Power Factor

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mull982

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I had a question in regards to power factor that I was hoping someone could help me out with. If I have a lagging power factor, lets say 80% I believe that this means that the voltage is lagging the current. Is this correct. Vise Versa if I have a leading power factor this means that the voltage is leading the current?

Is a lagging power factor caused by an inductive or capacitive circuit load. How about with a leading power factor, is it caused by an incuctive or capacitive circuit load? What circuit characteristics determine weather the power factor is leading or lagging?

Thanks for the help.

Mull982
 
Remember this: ELI the ICE man.

ELI: Voltage (E) leads the current (I) in an inductor (L).
ICE: Current (I) leads the voltage (E) in a capacitor (C).

It's easy to associate a "C" with a "Capacitor." I'm not sure how to suggest you associate, and remember the association of, "L" with "Inductor."
 
zog said:
L is a standard designation for inductance. Ex L=200mH
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I knew that. But the letter "L" is not used in the spelling of "inductance." I just don't know the origin of the use of "L" for this purpose. I suppose it may be because "I" had already been taken, and "L" looks like "I," expecially as a lower case letter. :roll: ;) :grin:
 
mull982 said:
I had a question in regards to power factor that I was hoping someone could help me out with. If I have a lagging power factor, lets say 80% I believe that this means that the voltage is lagging the current. Is this correct. Vise Versa if I have a leading power factor this means that the voltage is leading the current?

Is a lagging power factor caused by an inductive or capacitive circuit load. How about with a leading power factor, is it caused by an incuctive or capacitive circuit load? What circuit characteristics determine weather the power factor is leading or lagging?

Thanks for the help.

Mull982
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Lagging power factor means the current "I" lags the voltage. A leading power factor means current "I" leads the voltage.
 
... causes

... causes

mull982,

The presence of a lagging power factor is typically the result of motor loads.

Motor power factors are particularly low when a motor is lightly loaded, then increase to the nameplate pf when fully loaded.
Easy power factor correction is possible with older motors that typically had a power factor of 0.8, by installing a power factor correction capacitor energized with the motor by the motor contactor.
A rule-of-thumb number for the 0.8 power factor motors was that the capacitor VAR value be 20-25% of the HP rating of the motor, i.e. 100 HP motor, 20-25 kVAR capacitor.

Newer motors can be designed to deliver their power at a higher power factor, in which case the pf correction capacitor size for a 0.9 power factor motor is reduced to say 10% of the motor HP.

JM
 
So if the phase angle for the current is a (negative phase angle betwenn voltage and current) negative angle lets say negative 37 degrees, then the cosine of this angle would be about .79 which woud indicate a power factor of 79. Is this a leading or lagging power factor due to the fact that the angle is negative.

So if I understand this correctly a power factor is a lagging power factor when the current lags the voltage and this is casued by induction? Conversly when the power factor is leading it means that the the current leads the voltage and this is caused by capacitance?

Thanks
 
constants.

constants.

mull982 said:
So if the phase angle for the current is a (negative phase angle betwenn voltage and current) negative angle lets say negative 37 degrees, then the cosine of this angle would be about .79 which woud indicate a power factor of 79. Is this a leading or lagging power factor due to the fact that the angle is negative.

So if I understand this correctly a power factor is a lagging power factor when the current lags the voltage and this is casued by induction? Conversly when the power factor is leading it means that the the current leads the voltage and this is caused by capacitance?

Thanks
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In an electrical circuit, ELI the ICE man, The voltage will lead the current in an inductive circuit, ( the current shall lead the voltage in a capacitive circuit). ALWAYS, Just like 1.73 and 3.14 it is what it is. Hope this helps.
 
mull982 said:
So if the phase angle for the current is a (negative phase angle betwenn voltage and current) negative angle lets say negative 37 degrees, then the cosine of this angle would be about .79 which woud indicate a power factor of 79. Is this a leading or lagging power factor due to the fact that the angle is negative.

So if I understand this correctly a power factor is a lagging power factor when the current lags the voltage and this is casued by induction? Conversly when the power factor is leading it means that the the current leads the voltage and this is caused by capacitance?

Thanks
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Yes, that looks mostly correct. (Except you said the power factor is 79 instead of 0.79).

Also, you must be careful with the sign of the angle. You just have to keep track weather the PF is leading or lagging since cos x = cos -x.

cos 37 = .79

and

cos (-37) = .79

Steve
 
Thanks for all the help guys, its starting to become a lot clearer.

I understand that with a lagging power factor due to an inductive load or inductive circuit characteristics, the power factor can be corrected by adding a capacitor bank. Can the opposite be said for correcting a leading power factor. If you have a leading power factor caused by a capacitive load, can you correct this power factor by adding inductors into the circuit or system.

I've also been wondering where the factor of 1.73 comes from when dealing with three phase circuits. Is there a scientific explanation, or is this just one of those numbers you take for what it is?

Thanks for all the help guys.
 
View attachment 793

The value of the power factor is always positive, since we know that the cosine of a positive angle is equivalent to the cosine of a negative angle.

For example: cos(+10deg) = 0.985 and cos(-10deg) = 0.985

What differentiates between leading and lagging is knowing the relationship between the voltage and current angles. Therefore, when the difference is positive, it is said to be lagging, and when the difference is negative, it is said to be leading.

View attachment 794

For lagging or leading power factor; as the angle difference between the voltage and current approaches zero, the cosine of the angle approaches unity, or "1.0", which would be a highly desirable situation. Conversely, as the angle difference between the voltage and current becomes greater and approaches 90 degrees, then the cosine of the angle approaches zero.

In a capacitive circuit, the current leads the voltage by 90 deg.; in an inductive circuit the current lags the voltage by 90 degs. Thus, by placing a capacitor of exact equal value in parallel to the inductive load the the difference in angle between the voltage and current would be zero, creating a power factor equal to "1.0". This is the concept employed when power factor correction capacitors are added to motors, "to improve power factor".

A facility operating with a 0.79 lagging pf, draws power from the source, e.g. utility. This means that the facility requires not only real power (watts) but some portion of reactive power (vars) as well, because the power factor is less then 1.0. Think of the vars as wasted watts and the real power as usable watts, keeping in mind the customer pays for all the watts consumed.

View attachment 795

Improving the power factor of the overall facility is desirable and can be accomplished on a larger scale in the same manner as a single motor; by adding capacitance.
 
mull982 said:
Thanks for all the help guys, its starting to become a lot clearer.

I understand that with a lagging power factor due to an inductive load or inductive circuit characteristics, the power factor can be corrected by adding a capacitor bank. Can the opposite be said for correcting a leading power factor. If you have a leading power factor caused by a capacitive load, can you correct this power factor by adding inductors into the circuit or system.

I've also been wondering where the factor of 1.73 comes from when dealing with three phase circuits. Is there a scientific explanation, or is this just one of those numbers you take for what it is?

Thanks for all the help guys.
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Theoretically, one could correct a leading PF, but to my knowledge, this is never a problem.

The factor, 1.73, is derived mathematically. i.e.,

1.73 = 2cos(30)

You have to understand vectors, phasors, and trigonometry though to see this for yourself.
 
kingpb said:
Thus, by placing a capacitor of exact equal value in parallel to the inductive load the the difference in angle between the voltage and current would be zero, creating a power factor equal to "1.0". This is the concept employed when power factor correction capacitors are added to motors, "to improve power factor".
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Just to mention, the load itself still has the crappy power factor, it's just that you reduce the amount of conductor that has to carry the extra current to that between the low-PF load and the correction means.

That section of the circuit still has to be sized for both the Kvar's and watts; the improvement in power factor is seen only outside the load-and-corrective-means loop, and of course, by the power supply.
 
mull982 said:
Thanks for all the help guys, its starting to become a lot clearer.

I understand that with a lagging power factor due to an inductive load or inductive circuit characteristics, the power factor can be corrected by adding a capacitor bank. Can the opposite be said for correcting a leading power factor. If you have a leading power factor caused by a capacitive load, can you correct this power factor by adding inductors into the circuit or system.

I've also been wondering where the factor of 1.73 comes from when dealing with three phase circuits. Is there a scientific explanation, or is this just one of those numbers you take for what it is?

Thanks for all the help guys.
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what is the square root of 3? :smile:
 
mull982 said:
I've also been wondering where the factor of 1.73 comes from when dealing with three phase circuits. Is there a scientific explanation, or is this just one of those numbers you take for what it is?
Click to expand...
The technical answer would start by stating that voltage, as a function of time, is a sinusoidal wave form. It is usually expressed as a maximum value multiplied by the cosine of a term that includes time and includes a factor that makes the system operate at 60 hertz. The next statement is that current will have a similar wave form, with its own maximum value multiplied by a similar cosine function. However, the expression for current will include a factor that causes its peak value to occur at a different time than the peak value of voltage. Finally, you get a power function by multiplying the voltage and current functions. If you use trigonometry as the method of solving this equation, the value of the square root of three (about 1.732) will automatically present itself as a part of the solution.

The non-technical answer would be to ask you to draw, on a piece of paper, three arrows. I don?t have the ability to draw stuff and post it on this Forum, so perhaps someone will oblige me with a sketch. But the one you draw should have all three arrows beginning at the same point, and have the same length, and be separated from each other by 120 degrees. Now, measure the length of the arrows, and also measure the length from the tip of any one arrow to the tip of any other. The longer measurement should be about 1.732 times the shorter measurement. The length of a single arrow can be said to represent the value of voltage, in a WYE connection, from one phase to ground. The distance between the tips of two arrows can be said to represent the voltage phase to phase. And yes indeed, the phase to phase voltage in such a system is equal to the phase to ground voltage multiplied by the square root of three.
 
Just to clarify something, with a lagging power factor where the current lags the voltage, does this mean that the voltage waveform will reach its peak along the time access before the current waveform does? Looking at a time vs magnitude plot starting from 0s this would mean that the voltage waveform would reach its first peak at 1s and the current waveform would follow reaching its peak sometime later lets say 2s?

I assume a leading power factor would have the current waveform reach its first peak along the time access before the voltage waveform?

mull982
 
I prefer to think of it from the perspective of time. I never could get the "lead" or "lag" stuff. (Come to think of it, i never could figure out "Spring forward, Fall back." Was it me "springing forward in the time continuum, or was it the time continuum springing forward past me? It wasn't until i started relating all the time zones to GMT that i figured it out).

In an inductive circuit, the current has a delayed response to the voltage. Therefore, the peak of the voltage comes first and the peak of the current tags along behind. On a graph, this would show the voltage peak to the right of the associated current peak. (I wonder about Australia. Since everything is upside down... never mind). :-? :wink:
 
eric stromberg said:
In an inductive circuit, the current has a delayed response to the voltage. Therefore, the peak of the voltage comes first and the peak of the current tags along behind. On a graph, this would show the voltage peak to the right of the associated current peak. (I wonder about Australia. Since everything is upside down... never mind). :-? :wink:
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Wouldn't the voltage peak be to the left of the current peak because it occurs first with respect to time. Another words it occurs first in a shorter amount of time (time increasing from left to right) therefore I would think it would be to the left and before the current peak.
 
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