VA vs. Watts

[rattus]

Please give an example of a Complex number in 3 dimensions.

The product of 2 sinusoids with the same frequency is a pure sinusoid of frequency 2f with a bias. It as you say is not a phaser, but in power ElectricLand the angle resulting is the phase difference between the Voltage and Current.

See

http://books.google.com/books?id=vv...=X&oi=book_result&ct=result&resnum=1#PPA18,M1

Glad I don't have to deal with these things.

For a wave to be a sinusoid, it must be be shaped like a pure sine wave.

Now sin^2(wt) plots out as a string of positive lobes, which are shaped differently from the lobes of sin(wt). Furthermore, the plot never falls below zero. Try it.

Such a wave cannot be described with a magnitude and phase angle as in done with phasors.

 

[Cold Fusion]

---Now sin^2(wt) plots out as a string of positive lobes, which are shaped differently from the lobes of sin(wt). ---

You're right, sin^2 (wt) is shaped differently than sin(wt). Sin^2(wt) is the same shape as sin(2wt). I'd say that is sinusiodal, just a different frequency.

---Furthermore, the plot never falls below zero. Try it.---

Depends on the phase angle. At zero degrees, between E and I it is as you say. At 90 deg, half the plot falls below and half above. Try it

---Such a wave cannot be described with a magnitude and phase angle as in done with phasors.

News flash, power is not an E or I rotating vector. It is the product of the two. Use Eulers' formula multiply the two and convert back to rectangular. It will look like a vector, phasor, even first rank tensor - if you want. You choose

Integrate the power and the energy is still a vector.

The math model works. And you repeating, "It isn't a pure sinusoid because it has DC offset " doesn't change that.

cf

 

[Rick Christopherson]

Furthermore, the plot never falls below zero. Try it.

Nope. When you have a phase shift, there will be times when the load is a load and when it is a source of power. Energy is stored in the reactive element and this energy is returned to the system within the cycle.

Oh, by the way, this is still sinusoidal, and you will also note that the period has doubled (or is that cut in half, I forget). (Yeah, frequency is doubled, period is cut in half.)

 

[rattus]

Please note:

Please note:

Please note that my example is for sin^2(wt) which cannot have a negative value. The point is that there are no negative lobes, therefore the expression for power cannot be a sine wave, i.e., sinusoidal. Note also that the lobes of sin^2(wt) are sharper than those of sin(wt). Think about it. e.g., sin(30) = 0.5, sin^2(30) = 0.25

Also, someone had better look up the definition of "sinusoid".

 

[drbond24]

Also, someone had better look up the definition of "sinusoid".

Now there's an assignment I can handle!

si⋅nus⋅oid  /ˈsaɪnəˌsɔɪd/ [sahy-nuh-soid]
?noun Mathematics. a curve described by the equation y = a sin x, the ordinate being proportional to the sine of the abscissa.

And for those that said "Huh?" at the end of that definition like I did:

ab⋅scis⋅sa  /?bˈsɪsə/ [ab-sis-uh]
?noun, plural -scis⋅sas, -scis⋅sae  /-ˈsɪsi/ [-sis-ee]
Mathematics. (in plane Cartesian coordinates) the x-coordinate of a point: its distance from the y-axis measured parallel to the x-axis.

 

[jghrist]

Please note that my example is for sin^2(wt) which cannot have a negative value. The point is that there are no negative lobes, therefore the expression for power cannot be a sine wave, i.e., sinusoidal. Note also that the lobes of sin^2(wt) are sharper than those of sin(wt). Think about it. e.g., sin(30) = 0.5, sin^2(30) = 0.25

Also, someone had better look up the definition of "sinusoid".

sin? x = 0.5?[1 - cos(2x)]
See http://mathworld.wolfram.com/TrigonometricPowerFormulas.html

 

[charlie b]

Also, someone had better look up the definition of "sinusoid".

The following is from the McGraw-Hill Dictionary of Scientific and Technical Terms, though I don?t understand why you should offer the suggestion that it be looked up:

sinusoid [ANAT] Any of the relatively large spaces comprising part of the venous circulation in certain organs, such as the liver.

This dictionary has no other definition to offer for the single word ?sinusoid.?

For what it?s worth, however, the same dictionary also has the following definition for a similar sounding two word phrase:

sinusoidal function [MATH] The real or complex function sin(u) or any function with analogous continuous periodic behavior.

From this I infer that power, as a function of time, in a single phase system, being derived from the product of two sine waves of identical period, of different coefficients, and separated in time by a phase angle, is, in fact, a sinusoidal function. I have agreed with you in everything else you have posted in this thread, but I can?t agree with you here. That said, it is a minor point, and it does not diminish the strength of your reasoning on all other points.

 

[charlie b]

By the way, Dr Bond, where did you find your definition for sinusoid? It is incomplete, in that it does not address functions other than real functions of the form sin(x) (i.e. it leaves out complex functions), nor does it include functions with similar behavior. Please don't tell me you got it from wickedpedia.

 

[charlie b]

sin? x = 0.5?[1 - cos(2x)]

You will note that, since the cosine function never exceeds a value of 1.0, we must conclude that that function being subtracted from 1.0 will never yield a negative value. So you confirmed what Rattus had said.

 

[drbond24]

By the way, Dr Bond, where did you find your definition for sinusoid? It is incomplete, in that it does not address functions other than real functions of the form sin(x) (i.e. it leaves out complex functions), nor does it include functions with similar behavior. Please don't tell me you got it from wickedpedia.

Dictionary.com!

It will even say the word for you if you click on the little speaker.

That's better than wikipedia, isn't it? A tiny bit better at least.



What happened to the whole Joules per second thing? You guys have started another thread within this thread that has nothing to do with what we were talking about before as far as I can tell.

I think the pot needs stirred again: W = VA = VAr = J/s

I can hear Besoeker coming already. Haha!

 

[Cold Fusion]

---What happened to the whole Joules per second thing? ---

Here I'll help out.

I think it is cause the "Energy is not a vector" crowd and the "power is not a vector" crowd is in a corner.

Just looking at the math:
E is a vector (yes rattus, "phasor" is also okay)
I is a vector
E x I (complex power - not apparent power) is a vector (rattus - I'm not sure what term you like here. Pick one that says, 'can be described with cartesian coordinates, or magnitude/phase angle') Yes, it is allowed to have a DC offset

Integrate the power (E x I) and the result (energy) is a vector.

Pretty well leaves Joules as having a magnitude and phase angle, at least for this model

An interesting part to this is none of us have ever worked the math to this depth. The concepts are extremely useful for understanding and modeling power system behavior, but nothing I have ever had to do (nor any of the rest of us either)

cf

 

[shamsdebout]

CF what you just mentioned is so appropriate so that is why the math courses were stressed, and were prerequisites for many of the electrical courses. I may need to brush up on some of my math.

 

[steve66]

What happened to the whole Joules per second thing? You guys have started another thread within this thread that has nothing to do with what we were talking about before as far as I can tell.

That's how we roll :grin:

Steve

 

[drbond24]

One final note. The units of measure for the three lines described above are fundamentally the same. They all relate to the rate of use of energy, and can all be expressed in terms of ?joules of energy per second of time.? But to keep track of them separately, they are given separate names. The ?real power? unit (line 1-2) is expressed in ?watts (W)? or ?kilowatts (KW).? The ?reactive power? unit (line 2-3) is expressed in ?volt-amperes reactive (VAR)? or kilo-volt-amperes reactive (KVAR).? The ?apparent power? unit (line 1-3) is expressed in ?volt-amperes (VA),? or kilo-volt-amperes (KVA).?

This is what started the whole mess. Just so I'm clear on what is happening now, do you have a problem with this CF, or do you not? When you jumped in, you said it was right but you didn't like the way it sounded (I'm paraphrasing there). Would you suggest a better way to write the above paragraph without completely changing charlie b's point, or do you think it should be deleted from his narrative entirely? Remember, this was written to explain power factor to someone who isn't intricately familiar with electrical engineering principles, not to teach electrical engineering at MIT.

I'm just trying to get my feet back on the ground here since I've lost where this thread is going. Thanks.

 

[drbond24]

That's how we roll :grin:

Steve

Hey, that's fine with me. I just want to finish one arguement before we move onto another. I'll tackle global warming (or lack thereof) next if you want, but let's get the dissenters to admit that Volt-Amps have units of Joules per second first.

 

[markstg]

See

http://books.google.com/books?id=vv...=X&oi=book_result&ct=result&resnum=1#PPA18,M1

Glad I don't have to deal with these things.

For a wave to be a sinusoid, it must be be shaped like a pure sine wave.

Now sin^2(wt) plots out as a string of positive lobes, which are shaped differently from the lobes of sin(wt). Furthermore, the plot never falls below zero. Try it.

Such a wave cannot be described with a magnitude and phase angle as in done with phasors.

WOW complex numbers in 3D,

I don't think there is such a thing as a PURE Sinusoid.

And again, Apparent Power is a complex quantity and not a Phasor as you have said.

 

[rattus]

Someone isn't listening:

Someone isn't listening:

And again, Apparent Power is a complex quantity and not a Phasor as you have said.

No, apparent power is defined as the product of two magnitudes, therefore there are no phase angles involved. It is not inherently complex.

That being said, we can use complex numbers to break apparent power into real and reactive components with pseudovectors.

And, I have never said complex power is phasorial.

There may be various definitions of sinusoidal, but I prefer to use the one that says in so many words that a sinusoidal wave is a sine wave.

 

[markstg]

No, apparent power is defined as the product of two magnitudes, therefore there are no phase angles involved. It is not inherently complex.

That being said, we can use complex numbers to break apparent power into real and reactive components with pseudovectors.

And, I have never said complex power is phasorial.

There may be various definitions of sinusoidal, but I prefer to use the one that says in so many words that a sinusoidal wave is a sine wave.

No, I was saying you said Apparent Power WAS NOT a Phasor, Sheessssh I was agreeing with you and giving you the credit.

Apparant Power is defined as the product of the Phasor Voltage and the conjugate of the phasor current which is defined as the Complex Power

S=VI* = P + jQ

Reference: Engineering Circuit Analysis, Hayt and Kemmerly
Elements of Power System Analysis, William D. Stevenson, Jr.

Now how about that Beer.

 

[Rick Christopherson]

However, "concise" is not in my nature. :wink:

I wasn't paying attention to this discussion because Charlie's answer was so "concise" that I never made it all the way through. :grin::grin: However, now that you have my attention, I will weigh in on a few topics.

Actually I believe charlie b is right.

V = (kg*m^2) / (C*s^2)
A = C / s

V*A = (kg*m^2) / (s^3) = (kg*m^2) / (s^2) * (1/s) = J / s

Charlie is in fact correct. The units are and will always be joules per second. The reason why some posters here are getting this confused is because they are so accustomed to looking at secondary equations that have been simplified that they forget where all of this originates.

Must argue with the whistle blower.

The key to this discussion I think is that one VA "appears" to be one joule/sec, but it is not. For example, if the phase angle is 30 deg. and the apparent power is 1 VA, 0.866 joules/sec are transferred to the load while 0.5 joules/sec flow back and forth in the reactive portion of the load.

A Joule is the amount of energy required to move one coulomb of charge through 1 volt of potential difference. Even when the instantaneous power dips below the negative axis, work is still being performed, but it is going in the opposite direction. Work is always being performed throughout the cycle, but when examined over time, this small portion of negative work cancels out a portion of the positive work. This cancellation of the two over the time period is what makes it "Appear" that no net work has been performed for a portion of the cycle. It doesn't mean that there was no work during these time segments, only that from the time perspective that there was no net work.

It is also incorrect to state that this apparent j/s energy is simply bouncing around the reactive part of the load doing nothing. It only appears to be doing nothing when you look at the overall net result.

You are missing the point that a true vector--not a phasor--is a complex number expressing magnitude and direction, e.g., an electric field or magnetic field. Power has no directional angle, therefore it cannot be a vector.

You are confusing a "tool for the simplification of a problem" as being an absolute. Current and voltage are not vectors or phasors or even complex numbers. These are simply tools that we use to help us resolve complex problems. A vector is not a complex number, but we choose to represent it as a complex number to make it easier to solve vector analysis with simple equations. Moreover, a phasor is just another form for representing a vector.

Power is not sinusoidal and does not carry a phase angle, therefore it cannot be a phasor either.

Wrong. Power is sinusoidal. Just because it has a bias does not mean it is not sinusoidal. I think this has already been address by others.

You are also wrong about the phase angle. Because you assumed power was not sinusoidal, you failed to notice that its period is time-shifted from the baseline (in my example, the voltage sinusoid is what determined the baseline--v(t)=Vsin(wt)). I am not going to bother going through the math to find the exact phase shift, but from the graph you can see that the power is phase-shifted by approximately the same (but opposite) as the current's phase shift. Don't confuse the zero-crossing of the power function with its period origin.

Please note that my example is for sin^2(wt) which cannot have a negative value. The point is that there are no negative lobes, therefore the expression for power cannot be a sine wave, i.e., sinusoidal.

It is always amusing how quickly you can backpeddal. Considering that this thread is titled "VA vs Watts" it was not much of a stretch to assume you were speaking in the general sense.

Note also that the lobes of sin^2(wt) are sharper than those of sin(wt).

No, if you are referring to my previous drawing, that is actually my mistake in my original graph, which I drew many, many years ago without actually plotting the functions. So today I plotted the actual functions from Excel.

In this more accurate representation you can clearly see that the power function is a smooth sinusoid with a positive bias and a phase shift to the right. The period of the power function is 1/2 that of the current and voltage functions, but within the functions own period, the lobes are the same, and if follows the path of a standard sinusoidal function. The reason why I displayed the graph starting with negative time values was to make it easier to see how the power's sinusoid was shifted to the right.

 

[Cold Fusion]

One final note. The units of measure for the three lines described above are fundamentally the same. They all relate to the rate of use of energy, and can all be expressed in terms of ?joules of energy per second of time.? But to keep track of them separately, they are given separate names. The ?real power? unit (line 1-2) is expressed in ?watts (W)? or ?kilowatts (KW).? The ?reactive power? unit (line 2-3) is expressed in ?volt-amperes reactive (VAR)? or kilo-volt-amperes reactive (KVAR).? The ?apparent power? unit (line 1-3) is expressed in ?volt-amperes (VA),? or kilo-volt-amperes (KVA).?

--- do you have a problem with this CF, or do you not? When you jumped in, you said it was right but you didn't like the way it sounded (I'm paraphrasing there).---

Not really - it is still not wrong. I don't like that the phrasing looses the phase angle information. Complex power keeps this information intact. I am absolutely clear that me not liking it doesn't make it wrong. I'd have left it right there had charlie and rattus not jumped on me. The idea that power and energy are not vectors doesn't set well with me. This insistance on dwelling on 'apparent power' instead of 'complex power' is a bit baffling. Why would one purposely ignore the phase angle information?

---Would you suggest a better way to write the above paragraph without completely changing charlie b's point, or do you think it should be deleted from his narrative entirely? Remember, this was written to explain power factor to someone who isn't intricately familiar with electrical engineering principles, not to teach electrical engineering at MIT.---.

No and no - because, yes, I remember.

I likely would not have said anything had not several posters landed on Besoeker for differing with charlie. Rick did a fine job covering most all of these points in his last post.

---I'm just trying to get my feet back on the ground here since I've lost where this thread is going. Thanks.

So we have power that is wattless, energy that is pointless, Dr Bond is groundless, and the thread is unstitched. Sounds great - we have all done our jobs.

cf