Power Transformer Question: Why is core magnetic flux maximum at no load?

[killingtime]

[Re-Post as the original disappeared when the forum crashed]

Hi,

Can anyone explain why the magnetic flux in a mains power transformer is highest while in the unloaded state, and why it decreases when a secondary load is applied (and the primary current increases as the load is transferred to it)? There's no problem, just trying to further my understanding of power transformers so I can design one.

I've always understood magnetic fields and flux to vary according to conductor current as many of the equations a afunction of current (discussed further down). Then I stumbled on the article below. It's an interesting read on transformers from the perspective of someone that's done plenty of experimentation. Very little theory on the first page. More of a discussion really, but it all looks correct and confirms many of my actual experiences with Xmrs. Give it a read if you have the time.

https://sound-au.com/xfmr.htm

The piece starts off by asserting that:

"For any power transformer, the maximum flux density is obtained when the transformer is idle."

Well, let's look at a real world example to confirm this. If we take a microwave power transformer, leave the secondary unconnected (unloaded) and drive the primary at mains voltage and frequency (as it was designed), we see a primary current of around 2 to 3 Amps (very poor idle efficiency). That primary current isn't a clean sine wave, and that's because the transformer core (silicon steel) is designed to operate heavily in the saturated region. It's designed this way to save on core steel, copper and weight, a manufacturing win, but at the expense of efficiency. Magnetic saturation in a Xmr or inductor has the same effect as little or no magnetic core at all > inductance drops > impedance drops > current rises. When the core is completely saturated, winding current is only limited by the Ohmic resistance of the copper winding (an electrical short circuit).
Ok so far. Now load the secondary with say 700w. That load is transferred to the primary according to the turns ratio so the primary current goes up as well. If increased Xfmr load also increased core flux then the transformer wouldn't work, as it's already heavily magnetically saturated to start with at idle.

This leads me to believe that flux behaves somewhat independently of load current and is more related to rate of change of primary driving voltage. If correct, then that would explain why Xmr flux goes down at load. The driving voltage hasn't changed (mains) but there are Ohmic voltage losses on the primary winding which go up with the current meaning the Xmr sees a lower primary voltage.

If you need a primer on electromagnetism and equations, Surrey University has a good page with explanations and magnetic duality with the electric world (MMF -> EMF etc).

http://info.ee.surrey.ac.uk/Workshop/advice/coils/terms.html

Scroll down to the part titled "Magnetic Flux" (MF). MF is measured in Webers or Volt Seconds (rate of change of voltage). That's the give away, but it doesn't explain why the flux doesn't increase with current if (using the definitions from the above link):

Φ(flux) = V × T / N  and,
Φ(flux) = I × L / N 
V - voltage, T- time, N - coil turns, L - inductance

----------

Magnetic Field Strength: Whenever current flows it is always accompanied by a magnetic field.  The strength, or intensity, of this field surrounding a straight wire is given by:  H = I / (2 π r)
^^^ So magnetic field strength is a function of conductor current (I).

Magnetic Flux Density:  B=μrμ0H
^^^ So Magnetic Flux (Density) B is related to Field Strength and proportional to it according to the permeability of the material it's moving through (μr).

Given the Xmr core size is fixed, if flux density increases, so should the flux. Add retentivity and saturation to this and we end up the 'S' shaped B-H curve. I get this, I just don't see why core flux doesn't increase with current as the Xmr secondary is loaded and current (I) on both windings goes up.

Assuming both flux equations above the ---- line are correct (a university is unlikely to be wrong), the only way flux can decrease with increasing current in an Xmr is if the inductance (L) goes down with increasing current (I) as the Xmr is loaded (N remains constant). Inductance drops due to increased core saturation as the Xmr is loaded? Could this be the answer?

Thanks.

[Kleinstein]

The equation  flux = I x L / N only applies to a linear normal inductor. With a transformer one would have to use the difference between primary and secondary current (scaled with the turns number).

In a transformer the flux is kind of forced to follow the votlage. The current than reaches the value needed to cause the needed magentization.

[Benta]

For an ideal transformer, core flux is always the same at the same operating voltage/frequency regardless of load current. That's the beautiful thing about transformers.
The flux is maximum at no load is simply because maximum voltage is present at the primary (=minimum resistive voltage drop in the winding).

[schmitt trigger]

Exactly as Benta explained.

No or very small IR primary losses, allow the full applied terminal voltage to develop the flux.

[james_s]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

[langwadt]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

afaiu when you add load the primary and secondary balance out but the "idle" flux is still there

[Vovk_Z]

I don't know why TS need to deep into such a theory whili there are simplified formulas for engineer calculations.

"Φ(flux) = I × L / N" - a transformer is not a simple wire but is a two strong magnetically connected wires. That is why if we'll talk about this formula then a current 'I' has to be magnetising current but not wire current.

[Wolfram]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

The flux (or actually magnetizing force) of the primary and secondary cancel out, but the magnetizing current and flux are separate from this. You could say that the core flux is lower for a given primary current when there is secondary current. Which is true, but not very a very useful starting point for analyzing mains transformers, as they are fed from a fixed voltage, and primary current is a function of the secondary current.

I like to think of voltage fed transformers as follows: A fixed voltage at a fixed frequency is applied across the primary. Flux then comes from the time integral of volts per turn, and dividing this by the core cross section gives the flux density. Through the B-H curve of the transformer iron, you get the required magnetizing force, which gives the magnetizing current. This magnetizing current is phase shifted in relation to the voltage because the flux is the time integral of voltage, it's a purely reactive current. It also often contains harmonics of the applied voltage as most materials have non-linear B-H curves.

Any load current you draw from the secondary creates its own magnetizing force, that is then opposed by an equal magnetizing force from the primary, in an ideal transformer the flux density does not change at all. Real transformers have winding resistance, and the reflected load current in the primary will create a voltage drop across the wire resistance, this subtracts (in quadrature) from the applied voltage, reducing the applied magnetizing voltage and therefore also the flux.

[gcewing]

I just don't see why core flux doesn't increase with current as the Xmr secondary is loaded and current (I) on both windings goes up.

Although both currents go up, they produce flux in opposite directions, so it cancels out.

This raises another interesting question. Increased load means increased power being transferred from the primary to the secondary. But if the flux doesn't go up proportionally, it seems it can't be the flux that's transmitting the power. So what *is* carrying the power? 

[PKTKS]

I just don't see why core flux doesn't increase with current as the Xmr secondary is loaded and current (I) on both windings goes up.

Although both currents go up, they produce flux in opposite directions, so it cancels out.

This raises another interesting question. Increased load means increased power being transferred from the primary to the secondary. But if the flux doesn't go up proportionally, it seems it can't be the flux that's transmitting the power. So what *is* carrying the power? 

MAGNETIC FLUX  IS  ALWAYS CLOSED BY ITSELF

Implies the POWER relations to magnetic flux
Goes via Ampere relation direct application of magnetic OHM law
and equivalent magnetic proportions like reluctance and
isomorphic linearity

attached formal closed loop Ampere integral and OHM
equivalent by using Faraday relation

Power follows same electric principles applied to OHMs relation
but instead using the magnetic properties (reluctance and closed
loop physical constraints to solve ampere integral)
Paul

[PKTKS]

IMHO.. after re-reading that statement:
- it is very counter intuitive that thinking.

not only goes weird but also goes  against the Ampere
fundamental equation in which the induced flux is function of
coil current.

Obviously we should stick with Ampere fundamental relation
which goes to OHM magnetic circuit resolver...

Basic stuff .. those readings are really odd..

Paul

[killingtime]

Thank you for the replies.

After reading around this subject a bit more I found a useful illustration depicting how the flux at load cancels out in the Xmr core because the primary and secondary currents run in opposite directions (credit; Andy aka).



Interestingly, a higher inductance (provided you keep the same number of primary winding turns) doesn't increase core flux either. Inductance is defined as the total flux produced per amp i.e. a bigger inductor produces more flux per amp. However, when AC is used, an inductor that's twice as big produces half the current but, (as per the above definition) it produces twice the flux per amp and because the current has halved, the flux remains the same. Keep taking inductance up and up and flux remains the same.

[harerod]

Erickson's Fundamentals of Power Electronics is a good introduction.

https://link.springer.com/book/10.1007%2Fb100747

Sometime last year this book was -legally, some 'rona action- made freely available online by some institution. Maybe you can still find it. I was a bit annoyed, since I had recently shelled out the full price.

[David Hess]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

I always find transformer operation confusing.  If a load on the secondary cancelled the magnetizing flux, then the primary voltage could be raised before saturation occurs which is not the case.

[langwadt]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

I always find transformer operation confusing.  If a load on the secondary cancelled the magnetizing flux, then the primary voltage could be raised before saturation occurs which is not the case.

wasn't that sorta what the carver amplifiers did with a triac on the primary?

[David Hess]

I thought the back EMF from the secondary "fought" against the flux in the core from the primary, resulting in a lower total flux? Admittedly magnetics is not my specialty.

I always find transformer operation confusing.  If a load on the secondary cancelled the magnetizing flux, then the primary voltage could be raised before saturation occurs which is not the case.

wasn't that sorta what the carver amplifiers did with a triac on the primary?

I am not familiar with that but magnetic amplifiers exist where a control winding on the transformer drives it in and out of saturation producing amplification.

This used to be very common for producing the regulated 5 and 3.3 volt outputs in ATX power supplies with a simple low current error amplifier controlling the saturation of the "swinging inductor".

[bsfeechannel]

It's designed this way to save on core steel, copper and weight, a manufacturing win, but at the expense of efficiency..

It is a manufacturer win, but not exactly because of that. If you look closely at your MOT you will notice a strange feature that happens to be a magnetic shunt.



The equivalent circuit is therefore like that.



Lms is the equivalent magnetic shunt inductance which is in series with the primary of the ideal transformer. Rs represents the losses due to saturation and is in parallel.

If Vmains increases, Rs decreases. So the voltage drop Vms increases. The opposite is true. If Vmains decreases, Rs increases, and Vms decreases. This is totally undesirable in other transformers, but here its purpose is to form a crude but effective voltage regulator. The intention is to protect the single most expensive part of any MO: the magnetron. (It can also help to protect the transformer in case of a short on the secondary).

It's an old technology but it's dirt cheap and works. Saving on iron, copper and weight is unintentional, but desirable. Nowadays we're starting to see kW SMPS in place of the classical MOT.

[bsfeechannel]

Although both currents go up, they produce flux in opposite directions, so it cancels out.

This raises another interesting question. Increased load means increased power being transferred from the primary to the secondary. But if the flux doesn't go up proportionally, it seems it can't be the flux that's transmitting the power. So what *is* carrying the power? 

That's a very good question. The "residual" magnetic field inside the core of a linear transformer is the magnetizing field. You need it to induce the voltage on the secondary. However this field just stores energy, and it must be varying all the time, since the voltage induced on the secondary is proportional to rate of change of this magnetic field. In fact it stores energy coming from the voltage source on the primary for half a cycle, in case of a cyclical waveform, and returns it to the same voltage source on the following half cycle.

So nothing really is carrying the power. Because we are assuming that the power that goes into the primary immediately goes out at the secondary. No energy, except that of the magnetizing field, is stored in the transformer.

That's not the case, for instance, with SMPS flyback transformers, which do store energy from the source in the magnetizing field, but are "tricked" by the switches to deliver the stored energy to the load on the secondary.

[gcewing]

So nothing really is carrying the power. Because we are assuming that the power that goes into the primary immediately goes out at the secondary. No energy, except that of the magnetizing field, is stored in the transformer.

Energy can't just disappear from one place and instantly reappear in a distant place -- it has to pass through the intervening space.

What's more, it can't travel any faster than light, so if there is a nonzero distance between the primary and secondary, and power flowing from one to the other, there must be an amount of energy, proportional to the power, present in the space between at any given moment.

But what form is that energy in? We agree that it's not the magnetic field, so what is it?

[gcewing]

I think I've found the answer. Although the flux from the primary and secondary load currents cancels in the core, this is not true outside the core.

There are H fields in the space around the transformer due to the load currents, and there is also an E field circling the core due to the rate of change of flux in it. The cross product of these is the Poynting vector, which represents flow of energy. It points out into space away from the primary winding, and inwards into the secondary winding.

So the power doesn't go through the core, it goes through the space around the transformer!

There's an interesting paper here analysing the field patterns around a transformer with a long thin core and windings at each end. It turns out to be the same as for a pair of current-carrying wires, but with the E and H fields reversed.

https://www.researchgate.net/publication/43483876_Power_flow_in_transformers_via_the_poynting_vector

[bsfeechannel]

So the power doesn't go through the core, it goes through the space around the transformer!

There's an interesting paper here analysing the field patterns around a transformer with a long thin core and windings at each end. It turns out to be the same as for a pair of current-carrying wires, but with the E and H fields reversed.

https://www.researchgate.net/publication/43483876_Power_flow_in_transformers_via_the_poynting_vector

Brilliant!