# Thread: Power factor Vs Power angle

1. ## Power factor Vs Power angle

Greeting all,
Hope you are fine and well. I have been asked the below question

What is the difference between power factor and power angle.

I replied the below information and I need your suggestion and information regarding to this question

Power factor is the cosine of the angle between the current and voltage.

Power angle is the angle between a generator's internal voltage and its terminal voltage, or between the voltages at the source and load points of an electrical transmission line.

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Power factor is simply the ratio <real power delivered to load> / <apparent power delivered to load>

Apparent power is the product of RMS current and RMS voltage.

If current and voltage are pure sinusoids, then the real power delivered to the load is RMS current * RMS voltage * cosine (angle between voltage and current). Thus for pure sinusoids, the power factor is numerically equal to the cosine of the angle between voltage and current, as you say.

If voltage or current is nor sinusoidal, then you can have a power factor that is different than the cosine of the angle between voltage and current. For example, a single phase rectifier supplying a capacitive filter will draw extremely high peak currents right at the peak of the voltage sine wave, but will draw no current at other parts of the cycle. Such a rectifier load will have very poor power factor, but virtually no angle between voltage and current.

I have never heard the term 'power angle' used as you have described it. I would think that 'power angle' means the angle betwen voltage and current.

-Jon

3. Originally Posted by winnie
Power factor is simply the ratio <real power delivered to load> / <apparent power delivered to load>

I have never heard the term 'power angle' used as you have described it. I would think that 'power angle' means the angle betwen voltage and current.

-Jon
power angle is also called torque angle which is mostly less or equal 30 degree because of stability.

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Originally Posted by Hameedulla-Ekhlas
...What is the difference between power factor and power angle.

...Power angle is the angle between a generator's internal voltage and its terminal voltage, or between the voltages at the source and load points of an electrical transmission line.
ham -

Yes, you have the definition of "power angle" exactly correct - at least according to Grainger and Stevenson, Power Systems Analysis.

I'm assuming you don't need an answer, or explanation - you already understand it. Rather you are looking for a discussion.

Power angle is not something I have to deal with. I don't do transmission, and for all of the generators I work, the prime mover generally won't develop enough power to slip a pole. So with that in mind, my understanding is:

In order for the generator to push power out on the line, the generator prime mover throttle opens, pushing power into the generator shaft. The gen tries to speed up, but can't, it is stuck at synchronus speed with the buss. But the generator rotor rotating vector does pull ahead of the stator rotating vector. And that is the representation of the power angle.

Look at the generator impedances, transmission line impedance, load impedance. The are all in series. So the current is the same all the way through - same magnitude and phase angle. But the Voltage measured at different parts of the system has different magnitudes and phase angles.

Starting with the internal generator voltage, ahead of the generator reactance, E(i) leads the generator terminal voltage, V(t), which leads the far end of the transmission line. The angle of lead is the power angle.

So how did I do

cf

5. Sometimes I am reminded about how really ignorant I am

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Originally Posted by Hameedulla-Ekhlas
power angle is also called torque angle which is mostly less or equal 30 degree because of stability.
Looking at the power angle equations in Grainger and Stevenson:

At zero power output, the power angle is zero. At maximum powr output, the power angle is just shy of 90 deg. At 90 deg, the gen is unstable and is ready to slip poles or is slipping poles.

All of the generator curves I have seen, limit the power output for leading power factor (vars going into the generator) for stability. That make sense, because as the Gen output goes leading, the field current goes down to keep the voltage down. And the reduced field current reduces the magnetic field linkages to the stator which reduces the amount of power that can be transfered from the rotor to the stator.

cf

7. Originally Posted by Cold Fusion
ham -

Yes, you have the definition of "power angle" exactly correct - at least according to Grainger and Stevenson, Power Systems Analysis.

I'm assuming you don't need an answer, or explanation - you already understand it. Rather you are looking for a discussion.

cf

Yes, you are right. We all read books and always reply according books reference. But personally I may have read one, two or maximum three books regarding one topics. I want more information and specially reall and good practical experience answers I want which such guys are in this forum.

I just want to know practical aspect of topic and real experience.

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Originally Posted by augie47
Sometimes I am reminded about how really ignorant I am
Following is delivered in a stern, warning voice:
Stop that - we all have different areas of expertise. Regardless of what some our members think, the engineers need you guys just as much as you need us.

End of stern, warning voice - switch to conversational tone.

And, there a lot (read most days that I am working) of times where I say, "I didn't know that. Have you got any references I can look at - something on the practical, application level as opposed to the university level?" So yeah, I understand

cf

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This is consistent with everything said previously but in it simplest form, a generator that is not "islanded", in other words is tied to the grid has two controls. The field excitation which controls the reactive power flow and the prime mover power (gates on a hydro, steam valve on turbine etc) that controls real power generation. When you push more power from the prime mover into the generator the angle between the internal Eg to the terminal voltage Vt (called power angle, usually a lower case delta) changes (remember if you were islanded and you pushed more power from prime moved you would increase frequency). There are some other constraints that come into play that make up the "loading capability diagram" which you can find covered in Grainger and Stevenson. As you stated the term is also sometimes called "torque angle".

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I stand corrected on the 'power angle' term. I guess that I let myself get confused by the way it was set against power factor.

If I recall correctly, the two terms are actually somewhat inter-related, in that the excitation of a synchronous generator can be used to adjust the power factor of its output; if the generator is locked to the grid (thus fixing the rotor and prime mover to a single speed), and with fixed prime mover power (thus fixing the system power output), my understanding is that adjusting the excitation will change both the angle between rotor and rotating field as well as the power factor of the generator output.

-Jon

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