Transfomer Core size vs Power

[magnX]

Hello questions for the experts,

Is there a realationship between the core size of a transformer (single or three phase ) and its power rating? Please describe.

thx

 

[davidbeach]

Yes, the higher the power rating the bigger the core.

 

[prc]

Yes. The core size is increased when the power transferred magnetically is increased.( ie for an auto-transformer it depends on the self rating of the unit ie HV-LV/HV x line rating) Core size varies power rating raised to 0.75 for the same flux density, frequency and impedance range.

 

[waross]

Higher power = larger core.
Higher frequency = smaller core.

Bill
--------------------
"Why not the best?"
Jimmy Carter

 

[magnX]

Thank you all for the replies,

So obviously the question is yes, is there an equation that describes the correlation between Ac and Power?

thx

 

[oldfieldguy]

Over the years, improved iron chemistry has allowed greater power densities for a given core size, but for identical chemistries, the 'bigger means more rule' applies

old field guy

 

[bacon4life]

When we have specified "identical" power transformers for delivery over a contract period of several years, some manufacturers actually redesign the core size for each delivery based on the current price of copper vs core steel. Also, the supply chain for core steel is quite limited, so sometimes transformer manufactures make do with what they can find, rather than using the exact type of core steel they would prefer. The loss evaluation price, the specified impedance, or any sound level limits can also play a role in sizing the core.

The TAPs presentation on the IEEE transformer committee website is a very good explanation of the tradeoffs in transformer design, although the site may require a login.

http://grouper.ieee.org/groups/transformers/

 

[PHovnanian]

Its actually an indirect relationship.

The core area is proportional to the volts per turn generated in each winding. And inversely proportional to the frequency. It depends on the B-H curve of the core material as well. The core's length (and therefore its ultimate volume) is primarily determined by the dimensions needed to accommodate the necessary windings. Core length does have an effect on leakage flux and therefore the overall efficiency and impedance of the unit. So if you can keep the core length (and resulting volume) down with better winding designs and insulating materials, you can get better performance out of a 'smaller' core for the same power.

 

[prc]

The most important parameter in transformer design is per turn voltage. The per turn voltage (e) in volts = 0.7-0.9 square root KVA per wound limb.kVA should be the self rating in case of auto transformer.The rule is valid for the past 60 years and applies from 5 kVA to 1000 MVA. e ~ 4.44 xBxAXf where A= core area B=flux density F =frequency.B will not vary with the quality of CRGO, but will vary depending on the application of transformer and the capitalisation formula applicable.When load loss capitalisation is high ( ie designer wants low load losses) he selects a high e in the above band width, resulting in a bigger core ( for same B and f) and smaller copper ie it becomes a core machine, less height and more diameter. When capitalisation is low, the reverse happens resulting in a copper machine.Of course the cost of CRGO and copper also enters in to picture.Generally the design is optimum when the cost of making core equals cost of windings which may not be practicable always.

 

[magnX]

Thank you all for the interest in answering this question,
Prc, you brought up an interesting point which is very similar to what I found in the link below:

http://en.wikibooks.org/wiki/Electronics/Transformer_Design

At the section "simpler formula" they came to the conclusion that
area =0.17 *sqrt(Power) for 12 K-Guass which is 1.2T at 60Hz.

which is similar to what you described (I am not sure about the F.factor there though).

What's you guys thoughts?

 

[7anoter4]

I agree with prc, of course. In modern laminate saturation occurs at higher flux density.
The price of laminate against the price of copper [or aluminum] states [in a limited measure]the core cross-section.
From an old book [R.Richter vol.III ] we get these:
S=rated power [w]; f=frequency[Hz]; sc=core[column] cross-section [cm^2]
Single Phase Shell-Type sc=C*sqrt(S/f)
Single Phase Core-Type sc=C*sqrt(S/2/f)
Three Phases trf. sc=C*sqrt(S/3/f)
C=4-6 cm^2 for small and medium transformer
C=8 for large transformer.

 

[magnX]

Thank you 7anoter4,

In Three Phases trf. sc=C*sqrt(S/3/f)

what is trf? is it trf*SC? or TRF stands for something different?

 

[7anoter4]

I am sorry:
"Three Phases trf. sc=C*sqrt(S/3/f)"
has to be:
"on three-phase transformer sc[core cross-section]=C*sqrt(S/3/f)"
where C is the same constant as above it was mentioned.