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

[Sahib]

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.

Consider the case at full load.
Neglect the case at no load for the time being.
For B is particular about maintaining the same KVA capacity for 60hz and 50hz transformers.

 

[Sahib]

Golddigger:
You know that at no load any transformer current is rich in harmonics, due to core saturation. So in our case too, it may not do any harm at no load. Anyway, we may explore it later after B's conversion.

 

[GoldDigger]

Consider the case at full load.
Neglect the case at no load for the time being.
For B is particular about maintaining the same KVA capacity for 60hz and 50hz transformers.

If you neglect the case at no load, a core of the 60Hz size will saturate at 50Hz, guaranteed. So you cannot ignore it for very long.

You are relying on tweaking one value (primary winding wire resistance) at no load to fix saturation and then tweaking the same value at full load to maintain KVA capacity. You cannot have it both ways.

 

[Sahib]

GoldDigger:
Please see my last reply above.

 

[GoldDigger]

Golddigger:
You know that at no load any transformer current is rich in harmonics, due to core saturation. So in our case too, it may not do any harm at no load. Anyway, we may explore it later after B's conversion.

It is not rich in harmonics because of core saturation. It may be rich in harmonics because of core hysteresis, which is a different problem entirely. You do not want to saturate. (Because that will result in very high primary currents and will also interfere with transfer of power from the primary to secondary winding.)

 

[Sahib]

It is not rich in harmonics because of core saturation. It may be rich in harmonics because of core hysteresis, which is a different problem entirely. You do not want to saturate. (Because that will result in very high primary currents and will also interfere with transfer of power from the primary to secondary winding.)

So the no load case is out.
Only the full load case remains.............

 

[GoldDigger]

So the no load case is out.
Only the full load case remains.............

No, it is not out.
You still need to provide for a way to prevent saturation at no load using the same size core for a 50Hz transformer as you would for a 60Hz transformer. Please address that.
Unless you are now trying to say that a 50Hz transformer can be larger at no load but still be smaller at full load.

 

[Sahib]

No, it is not out.
You still need to provide for a way to prevent saturation at no load using the same size core for a 50Hz transformer as you would for a 60Hz transformer. Please address that.

I do not believe that 50hz operation of a 60hz transformer at no load will damage the transformer in the short run.

Unless you are now trying to say that a 50Hz transformer can be larger at no load but still be smaller at full load.

Great joke.:thumbsup:

 

[GoldDigger]

I do not believe that 50hz operation of a 60hz transformer at no load will damage the transformer in the short run.

Great joke.:thumbsup:

My assertion is that if the core saturates at no load it must also necessarily saturate at full load, interfering with proper energy transfer from primary to secondary.

 

[Besoeker]

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.

Please see post the Steinmetz equivalent circuit I presented for you showing exactly that in post #16 to refresh your memory.

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.

And end up with the same voltage across Xm?
Might I remind you of the ?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.? also in post#16?
The integral with respect to time of the applied voltage is greater at 50Hz than 60Hz. The flux is greater. To the point of probable saturation.
That's why the transformer designed for 50Hz is larger than that designed for 60Hz. A point you already accepted in post#7.

Why can't you now accept that, for the same reasons, you simply can not present 480V 50Hz to the Xm of a transformer designed for 60Hz?

 

[Besoeker]

I do not believe that 50hz operation of a 60hz transformer at no load will damage the transformer in the short run.

You really don't understand transformers.
It seems like a waste of effort trying. I gave you quite a full explanation in post #16. If you didn't understand it, and clearly you didn't, you could have asked pertinent questions which I would have been happy to answer.

Try this.
Consider the implications of 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 with respect to 60Hz and 50Hz.
Consider it seriously. Visualise a half sine wave of 50Hz superimposed on a half sine wave of 60Hz, both 480V. Better still, draw them out to scale.
Maybe then you might come to some understanding about the flux.

 

[Sahib]

My assertion is that if the core saturates at no load it must also necessarily saturate at full load, interfering with proper energy transfer from primary to secondary.

No, because at full load, sufficient voltage drop could occur across resistance and leakage reactance
so that magnetising current is at normal value just as a transformer operates under saturation at no load ( with no ill effects) but not at full load as I said in an earlier post.

 

[Sahib]

Better still, draw them out to scale.

I guess that you are going to do that yourself in your next post. :lol:

 

[GoldDigger]

Please see post the Steinmetz equivalent circuit I presented for you showing exactly that in post #16 to refresh your memory.


And end up with the same voltage across Xm?
Might I remind you of the ?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.? also in post#16?
The integral with respect to time of the applied voltage is greater at 50Hz than 60Hz. The flux is greater. To the point of probable saturation.
That's why the transformer designed for 50Hz is larger than that designed for 60Hz. A point you already accepted in post#7.

Why can't you now accept that, for the same reasons, you simply can not present 480V 50Hz to the Xm of a transformer designed for 60Hz?

Let me try to approach this in a different way:
Sahib is not arguing that he can present 50Hz to a transformer designed for 60Hz.
He is arguing that he can design a transformer specifically for 50Hz which is smaller than the equivalent 60Hz unit.
My painfully simple refutation of that is that I can then apply 60Hz to that transformer and have an equal sized comparable 60Hz transformer, which contradicts the original assumption.
By reduction ad absurdum the original assumption must be false.

I believe you made this argument already and Sahib simply ignored it.

 

[Sahib]

Golddigger:
Your logic is wonderful, though of no relevance.
I am just trying to understand the possibility or impossibility of 50hz operation of 60hz transformer.
Suppose a 6ohz transformer at no load is energized at 50hz. What then happens?

 

[Besoeker]

Golddigger:
Suppose a 6ohz transformer at no load is energized at 50hz. What then happens?

The core will most likely saturate, the current be excessive and either trip the protection or burn out the transformer.
I suggest you don't try it. But, if you must, make sure you have a CO₂ fire extinguisher to hand and that it is a small transformer (cheaper and easier to contain the conflagration).

 

[Sahib]

The core will most likely saturate, the current be excessive and either trip the protection or burn out the transformer.
I suggest you don't try it. But, if you must, make sure you have a CO₂ fire extinguisher to hand and that it is a small transformer (cheaper and easier to contain the conflagration).

At no load?
Unbelievable!
Please do not just draw any thing to scale to prove it .
Please do some calculations also to prove it, if you have that much expertise, as I requested many posts back.

 

[Besoeker]

At no load?
Unbelievable!
To you, perhaps.

Please do not just draw any thing to scale to prove it .

Did you give due consider the implications of 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 with respect to 60Hz and 50Hz?
I suspect not. Here is the time integral shown graphically to demonstrate the difference between that for 60 Hz and that for 50Hz.



It is perfectly clear that the 50Hz voltage time integral is greater than that for 60Hz.
The flux is thus demonstrably greater for 50Hz than 60Hz. I'm sure you can see that.

Please do some calculations also to prove it, if you have that much expertise, as I requested many posts back.

I already did. For a 480V 60Hz transformer to operate at design flux it would need to be energised at 400V on a 50Hz supply. It's that simple.

Let me give you another example.
The Steinmetz equivalent circuit I gave you also works for induction motors.
Induction motors are sometimes driven from variable frequency inverters. The most common mode of operation is constant voltage to frequency ratio. Constant V/f control.
So if you drop the frequency of a 480V 60Hz motor to 50Hz you also reduce the voltage to 50/60 of 480V which is 400V.
This keeps the operation in the constant flux region and the motor can generate rated torque at any speed.
If the voltage wasn't reduced, the motor magnetic circuit would saturate.

Normally, we charge a grand a day (Sterling) when I provide training for customers.
I have happily given you all this information/education in a way that I thought might be helpful to you. I think one of the great merits of this forum is that we can freely share knowledge.
Maybe, just maybe, it is time for you appreciate that rather that refuting it.

 

[GoldDigger]

At no load?
Unbelievable!
Please do not just draw any thing to scale to prove it .
Please do some calculations also to prove it, if you have that much expertise, as I requested many posts back.

I can give you some calculations if you are willing to accept some integral calculus rather than formulas from a handbook.

Let V₁ = 120 sin(w₁t)
and V₂ = 120 sin(w₂t)

The period of each of these waveforms is 2*pi/w, so the frequency is w/(2*pi).

For those two voltage waveforms, the core flux is (within a constant factor or two) the integral of V₁dt and V₂dt over time from t=0 to t=pi/w.

Now the indefinite integral of sin(wt) is (1/w)cos(wt) +C and the definite integral from 0 to pi/w is (1/w) (cos(0) - (cos(pi)) = 1/w (2) = 2/w.

In the two cases we need to look at, w₁ for 50Hz is 50/(2*pi) and w₂ for 60Hz is 60/(2*pi)

It seems pretty clear to me that the first integral, 240*2*pi/50 is greater than 240*2*pi/60. By a factor of 60/50, in fact.
This same result, including the factor of 60/50, can be also deduced from Besoeker's graphic.

 

[steve66]

For arc flash studies, to compare differences in 50Hz transformers vs. 60Hz, you only have to compare the transformer impedances.

If the 50Hz xformer and the 60Hz xformer have the same impedance (assuming same voltage and KVA), then wouldn't the arc flashes be very close to the same?