Transformer Loading:

[rattus]

From the discussions on other threads, I have concluded that transformer loading should always be computed to be the sum of Vphase x Iphase rather than summing up the individual loads. Why you ask?

It turns out that connecting unbalanced line to line loads on a 3-phase wye yields different loadings depending on the way you compute them. Take the infamous Oregon state test question involving the magic number, 1.154. The load thinks it is getting 208xI VA, but the transformer thinks it is delivering 2x120xI VA. How would you size the tranformer? Use the larger number of course.

I would expect however, that the loads would be more nearly balanced, and this would be less of a problem. Still, it makes sense to compute the loading from VphasexIphase.

This is the dead horse Ed brought up recently, but it is an important dead horse. One would not knowingly undersize a tranformer by 15%.

I expect to hear a bit of rebuttal on this.

 

[rbalex]

Re: Transformer Loading:

Part of the problem is that we tend to forget that, at its root, ?VA? is a fictitious scalar product of two vectors. If a three-phase transformer had the entire rated load connected between only two phases, it would be overloaded; and it wouldn?t matter if it were wye or delta connected.

However, for day-to-day practical applications the instruction to ?balance the kVA load on all three phases? works and minor ?imbalances? are within the operating tolerance of most transformers.

 

[charlie b]

Re: Transformer Loading:

Originally posted by rattus: From the discussions on other threads, I have concluded that transformer loading should always be computed to be the sum of Vphase x Iphase rather than summing up the individual loads.

I agree with Bob. The process you suggest is not possible, let alone practical, to implement. You know very well that every time you turn on a load, the voltage supplied to every other load will change slightly. Any value of ?VA? you calculated for any given load condition using ?the sum of Vphase x Iphase? would become invalid as each load is turned on or off.

 

[steve66]

Re: Transformer Loading:

Posted by Rattus:

The load thinks it is getting 208xI VA,

The load DOES get 208xI VA. But I think that's what you meant. We all know the load doesn't "think" about anything.

but the transformer thinks it is delivering 2x120xI VA

That's a little more subtle. Can you explain why you think that is the case? I'm not sure I agree with that statement, but I will think about it some.

I would expect however, that the loads would be more nearly balanced, and this would be less of a problem. Still, it makes sense to compute the loading from VphasexIphase.

Would you agree that if a completly balanced 3 phase load is connected, the sees the same KVA as the load?

Also, when you say "single phase loads", I'm not sure if you are talking about L-L loads, or L-N loads. (I am picturing a Y transformer).

Steve

 

[charlie b]

Re: Transformer Loading:

Originally posted by rattus: The load thinks it is getting 208xI VA, but the transformer thinks it is delivering 2x120xI VA.

Now that I?ve read Steve?s question about this statement, I see the error in your reasoning. The transformer thinks it is delivering 1 x 120 x I VA plus another 1 x 120 x I VA. But these two do not add up to 2 x 120 x I VA. Rather, they add up to 208 x I VA.

 

[rattus]

Re: Transformer Loading:

Originally posted by steve66:
Posted by Rattus:

but the transformer thinks it is delivering 2x120xI VA

That's a little more subtle. Can you explain why you think that is the case? I'm not sure I agree with that statement, but I will think about it some.

Reply: Treating this as one unit, the xfrmr knows its phase voltage and phase current, therefore it thinks it is producing Vphase x Iphase VA. The transformer does not know that the load is connected line to line, although it might suspect as much. If we use 208 instead of 240, our load computation will be some 15% low.

I would expect however, that the loads would be more nearly balanced, and this would be less of a problem. Still, it makes sense to compute the loading from VphasexIphase.

Would you agree that if a completly balanced 3 phase load is connected, the sees the same KVA as the load?

Reply: Without thinking about it, I would say yes, irrespective of the load configuration.

Also, when you say "single phase loads", I'm not sure if you are talking about L-L loads, or L-N loads. (I am picturing a Y transformer).

I don't think I used that term. L-L or L-N leave no doubt about the load configuration.

Steve

And for Charlie B.,

I do believe it is possible to compute the loading in this way, although, as you say, it might not be of any value since a properly designed system balances the loads reasonably well anyway.

 

[steve66]

Re: Transformer Loading:

Rattus:

It is certainly possible to overload one winding or phase of a transformer while still being below the transformer's "total" rating. But I don't think that's what you are talking about.

The idea that the transformer "sees" a load that is different that the actual load seems wrong. I suspect that you are missing something in you analysis.

Now I see Charlies reply. I am sure he is right, but it will take some time before the "how and why" sinks into my brain.

Steve

 

[rattus]

Re: Transformer Loading:

Steve,

Consider a load between Va and Vc:

A 20.8 Ohm @ 0 load connected across 208V. Now work out the currents and the power. The tendency is to say 2080VA.

Now consider separate loads across the two phase voltages:

A 12 Ohm @ -30 load from Va to neutral, and
A 12 Ohm @ 30 load from Vc to neutral.

Now work out the currents and the power.

You will find that the currents are exactly the same in both cases, but the xfrmr does not know the difference, nor does it care. It only knows it is being saddled with 1200VA per winding, not 1040VA.

To those who would say, "who cares?", I would reply that this is a mind exercise to help one get a grip on phase angles.

[ March 11, 2005, 04:23 PM: Message edited by: rattus ]

 

[rbalex]

Re: Transformer Loading:

AS I said originally "V-A" is a fictitious construct.

2 Watts + 2 Watts = 4 Watts, but
2 Volt-Amps + 2 Volt-Amps does not necessarily = 4 Volt-Amps unless they have exactly the same power factor. However, for common calculations it's usually close enough.

This discourse has spanned at least three threads. I believe we stipulated in one of them that the load was purely resistive and, at 10A and 208V L-L, was 2080 Watts. That is what a three-phase POWER (WATT) METER would indicate if it were properly installed.

I have occasionally installed VAR meters, but I don't believe I have ever even seen V-A meter - it would probably be meaningless.

An ideal transformer's throughput would be 2080 Watts and 1200 VARs for the connection we have been discussing.

 

[cpal]

Re: Transformer Loading:

2 Watts + 2 Watts = 4 Watts, but
2 Volt-Amps + 2 Volt-Amps does not necessarily = 4 Volt-Amps unless they have exactly the same power factor. However, for common calculations it's usually close enough.

and ultimately that is why transformers are rated in kVA rather than Watts. yes / no???Charlie P

 

[rattus]

Re: Transformer Loading:

Charlie P.,

As I see it, a xfrmr can stand just so much voltage (iron loss) and just so much current (copper loss). Together these maxima make up the KVA rating. And, since we usually operate at a fixed voltage, the KVA rating is essentially a current rating as has been pointed out.

 

[ray94553]

Re: Transformer Loading:

After all is said and done are we going to calculate according to the methods set forth in the NEC or make it up as we go along? I would agree with changing the NEC if there was a need to do so but so far that's not the case. Prior to the Oregon State Supervisors Licensing Examination, a test created by one or two individuals without review by any peer group, this was not an issue. The next thing you know we will need to know how to calculate the phase shift for line disturbances and changes in frequency.
If I use the infamous 1.154 correction factor to increase the size of the 208 wye transformer supplying the panel it still would not prevent over loading on any one phase. Performing the craft in a workmanship like manner is the only thing that will prevent that.
Throughout the NEC load calculations the use of volt amperes and kilovolt amperes indicates that APPARENT POWER is the acceptable method to be used for the calculation. And apparent power is calculated using the formula S = V*I , where S is in Volt Amperes (VA), V is the phase Voltage and I is the Current in that phase.(sorry, I don't know how to add sub and superscripts to this text format yet) I offer as a reference Introductory Circuit Analysis 6th Edition by Robert L Boylstead ? 1990, Chapter 23 Polyphase Systems. or any similar undergraduate text on electrical circuits. There are more advanced treaties on the subject but do we need a doctorate in electrical engineering in order to use the NEC?
Using methods and calculations that everyone in the industry knows and understands is the whole purpose of the Code. Isn't that why it is there? See; National Electric Code Examples D5(a) and D5(b). If it isn?t in the code it doesn?t necessarily mean that it isn?t a good idea but it isn?t required by the code.
And designing test questions that conjure obscure formulation that even some engineers have trouble explaining is contrary to the ideals and standards of the industry. Why would you want me to use methods or calculations that were not standard to the industry? Arguing an issue as a point of theory is all fine and good but to implement your pet methodologies without warrant is a violation of the ideals of a uniform standard.

[ March 04, 2005, 08:23 PM: Message edited by: ray94553 ]

 

[charlie b]

Re: Transformer Loading:

Sorry for the late reply. But I have been out of town, and am just getting a chance to read through the Forum discussions that I have missed.

Originally posted by rattus: As I see it, a xfrmr can stand just so much voltage (iron loss) and just so much current (copper loss). Together these maxima make up the KVA rating. And, since we usually operate at a fixed voltage, the KVA rating is essentially a current rating as has been pointed out.

Not so. The voltage rating is based on the ability of the insulation system to prevent leakage current from the conductor to the outside world. The current rating is based on the cross-sectional area of the conductor, which in turn impacts the amount of heat generated within the conductor. The KVA rating is based on the ability of the device to reject the internally-generated heat to the outside world, and takes into account such non-electrical physical considerations as the existence of ventilation louvers and space allocation within the enclosure.

 

[rattus]

Re: Transformer Loading:

Charlie B., you are ignoring iron loss, that is hysteresis and eddy currents. And there is the possibility of saturation in the iron. All these phenomena are affected by the voltage. There is more to the voltage rating than the insulation. Now, I must admit I do not know the relative amount of iron to copper loss in a well designed transformer. Anyone know?

 

[charlie b]

Re: Transformer Loading:

I am not ignoring them. I am saying that the single critical factor that determines the voltage rating is the ?resistance? of the insulation system. All the other things may be influenced by the applied voltage, but none of them has a sufficient impact to influence the voltage rating.

 

[rattus]

Re: Transformer Loading:

Charlie B.

Again, I beg to differ. From what I read, the core loss is significant and in some cases exceeds the winding loss. Check out:

http://www.energyusernews.com/CDA/Article_Information/Fundamentals_Item/0%2C2637%2C76086%2C00.html

Also,

[/qb][/QUOTE]Now that I?ve read Steve?s question about this statement, I see the error in your reasoning. The transformer thinks it is delivering 1 x 120 x I VA plus another 1 x 120 x I VA. But these two do not add up to 2 x 120 x I VA. Rather, they add up to 208 x I VA. [/QB][/QUOTE]

Yes, Charlie B., they do add up to 240V x I VA. That is the way apparent powers are added. You do not apply vector algebra to apparent powers. You would not say that for a wye connected load with the same current. The transformer does not know the difference. Each winding sees 120V x I, whatever the load configuration.

This is the whole point of the infamous Oregon factor, which does indeed have a technical basis. Don't you see that?

[ March 09, 2005, 10:43 AM: Message edited by: rattus ]

 

[ronaldrc]

Re: Transformer Loading:

Rattus

I know I'm just an electrcian and not an instructor or engineer but from what I have learned from this site from you and others I agree with Charlie.

You are forgetting about the time factor. At that point and time the alternator voltage of the two coils added together equal 208 and not 240 volts.

This graph shows three phase the way I understand it.

http://home.comcast.net/~ronaldrc/wsb/html/view.cgi-image.html--SiteID-2102494.html

Ronald

 

[rattus]

Re: Transformer Loading:

ronald, I understand all that perfectly. What many seem to be missing though is that the individual transformers see 120V x I VA as their apparent load. You do not apply vectors to apparent power. You add apparent power arithmetically. The transformers deliver 2400VA.

If one of the transformers feeds a black box with a load to neutral which delivers a current of say 10A, then you would say, correctly, the apparent power is 120V x 10A.

Then if someone replaces that load in the black box with a line to line load which also draws 10A, you would say the transformer delivers 120 V x 10A because the transformer does not know the difference.

This is all about transformer loading, and the test makers in Oregon have worked it into their tests.

What Charlie B. and others seem to be stuck on is the standard method for computing load, and this method works just fine in the real world. However, for this special case, which should never occur, the standard method is in error by some 15%.

It is tricky, but once you get your mind wrapped around it, you will understand 3-phase better.

 

[rbalex]

Re: Transformer Loading:

I think I've been consistent saying "V-A" is a useful, but fictitious construct. Where overall system power-factors are 0.85 or better "VA"s add arithmetically close enough for practical purposes.

It's been well over 25 years since I "designed" a transformer, but the "VA" limit is pretty much established by the maximum flux-density in the core steel below or just at "knee-point" saturation. That's why two transformers of the same "VA" rating are roughly the same size physically regardless of the primary or secondary voltages.

Once that is established, voltage ratings are established by insulation and current ratings by wire size.

Again, it isn't immediately obvious but ALL transformers are both VTs and CTs - it is simply a matter of application.

 

[jim dungar]

Re: Transformer Loading:

rattus,

Your/their reasoning is not tricky, it is wrong.
And yes, after applying transformers for 26 years, I do understand 3 phase perfectly fine.

Power factor is the phase angle difference between voltage (E) and current (I). It has nothing to do with the phase angle differences between voltages.

Also remember the relationship of phase to phase voltage (Epp) and phase to neutral voltages (Epn). These relationships are fixed and cannot be modified simply by dropping a phase or neutral connection.
Single phase: Epp = 2*Epn
three phase: Epp = 1.73*Epn