Why 3-Phase?

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philly

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I got to thiniking over the weekend why 3-phase electricity was adopted for use as the standard for multiphase electricity? Why was three phase adopted as opposed to 4-phase with phases being seperated by 90deg or some other multiple like say 5 or 6 phases? Is the 120deg offset the only phase difference that will work for balanced systems?

I understand most of the math behind three phase systems but wasn't sure if there was some underlying issue why 3-phase was an advantange of invening or adopting some other multi-phase system as mentioned.

Just something I was pondering and would be curious to hear if there were any explanations or references out there.
 
The best reason I can think of is that power is constant. I have a typed out document (MS Word file) that shows the derivation, and can send it to anyone who is interested. Send me a PM with an email address, and I'll pass it along.

Here is a summary: Start with three voltages and three currents, as follows:
Va(t) = VM cos (wt)
Vb(t) = VM cos (wt - 120)
Vc(t) = VM cos (wt - 240)
Ia(t) = IM cos (wt - u)
Ib(t) = IM cos (wt - u - 120)
Ic(t) = IM cos (wt - u - 240)


Multiply Va(t) times Ia(t), and then multiply Vb(t) times Ib(t), and multiply Vc(t) times Ic(t), and add those three things up. Perform some trigonometric magic, and all the terms that contain the variable "t" disappear. Thus, power as a function of time does not depend on time. It is constant. I don't think you can get there with any other number of phases, or with any other phase angle between votages or currents.
 
Somewhat related but here's something I've always wondered. Why is it single phase is called single phase when there are actually two phases?
 
This subject is near and dear to my wallet (I get paid to research 'high phase order' electric motors).

You can build a balanced polyphase system with any number of phases.

The initial 'polyphase' systems were _two_ phase; however they were either balanced (requiring 4 wires) or unblanced (requiring 3). It was quickly realized that with the same 3 wires you could supply balanced 3 phase power and deliver more power over the same wires.

Going to more than three phases adds to the cost of your transformers, switchgear, etc, and is of benefit only in specific circumstances.

EPRI tested out some high phase order power transmission systems. The benefit was that the phase-phase voltage was significantly reduced, so you could space the transmission wires more closely, thus with the same phase current and system voltage you could pack more power into the same right of way. This required transformer arrays to go between three phase and high phase; the thought was that this would be cheaper than the land for a wider transmission right of way.

In the motor realm, the high phase counts are produced by a specialized VSD, so you only have high phase counts between the VSD and the motor; it is still 3 phase power going into the system. The benefits there have to do with motor overload capability and inverter limitations.

-Jon
 
daleuger said:
Somewhat related but here's something I've always wondered. Why is it single phase is called single phase when there are actually two phases?
Click to expand...
Presuming you are talking about the common residential 120/240 volt system, it has is only one phase, not two. It is not uncommon to speak of A Phase loads and B Phase loads. But that is a conversational simplification, an easy way to keep track of loads, as you connect them and attempt to balance them. But looking at a perfectly balanced system, any current that leaves the main panel on Phase A will return to the main panel on Phase B; it is the same current. But since we select a point in the middle of the transformer, and connect that point to planet Earth, and measure each of the "two phases" with that point as the common reference, the two are out of phase with each other by 180 degrees. That is a mathematical result, but it does not change the fact that current leaving on one phase returns on the other, and they are the same current.

By contrast, current leaving a three phase panel on Phase A can return via either Phase B or Phase C or both, and they will appear separated by 120 degrees of phase. They are no longer the same current.
 
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charlie b said:

Presuming you are talking about the common residential 120/240 volt system, it has is only one phase, not two. It is not umcommon to speak of A Phase loads and B Phase loads. But that is a conversational simplification, an easy way to keep track of loads, as you connect them and attempt to balance them. But looking at a perfectly balanced system, any current that leaves the main panel on Phase A will return to the main panel on Phase B; it is the same current. But since we select a point in the middle of the transformer, and connect that point to planet Earth, and measure each of the "two phases" with that point as the common reference, the two are out of phase with each other by 180 degrees. That is a mathematical result, but it does not change the fact that current leaving on one phase returns on the other, and they are the same current.

By contrast, current leaving a three phase panel on Phase A can return via either Phase B or Phase C or both, and they will appear separated by 120 degrees of phase. They are no longer the same current.
Click to expand...

Ahhh....:grin:
 
Graphic Representation (Single vs Three Phase)

Graphic Representation (Single vs Three Phase)

I am no instructor, but this is a graphical representation I made up.
 
charlie b said:
Presuming you are talking about the common residential 120/240 volt system, it has is only one phase, not two. It is not uncommon to speak of A Phase loads and B Phase loads. But that is a conversational simplification, an easy way to keep track of loads, as you connect them and attempt to balance them.
Click to expand...

This why I prefer to call them Phase A conductor and Phase B conductor or Line A and Line B. In most electrical discussions the word 'phase' is highly context sensitive, but many people assume it to always mean a Line-Neutral circuit.
 
philly said:
I got to thiniking over the weekend why 3-phase electricity was adopted for use as the standard for multiphase electricity? Why was three phase adopted as opposed to 4-phase with phases being seperated by 90deg or some other multiple like say 5 or 6 phases? Is the 120deg offset the only phase difference that will work for balanced systems?

I understand most of the math behind three phase systems but wasn't sure if there was some underlying issue why 3-phase was an advantange of invening or adopting some other multi-phase system as mentioned.

Just something I was pondering and would be curious to hear if there were any explanations or references out there.
Click to expand...
The obvious merit of a three-phase system and possibly its raison d'etre is that four wires can be used - you need only one neutral.
It also means that line to line voltage is the same regardless of which two lines you use. I don't think any other polyphase system can do that.
With a four-phase system, you would have two different line to line voltages depending on which two lines you used.

We quite often use hexaphase (six-phase) unit transformers for high current rectifiers. Three centre-tapped secondary windings with the centre taps of each connected to a common give the six 60deg displaced phases.
That gives three different line to line voltages.

So, maybe three phase is optimum.
A related point might be the relative merits of power frequency.
Is 60 Hz better than 50 Hz? Would 100 Hz be better?
 
3 is balanced and stable just like a three leg table will never wobble. You can add a 4th but a properly designed 3 leg table is just as stable and equally effective. Why add the complication there is no need.
 
Graphic Updated

Graphic Updated

Besoeker said:
That's possibly as an illustration to make the point that there is a phase shift between each of the three phases.
But not accurate.
Your diagram shows a 60deg shift between the phases thus you have all three the same polarity at the same time.
It's more like this:
http://i36.photobucket.com/albums/e39/Besoeker/three-phase01
Click to expand...

Beoseker,

Good catch, I threw that one down in a huury after I read the OP. I have ammended my graphic to represent the 3-phase at 120 deg.

Thanks Again
 
IMM_Doctor said:
Beoseker,

Good catch, I threw that one down in a huury after I read the OP. I have ammended my graphic to represent the 3-phase at 120 deg.

Thanks Again
Click to expand...
And my link didn't work.:(

three-phase01.jpg
 
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