Transformer's Theory question 2

[mackmaster]

I have difficulty to understand the theory of how the transformer acually works and have a question regarding to that:

The primary winding of a transformer consists of two parts:

1- Primary leakage inductance Lp1

2-Primary coupling inductance L1

neglect the wiring resistance.

So the total primary inductance Lp=Lp1 + L1

The voltage across L1 must be constnat all the time = N1*d@m/dt

where @m is the mutual magnetizing flux, which is constant for all loads.

Now,if the primary is connected into a constant AC supply voltage V1 and the secondary is connected into resistive load,then:

V1 = Lp1*d i1/dt + N1*d@m/dt

V1 and N1*d@m/dt are constants while the first term of the equation Lp1*d i1/dt

is variable depends on the primary current !

Any one can explain that conflict in the equation ?

Thanks

 

[Skogsgurra]

I see no conflict. Increase load and you get more voltage drop across the leakage inductance. Typically, the so called regulation is 5 - 10 %. That means that your voltage drop is 5 - 10 percent compared to no-load voltage.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[mackmaster]

Thanks,but the voltage across the coupling inductance L1(E1)remains constant =N1(d@/dt)
So, the induced secondary voltage E2= E1(N2/N1)=N2(d@/dt) remains constant and does not depend on the voltage drop on the primary leakage inductace.
@ is the magnetizing flux which is constant.

 

[davidbeach]

Constant E1, variable load, variable E2. At least that's how real transformers work. I've never seen a transformer model that wouldn't have a voltage drop related to load.

 

[Skogsgurra]

Mackmaster, if you look at the voltage magnetizing the core, you will notice that the primary leakage inductance is in series with the primary winding.

Increased load current also means increased primary current (I really hope you agree to that). So, increased current in an inductor (the primary leakage inductance) means less voltage across the primary winding.

Why do you think that the magnetizing flux, which you for some strange reason call @, is constant? It is not!

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[mackmaster]

Skogsgurra thaks for help, the transformer theory indicates that the hysteresis loop does not change with the load current, so the magnetizing flux @ is assumed to be constant and so d@/dt is assumed to be costant.

 

[mackmaster]

We can put the question in different form:
Does the hysteresis loop change its shape and reduces its two peaks with the increase of the load current?

 

[boBK7IQ]

I think that what is happening is that the leakage inductance is not part of the magnetizing inductance, i.e. that inductance does not contribute to the flux in the core and so has a voltage drop, even without wire resistance. (I ~think~ I said that right)...

However, a real transformer does have winding resistance (until we have superconducting wire) and so even the flux on the core and the B-H curve (hysteresis etc) will change with load current.

boB

 

[mackmaster]

So,what I understand is that primary leakage inductance acts exactly as the primary wire resistance and it will cause the hysteresis loop to reduce its height as the load current increases-Is that what you mean?

 

[dpc]

I think you are taking the equivalent circuit too literally. The transformer equivalent circuit is useful in determining how the transformer behaves in the electrical circuit it is connected to, when viewed from the outside of the transformer. This is done in terms of parameters that are fairly easy to measure. It does not really help us with what is happening inside the transformer core. The resistance that is in parallel with the magnetizing reactance represents the core losses. There will be resistance in the leakage reactances that represent the winding load losses.

Any model is a simplified version of reality. It is important to understand the limitations of the model.

 

[Skogsgurra]

No need at all to involve B-H curve and hysterisis in this. As dpc says - you are making things much too complicated.

There are several levels of complication involved. Simplest model has no leakage inductance at all. And no resistance. Then flux ix constant when load changes.

Next model (a little more complicated, and closer to reality) contains primary and secondary leakage inductance. Those elements behave just as ordinary circuit elements and can be treated as such. You can use RMS and do not need to bother about B-H curve. This is the model used in most real-world calculations.

Next model contains more details - but still working with RMS and no B-H curve thinking involved.

Still higher in model complexity, you find differential equations and instantaneous values - but still no B-H curve involved. Core is regarded as lossless and linear.

It is only when you are doing doctorate work and pure research that you start bothering about hysterisis loops. You are then working with non-linear partial differential equations. You are a long way from that.

Accept simple and proven facts.

Gunnar Englund

http://www.gke.org

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100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[spinach]

Hi,

I read the theories with interest....but think of a common mode choke at the input of a switch mode power supply........

...That is a transformer, but since the Hot & Neutral are effectively "differential" lines, then which is the primary and which the secondary?

....And which coil is it that passes the magnetising current?....is it both?.

I know that the fields of each coil cancel each other out...but there must be some magnetising current whose flux is not cancelled else the thing wouldn't work as a transformer and NIp = NIs wouldn't apply.

This is one of the most confusing transformers of all...so you are right to get confused

 

[Skogsgurra]

"there must be some magnetising current whose flux is not cancelled"

That current is the common mode current. That is the high-frequency current leakage current, to which the common mode choke represents an inductance.

Normal mode currents are not affected by the choke. There's nothing mystical or confusing about that. Just pure physics.

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[DHambley]

The problem is that you said there are two constants (V1 and N1*d@m/dt) in your equation:

V1 = Lp1*d i1/dt + N1*d@m/dt

Both V1 and N1*d@m/dt cannot be constants.

Your rate of change of flux "d@m/dt" (or better written as simply "voltage per turn") is not constant, it is the load current times the load resistance.

DH

 

[7anoter4]

As Skogsgurra and dpc already said the actually [closer to actually!] diagram is as follows:

I1+I'2=Io1 where I'2 is I2 referred to primary and Io is a virtual parameter which means Io is I1 when I2=0.
If I1could be =0 [ideally] than U1=E1o [E=FEM]. As I1>0 then E1=U1-I1*(Rp+j*Xp) so E1<E1o.
Since E1=-ke*d (magnetic flux)/dt=ke*omega*Flux*no.turns1 [omega=2*pi*freq.] also the magnetic flux will less than Flux[o].
In order to balance the presence of I2 the transformer will draw more I1 from the Grid and if U1 will be the same:
I1+I'2=Io2 <Io1 .
The equilibrium is unsteady –steady for each value of I1 but for other E1 and Io.
Regards

 

[Skogsgurra]

Thanks 7-4!

This thread was tipping towards superstition. A PLS for you!

Gunnar Englund

http://www.gke.org

--------------------------------------
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

 

[7anoter4]

Many thanks,Skogsgurra!
Best Regards

 

[mackmaster]

Hi every one.
After this long round of discussion my origional question did not receive a clear definite answer:
Does the magnetizing current (Im) change with load current or it stays constant ?
That is my question- I wish to find clear answer.
Thanks

 

[davidbeach]

Yes, the magnetizing current changes with load current because the voltage across the magnetizing branch changes with load current and the magnetizing current is a function of that voltage.

 

[dau]

I agree with davidbeach.The magnetizing current is developed by the net-voltage over the magnetizing inductance.In an idle transformer there is little voltage drop over Lp1 or R1 because the magnetizing current is relatively small.When a load is connected to the secondary winding the secondary current develops a flux counteracting the original core flux.By this the primary induced voltage falls, causing a rise in primary current.This rise generates an equal and opposite flux which reestablishes the original flux.The only difference is that because of the higher primary current some voltage drops over Lp1/R1 and the core flux in a loaded transformer is a little bit lower than in idle state, depending on the amount of these parasitics.