# Power Factor - Leading/Lagging - Angles



## trying2pass

I thought I had this in the bag, but I've done more questions and it was opposite of what I was doing.

Can someone clear things up for me.

Leading and lagging power factors and their angles. I use a negative angle for a leading (+) pf and a positive angle for laggin (-) pf. Is this correct?

I've worked out other problems, where it is opposite. positive angle for leading (+) pf and negative angle for lagging (-) pf.

Which one is correct or are both correct?

Thanks in advance.


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## benbo

I'm going to take a guess, although I am horrible in power.

I believe the phase angle is always the angle theta(v)-theta(i)

For a leading circuit, the current leads the voltage. I think this is like a capacitor. So since the theta(i) &gt; theta(v) the phase angle will be negative.

For a lagging circuit, the current lags the voltage. Like an inductor. So, theta(i) &lt; theta(v) and the phase angle is positive.

Since the pf is the cosine of the phase angle, it could be positive in either case.

That's how I understand it, but I am really bad in power. I'm an electronics, communication, control guy.

Dark Knight, Wolverine, Flyer, Dustin, a few other - these guys are power experts. So I'm sure someone will answer. But I wanted to see how close I got.

:bananapowerslide:


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## Flyer_PE

Pretty close.

I'll take a stab at this even though I'll probably get it backwards. (I figure I have a 50/50 chance)

Benbo is correct in that for a leading power factor, the current waveform leads the voltage waveform and the opposite is true for the lagging value.

However, the value of theta is Theta(I) - Theta (V) so the angle between current and voltage for a leading (net capacitive) circuit is positive.

Where things usually get confusing is when the translation to power is made.

A lot of people (including myself recently) forget that S=VI*. If you are typically looking for magnitudes, you may forget that you need to use I conjugate instead of just I.

The result is that a positive theta between current and voltage (capacitive circuit) will have a negative power angle (i.e. value of Q will be negative). Likewise, a negative theta between current and voltage (inductive circuit) will have a positive power angle (i.e. value of Q will be positive).

Let me know how well I did. :brick:


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## z06dustin

I agree with everything Flyer said. Some things to add:

ELI the ICE man.

Voltage leads current in an inductor. (E before I in an L)

Current leads voltage in a cap. (I before E in a C)

Given that, use S=VI* and you can determine if the power vector (in VA) is leading or lagging.

I think if you see conflicting answers to this question in different sources, it's because it's really a confusing subject. I had teachers say leading/lagging referring to the current, and then another who referred it to the total power (S). Both are correct, but both are also opposite, so make sure you know what angle (current, impedance, or power?) it is that they're referencing.

Also, when I took the test, I had a master cheat sheet folder, which was basically 3 pages of stuff like this. Make sure you jot it down in a way you can remember, when it makes sense to you.

I applaud you looking into this now, the fact that you're figuring it out now means you WONT have to figure it out during the test! Every second counts.


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## trying2pass

z06dustin said:


> I agree with everything Flyer said. Some things to add:
> ELI the ICE man.
> 
> Voltage leads current in an inductor. (E before I in an L)
> 
> Current leads voltage in a cap. (I before E in a C)
> 
> Given that, use S=VI* and you can determine if the power vector (in VA) is leading or lagging.
> 
> I think if you see conflicting answers to this question in different sources, it's because it's really a confusing subject. I had teachers say leading/lagging referring to the current, and then another who referred it to the total power (S). Both are correct, but both are also opposite, so make sure you know what angle (current, impedance, or power?) it is that they're referencing.
> 
> Also, when I took the test, I had a master cheat sheet folder, which was basically 3 pages of stuff like this. Make sure you jot it down in a way you can remember, when it makes sense to you.
> 
> I applaud you looking into this now, the fact that you're figuring it out now means you WONT have to figure it out during the test! Every second counts.



I wasn't able to get online for a couple days. Thanks for your responses, but I'm still somewhat confused. If you take a look at NCEES #517 with the synch. motor at 8KVA with a leading .7pf(+) and induction motor at 14.43A with lagging .6pf(-), voltage is 480V. Question asked for the power factor. Solutions shows using a negative angle for the synch. motor with (+) pf and a positive angle for the induction motor with (-) pf. I got the right answer, but when I was doing NCEES #129 (question asked for voltage at Panel A), I got it wrong becuase I used a positive angle for the lagging .8pf(-). I don't see what the difference of the two. Not yet anyway.

Again, thanks!


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## Flyer_PE

trying2pass said:


> I wasn't able to get online for a couple days. Thanks for your responses, but I'm still somewhat confused. If you take a look at NCEES #517 with the synch. motor at 8KVA with a *leading .7pf(+)* and induction motor at 14.43A with *lagging .6pf(-)*, voltage is 480V. Question asked for the power factor. Solutions shows using a negative angle for the synch. motor with (+) pf and a positive angle for the induction motor with (-) pf. I got the right answer, but when I was doing NCEES #129 (question asked for voltage at Panel A), I got it wrong becuase I used a positive angle for the *lagging .8pf(-)*. I don't see what the difference of the two. Not yet anyway.
> Again, thanks!


For power, a leading power factor indicates a negative value of theta. If you look at the NCEES solution to #517, the angle for the synchronous motor is -45.6o. You can have it exactly backwards and still get the right answer for #517 because it's not directly asking for the sign of the angle. Between the synchronous and induction motors, so long as you have one positive and one negative, you'll get the magnitude correct. Also, so long as you stay consistent, you will even be able to tell, correctly, that the net power factor is lagging. What they don't ask, is the sign of the angle.

When looking at #129, the value they are giving you is current, not power. Remember that S=VI***. A lagging value in terms of current has a negative angle with respect to voltage. So 400 amps at 0.8 pf lagging is actually 400 amps at an angle of -36.9o.


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## trying2pass

Flyer_PE said:


> trying2pass said:
> 
> 
> 
> I wasn't able to get online for a couple days. Thanks for your responses, but I'm still somewhat confused. If you take a look at NCEES #517 with the synch. motor at 8KVA with a *leading .7pf(+)* and induction motor at 14.43A with *lagging .6pf(-)*, voltage is 480V. Question asked for the power factor. Solutions shows using a negative angle for the synch. motor with (+) pf and a positive angle for the induction motor with (-) pf. I got the right answer, but when I was doing NCEES #129 (question asked for voltage at Panel A), I got it wrong becuase I used a positive angle for the *lagging .8pf(-)*. I don't see what the difference of the two. Not yet anyway.
> Again, thanks!
> 
> 
> 
> For power, a leading power factor indicates a negative value of theta. If you look at the NCEES solution to #517, the angle for the synchronous motor is -45.6o. You can have it exactly backwards and still get the right answer for #517 because it's not directly asking for the sign of the angle. Between the synchronous and induction motors, so long as you have one positive and one negative, you'll get the magnitude correct. Also, so long as you stay consistent, you will even be able to tell, correctly, that the net power factor is lagging. What they don't ask, is the sign of the angle.
> 
> When looking at #129, the value they are giving you is current, not power. Remember that S=VI***. A lagging value in terms of current has a negative angle with respect to voltage. So 400 amps at 0.8 pf lagging is actually 400 amps at an angle of -36.9o.
Click to expand...


Thanks Flyer! That makes sense and definitely clears things up.


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## HornTootinEE

*Rule of Thumb:* Lead/Lag on a power factor will be referring to the angle of the current relative to it's respective voltage.

It is confusing with the conjugate in the apparent power magnitude equation.

If you see a lagging power factor, it means the current lags the voltage and since S=VI*, your load is consuming reactive power and the power angle (S-assuming current direction is flowing into the positive voltage terminal-passive sign convention) is positve. Your power triangle will have an opposite leg that is positive. Positive Watts (P) and Positive vars (Q).

If you see a leading power factor, it means the current leads the voltage and since S=VI*, your load is supplying reactive power and the power angle (S-assuming again the passive sign convention) is negative. Positive Watts and negative vars.

On a generator using the passive sign convention, You will see mostly negative quantites for S, P, and Q.

If you have a lagging power factor, on a real system the voltage is probably sagging a bit and you need to correct with capacitance. If you have a leading power factor, the voltage may be a little high, you'd need to correct with an inductor (reactor in the industry lingo).

Inductive motors (90% of motor loads) will almost always have lagging power factors-they "consume" reactive power (vars). I say almost simply because the motor itself will ALWAYS, but if it's connected with some sort of starter or VFD, it may look different to the system supplying the motor.


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