Using 175.68 instead of 208 volts to determine the VA load for B Phase (Hi Leg)

[IWIRE52]

I am trying to understand why the 175.68 volts instead of 208 volts works on the Hi Leg to calculate the correct total load for a 120/240 Hi Leg Delta system?

Example: You have 100 Amps of 1 phase 120/240 load and 50 amps of 3 phase 240 volt load. You normally calculate the 100 amps of 120/240 load as 24,000VA, and the 50 Amps of 240, 3 phase load as 50x240x1.732=20,784VA, for a total of load of 44,784VA.

Alternately if you calculate the phases independently by their voltage, you get the following:
A phase 150Ax120V=18,000VA
B phase 50Ax208V=10,400VA (Using 120V here as well, is incorrect)
C phase 150Ax120V=18,000VA
Total 18,000VA+10,400VA+18,000VA=46,400VA which is incorrect.

But if you calculate the phases independently this way the result is correct.
A phase 150Ax120V=18,000VA
B phase 50Ax175.68V=8,784VA
C phase 150Ax120V=18,000VA
Total 18,000VA+8,784VA+18,000VA=44,784VA, which is correct.

I have tried it on other configurations and it seems to work using the 175.68 Volts for B Phase (Hi Leg) but I am not sure why this works mathematically?

 

[wwhitney]

175.69 = 240 * (sqrt(3) - 1)

If the 3 phase line current is X, and if you include X in your A and C currents, you are already including 240 * X. The full 3 phase power is 240 * sqrt(3) * X. So the discrepancy is 240 * (sqrt(3) - 1) * X. Which is the amount your method assigns to the B phase.

Cheers, Wayne

 

[IWIRE52]

I am trying to understand why the 175.68 volts instead of 208 volts works on the Hi Leg to calculate the correct total load for a 120/240 Hi Leg Delta system?

Example: You have 100 Amps of 1 phase 120/240 load and 50 amps of 3 phase 240 volt load. You normally calculate the 100 amps of 120/240 load as 24,000VA, and the 50 Amps of 240, 3 phase load as 50x240x1.732=20,784VA, for a total of load of 44,784VA.

Alternately if you calculate the phases independently by their voltage, you get the following:
A phase 150Ax120V=18,000VA
B phase 50Ax208V=10,400VA (Using 120V here as well, is incorrect)
C phase 150Ax120V=18,000VA
Total 18,000VA+10,400VA+18,000VA=46,400VA which is incorrect.

But if you calculate the phases independently this way the result is correct.
A phase 150Ax120V=18,000VA
B phase 50Ax175.68V=8,784VA
C phase 150Ax120V=18,000VA
Total 18,000VA+8,784VA+18,000VA=44,784VA, which is correct.

I have tried it on other configurations and it seems to work using the 175.68 Volts for B Phase (Hi Leg) but I am not sure why this works mathematically?

175.69 = 240 * (sqrt(3) - 1)

If the 3 phase line current is X, and if you include X in your A and C currents, you are already including 240 * X. The full 3 phase power is 240 * sqrt(3) * X. So the discrepancy is 240 * (sqrt(3) - 1) * X. Which is the amount your method assigns to the B phase.

Cheers, Wayne

Wayne, Thanks for the info. I am still not sure how you came up with that math. Could you link me to a website or explain the how we get “-1” in the equation in a little more detail.

 

[wwhitney]

Could you link me to a website or explain the how we get “-1” in the equation in a little more detail.

You need to add sqrt(3) * something [where something = 240V * 3 phase line current]. You've already added something [which is the same as 1 * something]. And sqrt(3) * something - 1 * something = (sqrt(3) - 1) * something [multiplication distributes over addition/subtraction]. So that latter amount is how much more you need to add.

Cheers, Wayne