Relative size and Arc Flash Hazards of 50 Hz versus 60 Hz transformers at same KVA

[GoldDigger]

This is a continuation of a discussion started in another thread. Some starter quotes are provided here:

The article did not mention about installation practices.

With the same input and output voltages and same KVA, a 50Hz transformer is smaller than a 60Hz transformer and so the arc hazard is lesser.

For 60Hz, the current taken by the transformer is less.
For 50Hz, it is more requiring more iron as you stated.
But by using thinner coil wire, the current can be kept same as in 60Hz without increasing iron size. So the coil size would be smaller and so the overall size of 50Hz transformer is smaller and so the arc hazard is lesser.

Higher the frequency, lower the AC current in an inductive circuit. So to bring the higher value current at a lower frequency to the same value at the higher frequency for a given voltage and given output KVA at the higher frequency, the resistance of the inductive circuit need to be increased.

As in 60 Hz
1) Core size same.
2)Current same
3)No of turns same
4)KVA same for 50Hz transformer. Only cross sectional area of coil wire reduced. So core flux density does not change. Due to reduction in coil size, the overall size of 50 Hz transformer is smaller.

Reduction in size of 50Hz transformer due to decrease in coil size.
Decrease in coil sizer due to thinner coil wire.
Increase in resistance of coil wire due to thinner coil wire.
Lesser arc hazard due to increase in resistance of coil wire of 50 Hz transformer.

I think that you have two fundamental problems here:

1. For a higher frequency, the current in a given inductor for a given voltage will be lower. Therefore the magnetizing current in the 50 Hz transformer will be higher for the same voltage. That requires more current, not less, and more energy loss. Or else you increase the inductance, not the resistance.
2. The magnetizing current does not really matter. We are looking at the transferred power between primary and secondary, not the magnetizing current.
And there is no avoiding the fact that the power is V x I, which has no frequency dependence at all. The only thing that will change with frequency, all other things being equal, will be the power factor of the transformer input for a given power level.

For support, I refer to the following reference on the web sites of a transformer manufacturer, who should be expected to get this right:

http://www.tortran.com/transformer_design_guide.html

Step 2. Choose your Operating Frequency

The standard line operating frequency in North America is 60 Hz. The rest of the world operates at 50 Hz.

A transformer designed for 50 Hz will also work at 60 Hz but a transformer designed for 60 Hz will not work at 50 Hz.

A 50 Hz transformer is 20% larger than a 60 Hz design so allow space for a 50 Hz design if you plan to export your product at a future date.

400 Hz is used for weight sensitive airborne and seaborne applications as it allows the transformer to be about 1/3 smaller.

And, a fairly complete logical analysis which argues that the 60Hz transformer will be able to handle even higher power ratings with a proportionally smaller core size than a 60/50 Hz dual rated transformer, since the smaller core will allow shorter coil turns and fewer of them:
http://music-electronics-forum.com/t16277/#post132369

The facts is that power transformers must make a big enough primary inductance to limit the magnetizing current below some safe level. They must also provide a sufficient number of turns and core cross sectional area to limit the magnetic field intensity to below the saturation value. These two conditions are in fact two different ways of saying the same thing.

The limitation on the amount of power a transformer can provide is the internal temperature rise versus the temperatures the insulation system can withstand. In general, higher temperature insulation classes are more expensive, so the design optimization process tends to run the transformer right up against the edge of temperature rise for the given insulation class.

Given that, one has two choices when designing a power transformer to a particular insulation temperature rise/class. (1) Use enough core stack to work OK at 50Hz and make one model. If it works OK with low enough temp rise at 50Hz, it will have extra margin at 60Hz and one model fits all, except that you pay about 20% more for the iron and 10% more for the copper on every 60Hz transformer than you need to. (2) you can design one 50Hz device about 20/10% bigger/more expensive for the 50Hz market and another for the 60Hz market and get the lowest cost for each customized build. These are the competent engineering approaches. There are choices (3) through (N) which get cheap on some part of this. To the degree that the transformer runs hotter, its life will be shorter.

If a transformer runs OK at 50Hz, it will run OK at 60Hz at the same volts per turn, and will have a bigger power capability by the amount that the lower magnetizing current decreases heating, but will still not be as good as a 60Hz transformer specifically designed for that because the longer length per turn will cause additional resistive losses in the windings unless the core stack is also made bigger still to get fewer turns and get the copper losses lower.

A competent transformer designer can take this all into account depending on what he's told to design. A beginner will miss some things.

In general, for a given insulation class, the lower the lowest frequency on the primary, the bigger the transformer.

Your turn.

 

[Besoeker]

There is a good reason why aircraft use 400Hz.
Perhaps the good Maharajah would like to consider that.
And perhaps contemplate the raison d'etre for switch-mode power supplies. Why complicate the issue by using electronics to get high frequency upstream of the transformer? Since their use is ubiquitous, there must be a sound basis for this technique to be employed.

 

[Sahib]

Thanks Golddigger for all your valuable information.

The design stated in all your information is based on keeping the efficiency same for 50Hz and 60Hz transformers. What about the efficiency of 50Hz transformer to slide down to keep the size same as 60Hz by increasing coil wire resistance? This may also reduce the arc flash hazard associated with 50Hz transformer.

 

[GoldDigger]

Thanks Golddigger for all your valuable information.

The design stated in all your information is based on keeping the efficiency same for 50Hz and 60Hz transformers. What about the efficiency of 50Hz transformer to slide down to keep the size same as 60Hz by increasing coil wire resistance? This may also reduce the arc flash hazard associated with 50Hz transformer.

I considered the hypothetical case of two transformers with identical input and output voltages and identical power ratings to also assume identical or comparable efficiencies.
For you to assert that all 50Hz transformers are smaller (which you will find that you did if you look carefully) because everyone designs them for lower efficiency just does not make any sense.

Since the core size must be 20% larger, it will take a very large decrease in the wire size to come close to making up for that, and the resulting transformer's power handling ability (kVA rating) would end up being decreased because of the greater internal losses (both with and without load.)

 

[Sahib]

I considered the hypothetical case of two transformers with identical input and output voltages and identical power ratings to also assume identical or comparable efficiencies.

In which case the 50Hz transformer is larger in size.

For you to assert that all 50Hz transformers are smaller (which you will find that you did if you look carefully) because everyone designs them for lower efficiency just does not make any sense.

Our discussion here is to find out whether a 50 Hz transformer of smaller overall size is conceptually (theoretically) possible.

Since the core size must be 20% larger, it will take a very large decrease in the wire size to come close to making up for that, and the resulting transformer's power handling ability (kVA rating) would end up being decreased because of the greater internal losses (both with and without load.)

Why the core size must be 20% larger?
Because the frequency is lowered from 60hz to 50hz, the impedance of the transformer winding is reduced and so current is increased and with increase in current the core is driven into saturation and so to prevent it, the core size must be increased. But if the current of 50hz transformer is kept same as that of 60hz transformer by using thinner coil wire, there is no need to increase the core size. This will result only in loss of
efficiency ( slight, I would like to think ) but with smaller overall size and reduced arc hazard.

 

[Besoeker]

In which case the 50Hz transformer is larger in size.

Which directly contradicts your assertion:

With the same input and output voltages and same KVA, a 50Hz transformer is smaller than a 60Hz transformer

But at least you have had the good grace to nearly admit that your original assertion was not correct.

Our discussion here is to find out whether a 50 Hz transformer of smaller overall size is conceptually (theoretically) possible.[/qyote]
It is. And not just theoretical.
You could use better steel, run at a higher flux density, use higher temperature insulation, say class F instead of C for example, But if you applied thosw same measures to a 60Hz transformer it would still be smaller that the 50Hz unit of the same kVA and voltages.

Why the core size must be 20% larger?

To keep the flux density the same. Flux is dependent on the volts times time. At 50Hz the volt second area for any half cycle is 20% greater than at 60Hz. So, for the same flux density, you need 20% more core.

Because the frequency is lowered from 60hz to 50hz, the impedance of the transformer winding is reduced

Only if you applied it to the self same transformer. You might apply 60Hz to a 50Hz transformer - but not vice versa.

and so current is increased and with increase in current the core is driven into saturation and so to prevent it, the core size must be increased.

See previous comment. Thinner wire will not reduce the flux density. All that would achieve is a reduction in kVA rating. Don't muddle magnetising current with load current. Magnetising current is usually very low compared to load current. Thinner wire will have little effect on magnetising current and core flux density. But will reduce load capacity hence my comment about kVA rating.

there is no need to increase the core size.

There is. Lower frequency means bigger for the same performance.

Let me refer you back to a couple of my previous points.
Aircraft use 400Hz because electrical is smaller, therefore lighter.
Switch mode power supplies first convert mains frequency to some tens of kHz. This makes the transformer very small - and cheap.

 

[Sahib]

Which directly contradicts your assertion:

Yes. You are correct in the case that the transformers are supposed to have same efficiency.

You could use better steel, run at a higher flux density, use higher temperature insulation, say class F instead of C for example, But if you applied thosw same measures to a 60Hz transformer it would still be smaller that the 50Hz unit of the same kVA and voltages.

Agreed. It is to be seen what happens when the efficiency of 50hz transformer is allowed to slide by using thinner coil wire.

Flux is dependent on the volts times time. At 50Hz the volt second area for any half cycle is 20% greater than at 60Hz. So, for the same flux density, you need 20% more core.

The immediate factor causing flux is current. So if current can be limited by increasing the resistance of the coil wire, the core flux density may be kept at the same level.

Thinner wire will not reduce the flux density.

No it will, because the core flux density depends on the ampere-turns of the winding and so on the current. So the core flux density can be changed by changing the coil current.

 

[GoldDigger]

Yes. You are correct in the case that the transformers are supposed to have same efficiency.

Agreed. It is to be seen what happens when the efficiency of 50hz transformer is allowed to slide by using thinner coil wire.

The immediate factor causing flux is current. So if current can be limited by increasing the resistance of the coil wire, the core flux density may be kept at the same level.

No it will, because the core flux density depends on the ampere-turns of the winding and so on the current. So the core flux density can be changed by changing the coil current.

You are still missing the fact that the magnetizing current (idle current) in the transformer is controlled by the inductance, not by the wire resistance, while the working part of the current is fixed by the combination of voltage and power you need to transfer.
Also the magnetizing current depends on the inductance. The current at the peak of a cycle must be such that the core does not saturate, regardless of how many turns you use.
For the same number of turns, the di/dt times the inductance must equal the line voltage.
But at 50Hz the di/dt for a given current will be lower so the inductance must be higher. Now to get that higher inductance with the same peaks magnetic flux will require a larger core or a better magnetic material, as Besoeker stated.

 

[Sahib]

Golddigger:

The winding coil of a transformer has inductance.

The winding plus core combination has inductance.

The latter inductance is much larger than the former (below saturation).

A change in the resistance of the winding coli of the transformer and so a change in the coil current can change the inductance of the winding plus core combination and so the flux density in the core.

Please recall how magnetization curve of a ferromagnetic sample is drawn in this respect.

 

[Besoeker]

Yes. You are correct in the case that the transformers are supposed to have same efficiency.

Agreed. It is to be seen what happens when the efficiency of 50hz transformer is allowed to slide by using thinner coil wire.

It will get hotter for the same rating. Same goes for a 60Hz transformer.

The immediate factor causing flux is current. So if current can be limited by increasing the resistance of the coil wire, the core flux density may be kept at the same level.

The magnetising current for a transformer is a very small fraction compared to load current. Yes, you could decrease that by increasing the primary resistance. But then you would reduce the capability of that winding being able to handle load current. The transformer would no longer have the same kVA rating.

 

[mivey]

Sahib,

May I suggest you read the transformer chapters from:
"Electric Machinery" by Fitzgerald/Kingsley
"Electric Machines and Power Systems" by Del Toro

another text would be:
"Transformer Principles and Practice" by Gibbs

 

[Besoeker]

Sahib,

May I suggest you read the transformer chapters from:
"Electric Machinery" by Fitzgerald/Kingsley
"Electric Machines and Power Systems" by Del Toro

another text would be:
"Transformer Principles and Practice" by Gibbs

The "J&P Transformer Book" is also quite good.

 

[Sahib]

The magnetising current for a transformer is a very small fraction compared to load current. Yes, you could decrease that by increasing the primary resistance. But then you would reduce the capability of that winding being able to handle load current. The transformer would no longer have the same kVA rating.

It will be more convincing if you support your statements such as ''you would reduce the capability of that winding being able to handle load current'', ''The transformer would no longer have the same kVA rating.'' etc.,with calculations, for example from your favorite 'J&P Transformer Book', because the said windings, both primary and secondary, already have resistance in addition to inductance and we have to see to what extent further resistance may be added to the 60hz transformer to make it operate at 50hz without affecting its KVA capacity.

 

[Besoeker]

said windings, both primary and secondary, already have resistance in addition to inductance and we have to see to what extent further resistance may be added to the 60hz transformer to make it operate at 50hz without affecting its KVA capacity. [/COLOR]

You can't get the same capacity if you add resistance. Think about it. You would have to operate at 50/60 of the 60Hz voltage to prevent saturation.

 

[Sahib]

Sahib,

May I suggest you read the transformer chapters from:
"Electric Machinery" by Fitzgerald/Kingsley
"Electric Machines and Power Systems" by Del Toro

another text would be:
"Transformer Principles and Practice" by Gibbs

Thanks, mivey for your suggestion.
I have "Electric Machines and Power Systems" by Del Toro.
Take a look at the transfomer equivalent diagram in that book.
It has also resistance and leakage reactance values for the primary.
If we use 60hz transformer on 50 hz, the voltage drop across the leakage reactance is less. If the resistance value is increased so that the total voltage drop is the same as in 60hz, the voltage applied to the ideal transformer ( after primary resistance and leakage reactance) will be same as in 60hz and so the induced voltages both in the primary and secondary windings will be same as in 60hz and so the KVA capacity.

 

[Besoeker]

If we use 60hz transformer on 50 hz, the voltage drop across the leakage reactance is less. If the resistance value is increased so that the total voltage drop is the same as in 60hz, the voltage applied to the ideal transformer ( after primary resistance and leakage reactance) will be same as in 60hz and so the induced voltages both in the primary and secondary windings will be same as in 60hz and so the KVA capacity.

As I pointed out above, you simply can't do that,
You seem to be having difficulty grasping the basics.

I'll try again:

This is the Steinmetz equivalent circuit.



The applied voltage is on the left.
The values of X₁ and R₁ are small.
So the voltage arriving across X_m (the bit that has I_m in it) is close to the applied voltage.
If it the values weren't small, the voltage across X_m would vary with load resulting in poor voltage regulation on the output. Don't confuse voltage regulation with percentage impedance.

Regulation from no load to full load depends on a number of factors not least of which is load power factor. I've just done a calculation on a transformer we used and the regulation (change in output voltage) from no load to full load at 0.95pf is a little over 2.5%. On a 480V input transformer, we can thus see that most of that 480V will appear across X_m regardless of loading.

Flux.
I got a bit lazy with this. I have already mentioned that flux is proportional to the voltage time area under the curve. Wikipedia puts it thus:
?The time-derivative term in Faraday's Law shows that the flux in the core is the integral with respect to time of the applied voltage.?

For 50Hz, the time of the applied voltage is greater than 60Hz for the same voltage. If you simply applied 50Hz 480V to the 60Hz 480V transformer primary the flux would probably reach saturation levels which is unacceptable. To get the same flux as at 60Hz, the design flux of the transformer you would need to reduce the voltage by 20% to 400V to get the same volt time integral.
So now we have a transformer that will give a lower voltage output but no more current. So that alone would reduce the kVA available by 20% at a stroke.

But that?s not all. To get down to 400V by increasing the value of R₁ isn?t viable.
Suppose, for example, the magnetizing current is about 5% of rated current. The required resistance would have to drop 80V at that current to avoid overvoltage at the transformer terminals. Add any load current and the 80V increases. The voltage across X_m decreases, the output, already below the 60Hz value collapses even further ??

Can you see now why your idea of increased resistance can?t work?

 

[Sahib]

The values of X₁ and R₁ are small.
So the voltage arriving across X_m (the bit that has I_m in it) is close to the applied voltage.
If it the values weren't small, the voltage across X_m would vary with load resulting in poor voltage regulation on the output.

You should agree that there voltage drops across X₁ and R_1.
Let the sum (vectorial) of these voltage drops be Vd (at full load)
Let the line voltage be V.
Obviously, the net voltage applied to Xm or to ideal transformer (having no resistance or leakage reactance) is (V-Vd).
Suppose now that x1 decreases.
Increase the R1 in such a way that the sum of the voltage drops across the two remains the same and equal to Vd (at full load)
Then the net voltage applied to Xm or to ideal transformer (having no resistance or leakage reactance) is again (V-Vd) i.e remains the same as before.
Agree this far?

 

[Besoeker]

You should agree that there voltage drops across X₁ and R_1.
Let the sum (vectorial) of these voltage drops be Vd (at full load)
Let the line voltage be V.
Obviously, the net voltage applied to Xm or to ideal transformer (having no resistance or leakage reactance) is (V-Vd).

For the ideal transformer with no resistance or leakage reactance, there is no Vd as you have defined it.

Suppose now that x1 decreases.

Owing to a reduction in applied frequency one might assume?

Increase the R1 in such a way that the sum of the voltage drops across the two remains the same and equal to Vd (at full load)

Therein lies a problem. And the problem with your extra resistance ploy.
The difference between no load and full load is an order of magnitude then some. The voltage drop across R1 likewise. A consequence is that the voltage across Xm will vary more.

Then the net voltage applied to Xm or to ideal transformer (having no resistance or leakage reactance) is again (V-Vd) i.e remains the same as before.
Agree this far?

For the ideal transformer with no resistance or leakage reactance, there is no Vd as you have defined it.

 

[Sahib]

For the ideal transformer with no resistance or leakage reactance, there is no Vd as you have defined it.

A real transformer may be represented as a combination of an ideal transformer and the resistance and leakage reactance values of the real transformer. The voltage drops appear across the resistance and leakage reactance. Please see the J & P to refresh your memory.

Owing to a reduction in applied frequency one might assume?

Exactly

Therein lies a problem. And the problem with your extra resistance ploy.
The difference between no load and full load is an order of magnitude then some. The voltage drop across R1 likewise. A consequence is that the voltage across Xm will vary more.

No,because the resistance value is adjusted for full load to give the same total voltage drop (across R1 and X1) as in 60hz transformer at full load.

 

[GoldDigger]

No,because the resistance value is adjusted for full load to give the same total voltage drop (across R1 and X1) as in 60hz transformer at full load.

It cannot (as in can not) both drop the voltage at full load by the same amount and drop the voltage at idle magnetization current by the amount required to avoid saturation. The math for that is two incompatible equations in one unknown and has no solution.