# Calculate number of turns in transformer

Discussion in 'Homework Help' started by Deano123, Jul 16, 2009.

1. ### Deano123 Thread Starter New Member

Jul 16, 2009
1
0
I need to find the required number of turns on the primary and the secondary windings of a transformer.
Given it is single phase 110/25KV railway TX on a 50Hz system
the max flux density is 1.5Tesla when 1.13pu volts applied.
assuming a core area of 0.3m2.

How would I find this?? number of turns prim and sec

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Hi Deano123,

I get the following

Erms=222.14xNxAxBmax

Did you mean the primary is 110kV?

If it's 110kV (RMS) then for conditions at 1.13pu Vprim = 124.3kV

So Np=123.4x10^3/(222.14x0.3x1.5)=1243 turns

That's a big core CSA! [0.55mx0.55m]

For the 25kV secondary

Ns = 281 turns.

These are very sparse specs for such a big unit. You haven't specified whether there a limitations on magnetizing current, losses, efficiency and a whole lot of other stuff. Do you intend to build this?

3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Make that Ns=283 turns

4. ### kkazem Active Member

Jul 23, 2009
160
28
Hi Deano123,

Here is an answer from a top expert in the field, me! I have over 35+ years designing all kinds of transformers. I'm going to make it as simple as I can right now, as my time is very limited at the moment. This will require that you make a few conversions to use the CGS system, like 1.0 Tesla = 10,000 gauss.

Here is the formula for the first winding, based on the known input voltage. Normally the primary, so I'll use that term:

Np = number of primary turns.
Vp = known primary input voltage in volts. I'm assuming a sine wave input. If it's a square wave input, remove the factor of 1.11 from the denominator.
Bmax = maximum flux density in gauss.
Ac = effective core area in cm^2 (convert from m^2).
Fo = input frequency in Hz.

Np= (Vp X 10^8) / (4)*(1.11)*Fo*Ac*Bmax

In practice, you always round-up to the nearest integer turn. Then for the seconday turns, Ns = (Np*Vs)/Vp. This time, you can round up or down to the nearest integer turn, usually whichever is closest to the value you want.

In practice, the effective core area not only depends on the actual core area, but the type of core, like E-I laminations. Then it gets modified by the stacking factor; which depends on whether you interleave the laminations 1 by 1, 2 by 2, or butt-join them. It also depends on the lamination or tape-wound core tape thickness. The thinner the material, the closer to the actual measured core area.

That's probably more than you wanted to know. If you have more questions, please ask.

Good luck,
Kamran Kazem

5. ### bonjing Member

Dec 7, 2008
12
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hi

what is the recommended frequency for 110v Ac and 220v ac

6. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
783
Whether you use my formula or kkazems you'll get exactly the same answer.

Something is seriously wrong with your specification if you really mean 110V primary.

With a CSA of 0.3 m^2 at 50 Hz you'll need just 1.243 turns for the primary - even rounding up to 2 turns gives a ludicrous result. I think you need to re-check your spec. The CSA of 0.3m^2 is probably not what you intend.

7. ### bonjing Member

Dec 7, 2008
12
0
others they specify the frequency, 60Hz for 120volts ac and 50Hz for 220volts ac...