Transformer Question

[eHunter]

Also keep in mind that a three phase power source does not have a 180? phase displacement which would change things and allow each phase to only supply current to one phase at a time, they have a 120? phase displacement and because of this the adjoining phase will contribute current to to a single phase load between only two of the phases, this is why we see 86.6 amps at each phase when each load only pulls 50 amps when you have three equal 50 amp loads connected to all three phases, if you had a 0? displacement you would have 100 amps at each phase since each phase really supplies two loads, this is because while phase A is at it's voltage peak 90? phase B is at 330? and phase C will be at 210 in there phase cycle, maybe someone could point to a plot of a three phase sine wave that will give you a more visual reference to better wrap you mind around, to understand how vectors work in three phase supplies.

Maybe these visuals will help.




http://en.wikipedia.org/wiki/Three-phase_electric_power

 

[hurk27]

Maybe we could ask Smart $ to slow down his avatar by a factor of 10 or so?

I have seen a larger version of his avatar posted before, maybe I can find it?

I guess I should have added that since a three phase transformer that can supply a 120 volt load equally across all three phases will be a Wye 208/120, and if you figure the current at 208 volts you will get the 50 amps each single phase load will pull, 18,000/208/1.732 = 49.96 amps or 50 amps because of the rounding off in the equation.

When figuring the current of a transformer you must use the line to line voltage to get the correct current rating of the transformer, in my other post above I was figuring a line to line voltage of 120 volts for the three phase which might lead to some confusion since a transformer with this voltage would not be a commonly made transformer, calculating for a delta transformer with a center tap between A and C can even complicate things a little more because the line to neutral loads will not balance across all three phases as they are only connected from A to neutral and B to neutral, in this case you must figure your single phase line to neutral loads separately, then figure in the current with your other line to line loads to find the rating of the transformer needed or just add up the kva of all the loads to know what size transformer you need.

Lets say you have 18kva worth of loads that are line to neutral, this will place 75 amps between A and C phase or 9kva from A to neutral and 9kva from C to neutral and since these are equally balanced loads the neutral will not see any current, now add in two more 18kva 240 volt loads one between A and B and one between B and C, just to keep things balanced, if we add up the three 18kva figures we get 54kva, so we can take this figure to find our current each phase will see by 54,000/240/1.732 = 129.9 amps or 130 amps per phase the next size up common sized transformer will be a 75kva (unless they do make a 60kva which I have not seen other then a special order) which will provide 180.4 amps per phase so you will end up with 50.3 amps per phase extra for future loads, again this is only for a 4-wire delta with a high leg (B phase) but some of the math will apply to other three phase transformers also such as a 208/120Y when you have 120 volt loads only connected between two of the phases which would be uncommon, generally you would figure any balanced line to neutral loads at the 208 volt rating to get the phase current on the highest loaded phase to get the correct rating of the transformer needed, of course there are other figures you must use to find the correct kva rating the transformer will see such as the power factor rating and the transformer efficiency or the transformer impedance which will add to the size of the transformer needed for a given set of loads, but in trying to keep it simple as I can see that the OPer is struggling to wrap his head around this I was trying to keep it to the basics, once we see the OP has got this part down we can teach him how to add PF and transformer impedance or efficiency to the end results to figure how to size the transformer correctly which is the simple part.

 

[GalwayElectric]

Thanks. There's a lot of info for me to get my head around.

Why do you use the formula 18,000/208/1.732? Every time I saw a formula for transformers it was done by multiplying voltage by 1.73 not dividing

 

[GoldDigger]

Thanks. There's a lot of info for me to get my head around.

Why do you use the formula 18,000/208/1.732? Every time I saw a formula for transformers it was done by multiplying voltage by 1.73 not dividing

Careful with the maths there.
18,000/208/1.732 could be (18,000/208)/1.732 or it could be 18,000/(208/1.732), and the two give very different numbers.
The first one above is equal to 18,000/(208 x 1.732) = 49.96. Just like you remember.

 

[hurk27]

Careful with the maths there.
18,000/208/1.732 could be (18,000/208)/1.732 or it could be 18,000/(208/1.732), and the two give very different numbers.
The first one above is equal to 18,000/(208 x 1.732) = 49.96. Just like you remember.

Yes I'm very bad at expressing Algebraic notation and most times just put it the way I put it into my calculator, which is not a good thing when trying to teach someone how to work the math.

But yes (18000/208)/1.732 or 18000/(208x 1.732) is the correct expression that will give you the correct answer, with the first one easier to do on a non-scientific calculator as you can just enter it as I did, 18000 hit divide 208 hit divide 1.732 hit = 49.96

 

[Dave130]

Simplified -

Single phase 208A per phase = 1 * 208 = 208 Total single phase Amps

Three phase 120A per phase = 3 * 120 = 360 Total single phase Amps

 

[kwired]

Simplified -

Single phase 208A per phase = 1 * 208 = 208 Total single phase Amps

Three phase 120A per phase = 3 * 120 = 360 Total single phase Amps

voltage will remain constant, at least within a small tolerance, amps available will depend on the kVA rating of the unit.

Not sure what you were trying to say here, and the fact you used 120 and 208 in your example leads me to think you are getting volts and amps turned around somehow.

If you have 208 amps of load connected between two phase conductors - then yes you have 208 amps load, but if you have 3 separate single phase loads of 208 amps balanced across all three phases and clamp a meter around the supply conductors you will read 360 amps on each supply conductor.

 

[Dave130]

With a single phase 50kVA sub at 240V - max load 208A thereabouts
Two phase 50kVA 480V phase to phase Voltage you get 104A on A phase & 104A on B phase totalling 208A single phase load connected seperately on both phases
Three phase 50kVA 415V phase to phase Voltage you get 120A on A phase 120A on B phase & 120A on C phase totalling 360A single phase load connected seperately on all phases

All I was getting at was the benefit of three phase to single is that you can connect more single phase (which is 99.9% of installations) load to a three phase system than single phase which was the original question
Also you get less losses from three phase

 

[Dave130]

FYI I'm in Australia, principles are the same.

 

[Dave130]

Our distribution system is mostly 11kV with step down transformers to household use at phase to neutral voltage of 240V with a Delta/Star Transformer where the star point is earthed. We also use an MEN system where the neutral (connected to the star point) is also frequently Earthed on the low voltage system.
So, single/two phase subs used in rural areas only have two HV phases going in giving a phase to phase voltage of 480V/240V Phase to neutral. This method is more ecenomical and transformers can be converted to single phase only.
Three Phase subs have three HV phases going in (obviously) giving a phase to phase voltage of 415V between all phases and 240V phase to neutral on each phase.
Voltages are approx due to impedances in the line, transformers can be tapped up or down to correct this.


Voltages are not constant as calculations for Max load are derived from phase to phase voltages on the secondry.

 

[Dave130]

Sorry, I had a bit of a brain fart there, I was just using values given in the originl question. I thought the three phase Max amps was a bit high seeing as I do this every day. lol.

For three phase systems you also have to divide the phase to phase voltage by sq rt 3 (1.73) which gives a single phase Max load of 70A, X3 210A about the same as single phase 50kVA
Benifits being you can't run three phase equipment on single phase

I know this is a bit different to you guys over there 120/240 but other than the MEN system the principles are the same

 

[mivey]

totalling 360A single phase load connected seperately on all phases

You corrected the amps in a later post but totaling amps across phases is an odd expression. Totaling power is typical.

FYI I'm in Australia, principles are the same.

The expressions seem different.

 

[mivey]

Sorry, I had a bit of a brain fart there, I was just using values given in the originl question. I thought the three phase Max amps was a bit high seeing as I do this every day.

The original values were fine, it was the equation that was not clear.

For three phase systems you also have to divide the phase to phase voltage by sq rt 3 (1.73) which gives a single phase Max load of 70A, X3 210A about the same as single phase 50kVA

If you are comparing three-phase with single-phase L-G loads, but you could also have 416 volt single-phase.

Again, equating three phase current times three with single-phase current is odd, especially without the voltage referenced. Usually we compare the total power.

 

[Besoeker]

So Mivey are you saying that a 50kva transformer is delivering 50 kva per phase thus 150 kva total??

Then it wouldn't be a 50kVA transformer.

 

[mivey]

Then it wouldn't be a 50kVA transformer.

Thanks, I did not see that question. Bes is correct, we need (3) 50 kVA transformers to get 150 kVA.

 

[Dave130]

over here we calculate maximum demand in current and because most domestic installations are single phase loads I was just making the point that you could have 70A of single phase load connected per phase in the installation/s totalling 200A thereabouts I was just showing that you DO get much the same amperage out of a 50kVA single phase transformer as a 50kVA three phase transformer as is with all size transformers, which was the original question.

I don't need to use these calcs much anymore I just know (for us) what the max load for most of our distribution transformers is.

I understand other voltages are possible but I was only referring to the ones we use as outlined in above posts.