I don't know enough about transformers to provide any insight, but have been intrigued by the topic.

Modelling them in series certainly seems easy enough. In that model, assuming ideal, all of the current would be magnetizing into a flux defined through Maxwells.

In the non-ideal case, we would only deal with some of that flux being lost due to eddy currents, flux leakage etc.. and of course power loss due to resistance.

If what I just said applies, I think I'll also opt out of this conversation as it is non-intuitive for me to view the 'currents' from a perspective of core losses etc..

 

I am appending vector diagrams for both ideal and real transformers.

I have also provided an equivalent circuit and a differential equation for the real model.

primed (dashed) quantities are the image or induced values in the primary by action in the secondary.

In the ideal transformer E1 is the applied primary voltage and E2 the induced secondary.
E1 leads the flux by 90°. I2 is the secondary current , lagging E2 by angle β.
The secondary amp turns n2I2 are equal but of opposite sign to the induced current in the primary. I0 is the no load current which can be resolved into components of magnetising current and iron loss current.

The circuit model and vector diagram for the real transformer needs complex quantities to solve it. This is the model used to measure the complex impedances in two principal measurement tests

The Short Circuit Test
The No Load Test

 

Thanks for that mate.

That spawned me off to a whole other article of reading, supposed to be working!

Here is a paste from the follow up article I read, for Shahvir:

"Try to visualize what happens when the secondary current decreases. It may help to draw additional phasor diagrams. The difference between the terminal voltage V2 and the induced voltage E becomes less, and they approach one another. The magnetizing current becomes a larger part of the smaller primary current, which changes in phase accordingly. The flux, of course, remains the same. "

The last statement is what Shahvir was originally after. I understand this as follows:

1. Magnetizing current basically is a wetting flux, to get the core ready to move fluxes around.
2. Since I2 induces, what appears to me to be, an equal and opposite flux to that in I1, also seen in Studiot's phasors as equal and opposite directions of current and therefore flux, they more or less leave no 'net' additional flux, and rather the net flux is always that of the magnetizing current.

Does this sound appropriate?

 

Dear All,

I am pleased to note that my query has spawned a fruitful discussion amongst all! I think i have understood the concept.

Following is my interpretation;
1) There are 3 different currents at play in parallel with each other, viz. Load current 'IL', magnetizing 'Imag' and iron loss current 'Iw'.

2) Ii = Ir = Imag, since Ir becomes Imag as it passes through coil inductance 'Lc'.

3) The dampening or neutralizing of magnetic flux in ferrous core is due to the voltage drop across the impedances which appear in series with the windings of a 'non-ideal' transformer!
Please correct me if i am wrong!

I just want to understand why is 'Magnetic Hysteresis' represented by a resistance ? I also want to understand the physics behind the representation of magnetic hysteresis as a resistance (since it is practically difficult to visualize a magnetic parameter into an electrical one!)

Thanks & Regards,
Shahvir

 

Someone please reply!

Kind Regards,
Shahvir

 

I'm not going to delve into all the issues covered. Please read the following. This should answer your largest point of confusion concerning constant flux:

"Examining the magnetomotovei forces created by the primary and secondary windings, current I2 produces a secondary mmf N2I2. If it acted alone, this mmf would produce a profound change in the mutual flux Phim. But we just saw that Phim does __NOT__ change under load. Therefore flux Phim can only remain fixed if the primary develops a mmf which exactly counterbalances N2I2 at every instant. Thus, a primary current I1 must flow so that N1I1 = N2I2."

This is in agreeance with Studiot's phasor diagram and my attempt at intuitively reasoning it.

 

I also believe this 'mutual flux' to be a result of the magnetizing current. If that helps you intuitively understand. Basically it is just the flux needed to get things moving. Loading is considered separately as I just posted.

 

I'm not going to delve into all the issues covered. Please read the following. This should answer your largest point of confusion concerning constant flux:

"Examining the magnetomotovei forces created by the primary and secondary windings, current I2 produces a secondary mmf N2I2. If it acted alone, this mmf would produce a profound change in the mutual flux Phim. But we just saw that Phim does __NOT__ change under load. Therefore flux Phim can only remain fixed if the primary develops a mmf which exactly counterbalances N2I2 at every instant. Thus, a primary current I1 must flow so that N1I1 = N2I2."

This is in agreeance with Studiot's phasor diagram and my attempt at intuitively reasoning it.

Dear James,

Thanks. But this concept of constant magnetic flux in core is applicable to an ideal Voltage Transformer (VT). But as per Current Transformer (CT) theory, the core flux is neutralized by the secondary winding current MMF. Hence, the above concept cannot be applied to a CT and this is the reason for my query in the first place!

I think the explanation by BillO is correct, since it applies to both CT and VT. If the Xmer is non-ideal, then the magnetic flux in the core of a VT will also reduce (just as in case of a CT), since the magnetizing current will be dampened by the load which is connected in parallel with other parameters viz; inductance representing 'magnetizing current' branch and resistance representing 'core losses' current branch. The dampening/neutralizing of magnetic flux is the result of voltage drop across the series impedances in case of a non-ideal Xmer as explained by BillO (please refer non-ideal Xmer equivalent diagram provided by Studiot in the earlier post # 42).

P.S. Someone please explain the logic behind representation of 'Hysteresis Loss' by a resistance!
Please refer to my earlier post # 44 in this thread.

Kind Regards,
Shahvir

 

Can someone please respond to this thread also, very grateful

Kind Regards,
Shahvir

 

Shavir, I don't think there is anything left to say.

In a real-world application, resistance, primarily in the voltage source, but also in the primary windings of the transformer, will produce a reduction in the core flux as the transformer is heavily loaded. The reason is that the source voltage will drop as the current demand goes up.

CT applications generally have a primary of 1 or less windings. In the case of a current meter (the clamp-on type we are all familiar with), the primary is just a wire passing through the core. The secondary is usually heavily loaded - as close to a short circuit as possible.

The reason the flux in the core of the CT application gets reduced to zero (in a real transformer it would be finite but negligible ) is that there is no ability for the transformer to draw more current from the source as there is in the VT application. Plain and simple, but it's something you need to understand or you will never get this.

But this has all been said before.

 

no ability for the transformer to draw more current from the source as there is in the VT application. Plain and simple, but it's something you need to understand or you will never get this.
But this has all been said before.

Dear BillO,

Thanks, but i have already understood the concept. The reason for my recent postings was a brief discussion with Skeebopstop on the same.

But i think you must have missed out the part where i had requested about an explanation as regards the representation of 'Magnetic Hysteresis' as a resistance.

It is difficult to visualize a magnetic quantity into an electrical one and hence i had requested for a logical explanation for the same.
I would be grateful if someone could help me out in this!

Kind Regards,
Shahvir