Is There a Standard Power Factor Convention for Voltage and Current Angles?

[Marcin H]

Homework Statement

Is there a power factor convention when it comes to the angles of a given current and voltage? In one class I learned that PF = cos(θ_V - θ_I) but in another the professor claims (I still think he is wrong) the convention for that class is PF=cos(θ_I - θ_V).

Here is a example where I run into a problem with this:

Consider a circuit, where a 100-V source, rated at 3,000VA, supplies a single-phase electric motor. An ammeter on the motor load indicates that the current is 20A and lags by (pi/3) radians with respect to the voltage

Find the power factor and draw the power triangle.

Homework Equations

Power triangle
PF= I don't know what "convention" is correct if there even is one
S=VI* --> DEFINITION OF COMPLEX POWER.

The Attempt at a Solution

depending on the "convention" you use you will get either cos(π/3) or cos(-π/3) for the power factor which both equal 1/2. Now how do you determine whether the angle is positive or negative on your power triangle using this information? Because you will get 2 different answers according to the "different conventions"

What frustrates me the most is that if you use the DEFINITION of complex power, it is obvious that you will have a positive angle on the power triangle. By definition. And for this problem (on a quiz that I got wrong) a positive angle was marked as incorrect.

From the given information we have:

V=100V ∠ 0˚ (we can assume this is reference. We usually assume voltage as reference.)
I=20A ∠ -(π/3)˚ (current lags the voltage by π/3. Voltage is 0˚. This means that the angle on the current is negative.)

S=VI* (DEFINITION OF COMPLEX POWER...)

The conjugate of "I" will give you a POSITIVE angle for your complex power. Therefore you will have a positive angle (first quadrant) on your power triangle.

I asked the first professor that I agree with and he says that I am right and the other one is wrong. The other one claims it's just a "convention". I don't know what to do here and I am extremely frustrated because you can obviously see by definition that the complex power will have a positive angle.Here is another example from an old exam that does something similar. The power triangle they have or the complex power they found is not correct according to the definition of complex power. My professor (for a power and energy systems class ECE330@UIUC, taught over 40 years, department head, etc.,) said, "This ECE333 notation is contradictory to all legitimate textbooks on electric power and energy systems."

 

[cnh1995]

In one class I learned that PF = cos(θ_V - θ_I) but in another the professor claims (I still think he is wrong) the convention for that class is PF=cos(θ_I - θ_V).

Mathematically, it doesn't matter , since
cos(-θ)=cosθ.

But impedance Z is given as Z=V∠θ/I∠Φ.
∴Z=(V/I)∠(θ-Φ)
so the power factor is cos(θ-Φ) and as you can see, it is phase angle of voltage - phase angle of current.

V=100V ∠ 0˚ (we can assume this is reference. We usually assume voltage as reference.)
I=20A ∠ -(π/3)˚ (current lags the voltage by π/3. Voltage is 0˚. This means that the angle on the current is negative.)

Right. The complex power is indeed given by S=VI*, and it is NOT a convention. (I mean not using S=VI and using S=VI* is not a convention).

The complex power in this example would be S=100*20∠(π/3)
In rectangular form, it is S=1000+j1732.

Hence, you can see if the reactive power is positive, the current is lagging.

Take the same example, just change the phase angles of V and I. Take V=100∠30° and I=20∠-30°. Phase difference between both is still the same i.e. 60°.
See what you get when you use S=VI and when you use S=VI*.

In the other problem in your OP, the question says R and L are wired in parallel (typo?) but the circuit drawn is a series circuit and your calculations there look correct to me. With which part of that question does your professor have a problem?

 

[Marcin H]

The problem comes up when you are looking for your complex power or asked to draw a power triangle. One professor (the one that is incorrect) said that drawing the power triangle with a positive angle is WRONG. He claims that for that first problem that I mention that the angle is negative. This can be easily proven wrong by using S=VI* (a definition) but he claims that it is a convention in his class to use θi-θv which is why he is getting that angle. because of that ridiculous "convention", which I can't seem to find anywhere else on the internet or in other books, he says that for that first problem the imaginary power(Q) is negative, which is wrong. I don't understand why he is using θi-θv. Mathematically, yes it does not make a difference. but the PF angle (PF = cos(θ)) that θ will determine whether it's lagging or leading and with his method you get the exact opposite of what yo would get doing it the way everyone else and every other book does.

Edit* and yes i assume that was a typo. But the solution for that problem is also wrong for the same reason. This is an exam from the proffesor that uses θi-θv to find his PF angle. That is why he says his PF is cos(-45) instead of cos (45). But the power triangle is wrong. It should have a positive angle. not negative.

 

[cnh1995]

This is an exam from the proffesor that uses θi-θv to find his PF angle. That is why he says his PF is cos(-45) instead of cos (45). But the power triangle is wrong. It should have a positive angle. not negative.

Does your professor know this formula S=VI*? Has he ever used it in class?
Using this formula, it turns out that lagging VARs are positive and leading VARs are negative.

Your professor agrees that the current is 'lagging', but he thinks lagging current means negative VAR (sinΦ is negative according to his notation). This is OK as a convention, but he's probably the only one using it and it fails when you use S=VI* , as it contradicts his answer. According to his "convention", he would have to use S=IV* instead.
(I don't see the point in going against the convention though, that too in an EE class. The IEEE definition of complex power is S=VI*.)

So, for his class alone, take power factor angle as θ_i-θ_v and draw the power triangle accordingly (lagging VARs-negative and leading VARs-positive).
S=VI* would not work here, instead use S=IV*.

For the rest of your career as an EE, always use power factor angle as θ_v -θ_i and S=VI*.

 

[Marcin H]

Does your professor know this formula S=VI*? Has he ever used it in class?
Using this formula, it turns out that lagging VARs are positive and leading VARs are negative.

Your professor agrees that the current is 'lagging', but he thinks lagging current means negative VAR (sinΦ is negative according to his notation). This is OK as a convention, but he's probably the only one using it and it fails when you use S=VI* , as it contradicts his answer. According to his "convention", he would have to use S=IV* instead.
(I don't see the point in going against the convention though, that too in an EE class. The IEEE definition of complex power is S=VI*.)

So, for his class alone, take power factor angle as θ_i-θ_v and draw the power triangle accordingly (lagging VARs-negative and leading VARs-positive).
S=VI* would not work here, instead use S=IV*.

For the rest of your career as an EE, always use power factor angle as θ_v -θ_i and S=VI*.

Will do. Thanks. His only argument for using this "convention" is because the book uses it, but there is no such thing in the book like that. It is just infuriating that I got a problem correct on a quiz and I lost 40/200 for it. It's ridiculous that this is even being taught to students.

 

[cnh1995]

Will do. Thanks. His only argument for using this "convention" is because the book uses it, but there is no such thing in the book like that. It is just infuriating that I got a problem correct on a quiz and I lost 40/200 for it. It's ridiculous that this is even being taught to students.

See what he says about S=VI*. If he is insisting on using his "convention" , I believe he should also clarify that S=VI* is no longer applicable and one should use S=IV*. (This would mean he has thought this through and is not mistaken).
Otherwise, using different convention just for power factor is going to be very confusing for students.

 

[Marcin H]

See what he says about S=VI*. If he is insisting on using his "convention" , I believe he should also clarify that S=VI* is no longer applicable and one should use S=IV*. (This would mean he has thought this through and is not mistaken).
Otherwise, using different convention just for power factor is going to be very confusing for students.

Good news. The professor (ECE 330/the one that agrees with me) talked to the 333 professor (the wrong one) and it seems that he got him to admit that he is wrong about his convention. I'll have to wait till tomorrow to see what the 333 professor(the wrong one) says about my quiz and his "convention, but I will take that as a victory.