3-phase Delta power

[philly]

Ok so I know that to calculate the total power supplied by a balanced three phase wye source is to do one of two things. You can multiply the L-L voltages by the the line currents and then multiply by 1.73 to get the total power. Or you could add the individual powers across each wye brance and sum then together to get the total power. The power on each brance is calculated by multiplying the L-N voltage times the current on the branch.
An example of a 480V 100A system.

1) P = V(L-L)*A_line*1.73= 480*100*1.73 = 83.04kVA

2) P = V(L-N)*A_line*3 = (277)(100(3) = 83.1kVA

What about for a delta system? Can you simply take the power across each balanced delta element and sum them for the total power supplied by the system. I know you can find the total power by multiplying the L-L voltage by the line current and then multiplying by 1.73, but can you add each of the three power elements as well to arrive at the total power? My calculations below show that it looks like you can do it this way but I just wanted to verify?

1) P = V(L-L) * A_line*1.73 = 480 * 100 * 1.73 = 83.04kVA

2) A_load = A_line / 1.73 = 100 / 1.73 = 57.8A

P = V(L-L) * A_load * 3 = 480 * 57.8 * 3 = 83.23kVA

 

[LarryFine]

. . . can you add each of the three power elements as well to arrive at the total power?

Absolutely.

 

[philly]

I was told by someone at technical support for a Fluke power analyzer that you could not calculate delta power this way, which I did not believe.

They said thier analyzer uses the two wattmeter method for calculating total power and that you could not do as I stated and just add the individual powers.

I know because of the CT placement that the analyzer cannot measure L-L currents (or maybe it can calculate them) but I dont know why they just can use the line currents to calculate a total power, and rather use the two wattmeter method.

 

[Smart $]

I was told by someone at technical support for a Fluke power analyzer that you could not calculate delta power this way, which I did not believe.

They said thier analyzer uses the two wattmeter method for calculating total power and that you could not do as I stated and just add the individual powers.

I know because of the CT placement that the analyzer cannot measure L-L currents (or maybe it can calculate them) but I dont know why they just can use the line currents to calculate a total power, and rather use the two wattmeter method.

It's a matter of accuracy. Using line currents without their associated power factor introduces errors.

 

[philly]

It's a matter of accuracy. Using line currents without their associated power factor introduces errors.

In a wye configuration the meter or analyzer will directly measure the L-N voltage phase angle. Therefore is can compare the line current phase angle to the L-N voltage phase angle to calculate the power factor.

However I guess in a delta arrangement there is no direct input to the meter for a L-N voltage phase angle, it is only measuring L-L phase angles. Therefore the meter would have to assume that the L-N phase angle was 30deg ahead of the measured L-L phase angle and thus calculate power off of this assumed 30deg shift. This may or may not be accurate.

Is this what you were referring to regarding accuracy?

 

[Smart $]

In a wye configuration the meter or analyzer will directly measure the L-N voltage phase angle. Therefore is can compare the line current phase angle to the L-N voltage phase angle to calculate the power factor.

However I guess in a delta arrangement there is no direct input to the meter for a L-N voltage phase angle, it is only measuring L-L phase angles. Therefore the meter would have to assume that the L-N phase angle was 30deg ahead of the measured L-L phase angle and thus calculate power off of this assumed 30deg shift. This may or may not be accurate.

Is this what you were referring to regarding accuracy?

Well, sorta... My comment on accuracy was more that your OP was regarding kVA. When power factor enters the picture, we're talking power in Watts (i.e. W or kW), and I'm assuming tech support is taking the same position.

Otherwise, yes... but I assume the analyzer can also determine L-L voltage angles, so it does not have to assume a 30? phase shift. It simply calculates based on the relative phase shift of the line currents to L-L voltages. Additionally, even delta systems have a system neutral reference. There may be no connection for this reference, but it exists in [almost?] all other regards.

 

[philly]

Well, sorta... My comment on accuracy was more that your OP was regarding kVA.
.

What exactly was the accuracy that you were referring to.

Otherwise, yes... but I assume the analyzer can also determine L-L voltage angles, so it does not have to assume a 30? phase shift.
.

Yes but in a delta how does it measure a L-N voltage phase angle which is used for power factor calculation. Because there is no physical measurement in a delta, I was thinking that it was assumed.

There may be no connection for this reference, but it exists in [almost?] all other regards.

How is this exactly? Capacitive coupling?

 

[Smart $]

What exactly was the accuracy that you were referring to.



Yes but in a delta how does it measure a L-N voltage phase angle which is used for power factor calculation. Because there is no physical measurement in a delta, I was thinking that it was assumed.




How is this exactly? Capacitive coupling?

Simply the accuracy of power in terms of kVA versus kW, i.e apparent versus real.

Three phase systems, delta or wye configured have a circular voltage relationship. After all, the generated emf is a result of rotating windings in a magnetic field.

Given the preceding, plot the three voltage vectors of a either wye or delta or both. The neutral will always be at the center of a circle which intersects the three voltage points. Just the nature of the beast.

To verify, start with an energized delta secondary, grounded or not does not matter. Connect three appropriately-sized resistors (e.g. heating elements) of equal value in a wye configuration (or you could use a 3? wye-configured motor). Measure the voltage line to wye intersection. It will be, subject to practical tolerances, the line-to-line voltage divided by the square root of three. The phase angle will be halfway in between the line-to-line-to-line voltage angles. If line-to-line phase angles are measured, line-to-neutral phase angles can be calculated... no assumption required.