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I'm creating a simplified 2D model of 3 three-winding 132/22 kV, 40 MVA transformers that I'll use to calculate the magnetic field surrounding them.

Now, the turn ratio is of course 132/22, but is there a typical number of turns for such a transformer? Is it 132/22, 264/44, 1320/220, 13200/2200?

I realize this will vary, but does anyone have real-life examples where the number of turns is known? This can be from datasheets, test reports or simple experience.

J&P's transformer book says this (page 23):

Consider, for example, a transformer used to step down the 132 kV grid system voltage to 33 kV. At times of light system load when the 132 kV system might be operating at 132 kV plus 10%, to provide the nominal voltage of 33 kV on the low-voltage side would require the high-voltage winding to have a tapping for plus 10% volts. At times of high system load when the 132 kV system voltage has fallen to nominal it might be desirable to provide a voltage higher than 33 kV on the low-voltage side to allow for the regulation which will take place on the 33 kV system as well as the regulation internal to the transformer. In order to provide the facility to output a voltage of up to 10% above nominal with nominal voltage applied to the high-voltage winding and allow for up to 5% regulation occurring within the transformer would require that a tapping be provided on the high-voltage winding at about -13%. Thus the volts per turn within the transformer will be: 100/87 = 1.15 approx. so that the 33 kV system voltage will be boosted overall by the required 15%.

On page 331 we have:

[...] even in quite large transformers, the volts per turn is rarely more than 200, and on many occasions considerably less.

And this on page 136:

The frame size used depends on the rating of the transformer but, since, as the rating increases the voltage class also tends to increase, the volts per turn usually gives an LV winding with a hundred or so turns and an HV winding with a thousand or more.

Stewie Griffin
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  • It can be calculated from the operating frequency, the core cross section, the core maximum flux, and the winding voltage. Do you have that data? Double the linear size of the transformer, the core area increases by a factor 4, the number of windings falls by the same factor, for the same voltage, frequency, and max flux. – Neil_UK Aug 18 '22 at 10:11
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    I suggest using a volt/turn value close to 50. – Luiz Oliveira Aug 18 '22 at 11:11
  • https://www.quora.com/What-is-the-turn-per-volt-formula-in-a-transformer – Antonio51 Aug 18 '22 at 11:17
  • @Neil_UK, the transformer isn't purchased yet. I have no information, unfortunately. I know it's impossible to give an answer for "my" transformer, but data for a similar transformer will help. – Stewie Griffin Aug 18 '22 at 11:39
  • @Antonio51 I know I can calculate this, but unfortunately, I don't have any of the information I need. That's why I ask for typical or example values. – Stewie Griffin Aug 18 '22 at 11:40
  • @LuizOliveira thanks! This sounds like a reasonable value. May I ask where you have that number from? – Stewie Griffin Aug 18 '22 at 11:41
  • Do you need something as this (some electrical datas inside, must "search" ...) https://optcl.co.in/writereaddata/Tender/103918113914Technical_specification_24052018.pdf – Antonio51 Aug 18 '22 at 12:08
  • @Antonio51 thank you. This contains some useful information. Unfortunately, the number of turns is not specified: _"For determination of number of turns in the windings, the manufacturer shall provide dummy core, so as to accommodate the winding and determining the ratio between the unknown No. of turns (winding) and known No. of turns, wrapped around the winding."_ – Stewie Griffin Aug 18 '22 at 12:15
  • B=1.5 T. After calculus (EE&O), found 83 V/ turn ... – Antonio51 Aug 18 '22 at 14:29
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    @StewieGriffin, I worked as a power transformer design engineer for many years. – Luiz Oliveira Aug 18 '22 at 18:25
  • The specific construction of transformer windings is a matter for the transformer designer and not so much for the end user. Such design information will rarely (if ever) appear in the drawings, datasheets, and specifications for the end user. You are already reading the J&P book, and have a response from Luiz, who is much more qualified than I, so there's not much more I can add. – Li-aung Yip Aug 20 '22 at 09:17
  • Note that V/turn is influenced by B chosen, and also the current density ... – Antonio51 Aug 29 '22 at 12:29

3 Answers3

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This varies, and I'm assuming Luiz Oliveira's suggestion using 50 V/turn is correct for many transformers.

However, I just got a reply from one of the world's leading transformer manufacturers with the numbers for a transformer with the same specifications:

  • LV-winding: 127 turns
  • HV-winding: 730 turns
  • Regulating winding: 8 x 12 turns.

This gives a ratio of approx. 180 V/turn

Stewie Griffin
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  • Well.. I have checked here and 50V/turn is too small for a 40 MVA transformer, but 180V/turn is too high. Although, both are feasible, they wil lead to a very small (<4%) or a very high (>15%) impedance. In fact, V/turn is a secondary parameter when designing transformers. I mean, it's important to the manufacturers but has nothing to do with the technical specifications received from customer. – Luiz Oliveira Aug 21 '22 at 19:52
  • It's possible that the customer specified a high impedance to reduce the max short circuit currents. I have specified z>16% for a site where several transformers could be operated in parallel in certain situations. It was either high impedance, current limiting reactor in series or expensive switchgear etc. – Stewie Griffin Aug 21 '22 at 21:37
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    @LuizOliveira it's useful to know that 50 is low and 180 is high! That's more useful information than just a single number. :) – Stewie Griffin Aug 21 '22 at 21:38
  • That one comment about high and low impedance was very interesting by the way! – Stewie Griffin Aug 21 '22 at 21:48
  • It's not often you get a reply from someone who **really** knows how things work. I'd be happy to put a bounty on this question if you care to give some more insight into transformer design principles. – Stewie Griffin Aug 21 '22 at 21:53
  • No need of bounty, I'm happy to help a little. I can suggest you some books about transformer design, as Kulkarni and Del Vecchio. But you can have in mind that the choice of the number of turns in a transformers is always a compromise, where you try to fulfill the needs of your customers and standards requirements and, at the same time, minimize costs. Increasing the number of turns, usually lead to bigger windings, a smaller core and bigger impedance. Reducing number of turns goes in the opposite direction. – Luiz Oliveira Aug 21 '22 at 22:19
  • Thank Luiz. I'll check out the books. It's really the "silent knowledge" that's most interesting. The stuff you know and estimates you can make of the top of your head, such as typical values, how things are usually done etc. In my experience, books give the principles, equations and explain how to design a [something], but not rules of thumb etc. Example: I can probably design a core and winding configuration that gives me the desired voltage, impedanse, current rating etc. based on a book, but I wouldn't have a clue what iteration 1 should look like. – Stewie Griffin Aug 22 '22 at 08:03
  • Say I want an x MVA, v1/v2 kV, z=z% transformer. Where to start? Core cross-section: 10 cm2? 100 cm2? 1000cm2? Copper crossection: 100 mm2? 1000mm2? When should I start with a V/turn = 5 and when should I start with 150? This is obviously too much to answer in a comment, and I don't expect you to, but I find it really interesting :) – Stewie Griffin Aug 22 '22 at 08:55
  • I'll add an answer with the rule of thumb. – Luiz Oliveira Aug 22 '22 at 11:53
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As a rule of thumb, you can use the following formula for the first guess of V/turn:

$$V/turn=\sqrt{0.24\ S}$$

where S is the transformer rated power, in kVA.

For our example of a 40MVA, you will find ~98 V/turn.

Luiz Oliveira
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  • Do you have a reference for that? – D Duck Aug 24 '22 at 11:05
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    @DDuck, sorry but no. I learn it from another guy that worked in my company some years ago. I assume he used several transformer designs to fit a curve and then found this formula. – Luiz Oliveira Aug 24 '22 at 12:54
  • I accepted this, even though I have an "accurate" answer from Hitachi. This answer, assuming it's correct, is probably more useful for others with a similar question. – Stewie Griffin Aug 24 '22 at 13:03
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EE&O ...

Here is a Maple sheet for "calculating" the "Volt/turn".

enter image description here

Cu area primary + secondary (Scu) must be less than Awin (window of the transformer).

Antonio51
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