Single phase vs 3 phase efficiency

[electrofelon]

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

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

No way, get real, we all know a pound of feathers weighs less than a pound of steel.

 

[winnie]

A kilogram of feathers definitely weighs less than a kilogram of steel. At least if you are weighing things in an atmosphere...

 

[kwired]

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

Which may end up being less copper overall.

 

[kwired]

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

Now consider that for most part you will need 14 AWG conductors to comply with NEC in either situation but the three phase application needs three of them instead of two. This isn't as big of an impact on circuits that have smaller conductors to begin with

But then compare the difference with say a circuit that draws 100 amps per line in three phase configuration. You went from 3 -3 AWG for three phase to 2- 2/0 AWG to handle same load at single phase at same voltage. Which is 266200 circular mils vs 108340 in total cross section of the copper portion of conductors. Also need larger raceway to contain the single phase than the three phase conductors.

 

[kwired]

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?

If you have a heater assembly with three identical elements all connected in parallel across a single phase source current of supply conductors is 3 times the current of an individual element. Connect them in delta to to a three phase source of same voltage and supply conductors are carrying 1.73 times the current of an individual element - still delivering same power.

If you would happen to connect those three elements in wye instead of delta still delivering same volts you would have less power as there would only be 58% of rated voltage across each individual element in that configuration.

 

[electrofelon]

If you have a heater assembly with three identical elements all connected in parallel across a single phase source current of supply conductors is 3 times the current of an individual element. Connect them in delta to to a three phase source of same voltage and supply conductors are carrying 1.73 times the current of an individual element - still delivering same power.

If you would happen to connect those three elements in wye instead of delta still delivering same volts you would have less power as there would only be 58% of rated voltage across each individual element in that configuration.

You missed this part of my post, neither one of those situation was what I was saying

assuming a reconfigurable load) with the same current X on all three legs

 

[tortuga]

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

I tend to think of it in 'electrical degrees'.

Phase Wires​	Electrical Degrees​	Power​
2​	180°​	1​
3​	120°​	1.732​
4​	90°​	1.414​

 

[wwhitney]

I tend to think of it in 'electrical degrees'.

I don't think the lower right entry is correct, probably you want "2" there. But maybe you can define what you mean by "power" to confirm.

Cheers, Wayne

 

[tortuga]

I don't think the lower right entry is correct, probably you want "2" there. But maybe you can define what you mean by "power" to confirm.

Cheers, Wayne

Good catch, I was thinking a two phase system would be sqrt 2 like a three phase system is sqrt 3.
But that would only apply for a 3 wire two phase as noted in T430.249. Even then a two phase 3-wire 1.414 would only apply to the 'common' wire of the two phases.

Phase​	Wires (L-L load)​	Watts​	Volts (V)​	Multiplier (M)​	V X M​	Amps per wire​
Single (180°)​	2​	1000​	480​	1​	480​	2.08​
Two (90°)​	3​	1000​	480​	1.414​	678.72​	1.47​
Three (120°)​	3​	1000​	480​	1.732​	831.36​	1.2​
Two (90°)​	4​	1000​	480​	2​	960​	1.04​

 

[tortuga]

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

Looking at the motor tables in the code for compassion of 1 HP 240V motors, assuming PF is equal or negligible there seems to be a pretty big spread of efficiency;

Phase​	Wires (L-L load)​	HP​	VA (V X A)​	L-L Volts (E)​	Voltage Multiplier (M)​	V= (E X M)​	Max Amps per wire​
Single (180°)​	2​	1​	1920​	240​	1​	240​	8​
Three (120°)​	3​	1​	1746​	240​	1.732​	415.68​	4.2​
Two (90°)​	4​	1​	1536​	240​	2​	480​	3.2​
Two (90°)​	3​	1​	1527​	240​	1.414​	339.36​	4.5​
DC​	2​	1​	1128​	240​	1​	1​	4.7​