Why not transmit electricity in 4-phase?

[GregValcourt]

Or even better, generate in 4-Phase, convert to two-phase for transmission. Even number phases cancel out nicely (contrary to popular belief, 3-phase does not actually cancel out). 2-phase might be convertible back to four phase for the purpose of industrial motors.

Forgive me for speaking out of ignorance, I'm not an electrician or engineer. Mathematically, an even number of phases seems better for transmission (in terms of loss).

Mathematical graph of 3 sine waves 120 degrees apart, with resultant wave:

 

[Averagesupernova]

Those 3 sine waves don't look 120 degrees apart to me.

 

[Baluncore]

The sum of the instantaneous currents in all three phases should always be close to zero. That reduces the magnetic radiation from the transmission line.

Given a minimum of three phases and by using transformers, any number of other phase combinations can be generated. For a simple example see; https://en.wikipedia.org/wiki/Scott-T_transformer

The sum of cross sections of conductors in a transmission line is independent of the number of phases, but the cost of insulators is 33% higher for a 4 phase line than for a 3 phase line.

 

[andrewkirk]

Here's why 3-phase cancels:
$$\sin(x-120)+\sin x+\sin(x+120)=\sin x\cos (-120)+\cos x\sin (-120)+\sin x+\sin x\cos 120+\cos x\sin 120$$

$$=-\sin x\cos 60+-\cos x\sin 60+\sin x-\sin x\cos 60+\cos x\sin 60$$
$$=-\sin x\cos 60+\sin x-\sin x\cos 60
=-\tfrac{1}{2}\sin x+\sin x-\tfrac{1}{2}\sin x=0$$

Picking up on the obaservation of @Averagesupernova, the blue and green curves in the graph are 90 degrees out of phase, not 120.

 

[anorlunda]

OP, you really blew it when you said three phases don't add to zero. Ignoring that, high phase order transmission has been studied many times. The short answer is that the added benefits do not outweigh the added costs.

Google the phrase high phase order transmission.

 

[cabraham]

Settled science. Single phase requires 2 wires. Two phase requires 3 wires. Three phase also needs 3 wires, 4 phase needs 4. Computing losses, you will find that to transmit a given amount of power from point A to point B with a given loss, 3 phase requires only 75% the copper area/weight as 1 or 2 phase. Increasing to 4 phase or more does not reduce copper needed, I can look it up later, but more phases may even need more copper than with 3 phases.

Three phase is optimum regarding maximum power ability, for a given amount of loss, with minimum copper consumed. The utility companies have studied this issue since the late 19th century. If a different number of phases is really better, it would have been done decades ago.

Claude

 

[Baluncore]

I can look it up later, but more phases may even need more copper than with 3 phases.

I believed that the total section of copper needed remained the same for 3PH and above, while the number, mass and cost of insulators increased.
If anything I would expect total copper mass to fall slightly for more phases due to the skin effect not fully utilising the centre of thick conductors needed for 3PH.
Can you give a reference to the weight of copper needed for polyphase lines of three and above ?

 

[The Electrician]

From the first paragraph here: https://en.wikipedia.org/wiki/Polyphase_system

"A major advantage of three phase power transmission (using three conductors, as opposed to a single phase power transmission, which uses two conductors), is that, since the remaining conductors act as the return path for any single conductor, the power transmitted by a balanced three phase system is three times that of a single phase transmission but only one extra conductor is used. Thus, a 50% / 1.5x increase in the transmission costs achieves a 200% / 3.0x increase in the power transmitted."

 

[cabraham]

Wikipedia is incorrect here. I will find or recompute, then post. Here is the conclusion, I know this is right. For transmitting power from A to B, same amount using 1-phase & 3-phase, with equal power lost in transmission, a 3-ph system uses 75% the copper of 1-ph, as well as 2-ph.

 

[anorlunda]

hus, a 50% / 1.5x increase in the transmission costs achieves a 200% / 3.0x increase in the power transmitted."

For transmitting power from A to B, same amount using 1-phase & 3-phase, with equal power lost in transmission, a 3-ph system uses 75% the copper of 1-ph, as well as 2-ph.

Can't you both be right?

• The Electrician holds wire diameter constant and increases the power transmitted, holding watts/(mile*phase) constant.
• Cabraham holds power and losses constant and decreases wire diameter.

Edit: By the way, high phase order transmission is interesting not only because of losses, but also because of series reactance.

 

[cabraham]

Here is a 2-page computation for copper needed re 1-phase, 3-ph, and 4-ph transmission. Here is the synopsis. The generated power is 1.000 watt per unit, the power loss in cables in 0.010 watts per unit, and the load power is 0.990 watts per unit. These values were held constant for comparison purposes. Also, maximum line to line voltages were fixed at 1.0 volts per unit.

The result is what I seem to recall. The copper requirement for 1-phase is set at 100% as the reference. A 3-phase system requires just 75% the copper of 1-phase, a considerable savings. But, a 4-phase system did not improve on the 75% figure. Actually it came in at 100%, identical to 1 phase. I remember computing the general relation for any number of phases, i.e. "n-phase". For any value of "n" other than 3, the result is the same, the same amount of copper, i.e. 100%, is needed. If n=3, then 75% of the copper weight is needed.

I'm not surprised, because if 4 phases, or 5, 6, 10, whatever, saved on copper usage, the power companies & others would have quickly done it. I've heard of 6, 12, 24, & even 36 phase power employed. But it's advantage is usually very low ac ripple after rectification negating the need for large smoothing capacitors. But for long distance power transmission, 3 phase is pretty much the only game in town. Comments/feedback/questions welcome. Best regards.

Claude

 

[mheslep]

...But for long distance power transmission, 3 phase is pretty much the only game in town. Comments/feedback/questions welcome. Best regards.

Claude

Or HVDC.

 

[GregValcourt]

Those 3 sine waves don't look 120 degrees apart to me.

Your right, I must have did something wrong when building the spreadsheet. The second time I did it, 3-phase does cancel out.