Single phase vs 3 phase efficiency

[drcampbell]

In practice you will find a three phase load of the same KW will require less conductor. This is because ampacity is not linear with conductor size. A three phase load will have smaller conductors, and even though there are 50% more conductors, the total area will still be less. For example consider a 48 KW load. At 240 single phase this would be 200 amps or 3/0 CU, for a total circular mail area of 335600. For three phase that would be 115 amps , #2 CU, for a total circular mail area of 199080. Of course one could theoretically parallel smaller conductors for the single phase case, but there is of course the NEC 1/0 limit for paralleling and even above that in many cases it would not be done.

Which is precisely why 3-phase power systems have been almost-universally adopted: More power can be transmitted over less wire.

 

[LarryFine]

Where you _might_ see a difference is in 'efficacy', in terms of producing the desired result of room occupants feeling comfortably warm. It might be the case that a different type of heater needs to put fewer BTU into the room for the occupant to feel comfortable. The big radiant panel, for example, might make people feel comfortable while leaving the air cooler.

 

[LarryFine]

Wouldnt the single phase heater be hooked up to 2 legs or line wires out of the 3 legs from the 3 phase system and therefore still have those same number of wires? Stoves placed on a 3 phase service are done this way and equally distributed.

Yes, multiple 1ph heaters or stoves can be distributed among 3ph supplies, but the single heater in question must be re-wire-able between 1ph and 3ph for this discussion to even have any purpose.

Of course nothing would be any different if we were discussing supplying a single 1ph heater with 480v 1ph vs supplying it with two lines of a 480v 3ph source. I hope everyone understands all of that.

So, we must ask the OP to clarify whether the heater in question would be re-configured to be powered by all three lines if connected to 3ph. If so, then my responses apply; if not, then they do not.

 

[LarryFine]

Ok I see what you mean. There can be single phase heaters wired from 2 legs of a three phase source or a three phase heating element wired in either delta or wye from all 3 phases?

Yes, if the heater in question can be internally rewired, like much commercial cooking equipment can.

 

[LarryFine]

I happened upon these pics. You can see that any of them could be supplied by 1ph by simply paralleling the three elements.

 

[wwhitney]

In practice you will find a three phase load of the same KW will require less conductor. This is because ampacity is not linear with conductor size.

That's not the primary reason; that's just a secondary benefit.

Even if you just look at ampacity, the 3 phase load will require a lower total ampacity of conductors. As 3 (conductors) / sqrt(3) = sqrt(3) < 2 (conductors).

Cheers, Wayne

 

[winnie]

Huh. That is one of those 'I should have known but I didn't know.'

1000W delivered with 2 wires at 480V requires 2.08A. You have to carry 2.08A out and 2.08A back, for a total 'aggregate conductor capacity needed' of 4.16A

1000W delivered with 3 wires at 480V requires 1.2A on each of 3 wires, for a total 'aggregate conductor capacity needed' of 3.61A.

-Jon

 

[wwhitney]

Right. And 4.16 / 3.61 = 1.15 = 2 / sqrt(3). Which is the ratio you'll always get from such a computation, independent of voltage and load.

Cheers, Wayne

 

[electrofelon]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y. Where is that extra capacity coming from? Arnt there extra losses with a third conductor now?

 

[jaggedben]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y. Where is that extra capacity coming from? Arnt there extra losses with a third conductor now?

Your losses increase by 50% even though your capacity increases by 73%. Still a net gain in efficiency. But a very marginal one. (Say, if losses were 1% before, your losses are now 0.87%, a difference of 0.13%).

...

Also while that's all very interesting let's not confuse cost effectiveness of installation with the efficiency of power delivery over conductors or the efficiency of appliances use of energy. The latter are much more important advatanges of three phase than conductor losses.

 

[wwhitney]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y.

That assumes you are going to use 3 phase power on your 3 conductors. If you instead use a split phase arrangement, where one of the original conductors is now the neutral, you get 200% of the power with 150% of the conductor area. But maybe that's cheating in some sense, as it increases the maximum L-L voltage. Although you don't need to use L-L loads to realize the additional power.

Where is that extra capacity coming from?

Good question, but I'm not sure it has a good answer.

Let say you run just one conductor, the total power is 0. Now you add a second conductor to carry current X and total power Y. Where did the extra capacity come from? : - )

Here's a little chart of number of conductors vs power they can carry, where the L-L voltage is limited to some fixed maximum, likewise the current on each conductor is limited. Power values are scaled so the first non-zero entry is 1.

Conductors : Power
1 : 0
2 : 1
3 : sqrt(3) = 1.73
4 : 2
5 : 5 / (2 * cos(18 deg)) = 2.63
2n : n

Cheers, Wayne

 

[Hv&Lv]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y. Where is that extra capacity coming from? Arnt there extra losses with a third conductor now?

I want to try..

So single phase power 20 amps x 240 volts is 4800 amps.
Three phase power (20/1.732 =11.55) x 240 = 4801.

There isn’t extra power. The power is the same, the currents go down and for a motor there is always power being delivered at 120 degree separation for the three phase vs single phase where there is the lull with 180 degrees separation

Does this make sense or is this even what you were looking for?

 

[LarryFine]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y. Where is that extra capacity coming from? Arnt there extra losses with a third conductor now?

Except that the power, not the current, would remain the same, resulting in less current over more wires.

 

[winnie]

Ok so say I have a set of single phase conductors running a load with current X and total power Y. Now I add a third conductor. My total conductor area is now 150% of what it was originally. My power (assuming a reconfigurable load) with the same current X on all three legs is now 173% of Y. Where is that extra capacity coming from? Arnt there extra losses with a third conductor now?

I'm still scratching my head about this myself.

Here is a thought: Assign a value for the power delivered by each wire, by multiplying the current in the wire by the voltage relative to an arbitrary reference point. This is an instantaneous product, to get instantaneous power which you would then have to average over time. Alternatively you could consider the phase angle between voltage and current and include power factor in your calculation.

The reference point could be arbitrary, including defining one wire as '0V'.

This is completely analogous to using a Blondel compliant metering setup.

Let's pick the neutral point of our supply wires. In the case of 480V single phase, our line-reference neutral voltage is 240V. Add the third wire, and your line-reference neutral voltage climbs to 277V.

Consider the inverse case: compare a two wires supplied from a 120/240V split phase system vs 3 wires from a 208/120V three phase system. Same L-N voltage, same power delivered per conductor amp.

-Jonathan

 

[electrofelon]

Except that the power, not the current, would remain the same, resulting in less current over more wires.

Ok everyone seems confused by this, not sure why. I am thinking in terms of capacity. Assume our conductors have a max voltage of 240, and can carry 20 amps. I was thinking watts that can be supplied with those parameters in the single and three phase case. I never said anything about how many amps for the same KW in each case.

 

[LarryFine]

Ok everyone seems confused by this, not sure why. I am thinking in terms of capacity. Assume our conductors have a max voltage of 240, and can carry 20 amps. I was thinking watts that can be supplied with those parameters in the single and three phase case. I never said anything about how many amps for the same KW in each case.

Yes, but we normally design a circuit to supply a given load, and rarely design a load to suit a given circuit.

I try to remember which are the constants and which are the variables for a given theoretical example.

 

[winnie]

Ok. Assume a fixed maximum current per conductor of 20A, and assume a maximum voltage between any two conductors of 240V.

I think this just repeats the table in post 31: https://forums.mikeholt.com/threads/single-phase-vs-3-phase-efficiency.2580401/post-2912834

wires	power	power per wire
1	0	0
2	4800W	2400W
3	8314W	2771W
4	9600W	2400W
5	12618W	2523W

 

[gadfly56]

The difficulty here I think is that a poor example was chosen. Resistance heaters will always be 100% efficient. Now, if you wanted to talk about motors, that's different. Way back when we covered pumps in ChemE, the professor made a point that polyphase motors were more efficient than single phase motors, and the more the merrier. Also, something, something, startup torque. Do I recall correctly?

 

[winnie]

3 phase motors are slightly more efficient than similarly sized single phase motors.

Higher phase counts can provide tiny efficiency improvements, by reducing winding distribution factors and the like.

But the efficiency change is tiny at best.

Jonathan

 

[Jraef]

What's the wattage of a 1000W 480V 3 phase heater?

Now what's the wattage of a 1000W 480V single phase heater?


Answer: they are both 1000W... watts are watts are watts, it has nothing to do with efficiency, and yes, ALL electric heating is 100% efficient, because ALL of the electrical energy consumed by the device is converted to heat. There is zero waste.

CURRENT is different, but we don't PAY for current, we pay for watts. Wire size would be SMALLER, but you have MORE WIRES.