anyone care to summarize a brief explanation of the difference? In my limited training I was always lead to believe the two were fairly synonymous.

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

I recall the thread, but in I my limited training I was also lead to believe the two were fairly synonymous and I embarrassed myself somewhat. I think you would find that previous thread more confusing than helpful. I have since spent some time re-educating myself on this topic.

The impedance of a transformer is the vector sum of the resistance and the reactance.

With loads of unity power factor the resistance is the predominant voltage drop. The reactive voltage drop is acting at right angles and has little effect. As the load becomes more inductive the resistive voltage drop becomes less effective and the reactive voltage drop becomes more predominant.

In practice, transformers of similar percent impedances may have similar X/R ratios and similar regulation, and so impedance ratings are commonly used to match transformers even though it may not produce a perfect match.

Re: transformers and transformer banks.

a delta bank may be considered as a virtual transformer formed by two transformers in open delta in parallel with a third transformer. When a balanced delta bank has a single phase load with unity power factor connected, the in phase transformer will supply half the current and the virtual open delta transformer will supply half the current. If the transformers are not balance, the load sharing will not be equal and the transformer with the best regulation will take a greater share of the load.

respectfully

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

Vdrop = |Vsource|- |Zxfmr| x |Iload|

leads to some excessive anticipation of voltage drop. I think I took realistic load flow and realistic impedances, and found that the voltage unbalance due to different xfmr reactances is rather small, when you do the math vectorially.

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

1. Voltage ratings are identical.

2. Tap settings are identical.

3. Percent Z of one is between 92.5% and 107.5% of the other.

4. Frequency ratings are identical.

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

1) Permissible tolerance on specified impedance values as per IEC 60076-1 (Table 1 of clause 9)

+,- 7.5 % for impedace values of 10 % or more

+,- 10% for values less than 10 %

2) As per ANSI/IEEE C57.12.00 (clause 9.2)

+,- 7.5 % for values more than 2.5 %

+,- 10 % for values 2.5 % and less

But for auto trfs and zigzag connected tolerance is +,-10 %

Difference of impedance between units manufactured by a vendor at same time shall be within 7.5 %( or 10 % of specified value

3) Voltage drop ie regulation at full load in a transformer is IR cos fi+IX sin fi where IR is the copper loss expressed as a %of rated KW ( up to 3MVA 1.5-1 %,3-100 MVA 1-0.3 %,100-400 MVA -0.3-0.15 %) IX is square root of IZ square-IR square.For large trfs IX is almost same as IZ (ie % impedance) as IR is negligible .Fi is the angle between load current to voltage.At unity power factor,voltage drop will be IR only ie reactance has no effect.

4) Voltage drop depends on I also.ie if I is half (load =half of rating)voltage drop will be half of at rated load.

5)Transformers can be parallel operated if the percentage impedances at their own ratings are with in the above tolerances.But then also,trf with lower impedance will share more load than the other unit.Because of this reason trfs with substantial difference in rating ( say a 10 kVA with 100 kVA) shall not be parallel operated. IEC 60076-8 recommends a maximum limit of 1:2 in rating.

Any further queries on the subject?

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

## RE: Transformer Impedance Mismatch in 3-Phase Transformer Bank

But when we consider lots from different make /made at different time, permissible tolerance limit is +,- 7.5 or 10 %,depending on impedance value.ie whether for paralling or forming a three phase bank, permissible impedance tolerance is same.But normally paralleling is critical.A difference in impedance between phases can result in minor change in secondray phase voltages under load due to unequal voltage drop.This is negligible compared to the effect of the unbalanced loading any grid has to cater to.

In India, one utility when they order a set of single phase generator transformers (pretty big ones) used to insist for a max impedance variation of +- 5 % among them.this figure is same as stipulated by IEEE.

To the specific original question,impedance variation in this case is within +-5 % and hence banking can be done without any worry.