208V/1P - convert using square root of 3?

[malachi constant]

I have some 208V/1P air conditioners that need factored into service sizes on a large multi-family development. The manufacturer's literature provides loads in MCA. Let's say an MCA is 11.6A.

The formula I know for converting into VA is: A*V*sqrt(PH)=VA. I've always assumed on a 208V/1P branch circuit that the phase is 1, so in this case the VA would be 11.6A*208V*sqrt(1)=2413VA. However I recently heard a respected engineer comment that this (or something similar to it) is a common mistake, and that the square root of three should be used. So VA would be 11.6A*208V*sqrt(3)=4174VA.

Obviously this makes a noticeable difference in load calcs when adding 200+ of these onto a pair of 208V/3P transformers. I've always calculated it using square root of 1, and never had anyone question me (or have services be overloaded) so I think sqrt(1) is correct. Anyone want to chime in? Is there an instance where sqrt(3) -should- be used in a single phase application?

Thanks!

 

[jumper]

Ack! I am having a senior moment!

There is something about 1 phase loads on 3 phase services in the load calcs in 220. You gotta double the conductor size or something like that.

Dryers,ranges, or something similar?

 

[david luchini]

Your approach is correct. The VA of a 208V-1ph unit using 11.6A is 2412.8VA.

If you have three units balanced on a 3 phase system, the total VA of the units would be 3*2412.8=7238.4VA. The current of the 3 units on the 3 phase system would then be 7238.4VA/208V/Sqrt(3)=20.1Amps. That is where the Sqrt of 3 comes into the equation.

 

[jghrist]

The VA for each load is the voltage across the load times the load current.

For a single phase load connected ?-?, this is simply the ?-? voltage times the current. 208 x 11.6 = 2412.8 VA. Since this is on two breaker poles, you would put half of this VA on each pole. The total for the panel will add both to get the full 2412.8 VA.

If this were a ?-n load, you would use the ?-n voltage times the load current. VA = 11.6 x 120 = 11.6 x 208 ? sqrt(3) = 1392. You would put this on one breaker.

If this were a 3? load, you would use the ?-n voltage times the load current. You would put this on each of three breaker poles.

Total of all three poles would be
VA = 3 x 11.6 x 120 = 3 x 11.6 x 208 ? sqrt(3) = 4176
Since 3 ? sqrt(3) = sqrt (3), this is the same as
Total VA = sqrt(3) x 11.6 x 208 ~ 4176

I hope this doesn't confuse things.

 

[malachi constant]

Thanks all - glad to see I am not crazy after all. Have a good and long weekend!