Calculating Reactive Power

[Student323]

Hi everyone, I am studying for the FE exam and the concept of apparent power, real power, and reactive power is still somewhat shaky for me.
Problem:

I tried solving the problem above as follows:



The book solution is as follows:


Is there a way to do it the same method I did but fix it to match the final solution? I wasn't sure how to go about doing that. Any insight will be greatly appreciated. I am trying to understand the concepts of intelligibly using apparent, real, and reactive power equations instead of just getting solutions. The book solution is confusing.

This problem is from the book " FE Electrical and Computer Review Manual"

 

[wwhitney]

Is there a way to do it the same method I did but fix it to match the final solution?

Your approach would work if you find the reactive power of each load in isolation, and then take the difference of the reactive powers, since one load is lagging and one load is leading.

That's sort of the point--apparent powers don't add and subtract normally, but the individual components consisting of real power and reactive power do.

Cheers, Wayne

 

[jim dungar]

Your method might have worked if both PF had been leading or lagging. Notice how their solution subtracted the Q values.

 

[Student323]

Your approach would work if you find the reactive power of each load in isolation, and then take the difference of the reactive powers, since one load is lagging and one load is leading.

That's sort of the point--apparent powers don't add and subtract normally, but the individual components consisting of real power and reactive power do.

Cheers, Wayne

So, just to clarify To find the reactive power would I need to use Q=IVSine(Theta) or Q=PTan(Theta)? I get confused on when to use each one.

 

[wwhitney]

Your method might have worked if both PF had been leading or lagging.

To be exact, you'd also need both PFs to be identical. Of course if they differ only slightly, the error from the OP's approach would be small.

Cheers, Wayne

 

[Student323]

Your method might have worked if both PF had been leading or lagging. Notice how their solution subtracted the Q values.

Thanks, I didn't know that. I will keep that in mind for the exam

 

[wwhitney]

So, just to clarify To find the reactive power would I need to use Q=IVSine(Theta) or Q=PTan(Theta)?

Assuming those are the correct formulas (I didn't check), you could use either.

But I was saying you can also just use the same approach you had. Your equation Qtotal = sqrt(Stotal^2 - Ptotal^2) is not correct. But it still works for each load individually, i.e. Q1 = sqrt(S1^2 - P1^2), likewise for Q2, S2, and P2.

So you can do that for each of the two loads, and then recognize that this formula for Q doesn't give you the sign of Q. Since one is leading and one is lagging, one has a minus sign and one has a plus sign. That means when you add up the reactive powers, you end up subtracting the magnitudes. Since the question only asks about the magnitude of the result, you don't have to worry about which one is positive and which one is negative (I don't actually know the convention), just that the signs are opposite.

Cheers, Wayne

 

[Student323]

Assuming those are the correct formulas (I didn't check), you could use either.

But I was saying you can also just use the same approach you had. Your equation Qtotal = sqrt(Stotal^2 - Ptotal^2) is not correct. But it still works for each load individually, i.e. Q1 = sqrt(S1^2 - P1^2), likewise for Q2, S2, and P2.

So you can do that for each of the two loads, and then recognize that this formula for Q doesn't give you the sign of Q. Since one is leading and one is lagging, one has a minus sign and one has a plus sign. That means when you add up the reactive powers, you end up subtracting the magnitudes. Since the question only asks about the magnitude of the result, you don't have to worry about which one is positive and which one is negative (I don't actually know the convention), just that the signs are opposite.

Cheers, Wayne

I think i see your point now. I got the same answer after doing them individually, thanks!

 

[Carultch]

Here's a visual that shows the way the loads add up as vectors in the phase space, drawn to scale with this problem's data.