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Permissible flux density of transformer core

Permissible flux density of transformer core

Permissible flux density of transformer core

I would need advice from esteemed experts on this forum.
It concerns the custom design of a dry, low-voltage power transformer with an approximate power rating of 1 to 3 kVA.
The issue at hand is that we have several sizes of new "EI" transformer cores of unknown quality and manufacturer, in our warehouse, which we occasionally need to use to build a transformer for a specific application.
The problem lies in the fact that we have no information about the core quality, particularly the permissible flux density, so we are unable to calculate the "turns per Volt" and maximum kVA.
We know that the flux density can vary within a very wide range (from 0.8 to 1.7 Tesla), which is not particularly helpful.
I'm wondering if there is a test through which we can measure and determine an approximate value for the permissible flux density so that we don't have to guess randomly. This wouldn't be a problem if we were dealing with a series of transformers, but in principle, it's always a single transformer for a specific purpose.
Any help would be greatly appreciated.

RE: Permissible flux density of transformer core

Take the following for what it's worth: I design, manufacture, and repair rotating "transformers" all the time.

The flux density "range" is dependent on the material chemistry (as it affects magnetic saturation characteristics), material "thickness", and intended operating parameters (i.e., load flow). In general, something with higher silicon content will have a higher initial magnetizing current and exhibit lower core losses when unsaturated. Thinner laminations will give more-or-less the same result. Grain-oriented material (arranged so the grain is parallel to the flux path across the air gap) will also help.

If the manufacturing details (material chemistry, lamination thickness and grain orientation) are unknown, then the simple answer is to develop a test setup (similar to a core loss tester) that is capable of intentionally driving a subject transformer core into saturation. Measure and record the saturation curve thus obtained, and work backward to see where it lies on the proposed design rating (MVA).

Converting energy to motion for more than half a century

RE: Permissible flux density of transformer core

Irrespective of the grades or thickness of cold rolled grain oriented steel laminations, the saturation flux density is 1.9 T. Giving an allowance for 10% over voltage or under frequency conditions, one can go up to 1.7 T for rated conditions. Considering noise levels, dry trf etc, you can limit to a safe value of 1.6 T.

RE: Permissible flux density of transformer core

Thank you all for the very helpful advice.
There is one more thing I should ask since I have found quite different recommendations in the books.
It concerns the relationship between the cross-sectional area of the core and the power of the transformer.
Is there any reliable formula, theoretical or empirical, for that?

Also, there are varying data on permissible current density and tables with average transformer efficiency values.
Are there any recommendations on that?
I would like to note that I am primarily interested in single-phase, air-cooled transformers with an EI core in the power range of 100 to 3000 VA, 50 Hz.
Thank you in advance

RE: Permissible flux density of transformer core

It is true. As rating kVA goes up the area of cross section goes up along with the per turn voltage. The. Famous formula is per turn voltage= 4.44x B ( flux density) x area of cross section x frequency x10-8
Consider a 1, 10, 100, 1000 kVA of same voltage ratio and impedance. The only item going up with kVA is per turn voltage. Since flux density and frequency are same, the only item going up when per turn voltage goes up is area of cross section of core.

RE: Permissible flux density of transformer core

Hi, prc,
Thank you for the quick response. I have to admit that from the given formula, I don't see a clear relationship between power and the cross-sectional area of the core.
Also, I wonder if the formula for transformer power should include the cross-sectional area of the core window. Could I get a bit more explanation? Thank you.

RE: Permissible flux density of transformer core

Let me explain in a simple way without formulae:
Rating in kVA= voltage x current
So for an increased kVA rating with the same voltages, the current has to be increased ie the winding cross-sectional area has to be increased for the same current density. But then you will find the impedance drop will be very high (your secondary voltage will be very low after the drop) due to the increased physical size of the winding. To avoid this, when the rating (current) goes up, the turns in the winding have to be reduced. Impedance and hence impedance drop varies as the square of the number of turns.

When turns are reduced, the per-turn voltage goes up ie for the same flux density and frequency, the cross-sectional area of the core goes up.

RE: Permissible flux density of transformer core

The sizing of the transformer depends on two main factors- the volume of iron and the volume of copper. When you keep flux density lower, you will have to increase the number of turns to get the desired voltage. The increased number of turns causes more copper loss and the size of the transformer also get increased. Therefore, we need to trade-off between the flux density and winding turns.

The efficiency of the transformer lowers with a change in the flux density. The core loss decreases with the reduction of flux density but the copper loss will increase for delivering the same KVA. The transformer when loaded at about 40% gives the best efficiency. The flux density of the transformer core if kept between 1.6 to 1.8 Tesla will give optimal efficiency. This article may be useful for better understanding- Overfluxing in transformer

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