Do harmonics cause stray flux losses in transformers?

[tim9000]

I read here:
http://static.schneider-electric.us/docs/Motor Control/AC Drives/8803PD9402.pdf

that harmonics cause stray flux losses in transformers, how is this so?

Thanks

 

[Jeff Rosenbury]

Hi Tim.

The energy is carried not by the flux, but by the rate of flux change. Harmonics are at a higher frequency and thus change faster. Since they don't carry motive power (in general) they cause eddy currents, etc. without contributing. Also, a well designed motor will operate near core saturation. Harmonics can force the core into saturation. There may be other factors I don't know. Also I'm not qualified for a quantitative discussion. Perhaps someone smarter knows those answers?

 

[jim hardy]

Cause losses or exaggerate them ?

Does Steinmetz equation have a term for frequency?

voltage induced in tank walls and support structures is dΦ/dt .

You knew that already.

 

[tim9000]

Sorry I have a lot of question-ie aspects (blanks that need to be filled in)

Hi Tim.

The energy is carried not by the flux, but by the rate of flux change. Harmonics are at a higher frequency and thus change faster. Since they don't carry motive power (in general) they cause eddy currents, etc. without contributing. Also, a well designed motor will operate near core saturation. Harmonics can force the core into saturation. There may be other factors I don't know. Also I'm not qualified for a quantitative discussion. Perhaps someone smarter knows those answers?

Cause losses or exaggerate them ?

Does Steinmetz equation have a term for frequency?

voltage induced in tank walls and support structures is dΦ/dt .

You knew that already.

Hey!
Yeah what befuddled me was they discussed eddy current (iron) and copper losses, then they also said stray flux losses.
I don't really remember (using) Steinmetz much, maybe this: https://upload.wikimedia.org/math/b/b/5/bb544bd4abdacdf8ce85f1cb2e3ea3de.png
But not https://upload.wikimedia.org/math/3/4/1/3413e0bb43566d9a098c4ca64b1e7bd1.png
in fact side question, does anyone know a resource that talks about how to find the hysteresis coefficient?
But it does only work for sineusoids, but independent of frequency.
I wonder how the hysteresis of coefficient is replaced by the derivative of B. Can anyone shed some light on how you would actually evaluate:
https://upload.wikimedia.org/math/d/f/d/dfdee1c046405cacd93bc953de64dde8.png

So to use Steinmetz you have to actually take the measurements, plot B H and get a and b from curve fitting, I assume.

So I'm assuming they exaggerate iron and copper losses, not change the amount of stray flux?
Also what did you mean by tank walls and support structures, I'm not sure what your analogy(?) is getting at.

A layman explanation of Steinmetz would be tres helpful.
So yeah energy is rate of change of flux, but I don't really understand the extent of how the increased rate of change due to harmonics causes loss. If I had a CRO and a TX and a signal generator I could do some investigating, but like if a dirty signal (say single phase) with harmonics is put into a transformer, how much will be trapped and how much will be transmitted through to the secondary? Is there some frequency response thresh-hold the core material will permit?Thanks

 

[jim hardy]

Stray losses i take to mean losses in parts other than the core, from flux that's leaked out of the core or around it ...

A concept we'd overlook just studying traditional textbooks.

Search and read on some buzzwords from links like these until it starts to make sense
http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=5607891&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D5607891

https://bib.irb.hr/datoteka/254695.325_Stray_losses_in_Transformer_Clamping_Plate.pdf

http://www.infolytica.com/en/applications/ex0192/

https://www.jmag-international.com/catalog/146_Transformer_StrayLoss.htmlNow
Steinmetz has the form p = f^α X B^β

since loss is a function frequency , moving part of the flux from f₀ to nth harmonic f_n will give it a bigger share .

That's all i was saying.

 

[jim hardy]

I've had the good fortune to wander around a power plant with a search coil and oscilloscope looking at line frequency fields.

Transformers do a good job of containing the flux
the lower the flux the better they are at containing it

you should try that on your core. You'll find leakage flux far from sinusoidal because it gets squeezed out as you approach the knee of BH curve.

My 894 MVA generator had almost no magnetic field outside its case, walking around it at centerline level with my search coil.
But underneath where the individual phase leads leads come out there's 0.2 volts per turn sinewave induced in a 0,1 square meter coil. Those leads are surrounded by aluminum so flux comes on through.

e= n dΦ/dt = 0.28 cosωt,, so Φ = 0.28/ω sin ωt ? 60 hz here so ω=377
That'd be 0.28/377 = .0.743 , ~around 3/4 a milliweber in 1/10 meter² = 7.5 milliTeslas? ~100X Earth's magnetic field? check my arithmetic...

So to use Steinmetz you have to actually take the measurements, plot B H and get a and b from curve fitting, I assume.

Put yourself in his shoes - it's 1880 and you have only voltmeters and ammeters. Electron is not yet discoverd.

 

[tim9000]

Thanks for the links

Put yourself in his shoes - it's 1880 and you have only voltmeters and ammeters. Electron is not yet discoverd.

Yeah I know how useful volt / ammeters are, there is a lot you can infer. But in practice what is the curve that is being fit?

you should try that on your core. You'll find leakage flux far from sinusoidal because it gets squeezed out as you approach the knee of BH curve.

Unfortunately I'm not able to access a core etc. at the moment. So the amount of leakage flux increases as the core saturates?
What I was saying was: If I'm putting on a sineusoid with some high frequency harmonics into he primary, and I'm looking at the secondary, I'd expect that the transformer wouldn't transmit through the harmonics very well because (gut feeling) the steel won't be able to react fast enough magnetically to cope with the d(fi)/dt to reproduce the harmonics on the secondary side? Something like that, and that extra energy just gets burnt as heat in the core?

So is there a simple explanation about what the maths of that more complicated Steinmetz equation is telling us, or what the hysteresis coefficient is?
I'm having trouble picturing the meaning...

Cheers

 

[jim hardy]

What I was saying was: If I'm putting on a sineusoid with some high frequency harmonics into he primary, and I'm looking at the secondary, I'd expect that the transformer wouldn't transmit through the harmonics very well because (gut feeling) the steel won't be able to react fast enough magnetically to cope with the d(fi)/dt to reproduce the harmonics on the secondary side? Something like that, and that extra energy just gets burnt as heat in the core?

Yes the harmonics aren't transmitted over to secondary so completely as is the fundamental.
Remember secondary mmf cancels primary mmf
looking in through the primary connection though, you can't tell whether that mmf arises from load currents in the secondary winding or from eddy currents in the core, that's why core loss is represented in parallel (in the transformer model)

recall core material has different effective permeabilities at DC and line frequency

laminating the core reduces eddy current effects to a level suitable for the frequency of operation

So is there a simple explanation about what the maths of that more complicated Steinmetz equation is telling us, or what the hysteresis coefficient is?
I'm having trouble picturing the meaning...

I think they're trying to modify Steinmetz's empirical equation for non sinewaves at frequencies he could only dream of.

I've never delved there.

You do remember this old photo
three frequencies, same transformer, with unlaminated steel bar for a core
upper trace in each is primary current, lower is secondary voltage

think of it as a low pass filter
mmf of fundamental is passed
at 3 hz, top trace, higher harmonics of primary mmf are passed on to secondary so we get a reasonable square wave over there
.. which is the proper e=Ldi/dt for triangle wave current
at 10 hz , middle trace, higher harmonics are beyond ability of core to pass on to secondary , they're attenuated, so voltage wave looks less squareat 60 hz bottom trace pretty much only the fundamental is passed

from another measurement, above 400 hz this transformer was oblivious to presence or absence of its core
7th Fourier term of 60 hz won't get through any stronger than air core because its>400
but at 3 hz that'd be the 133rd Fourier term. it's late and i hope this makes sense
sorry I'm not more academic

 

[tim9000]

Yes the harmonics aren't transmitted over to secondary so completely as is the fundamental.
Remember secondary mmf cancels primary mmf
looking in through the primary connection though, you can't tell whether that mmf arises from load currents in the secondary winding or from eddy currents in the core, that's why core loss is represented in parallel (in the transformer model)

recall core material has different effective permeabilities at DC and line frequency

laminating the core reduces eddy current effects to a level suitable for the frequency of operation
I think they're trying to modify Steinmetz's empirical equation for non sinewaves at frequencies he could only dream of.

I've never delved there.

You do remember this old photo
three frequencies, same transformer, with unlaminated steel bar for a core
upper trace in each is primary current, lower is secondary voltagethink of it as a low pass filter
mmf of fundamental is passed
at 3 hz, top trace, higher harmonics of primary mmf are passed on to secondary so we get a reasonable square wave over there
.. which is the proper e=Ldi/dt for triangle wave current
at 10 hz , middle trace, higher harmonics are beyond ability of core to pass on to secondary , they're attenuated, so voltage wave looks less squareat 60 hz bottom trace pretty much only the fundamental is passed

from another measurement, above 400 hz this transformer was oblivious to presence or absence of its core
7th Fourier term of 60 hz won't get through any stronger than air core because its>400
but at 3 hz that'd be the 133rd Fourier term.it's late and i hope this makes sense
sorry I'm not more academic

Jim you always help me keep perspective. Yes a filter is what it is! So I suppose if I was testing a core I could graph the frequency response curve to find the -2 dB point for the type of steel (by varying the frequency of the primary source).

So are you saying that if I have a core with a permeability at an RMS voltage and the same core at the equivalent DC voltage that the effective permeability will be different? I don't have a hard time accepting that, but I can't really justify why?

Ok so back to the topic of the thread. Core loss is a function of frequency, which goes up with harmonics, but because harmonics push a core into saturation, and saturation means that the flux is less contained. So harmonics exaggerate eddy current losses, and copper losses (via skin depth) and they are detremental to efficiency because stray flux doesn't transmit to secondary, but it is disingenuous to say that stray flux contributes to losses?

Thanks again for those pictures! (they've come in very handy)

 

[jim hardy]

effective permeability will be different? I don't have a hard time accepting that, but I can't really justify why?

eddy currents cancel out primary mmf so you get less flux per ampere with AC

harmonics push a core into saturation,

where did that come from ?

stray flux doesn't transmit to secondary,

stray flux is flux outside the core

Core loss is a function of frequency, which goes up with harmonics, but because harmonics push a core into saturation, and saturation means that the flux is less contained.

Go back to one thought per sentence.

 

[jim hardy]

So I suppose if I was testing a core I could graph the frequency response curve to find the -2 dB point for the type of steel (by varying the frequency of the primary source).

It's a bit sloppy and difficult to get a precise measurement. Affected by type of steel, thickness of its laminations, temperature(resistivity), and flux level
read carefully the specsheets for that solenoid stainless alloy we looked at, they brag on its high resistivity

 

[tim9000]

eddy currents cancel out primary mmf so you get less flux per ampere with AC

Yeah I remember how the more current in the secondary, the less net flux in the core, and thus the higher the permeability. But I'm a bit confused because wouldn't any amount of DC integrate over time to saturate? (I'm having a total memory failure)

where did that come from ?

It came from here:

Harmonics can force the core into saturation.

stray flux is flux outside the core

Yeah, what I mean is that since harmonics cause flux to be present outside the core, which doesn't couple to the secondary, it means that harmonic energy doesn't do work in the load. (?)

Go back to one thought per sentence.

Sorry, sorry. Poorly worded, I'm making the assumption that harmonics are causing the core to go into saturation, which in turn is making some flux leak and not couple to the secondary. Which means that harmonics make the transformer less efficient.
But also as a side observation, since harmonics are by nature high frequency multiples, and because eddy losses are proportional to frequency, harmonics also exaggerate losses.
So two detriments due to harmonics.

It's a bit sloppy and difficult to get a precise measurement. Affected by type of steel, thickness of its laminations, temperature(resistivity), and flux level
read carefully the specsheets for that solenoid stainless alloy we looked at, they brag on its high resistivity

H'mm, ok, well so if I set up a signal generator and fed it into a transformer, as I increased the frequency I could get a nice frequency response curve for that specific core (with it's specific lamination size at that B) but it may be only of use for operation at that temperature? Hence it isn't much use having a response graph for the steel because there are other variables unaccounted for.

 

[jim hardy]

But I'm a bit confused because wouldn't any amount of DC integrate over time to saturate? (I'm having a total memory failure)

two diferent tests
1 amp AC gives A units of flux
1 amp DC gives D units of flux
A ≠ D

Yeah, what I mean is that since harmonics cause flux to be present outside the core,

you have a misconception.

MMF pushes flux outside of the core.
From that link https://www.jmag-international.com/catalog/146_Transformer_StrayLoss.html

this would be true at DC.
But DC does not induce current (steady state current anyway )in the tank so there's no heat.

which doesn't couple to the secondary, it means that harmonic energy doesn't do work in the load. (?)

Harmonics that make it through the core of course couple to secondary where they contribute to RMS voltage and current hence power

I'm making the assumption that harmonics are causing the core to go into saturation,

i disagree

since harmonics are by nature high frequency multiples, and because eddy losses are proportional to frequency, harmonics also exaggerate losses.

i agree

H'mm, ok, well so if I set up a signal generator and fed it into a transformer, as I increased the frequency I could get a nice frequency response curve for that specific core (with it's specific lamination size at that B) but it may be only of use for operation at that temperature?

Temperature effect is not huge but easily measurable with ordinary DMM's . If you need an approximate curve ignore temperature. If you need a precise one, control temperature.

Hence it isn't much use having a response graph for the steel because there are other variables unaccounted for.

Agreed
You should measure in a configuration similar to how it'll be used, A solid cube of steel won't behave same as the transformer core tape made by hotrolling that cube into a thin sheet and cutting that into narrow strips.
.

 

[tim9000]

I'm glad we're mostly on the same page.

two diferent tests
1 amp AC gives A units of flux
1 amp DC gives D units of flux
A ≠ D

Intriguing, so are you saying AC gives magnetic flux in units of amps, and DC gives electric flux?

I understand that DC doesn't cause eddy currents, but (as I say, brain failure) since flux = ∫ Voltage dt if you have a relatively small DC on the AC signal, isn't that going to saturate the core by steady-state?

i disagree

I'll give an example to highlight my confusion, say you have an inductor and you're putting an MMF over it, then you have the same inductor and you put the same MMF over it, but it is partly saturated because this time there are harmonics in your supply; is there more leakage flux now?

Thank you kindly!

 

[Jeff Rosenbury]

Jim:

While small amounts of harmonics (compared to the main power) won't saturate the core, why wouldn't large amounts of harmonics (particularly the odd harmonics)? For at least part of the cycle they would be adding wouldn't they?

Of course this assumes the core is operating near saturation to start with.

 

[jim hardy]

Intriguing, so are you saying AC gives magnetic flux in units of amps, and DC gives electric flux?

? apply amp-turns and you get webers .

I understand that DC doesn't cause eddy currents, but (as I say, brain failure) since flux = ∫ Voltage dt if you have a relatively small DC on the AC signal, isn't that going to saturate the core by steady-state?

Listen to your words.
You've changed the experiment by applying DC volts instead of DC amps .
Of course DC voltage applied to inductance gives constant di/dt and current will approach infinity. Flux will follow current until saturation .

I'll give an example to highlight my confusion, say you have an inductor and you're putting an MMF over it, then you have the same inductor and you put the same MMF over it, but it is partly saturated because this time there are harmonics in your supply; is there more leakage flux now?

1. Explain that causation?

2. Same MMF ? Think about your statement. Leakage flux is through air , and flux through air is MMF/reluctance of air path.
Your statement is contradictory - if this time there are harmonics in supply then mmf is not the same.

 

[tim9000]

? apply amp-turns and you get webers .

Yeah I know that, but what's D than if not related to electric flux?

Listen to your words.
You've changed the experiment by applying DC volts instead of DC amps .
Of course DC voltage applied to inductance gives constant di/dt and current will approach infinity. Flux will follow current until saturation .

Oh...oh. You're right. Ok, well what's the difference magnetically with dc current than AC current? Also, how would you get DC current without DC 'volts'?

1. Explain that causation?

2. Same MMF ? Think about your statement. Leakage flux is through air , and flux through air is MMF/reluctance of air path.
Your statement is contradictory - if this time there are harmonics in supply then mmf is not the same.

Good point old boy!
But the penny hasn't dropped quite yet. So what I was thinking was that say I'd put the same current through it (same RMS or something), but this time it a harmonic component, isn't that the same amp-turns but the permeability of the core has changed (owing to the possible saturation induced by a dc component in the harmonics, *premise still up for discussion*). So isn't it just the reluctance of the return path that's changed, and the MMF is unaffected because the current is still the same? (or does the harmonics mean the current is changed?)

Thanks

 

[jim hardy]

Yeah I know that, but what's D than if not related to electric flux?

Was D a poor name? Shame onme - Laviosier cautioned to choose names with care. Mnemonic is the term for good naming..
I intended in my example
for A to be amplitude of flux you'd get for an amp of AC current, Asin(wt) webers
and D to be magnitude of flux you'd get for an amp of DC current , D webers
both by u_effectiveu₀NIA/path-length
u_effective being a little different for AC and DC cases because of eddy currents, hysteresis, whatever other magnetic phenomena go on in iron. Hence A≠D .

Ok, well what's the difference magnetically with dc current than AC current?

eddy currents, hysteresis, whatever other magnetic phenomena go on in iron.

Also, how would you get DC current without DC 'volts'?

Ohm's law on inductance. DC current is when di/dt = 0. E = L X di/dt = 0

So what I was thinking was that say I'd put the same current through it (same RMS or something), but this time it a harmonic component, isn't that the same amp-turns but the permeability of the core has changed (owing to the possible saturation induced by a dc component in the harmonics, *premise still up for discussion*). So isn't it just the reluctance of the return path that's changed, and the MMF is unaffected because the current is still the same? (or does the harmonics mean the current is changed?)

http://www.dspguide.com/ch13/4.htm

DC term is a₀
and it's just the average value

RMS is per planet math (i expected a √ - i love math but just kicks sand in my face)

If you reduce the higher ordered a's and raise a₀ to restore RMS
is current changed? Not by an RMS meter i suppose . By a FFT meter or oscilloscope most certainly.

I might see where you're coming from though
i posited current as controlled variable with fixed amplitude
if the core saturates its permeability goes down so AC flux decreases
but mmf across both core and leakage path through air are unchanged
and flux through air is mmf/u₀ , both unchanged

you seem headed back to voltage as controlled variable with fixed amplitude
if the core saturates its permeability goes down so AC flux decreases, current immediately goes up to restore counter emf
raising mmf across both core and leakage path through air.

 

[tim9000]

Was D a poor name? Shame onme - Laviosier cautioned to choose names with care. Mnemonic is the term for good naming..
I intended in my example
for A to be amplitude of flux you'd get for an amp of AC current, Asin(wt) webers
and D to be magnitude of flux you'd get for an amp of DC current , D webers
both by ueffectiveu0NIA/path-length
ueffective being a little different for AC and DC cases because of eddy currents, hysteresis, whatever other magnetic phenomena go on in iron. Hence A≠D .

Damn, I thought I was going to learn something profound I'd never realized.

eddy currents, hysteresis, whatever other magnetic phenomena go on in iron.
...
Ohm's law on inductance. DC current is when di/dt = 0. E = L X di/dt = 0

Ok, what you were saying was a lot more simple than I expected. So this DC current is in the coil and no voltages are produced in any surrounding conductors. Is this all your way of saying that harmonics (with a DC component) don't push the permeability further into saturation? What I'm confused about is if you have a supply voltage, which contains some harmonics including a DC component, is there no voltage associated with the DC part?

I understand that DC doesn't cause eddy currents, but (as I say, brain failure) since flux = ∫ Voltage_dc dt if you have a relatively small DC on the AC signal, isn't that going to saturate the core by steady-state?

That would integrate up to saturate over time.

I like where you're going with this, very methodical;

If you reduce the higher ordered a's and raise a0 to restore RMS
is current changed? Not by an RMS meter i suppose . By a FFT meter or oscilloscope most certainly.

So are we talking about if we maintain the Same RMS but with different levels of higher harmonics?
Because that is what I'm wondering what will happen to the permeability and if this will integrate over time to saturate, or if not, even still, what effects this will have. (I was sort of thinking of a₀ as a biproduct of higher harmonics, but I suppose you actually need to introduce a DC offset)

I was trying to think of it as the RMS current was the control variable, but I didn't consider that, that may be closer to having voltage as the control variable:

you seem headed back to voltage as controlled variable with fixed amplitude
if the core saturates its permeability goes down so AC flux decreases, current immediately goes up to restore counter emf
raising mmf across both core and leakage path through air.

I think I need to get my head around the previous Fourier Vs. RMS paragraph affect on permeability...

I might see where you're coming from though
i posited current as controlled variable with fixed amplitude
if the core saturates its permeability goes down so AC flux decreases
but mmf across both core and leakage path through air are unchanged
and flux through air is mmf/u0 , both unchanged

Oh, yeah so to have constant current amplitude and you started making the frequency longer, that would necessitate mmf staying the same, so even though the flux through the core has changed, so the leakage flux will stay the same.

 

[jim hardy]

What I'm confused about is if you have a supply voltage, which contains some harmonics including a DC component, is there no voltage associated with the DC part?

How can there be ? Derivative of DC component is zero. Well , that is after initial transients settle , in which case i guess you'd call it a step? 1/s ?

So are we talking about if we maintain the Same RMS but with different levels of higher harmonics?

That's what i understood

Because that is what I'm wondering what will happen to the permeability and if this will integrate over time to saturate,

For current i don't see how it would guarantee or assure saturation, though one might get unlucky.. The retentivity and time characteristic will of course walk you some distance up the curve for whatever iron it is. Look up "degaussing current transformers" .

(I was sort of thinking of a0 as a biproduct of higher harmonics, but I suppose you actually need to introduce a DC offset)

i think a₀ is just average which for any integral number of cycles is zero

so it must be the DC offset

I was trying to think of it as the RMS current was the control variable, but I didn't consider that, that may be closer to having voltage as the control variable:

there's times it's convenient to think current because there's no derivative between it and mmf
when you can flip back and forth and the derivative-integral follows in your mental model you're getting to Lord Kelvin's "primitive understanding" . When we can put numbers on it we are getting to his definition of real understanding. Sadly I'm so awkward with math I'm stuck in the remedial classes... so i plod along.

Oh, yeah so to have constant current amplitude and you started making the frequency longer, that would necessitate mmf staying the same, so even though the flux through the core has changed, so the leakage flux will stay the same.

yes . Whatever happened to cause saturation in the core we did not say, My point was mmf is equivalent to current , after all its unit IS the amp-turn.
Frequency was a non-sequitur unless i missed a step .

 

[tim9000]

How can there be ? Derivative of DC component is zero. Well , that is after initial transients settle , in which case i guess you'd call it a step? 1/s ?

I think I've let a lack of specificity creep in here, are you talking about voltage in the surrounding case/tank, or in the coil itself?
Because I'm saying in the source / supply, you've got some dc current through the TX coil, surely there is a voltage associated with that DC current, otherwise how would it get there?
Anyway, what I'm taking away from what you just said is that Φ = ∫ V dt, is only for AC Φ, and and V_AC,
not Φ_DC, so dΦ/dt = 0 means no eddy currents are induced in the core, which means that it won't saturate over time. So I suppose this means that if there is a DC component in the TX supply it will only SHIFT the hysteresis curve up, and not saturate it over time.
So high frequency harmonics with a DC component or otherwise won't saturate the core, no matter how bad they are. In fact wouldn't a dirty harmonic supply into a core actually mean there is less V.s and thus possibly raise the permeability?

Yeah I remember talking about the phase of the MMF with current with you previously, the question about whether a type of DC voltage exists or not aside, I suppose the current signal would be the voltage signal but phase shifted and passed through a low pass filter?

Thanks