Come on HE. Lets not start these short cuts with the english language.
Power factor and VA vs Watts
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Come on HE. Lets not start these short cuts with the english language.
winnie
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I disagree in part. Steve66 gave a very good explanation of what is known as 'displacement power factor'.
gar's definition in post 16 gives the more general case.
When we deal with AC circuits, we use 'RMS' values for voltage and current. RMS values are single numbers that describe the constantly changing voltage or current present in AC circuits. RMS values are tremendously useful, because many devices respond to AC of a given RMS value in the same way they will respond to DC of that value; this simplifies the analysis of systems.
For example, the heating of a wire carrying AC current of 10A RMS is very similar to the heating of the same wire carrying 10A DC. A light bulb connected to AC of 120V will light up very similarly to the same bulb connected to DC of 120V.
One place where the RMS analogy to DC falls apart is that RMS current * RMS amps does not equal power delivered to the load. Power is always given by the _instantaneous_ product of voltage and current, and properly the way to calculate the power going to a load you need to take the product of a continuous set of measurements.
Power factor in its most general sense tells us the difference between the actual power delivered to the load and the apparent power (RMS current * RMS volts) being supplied by the power system.
One reason for the difference between apparent power and real power is the displacement power factor that Steve66 described. During part of the AC cycle, current is used carrying power to the load, during other parts of the AC cycle, current is being used to carry power from the load back to the source. With these types of load, the current waveform is out of phase with the voltage waveform, and for those part of the cycle where they have 'opposite' sign, power is flowing in the 'reverse' direction. If you look at the instantaneous measurements, sometimes power is positive, and sometimes negative. Because phase of sine waves can be described in terms of angles and vector math, these are often used to describe displacement power factor.
A _different_ way that RMS voltage * RMS current will not equal power delivered to the load is if the current waveform has a different _shape_ than the voltage waveform. This is called distortion power factor. For a given total power delivered to the load, the distorted current waveform will have a higher RMS value than the non-distorted waveform. Gar gave the example of a diode rectifier feeding a capacitor, where extremely high current will be drawn right at the peak of the AC voltage cycle, with no current flow at other times. The pulse will be almost perfectly 'in phase' with the supply voltage, and power is only flowing during the pulse, not shuttling back and forth. Such a load will have poor power factor, but with almost no angular displacement.
The two different types of power factor can be described in a unified fashion if you use harmonic analysis, which PowerQualityDoctor noted.
-Jon
Cold Fusion
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I saw that you had the current leading the voltage by 90 deg. I figured it was just a mistype.
Yes, of course that would be the one that explodes....And, it is actually at the current's zero crossings that impedance goes off the chart (a fold in the whole space-time contiuum, because it is both positive and negative infinity at the same time)...
It is an interesting mathematical model. However, you may be the only one in the world that uses it. Most everyone else, when dealing with sinusiods, uses:
Z = R +jX
Where jX =jwL or 1/(jwC),
For the general case, another model would be:
V= Ldi/dt
I = Cdv/dt
The model you are using is, well, pretty unusable. And I thinking you already knew all of this.
cf
Hmmm... don't see it. Current lags voltage on both pages.
I agree. It is an interesting mathematical model. But no, I do not use it as such. It is just interesting, and the purpose for presenting it, to see by graphical representation how the impedance varies, along with it going negative (returning the "absorbed" power back to the source). I thought the graphical presentation would help some who are not so versed in the math to better imagine what is happening. I don't know about you, but I can't visualize the impedance waveforms using the proper equations.
Cold Fusion
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Note: Limiting my discussion to sinusoidal functions, fundamental only - just to keep it what .... bounded? maybe.
The view that I would be more comfortable with is:
The impedance is fixed: Z = jwL and that causes the current to lag the voltage.
The physical property causing the phase shift is the current builds a magnetic field in the inductor and that stores energy. Energy is pumped into the inductor magnetic field when the current is increasing. And when the current decreases, the magnetic field collapses, and dumps the energy back into the system. And it takes a phase shift to make this happen.
And again - I knew you already knew this
But if I apply Euler's formula and make them vectors (or rotating vectors, or phasors - what ever term you like) then I can see them.
No question, your pictures look prettier than mine
cf
Absolutely true - don't know what I was thinking.
Yeah, that is the interesting part. Looking at it from the point of view that the impedance changes depending on which part of the cycle the current is in -- that's a new concept for me.
The view that I would be more comfortable with is:
The impedance is fixed: Z = jwL and that causes the current to lag the voltage.
The physical property causing the phase shift is the current builds a magnetic field in the inductor and that stores energy. Energy is pumped into the inductor magnetic field when the current is increasing. And when the current decreases, the magnetic field collapses, and dumps the energy back into the system. And it takes a phase shift to make this happen.
And again - I knew you already knew this
I don't know what "impedance waveforms" are (is?).
But if I apply Euler's formula and make them vectors (or rotating vectors, or phasors - what ever term you like) then I can see them.
No question, your pictures look prettier than mine
cf
Smart:
I think you are missing the fact that inductors and capacitors can have a voltage across them even when the circuit current is zero.
Say for example that your graph shows input voltage vs. current for a single inductor. When the input voltage is max., and the current is zero, the voltage across the inductor is equal and opposite to the input voltage. So the net voltage around the circuit is zero. If you tried to calculate an impedence, you would have 0 Volts/0 Amps = Z, which would be indeterminate.
Its different than a resistor, which would always have 0 volts across it when the current is zero.
I guess you could say that your impedence (maybe we should call it an instantaneous impedence) also includes the voltage developed across that impedence. But like Cold, I don't see much advantage in looking at this instantaneous impedence. I don't see an advantage because the value of this instantaneous impedence also depends on the past history of current or voltage - how much a capacitor has charged, or how much energy is stored in the magentic field of a inductor.
At any rate, its certainly not the same impedence that most people are used to dealing with.
Steve
Not really a new concept... just that your conventional education keeps you thinking in the box. You are permitted to think outside the box, just in case you didn't know
As a consolation, I'll get around to aligning in the box with outside the box here in a little bit
...and this fixed Z is to instantaneous Z as 120VAC is to instantaneous voltage.
The only problem here is that your stated premise has the phase shift as the cause. It is not. Phase shift is the effect.
Let's use an analogy of connecting two identical batteries in parallel. There is a conductive circuit pathway, but the emf of each battery opposes the other, so no current flows. If one of the batteries had a lesser charge, current would flow until equilibrium was achieved. In this scenario, think of the opposition to current flow as impedance.
In the case of the inductor, on the application of a voltage across its terminals, it instaneous creates a counter emf to oppose current flow, essentially the same as the two identical battery scenario above. Note this is the start of the phase shift, because current is at zero when the voltage is applied. If the voltage were maintained steady state, the counter emf would subside because there is no current to maintain the field (the physical characterictic of an inductor that you speak of)... for it is the change in voltage which creates the counter emf. Therefore, the counter emf subsides, and current flows. This is comparable to the inductor being the second battery having a lesser charge.
I could continue this analysis, but I think you know how it goes
I think it should be noted here, though, that the graphs in my pdf indicate impedance as seen by the voltage source, not the entire circuit. The inductor is essentially equivalent to a second source, similar to the two battery analogy above.
Well, I guess technically they are not waveforms.
They are however a graphic plot of instantaneous values and not so much a wavy appearance.
Sorry, but you are getting into my too-rusty-to-follow area. So what do they look like?
Thx...
So attached is a modified pdf to mimic your shading. Note how my impedance plots indicate a negative impedance where P (power) is negative as in your plots.
Nope. Not missing any facts... but I'll be modest and say I'm open to correction. In the meantime, please review my graphs. In both instances the plots indicate an input voltage present when current is zero.
Indeterminate by the simple math. But taking before and after into account, and the rate of change of the impedance, all indications have the impedance at plus and minus infinity when current is zero.
Since it apparently isn't readily apparent to you, I already know this
I explained the advantage earlier. It is not meant to represent some new math model to work by. Rather it is simply a graphical representation.
Please show me a plot of the impedance you refer to...
Cold Fusion
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Part one
This is the part I'm having trouble with.
Like it or not, your "simply a graphical representation" is a model.
And I don't see any advantage. I can't explain anything with it. I can't show how the physical properties interact. I certainly would not use the "graphical representation" to teach (or explain) the concepts of complex power.
cf
I don't think you are missing any facts either. You get it. No correction from me.
This is the part I'm having trouble with.
Like it or not, your "simply a graphical representation" is a model.
And I don't see any advantage. I can't explain anything with it. I can't show how the physical properties interact. I certainly would not use the "graphical representation" to teach (or explain) the concepts of complex power.
cf
Cold Fusion
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Part 2
Okay, that's done - not even bleeding much.
Well, I would say that I am pretty comfortable with thinking outside of my box. I am pretty sure that all of my thinking is outside of your box (and thankfully so).
My conventional education gives me the tools to formulate and use models that will solve real world problems and offer an explanation as to why the physical phenomena interact the way they do.
And yes, your concept of an inductor having a real, variable, impedance, that ranges from a positive infinity to negative infinity, when excited by a sinusiod would be considered a new concept by most anyone that I know in the field.
The concept of "instantaneous impedance" as defined by your model appears to be:
Take the sinusiod voltage value:
V(inst) = Vsin(wt)
and divide it by the phase shifted sinusoid current value. And since you are using a inductor, the current is shifted 90 degrees lagging. So the current value is:
I(inst) = I sin(wt + pi/2) = I cos (wt)
(slopy interchange of degrees and radians, and I hope I didn't slop my math up too much - but I think you are translating okay)
So Z = (V sin (wt))/(I cos (wt))
and that, amazingly enough, is:
Z = (V/I ) tan (wt)
and that will go to infinity every 90 deg.
That part of what you are doing is not new - just falls out from your model definitions.
Plotting this Z on a time domain graph is the "impedance wave form".
The model I use has sinusiodal voltage and current, measured property called inductance, expanding and collapsing magnetic fields, phase shifted voltage and current, energy being pumped back and forth. We can't see any of these. All we can do is measure the effects, and formulate a "model" (read "equations") to describe their behavior. You can pick anyone you want as the cause and assign the rest to effects. My model doesn't change a bit.
You have a valid model. I just don't know what one could use it for.
cf
Ouch - hang on a minute while I pull the knife out of my back.
Okay, that's done - not even bleeding much.
Well, I would say that I am pretty comfortable with thinking outside of my box. I am pretty sure that all of my thinking is outside of your box (and thankfully so).
My conventional education gives me the tools to formulate and use models that will solve real world problems and offer an explanation as to why the physical phenomena interact the way they do.
And yes, your concept of an inductor having a real, variable, impedance, that ranges from a positive infinity to negative infinity, when excited by a sinusiod would be considered a new concept by most anyone that I know in the field.
Okay. However, as I stated in an earlier post, I think I understand your model. You are exciting an inductor with a sinusiod, measuring the instantaneous voltage and current. The measured values are real (scalar)values. There are no vector components, the concept of reactive impedance is ignored. Then dividing the measured voltage by the measured current, and calling the result the inductor impedance. Isn't that your model?
I have no clue as to what this means. To get the RMS voltage, one integrates the square of the instantaneous voltage over one period and then takes the square root. I have no clue as to how that applies to what you are doing to the inductive impedance.
The concept of "instantaneous impedance" as defined by your model appears to be:
Take the sinusiod voltage value:
V(inst) = Vsin(wt)
and divide it by the phase shifted sinusoid current value. And since you are using a inductor, the current is shifted 90 degrees lagging. So the current value is:
I(inst) = I sin(wt + pi/2) = I cos (wt)
(slopy interchange of degrees and radians, and I hope I didn't slop my math up too much - but I think you are translating okay)
So Z = (V sin (wt))/(I cos (wt))
and that, amazingly enough, is:
Z = (V/I ) tan (wt)
and that will go to infinity every 90 deg.
That part of what you are doing is not new - just falls out from your model definitions.
Plotting this Z on a time domain graph is the "impedance wave form".
That is not a problem for me. I'm okay anyway you want this one.
The model I use has sinusiodal voltage and current, measured property called inductance, expanding and collapsing magnetic fields, phase shifted voltage and current, energy being pumped back and forth. We can't see any of these. All we can do is measure the effects, and formulate a "model" (read "equations") to describe their behavior. You can pick anyone you want as the cause and assign the rest to effects. My model doesn't change a bit.
I'll let this analogy go. You have conotations of negative resistance and inductors as power sources. There is steadystate sinusiod mixed with sinusiod initial conditions, DC steady state, DC initial conditions. And a minor physics flaw.
You have a valid model. I just don't know what one could use it for.
cf
Cold Fusion
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Part 3
Smart - None of this is news to you. I got that.
So, as you know, one would not put the impedance vector on the same plot as the voltage or current phasors. All values are expressed as complex numbers.
If the impedance is defined as:
Z = 0 + j|Z|
where
j|Z| = jwL
and
V(phasor) = |V| + j0
then
I(phasor) = V(phasor)/Z
Since it is hard to divide vectors in rectangular coordinates, switch V(phasor) and Z to polar coordinates.
Note: Notation "<xx" is "phase ange xx degrees"
Z = |Z|<90
V(phasor) = |V|<0
I(phasor) = (|V|<0)/(|Z|<90) = (|V| / |Z|)<-90
None of the plots (graphical representations) are on a time domain plot. All are on R - j cartesian.
What do you think - Is it possibly a little cleaner model than "impedance wave forms' that explode to infinity?
cf
Smart - None of this is news to you. I got that.
So, as you know, one would not put the impedance vector on the same plot as the voltage or current phasors. All values are expressed as complex numbers.
If the impedance is defined as:
Z = 0 + j|Z|
where
j|Z| = jwL
and
V(phasor) = |V| + j0
then
I(phasor) = V(phasor)/Z
Since it is hard to divide vectors in rectangular coordinates, switch V(phasor) and Z to polar coordinates.
Note: Notation "<xx" is "phase ange xx degrees"
Z = |Z|<90
V(phasor) = |V|<0
I(phasor) = (|V|<0)/(|Z|<90) = (|V| / |Z|)<-90
None of the plots (graphical representations) are on a time domain plot. All are on R - j cartesian.
What do you think - Is it possibly a little cleaner model than "impedance wave forms' that explode to infinity?
cf
weressl
Esteemed Member
I do not. Pretty basic, and straight to the point. All the calculation stuff isn't necessary to understand the concept
That may be the case, but all the understanding stands on a pretty weak ground if you can't prove it by 'calculations'.
Does any one disagree with this?!
Cold Fusion
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Uhh .... My comment didn't fit the discussion. Please let this one go. Sorry
cf
Cold Fusion
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(rotfl)
I've got this picture in my head of you standing there, fists all bunched up, adversarial look, defending your line in the sand.:grin:
Gives me a nearly uncontrollable urge to kick sand all over your line:roll:
(laughing to hard to type)
Well, in one specific area, you are right.
In two other specific areas, you are wrong
So, two to one, I disagree.
cf
I think it is time to let this go, if you have no objections.
My intent was simple, but you want to take it to the complex... in more ways than one. You want to exhibit being able to think outside the box, but yet to explain any concept of the phenomenon, you immediately resort to the complex calculations (see middle of Part 2). What is so hard to understand about Z = V/I and plotting it? (That's a rhetorical question, btw)
My initial intent was to simply point out that impedance is not steady state as the basic calculations lead one to believe. You cannot prove otherwise if you adhere to your statement I have a valid model. My point is made. The rest is rhetoric.
Perhaps it will help someone understand what happens without getting into all the [unnecessarily] complex calculations. Perhaps in time you'll see it. I don't think you can now because you already have a firm grasp of the complex side of the phenomenon. I believe it very difficult to be retrogressive intentionally and without good cause... and this is what you are exhibiting
Yes, I disagree... in a sense.
Proof is in empirical evidence.
Calculations are just a means to determine values when empirical evidence is not available.
If the calculations don't match the empirical evidence, what good are the calculations?
Granted we have a fair or better understanding of electrical phenomenon, and calculations to match, but someone first had to compare the calculation results to empirical evidence so as to affirm the validity.
weressl
Esteemed Member
I believe the superiority of numbers.
If a scientific idea can not be expressed mathematically, it remains an unproven theory.
This is the fundamental principle of science as it stands today.
Am I wrong?
ggunn
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This gets into the realm of the philosophical, IMO. Are instantaneous values of impedance important in an AC environment, anyway, and/or do they even have any real meaning?
Of course, one can look at the plot of I and V in the time domain when an AC voltage is applied across the terminals of an inductor and see that V is nonzero when I crosses zero. Calculating V/I yields a divide by zero every time this happens. Does that mean that impedance is infinite at those points in time? It depends on how you look at impedance, I guess; it just means that at the point in time when the current through the inductor is zero, the collapsing magnetic field in the inductor is creating a current flow in the opposite direction from the applied voltage that exactly cancels it out. Is it two currents equal in amplitude and opposite in direction, or is it one current with an amplitude of zero? What is the sound of one hand clapping?
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weressl
Esteemed Member
Empirical evidence is no proof that an exception does not exist. Does not matter how many times you repeat the same test with the results you would have no proof that an exception does not exist.
Calculations ARE proof that an empirical evidence holds up as as an absolute truth.
Your argument only proves the same. If the empirical evidence does not match the calculations then the base of the empirical evidence is unsound. In otehr words your evidence may appear to be empirical in quantity but has a qualitive failure in some of its assumptions and theories.
Empirical evidence is only accepted in soft sciences, such as medicine where the variables are just so great that even with supercomputing capability we are unable to assemble the right formulas.
Cold Fusion
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