Coupling coefficient of industrial transformers

Discussion in 'Electronic Design' started by orvillefpike, Apr 7, 2007.

1. orvillefpikeGuest

Would anybody know what is the coupling coefficient of step-down,
commercial type, transformers like the ones used in shops, like a
three phase 15 Kva or a 30 Kva?
Thanks

2. Tim WilliamsGuest

Might be 0.99, or better.

Tim

3. Tom BruhnsGuest

So, measure one.

I'd bet it's higher than Tim's guess. I've measured RF transformers
with better coefficients than .99, and with the much higher
permeability of mains-frequency cores, it should be easy to get over .
99. Admittedly, the RF transformers are wound specifically for tight
coupling.

Cheers,
Tom

4. orvillefpikeGuest

How do I measure it?
In the simulation, if the transformer has .990, it's a lot different
than .995, for example.
Thanks

5. BFoelschGuest

Exactly what are you trying to calculate/simulate? Coefficient of
coupling is not a useful concept when discussing power transformers;
it is assumed to approach 1.

6. The PhantomGuest

I can't speak to the size transformer you have cited, but a 3 kW single
phase transformer I have on hand has a measured k of .999883

7. orvillefpikeGuest

Because I am feeding it with a square wave, the shape and the
amplitude of the output is very different whether the coupling
coefficient is .990or .995.
Thanks

8. john jardineGuest

Thanks for that figure!.
It's the first time I've -ever- seen a real "k" quoted for power equipment.
When forced to, I use an arbitrary value of 0.999 as it's physical symptoms
seem to correspond well with reality but have [was!] always been leery of
working with a number so near to 'perfection'.

9. orvillefpikeGuest

Also, the smaller the coupling coefficient, the bigger the leakage
inductance, which causes voltage spikes. Once I know the magnitude of
the voltage, I can design a snubber circuit if there is a need for it.
Thanks

10. The PhantomGuest

There have been threads on this topic fairly recently.

To measure the coupling coefficient (of an iron core transformer) without
making an inductance measurement, do this:

Apply rated voltage (sine wave) at one winding, and measure the open
circuit voltage at the other, getting the ratio V2/V1'. V1' means that
winding 1 was excited.

Now excite winding two and measure the open circuit voltage at the other
winding, getting the ratio V1/V2'.

The coupling coefficient is very nearly SQRT(V2/V1' * V1/V2')

The turns ratio is very nearly SQRT(V2/V1' / V1/V2')

I just did this measurement on a 25 VA filament transformer and got k =
..99767

11. Tom BruhnsGuest

OK, if your simulation shows different results if it's .99 versus if
it's .995, that's exactly a clue how to measure it. Simulate a
circuit you can measure, and trim the simulation until it matches the
measurement.

One way to do this: remember that the coefficient of coupling is the
fraction of magnetic field shared by two coils. If the two coils have
exactly the same number of turns, and you apply 1V to L1, assuming
that you load L2 very lightly, and that the resistance of L1 is low
enough that there is insignificant drop in that resistance due to the
current through L1 when it's excited, the voltage you'll see at L2
will be just the coefficient of coupling. But of course there's no
guarantee the number of turns will be EXACTLY the same. However, if
you measure L2 with L1 excited, and then measure L1 with L2 excited,
you can resolve both the coupling coefficient and the turns ratio.
You can add measurements to resolve other things: you can change
frequency to see effects due to resistance of the windings and
capacitance across the windings.

Another way: you can measure the leakage inductance and figure out
the coupling from that. It likely will be important to also know the
AC resistance of the windings at the frequency of measurement, though.

I don't claim to have given you a recipe here...only hints. Keep your
wits about you and account for parasitic effects like winding
resistance and capacitance, and possibly even nonlinearities in the
core.

Cheers,
Tom

12. orvillefpikeGuest

How did you come up which such a precise number?
Thanks

13. orvillefpikeGuest

Would this method work if I don't feed the transformer at its nominal
voltage, because this transformer was ment to be connected at 600
Volts on its primary side.
Thanks

14. The PhantomGuest

Because the permeability of the silicon steel core varies somewhat with flux
density, k will vary a little with excitation level, but I think you will get
usable results with a reduced excitation level.

15. The PhantomGuest

Don't be fooled by the 3 leading 9's. That number only has 3 significant
digits.

And with an iron core transformer, such a measurement is probably not
repeatable to 3 digits, but that's the result of the measurement at the time.
Temperature and magnetic history of the core can affect the measurement.

16. orvillefpikeGuest

Correct me if I am wrong but I would think that it's even harder to
"measure" the leakage inductance. I don't think that you could
"measure" the leakage inductance without figuring it out from other
measurements in some kind of test under certain condition.
Thanks

17. Tim WilliamsGuest

Not really...short the secondary...

Tim

18. Tom BruhnsGuest

As Tim wrote, short the secondary, measure the primary. That's not
quite all there is to it, since you can't really short the secondary
inductance; you're putting a resistance equal to the winding
resistance across it. But yes, you can do it if you think about it
carefully.

I think the measurement of the secondary voltage with the primary
excited, and vice-versa, is a better way, though there you technically
need to compensate for the drop in the resistance of the excited
winding because of the current through the winding. That is, the
voltage across the pure inductance is less than what's applied to the
winding. I'm not sure you got a proper answer to the question about
how to measure the coupling so precisely. Consider if the transformer
is 1:1; you could connect the windings so that you only have to
measure the difference between them to know how much lower the
secondary is. You do need to account for the case where the
transformer is, say, 1.001:1 turns ratio. Then when you reverse the
windings, be sure that you know which winding has the higher voltage.
You loose the polarity of the difference when you're only measuring an
AC amplitude. If the transformer isn't 1:1, you can still do it if
you use an accurate voltage divider... -- I haven't actually done
this with mains-frequency transformers, so I may be missing some
practical aspects...I normally work with things at 100kHz up into many
MHz, where there are ways to deduce the coupling, also, and I do have
some experience with those.

Cheers,
Tom

19. The PhantomGuest

Go look up the thread with the subject line:

that I started on March 1, 2007. Read my first post and Tony Williams'
response to my questions.

Each winding in the transformer has a leakage inductance associated with
it, and determining the individual leakage inductances from measurements is
difficult with an iron cored mains frequency transformer. Shorting one
winding and making measurements at another winding gives a result that
combines the effect of the separate leakage inductances, and very often
this is all that is needed.

20. The PhantomGuest

Are you referring here to the post where, after I gave the OP a k of
..999883, he said:

"How did you come up which such a precise number?"

I suspected that he saw the number .999883 and thought, six significant
digits. I wanted him to know that that value only has three significant
digits.

If the question is, how did I get even a three significant digit
measurement, that's easy to do with good DVM's using the method I described
to him (and which you are recommending).

On the other hand, trying to get more than about 1 significant digit by
some method involving leakage inductance will be difficult with a mains
frequency iron core transformer.

But if you ask me if I believe the k value of .999883 is *accurate* to 3
significant digits, that's another question. The OP didn't ask that; he
just asked how I got "such a precise number", and I wanted to be sure that
he understood that .999883 is not *precise* to 6 digits.

Trying to get repeatable measurements from a mains frequency iron core
transformer is not easy. I find that if I just try to measure the
self-inductance of a winding at 60 Hz and some excitation level, the
reading will drift for many minutes, sometimes taking 5 minutes or more
before the measurement is stable to 3 digits. Apparently the initial
transient of connecting the meter tweaks the core and it takes a while to
relax, and if the transformer has just been connected to line power, it can
take even longer!

I mentioned that flux density at the excitation level of the measurement,
temperature and magnetic history of the core could affect measured k. How
much would depend on the particular transformer, of course.

The 1943 book I refer to in the earlier thread says it well (about a method
for measuring leakage inductance):

"...this method is inherently inaccurate when used with *measured* values
of the self- and mutual inductances of iron-core transformers. The leakage
inductance of one winding of such a transformer often may be as small as
0.2 per cent of its self-inductance. For example, if the self-inductance
of winding 1 is 10 henries, its leakage inductance may be about 0.02 henry.
If the value of the leakage inductance is to be determined from Eq. 91, to
the nearest millihenry--or within about 5 per cent of its true value--the
value of the self-inductance must measured to the nearest millihenry, or
within 0.01 per cent of its true value, and the mutual inductance must be
measured with the same per cent accuracy. Such precise measurements are
impossible with iron-core transformers."