# Unbalanced Three Phase Power Calculations

#### threePhase

Joined May 3, 2018
4
How to calculate total three phase Active Power, Reactive Power and Apparent Power if active, reactive and apparent power of each phase are given:

Active power phase1: 2432.96 W
Active power phase2: 2012.01 W
Active power phase3: 1843.34 W

Reactive Power phase1: 1339.46 VAR
Reactive Power phase2: 1146.34 VAR
Reactive Power phase3: 1076.47 VAR

Apparent Power phase1: 2777.31 VA
Apparent Power phase2: 2315.66 VA
Apparent Power phase3: 2134.64 VA

What would be total 3 phase Active Power, 3 phase Reactive Power, 3 phase Apparent Power?
• Total three phase active power = Active Power phase1 + Active Power phase2 + Active Power phase3
• Total three phase reactive power = Reactive Power phase1 + Reactive Power phase2 + Reactive Power phase3
• Total three phase apparent power = Apparent Power phase1 + Apparent Power phase2 + Apparent Power phase3
Anyone know if this is correct ?

#### WBahn

Joined Mar 31, 2012
24,854
MOD NOTE: You already had another thread on this problem (that I moved to Homework Help). It would have been better to just keep things to that one thread. But since you started this one with additional information, I've closed the other one in favor of this one.

#### WBahn

Joined Mar 31, 2012
24,854
How to calculate total three phase Active Power, Reactive Power and Apparent Power if active, reactive and apparent power of each phase are given:

Active power phase1: 2432.96 W
Active power phase2: 2012.01 W
Active power phase3: 1843.34 W

Reactive Power phase1: 1339.46 VAR
Reactive Power phase2: 1146.34 VAR
Reactive Power phase3: 1076.47 VAR

Apparent Power phase1: 2777.31 VA
Apparent Power phase2: 2315.66 VA
Apparent Power phase3: 2134.64 VA

What would be total 3 phase Active Power, 3 phase Reactive Power, 3 phase Apparent Power?
• Total three phase active power = Active Power phase1 + Active Power phase2 + Active Power phase3
• Total three phase reactive power = Reactive Power phase1 + Reactive Power phase2 + Reactive Power phase3
• Total three phase apparent power = Apparent Power phase1 + Apparent Power phase2 + Apparent Power phase3
Anyone know if this is correct ?
You have part of it correct, but if I tell you which parts I don't think that will help you because I don't get the feeling you would understand why the parts that are correct are correct and why the rest isn't.

So this is what I would recommend you do.

Take a single phase circuit with two parallel load, one inductive and one reactive but both with a series resistive element. Choose the components so that all of the powers are markedly different but within a factor of two or three.

Figure out the various powers for the individual loads and for the combined load.

Look at the results and see if you can figure the relationships that hold and why they hold.

If you are still confused, try another case by putting these same two loads in series and repeating the analysis.

#### threePhase

Joined May 3, 2018
4
It’s not about combined loads at single phase. It’s about unbalanced three phase system which means three power triangles need to be solved.
Active and Reactive power being the X and Y projection of apparent power must be added respectively.
So
3 phase active power = 2432.96 + 2012.01 + 1843.34 = 6288.31 W
3 phase reactive power = 1339.46 + 1146.34 + 1076.47 = 3562.27 VAR

Where 3 phase apparent power = sqrt(3phaseActivePower^2 + 3phaseReactivePower^2)= 7227.233 VA

But if we add apparent power per phase we get the same result.
3 phase apparent power=2777.3 + 2315.66 + 2134.64 = 7227.6

Do I approach it correctly?

#### WBahn

Joined Mar 31, 2012
24,854
It’s not about combined loads at single phase. It’s about unbalanced three phase system which means three power triangles need to be solved.
That you seem to think that there is something fundamentally different between single-phase power and three-phase power suggests that your understanding of the material is based on rote memorization of formulas and not on any understanding of the underlying fundamental principles.

How does the load on one phase know anything about the load on the other phases? Each load thinks its on a single phase circuit.

Active and Reactive power being the X and Y projection of apparent power must be added respectively.
So
3 phase active power = 2432.96 + 2012.01 + 1843.34 = 6288.31 W
3 phase reactive power = 1339.46 + 1146.34 + 1076.47 = 3562.27 VAR

Where 3 phase apparent power = sqrt(3phaseActivePower^2 + 3phaseReactivePower^2)= 7227.233 VA

But if we add apparent power per phase we get the same result.
3 phase apparent power=2777.3 + 2315.66 + 2134.64 = 7227.6

Do I approach it correctly?
DO you get the same result? Your data claims to be accurate to six significant figures? Do your answers agree to a comparable level?

As I said before, you have a mix of things that are correct and things that aren't.

The data for this problem was carefully chosen so that you could work the problem the right way and get the correct answer or you could work it the wrong way and get almost the correct answer.

Since you don't know which is the correct way and which is the wrong way, you think you are getting the same result with both. But while one really is correct, the other is only numerically very close due to pure coincidence (well, because the person designing the problem set about to force that coincidence to happen).

In order to figure it out which is which, if you don't understand the concepts well enough to do so from a theoretical basis, use an example that is extremely unlikely to have such a coincidence. Because real power is real power and reactive power is reactive power, it doesn't matter whether you use single phase or three phase for your example. Single phase is a lot easier to work with. But since you don't grasp this, you can certainly come up with a three phase problem and work it, instead.