Amperage calculation

[david luchini]

Forget the the load "end" for a minute. What are the apparent and real power values of each secondary winding?

Each winding would deliver 1040 Watts and 0 Vars to the load. The power factor is still 1.

The circuit in question does not consist of a single resistor. At a minimum it consists of a resistor and _two_ transformer secondary coils.

Yes, I suggested a Wye source. That doesn't change the power factor of the circuit.

The power factor in the resistor is 1; I agree with your calculation above for this _portion_ of the circuit.

The power factor in each of the transformer secondary coils is less than 1.

The unbalanced loading on the three phase source causes this power factor to be present _on the source_.

The power factor of the source as a whole is 1. NO vars are being delivered to the load.

A single phase _resistive_ load will have unity power factor as compared to the line-line voltage, but a 0.86 power factor when referenced to the line-neutral voltages.

The power factor doesn't change with different voltage references. Power factor is the ratio of real power to apparent power. The are 0 vars at the load and there are 0 vars at the "lines," therefore the power factor is 1 at both the load and the "line."

Try this. Add a 5A resistive load connected A-N together with the 10A resistive load connected A-B in the previous example. Both loads are still purely resistive with no reactive power. But in this case, line A current will be 14.55<-9.9 and line B current will be 10<180. Would you suggest that line A and line B have different power factors as well as being different from the loads? Would you suggest that the load from A-N has a non unity power factor with respect to voltage A-B?

 

[GoldDigger]

Yes.

Tapatalk!

 

[charlie b]

I have to disagree on this point. The current through a resistive load will be in phase with the voltage applied to that load, and thus in phase with the A to B voltage. For a single circuit, the current must be the same throughout, and _not_ in phase with either of the phase to neutral voltages.

I concede this point. I was in error to compare the phase angle of the current in the resistor with the line to neutral voltages.

A single phase _resistive_ load will have unity power factor as compared to the line-line voltage, but a 0.86 power factor when referenced to the line-neutral voltages.

Again, I concede this point. But this one I will call irrelevant. There is no meaning to a comparison between the phase angle of a current with the phase angle of a voltage that is not the voltage that is driving the current.

 

[GoldDigger]

Au Contraire!
There is always a (formal) relevance to the phase relationship between the current at a point and the voltage (relative to any selected reference point you choose) at that same point.
It determines the magnitude and direction of the power flow past that point.
What is interesting is that although that number will vary with the choice of voltage reference point, the total power going into a load or coming out of a source will be exactly the same independent of reference point.

When you talk about the voltage driving the current, you are explicitly adding the "power flow" values from each end of the load to find out how much power (net) goes into the load. But that does not mean that any other analysis that gives the same result is not equally valid.

Tapatalk!

 

[Smart $]

Forget the the load "end" for a minute. What are the apparent and real power values of each secondary winding?

Each winding would deliver 1040 Watts and 0 Vars to the load. The power factor is still 1.

...

How did you get 1040W for each winding if the load is 2000W???

Where the secondary is 480/277V and the load is 480V 1? 2000W resistive...

2000VA?480V=4.17A

The apparent power of each winding is...

4.17A?277V=1155VA

Reactive power is realized by each winding though the neutral node. The load and its wiring do not "see" the reactive power, but the transformer primary does.

 

[GoldDigger]

And I counter with the statement that if you can only consider the current relative to the voltage across the load, you are equally constrained to consider the current relative to the individual coil voltage for each of the two wye coils that drive that load.
You cannot have your cake and Edith too.

Tapatalk!

 

[david luchini]

How did you get 1040W for each winding if the load is 2000W???

Sorry...two different examples going on concurrently....

Consider a load that is 10A, 208V, single phase, or 2080VA.

Reactive power is realized by each winding though the neutral node. The load and its wiring do not "see" the reactive power

Exactly...The reactive power is contained to the source...It does NOT flow to the load, and it does NOT create a different power factor on the wiring to the load, as was suggested in post 3.

 

[Besoeker]

Charlie, consider a three phase wye system.
Now connect one line to line resistive load to it.
Look at the phase angle of the line current relative to the line to neutral voltage.

For a line to kine load, the line to neutral voltage is irrelevant.

 

[GoldDigger]

For a line to kine load, the line to neutral voltage is irrelevant.

It is irrelevant to the load. It may be very relevant to the source! (Such as a wye ouput generator).

The principle that I am trying to follow is that if you do the calculations consistently and correctly, all of the various ways of looking at it will give the same result in terms of the power in the load and the power taken from the source.
If you do not follow a consistent process, you will eventually find yourself in a situation where you have to choose between two different results that both seem plausible but cannot both be right.

Using my analysis, there is reactive VA in both of the wye windings supplying the line to line load, but that reactive VA cancels out between the two coils, and you have the same situation (at the load) as if you had a delta winding instead.

You cannot avoid the fact that the VA in each wye winding is greater than half of the load power.
If you wanted to, you could cancel this reactive power out with a combination of inductor on one winding and capacitor on the other winding. And it would make no difference to the operation of the load but would increase the IR losses in the generator.

 

[david luchini]

The principle that I am trying to follow is that if you do the calculations consistently and correctly, all of the various ways of looking at it will give the same result in terms of the power in the load and the power taken from the source.

Neither the power "in the load" nor the power "taken from the source" include any Vars. It is purely resistive. So P/S = 1...The power factor is unity.

Using my analysis, there is reactive VA in both of the wye windings supplying the line to line load, but that reactive VA cancels out between the two coils, and you have the same situation (at the load) as if you had a delta winding instead.

Yes, the reactive power at the source cancels out between the two coils...none of it is delivered to the load. But that does not make this statement any less correct.

But the power factor of the line current will not be 1.

This is no reactive power associated with the line current to the load.

 

[Besoeker]

It is irrelevant to the load.

Wasn't the original question about that?

 

[Smart $]

...
This is no reactive power associated with the line current to the load.

No significant reactive power. There may be a trivial amount as a result of wiring method and heater housing.

 

[Besoeker]

No significant reactive power. There may be a trivial amount as a result of wiring method and heater housing.

A little pedantic if I may say so............

 

[Smart $]

A little pedantic if I may say so............

Just a tad. I was bored at that instant...

 

[GoldDigger]

Wasn't the original question about that?

Well, IIRC, the original question was about the line current. The power factor came up in the process of trying to give a general answer.

 

[Pharon]

It sounds like the original question (before 4 pages of nuance) was asking how to calculate the line current, which would be 104.2A, or 52A per phase. I'm guessing that the OP is trying to figure out what size OCPD and/or wire to run in order to support the load.

 

[GoldDigger]

It sounds like the original question (before 4 pages of nuance) was asking how to calculate the line current, which would be 104.2A, or 52A per phase. I'm guessing that the OP is trying to figure out what size OCPD and/or wire to run in order to support the load.

But the OP left himself vulnerable to nuance by including a comment about power factor in the original question.
PF is not relevant to the answer the OP was looking for, but it was relevant to one of several ways of getting that result and it is very relevant to why the 1.73 does not come into play in any form in the final result.

 

[Pharon]

But the OP left himself vulnerable to nuance by including a comment about power factor in the original question.
PF is not relevant to the answer the OP was looking for, but it was relevant to one of several ways of getting that result and it is very relevant to why the 1.73 does not come into play in any form in the final result.

The only reason he brought up PF was to double check his (correct) assumption that resistive loads are 1.0. And it does not factor into a change in wire size or OCPD with respect to the answer he was seeking.

While I will admit that the ensuing conversation was enlightening, I don't see how it helped the OP get an answer to his question. That's all I'm saying.

 

[Pharon]

By the way, I'm not sure what possessed me to write 52A per phase. The ampacity of the conductors and OCPD should be based on 104A, not 52A. Taking into account potential continuous duty, voltage drop, derating, etc.