# What is the zero-sequence equivalent of a YNy0 transformer?

The zero sequence equivalent network of a YNy0 transformer with grounded primary is shown below (source).

It looks like there is no connection between the primary and secondary side of the transformer. This means that, if a line-ground short circuit occur on the primary side of the transformer, there won't be a fault current from the transformer.

From several simulation tools, I've concluded that this is not correct. I've included a screenshot from one (Paladin Designbase). As you can see, by running an short circuit analysis (using IEC 61363). Running an analysis using standard IEC 60909, there is no line-ground fault current.

What I'm wondering is: What is the zero sequence equivalent of a YNy0 transformer, and how can I use it to calculate the fault current?

The first question to ask is: have you got, or can you obtain, the transformer's test certificate?

Zero sequence impedance may have been measured during the transformer's factory tests. It may be on a separate test certificate specifically for zero sequence impedance. If you can find the measured Z0 from tests, you don't need to delve into the following theory.

In IEC land (where transformers are built and tested to IEC 60076), zero sequence impedance measurement is not a "routine test" so it has to be specially requested. (Hint: If you are specifying a transformer, please ask for the test! It doesn't cost much to run at the factory, and it's quite helpful.)

The second question to ask is: does the transformer have neutral earthing resistors (i.e. LV star point earthed by a 750 amp NER)? It would be unusual (unsafe?) to have a completely floating LV star point.

The third question to ask is: does your transformer have a buried delta tertiary? That considerably changes the answer.

Notwithstanding the above, the full theory is below.

The zero sequence impedance of a Y-Y transformer depends on the transformer's construction and how the windings are earthed.

The case of interest to you is when only one winding of a wye-wye transformer is earthed, i.e. HV grounded-wye, LV ungrounded-wye, or vice-versa. For brevity's sake I'll call this a "YNy0" transformer for the remainder of this post.

NB: technically, it's possible for a YNyn0 transformer to have the LV star point brought out to a bushing, but not connected to anything, so it could also be operated in this way.

Paul M. Anderson's Analysis of Faulted Power Systems, chapter 7.9 Zero Sequence Impedance of Three-Phase Transformers, covers the topic.

Even though the zero-sequence impedance of a theoretical YNy0 transformer is infinite, in practice, the tank of the transformer acts as a weak kind of delta winding. This is the so-called "tank delta" effect.

The table at the end of the chapter essentially says that, for a wye-wye transformer with one of the star points earthed, $Z_0 \approx 5 \times Z_1$.

A document I have from Eskom (South African power utility) says that a YNy0 transformer has $Z_0 \approx 10 \times Z_1$, again citing the tank delta effect.

The following text is quoted from Eskom DGL 34-617, "Network planning guideline for transformers".

### 4.5.2 Transformer zero sequence impedances

The zero sequence impedance of a transformer installation is dependent on:

• The transformer zero sequence impedance Z0.
• Transformer star point earthing and NEC, NECR earthing.
• Earthing impedances.

In modern PSST software each of the above elements is modelled explicitly. By specifying the transformer zero sequence impedance and it’s earthing (with any associated impedances) the total zero sequence model of the entire transformer installation is simulated in the PSST. In cases where test sheet data is not available, the assumptions below are commonly applied for transformer zero sequence impedance (these are zero sequence values for the transformers. Any grounding impedance must also be modelled in the PSST, and is entered separately):

• Star/Delta and Delta Star: Z0 = 0.9Z1.
• Star/Zig-zag: Z0 = 0.091Z1.
• Star/Star with both star points earthed: Z0 = 0.85Z1.
• Star/Star with only one star point earthed: Z0 = 10Z1. This is the “tank delta” effect whereby the transformer tank provides a delta winding effect.

It is important to note that with Star/Star transformers the transformer zero sequence impedance is dependent on the star point earthing. In all other cases the transformer zero sequence impedance is not dependent on transformer earthing.

Finally we have old faithful, the J&P Transformer Handbook.

From the J&P Transformer Handbook, 12e:

## 2.7 ZERO-SEQUENCE IMPEDANCE

... the zero-sequence impedance varies considerably according to the construction of the transformer and the presence, or otherwise, of a delta winding.

The zero-sequence impedance of a star winding will be very high if no delta winding is present. The actual value will depend on whether there is a low reluctance return path for the third-harmonic flux.

For three-limb designs without a delta, where the return-flux path is through the air, the determining feature is usually the tank, and possibly the core support framework, where this flux creates a circulating current around the tank and/or core framework. The impedance of such winding arrangements is likely to be in the order of 75 to 200% of the positive-sequence impedance between primary and secondary windings. For five-limb cores and three-phase banks of single-phase units, the zero-sequence impedance will be the magnetising impedance for the core configuration.

Should a delta winding exist, then the third harmonic flux will create a circu lating current around the delta, and the zero-sequence impedance is determined by the leakage field between the star and the delta windings. Again the type of core will influence the magnitude of the impedance because of the effect it has on the leakage field between the windings. Typical values for three limb transformers having a winding configuration of core/tertiary/star LV/star HV are:

[Z0]LV approximately equal to 80 to 90% of positive-sequence impedance LV/tertiary

[Z0]HV approximately equal to 85 to 95% of positive-sequence impedance HV/tertiary

where Z0 = zero-sequence impedance.

Five-limb transformers have their zero-sequence impedances substantially equal to their positive-sequence impedance between the relative star and delta windings.

The assumption I have seen used most often is that a YNy0 transformer has $Z_0 = 5 - 10 \times Z_1$.

At least one piece of software has this as the default, if you select a "core type" wye-wye transformer (as opposed to "shell type".)

• Awesome answer! I love how you always include great references in the answers! =) I do have test reports with zero-sequence data for 75% of the transformers. I'm using 6-7*Z+ for Yy, and 0.9 for Yd for the others, so pretty much the same as you recommend. Part of why I asked was because I wanted to draw the equivalent circuit. The figure I posted shows an open circuit, not connected to ground, which can't be right...? Is it correct if I just simply put a ground-symbol after the impedance? – Stewie Griffin Oct 14 '15 at 15:39
• Without a sketch I'm not quite sure what you're suggesting. Off the cuff, I would bridge the "gap" with a large impedance, 6 - 7 times Z1 as you have suggested. – Li-aung Yip Oct 14 '15 at 15:43
• This would represent the "tank delta" effect which bridges the two cores with a high impedance. (Impedance is high due to air gap, and the tank not really being designed as an efficient magnetic flux path.) – Li-aung Yip Oct 14 '15 at 15:49
• Small question (couldn't find you in chat): Synchronized phase-by-phase transformer connection to reduce inrush currents... Do you know what words I can search for on google? I can't find any information about it (my vocabulary is limited I'm afraid). – Stewie Griffin Sep 2 '16 at 11:38
• @StewieGriffin single pole closure? – Li-aung Yip Sep 2 '16 at 11:39