Three Phase Ampacity Calculations

[donf]

I sent this question directly to Mike although I believe this is the correct process, I apologize for my error!

A student posed a question that I cannot answer other to say, "That's the way it is."

Appendix "D", Sample D3 (a). The method used to calculate the Ampacity of the 3p load. Subtotal, actual load (actual load in amperes) formula

99,000 VA / (480V * 1,732) = Ampacity
99,000/ 831 = 119 Amps

The question is, why are we multiplying a 3p voltage, 480V by 1.732 because 480V is already a 3p voltage.

Can anyone answer this question, please.

 

[don_resqcapt19]

To account for the current per phase. With a single phase system, the current for the 99,000 vA would be 206.25 amps, but for a 3 three phase system you divide the single phase current by the square root of 3, resulting in a current of 119 amps. The square root of 3 plays a part in all 3 phase calculations.

 

[infinity]

The question is, why are we multiplying a 3p voltage, 480V by 1.732 because 480V is already a 3p voltage

Yes it's 480 volts but it can be 480 volt single phase or 480 3 phase. For single phase the 1.73 factor is not used but for 3 phase it is used. 1.73 is equal to the square root of 3 which has to do with the phase angle of the 3 phase voltage.

 

[d0nut]

The square root of 3 (1.732) factor comes is due to the 120 degree phase shift between the phases. If you actually calculate the current of each phase as a vector, you will see where the square root of 3 comes into play.

 

[donf]

Thank you!

 

[don_resqcapt19]

Some prefer to do the calculation by dividing the load by 3, and then dividing that by the line to neutral voltage of 277.
99,000/3/277=119amps

 

[d0nut]

Some prefer to do the calculation by dividing the load by 3, and then dividing that by the line to neutral voltage of 277.
99,000/3/277=119amps

Exactly. Another way to say the exact same thing. 277*3=480*Sqrt(3)=831.