Instantaneous 3-phase power:

[crossman]

Re: Instantaneous 3-phase power:

Side note: Rattus, you have not offended me. I want to apologize to all of you for sticking my "off-the-top-of-my-head" thoughts into this. Obviously you guys are much more learned with the math than I am. I want to learn all I can. The way I can learn is to think deeply on these things and then throw my thoughts out there for yall to critique.

Because my knowledge is less than yall's, I feel like I may intruding in this thread, so if I am, I apologize for that also.

 

[rattus]

Re: Instantaneous 3-phase power:

To all:

I have just spoken with Dr. K. W. Heizer who taught AC Circuits to me 49 years ago.

He agrees that impedance and reactance cannot be used in a time domain analysis.

Enough said. You cannot argue with an 80 year old retired EE professor with a Phd.

This is not unlike the episode on "All in the Family" when Archie found out that you cannot argue with a station wagon full of nuns!

[ January 27, 2005, 08:48 PM: Message edited by: rattus ]

 

[crossman]

Re: Instantaneous 3-phase power:

oh! oh! I said that way back on the 2nd page of this thread!

Originally posted by crossman:
You cannot use Z for instantaneous computations because Z is in actuality an RMS quantity. Does that sound right?

But it is possible to have an "instantaneous impedance" that can be defined mathematically and this "instantaneous impedance" can be used in the calculations.

Now someone tell me there is no such thing as "instantaneous impedance" because it isn't in the books. Oh? Well, let me define it for you, which I already have. It is the instantaneous source voltage divided by the instantaneous current at that particular instant.

So now there is a definition. You say I am full of it? Well, Inductive reactance did not exist until someone defined it and named it years ago. The effects of inductance on current have nothing to do with ohms. Inductive reactance is an artificial construct designed solely to make the computations of the magnitudes of current easier to calculate. It tells us nothing about what the electrons are actually doing in that circuit. It gives us a magnitude, but that is it.

And sometimes we get the cart before the horse.

We assume that electricity works like it does because the formulas say so. But it doesn't. Electricity works because of the basic laws of physics that deal with particles. The formulas are just ways that were discovered to model the circuits and to give us numbers that we can grasp given our human limitations. But the math does sometimes get in our way of what is really happening.

Here's one: If I asked "Why is the current in an inductor zero when the source voltage is at its peak?" The most likely answer will be "Because voltage and current are 90 degrees out of phase in an inductor."

But that is wrong. That is not an explanation of why. Actually, the fact that the current is zero when the voltage is at peak is how it was determined that there is a 90 degree phase shift. Our thinking is backward.

You may ask, "what is your point? The math still works"

The point is that sometimes we get too wrapped up in math that is only an analogy of what is really happening in the circuit. We start believing that the MATH is what is controlling the circuit. The formulas cloud us and we forget that all there is in a circuit is voltage and resistance and current and the effects thereof.

We start believing that source voltage and current at an instant can have a REAL phase angle of 37 degrees. But it can't. At a single instant, they are either in phase or 180 degrees out of phase. The 37 degrees is just a mathematical relation between the magnitude of current and the magnitude of voltage. There is no actual 37 degree relation between the EMF and the electrons that it is pushing at that given instant. Are the electrons are traveling at an angle in the wire? No.

At any given instant on the sine wave, there are only two possibilities (discounting the zero crossings): The current is traveling in the direction that the source voltage is "pushing" or the current is traveling against the direction the source voltage is "pushing." Either in phase or 180 degrees out of phase at any given instant.

Phase angle for instants of time? I don't think so. Because, to define a phase angle, you are talking about TIME. And when dealing with instants, we are not looking at other times, we are dealing with that specific time only. To define phase angle, for example, you would look at the source voltage peak, and then you would look atthe current peak, and say "okay, there is 37 degrees between the peaks, therefore the sine waves are 37 degrees out of phase." But does this have meaning for the electrons? Are the actual electrons 37 degrees out of phase with the source voltage at a GIVEN INSTANT in time? I don't think so. No, all the 37 degrees gives us is a relation of the magnitude of the current to the magnitude of the voltage.

Take a single instant in time. Let's say that the current is of the same polarity as the polarity of the source. Is the source voltage constant during that instant? Is the current constant in that instant?

If anyone has read this far, I wish you would answer at least the last question.

[ January 27, 2005, 07:55 PM: Message edited by: crossman ]

 

[Ed MacLaren]

Re: Instantaneous 3-phase power:

Take a single instant in time. Let's say that the current is of the same polarity as the polarity of the source. Is the source voltage constant during that instant? Is the current constant in that instant?

If anyone has read this far, I wish you would answer at least the last question.

Yes, if an "instant" is defined as an infinitely short period of time.

Of course, there would be an infinitely large number of these instantaneous values in one cycle.

H*ll, I'm just making conversation.

Ed

 

[steve66]

Re: Instantaneous 3-phase power:

Rattus:

I think the phrase "time domain analysis" is somewhat vague. Let me make my claim very simple with all the fat trimmed away, and please tell me if you agree or disagree:

Assume a sinusoidal steady state circuit with linear circuit elements. Assume the applied voltage v(t) = Vp sin(wt).

We can represent v(t) by Vp@0 where Vp is the peak magnitude and 0 is an angle. (I'm not going to call them vecotrs or phasors, it doesn't matter what they are called. It is just a shorthand for the equation for the voltage).

Now we apply v(t) to a circuit of resistance and reactance. We can represent the resistance and reactance by a magnitude and an angle, Z@u.

The current can also be represented by a magnitude and an angle, I@x. Then, by ohms law:

I@x=Vp@0/Z@u.

Once we calculate I@x, we can change it back to its long form:

i(t)=I sin(wt+x)

This allows us to find the current at any point in time. Or we can leave it as written above where current is a function of time.

You can say this is wrong all you want, but if you try it, it works.

P.S. Sorry Physis, I guess I lied. This is starting to look like another infinite thread

 

[rattus]

Re: Instantaneous 3-phase power:

Steve, you can switch back and forth as much as you wish, but you cannot mix the two methodologies. Furthermore, I see no reason to switch back and forth; you are merely muddying the water by doing so. Certainly not in my proof which is purposely brief and concise.

Vector analysis is an outgrowth of time domain analysis which is not vague. One may have a vague understanding, but the methodology must be exact in order to be of use.

No doubt you have seen my post referring to Dr. Heizer who I assure you knows this subject ten times as well as I do.

 

[rattus]

Re: Instantaneous 3-phase power:

Correction Please:

"Charlie B. insists that I did not ignore the reactive current. My proof has no equation for current anywhere, resistive or otherwise. That is about is ignorant as one can be!"

This quote from me might be interpreted as my calling Charlie B. ignorant. It should have been written,

"That as about as ignorant as I can be."

That is to say I was ignorant of the reactive currents, not Charlie B. My apologies Charlie for the poor wording.

 

[physis]

Re: Instantaneous 3-phase power:

So I finally can't take it anymore and reluctantly decide to look at Charlies math, cause I'm curios anyway. I'm still on the first page and I'm already in trouble.

I haven't read that much of the volumes you guys have written so I have no idea if this has come up. It's probably just me missing something obvious or lacking sufficient knowledge but here's my problem.

Sin wt. That's my problem. Sin wt.

w = 2*Pi*f

sin operates on angle. Radians are obviously related to angle. But a number of radians isn't an angle.

Using 60 cycles, starting at 0?

Sin 0 = 0. That's fine for sin angle and sin wt.

It takes .004166... seconds for 60 Hz. to reach 90?. After that much time passes my calculator says this:

2*Pi*f = (6.283....) * 60 = 376.991...
(376.991...) * (.004166...) = 1.5707...
That's: w = 376.991 and
wt = 1.5707... while the angle = 90

Sin 90 = 1
Sin 1.5707... = .0274...

After 1 second:

Sin 21600 = 0
Sin 376.991... = .292...

For Phase A, power equals Vmax sin (wt) times Imax sin (wt - @)

Using 340v. at .707 amp, @ = 15 (phase angle between V and I). (I already used 480 but didn't change it from RMS so it's 340, same with current)

At .004166... second (t = .004166...). The time between 0? and 90?.

480 x sin (376.99 x 004167) x 1 x sin ((376.99 x .004167) - 15) =

480 x sin 1.5709 x 1 x sin -13.429 =

480 x .0274 x 1 x -.2322 = -3.05 watts.

At 1 second (t = 1)

480 x sin (376.99 x 1) x 1 x sin (376.99 x 1 - 15) =

480 x (.292) x 1 x (361.99) = 50,736.5 watts.

I only used one from Charlie because it was the first occurence.

I don't have any doubt that I'm just demonstrating my ignorance and somebody's gonna point to something simple and I'll feel stupid. But, the concept of 2 Pi radians in a circle is far from news to me and I just can't find how to resolve the math without converting radians back to an angle.



Edit : I changed it to address sin wt instead of sin w (your're right Rattus, it doesn't make sense without the t)

[ January 29, 2005, 01:08 PM: Message edited by: physis ]

 

[rattus]

Re: Instantaneous 3-phase power:

Sam, sin(w) is meaningless because w is the radian frequency, not the angle.

sin(wt) does mean something because the argument, wt, is in radians.

For every period, T, wt goes from zero to 2*pi, and sin(wt) goes from zero to 1, to zero again, to -1, and then back to zero to complete the cycle.

 

[physis]

Re: Instantaneous 3-phase power:

I knew the sin w without the t would come up. I left t out because it's the radians part of w I'm lost on. "sin (radians)".

Would I be correct if I assumed that t is used as a variable and isn't measured in seconds?.

Like 1/f is an amount of time.

 

[rattus]

Re: Instantaneous 3-phase power:

Sam,
radians are just another way to measure angles, and the reason is that the 2*pi factor falls out of the mathematics in some applications.

Just remember that pi radians are equivalent to 180 degrees. Remember also that t is the independent variable and is always measured in seconds in most if not all technical work, and w is a constant except in frequency domain analysis, but we will save that for another day!

 

[physis]

Re: Instantaneous 3-phase power:

I know that two times the radius times Pi is the circumferance.

I must have an error in the application of the math I posted. Otherwise it would have to be the equation.

If t is in seconds, w is 2Pif and @ is the phase angle between V and I then am I calculating wrong?

 

[rattus]

Re: Instantaneous 3-phase power:

K.I.S.S.

That means Keep It Simple Sam, not the S word.

An example:

v(t) = Vp[sin(wt)]

i(t) = Ip[sin(wt + @)]

w in radians/sec times t in seconds = radians.

@ is also expressed in radians.

It is that simple.

 

[physis]

Re: Instantaneous 3-phase power:

I haven't studied your reply yet but I had to take a minute to say that I thought that plugging values into variables was simple.

 

[physis]

Re: Instantaneous 3-phase power:

Let's take this one:

v(t) = Vp[sin(wt)]

Goof it all up with my math:

The same values I used above: 340v RMS, 60 Hz., t = .004167 (for 90?)

Vt = 480 sin(wt) =

Vt = 480 sin(376.99 x .004167) =

Vt = 480 x 1.5709 =

Vt = 480 x .0274 =

Vt = 13.152 =

V = 3156

But V = 480 at 90?

w in radians/sec times t in seconds = radians.

I know. Sin (radians). But sine doesn't know that 12.566 represents 0?. In fact, it thinks it's 12.566?. Or is this where my problem is? Is it implied that radians are converted to an angle?

[ January 29, 2005, 12:52 PM: Message edited by: physis ]

 

[rattus]

Re: Instantaneous 3-phase power:

Sam, I was merely trying to emphasize in general terms the relationships you are struggling with without cluttering it up with numbers. Now we can get on with your example.

Your error is that you have sin(wt) > 1. This can never be. You should have,

sin(1.57rad) = 1.0

BTW, you should note that 1.57 rad = pi/2 rad = 90 deg.

[ January 29, 2005, 11:24 AM: Message edited by: rattus ]

 

[physis]

Re: Instantaneous 3-phase power:

Your error is that you have sin(wt) > 1. This can never be. You should have,

sin(1.57rad) = 1.0

That was an error. I neglected to take it's sine. It's value should be .027. The equation still fails.

BTW, you should note that 1.57 rad = pi/2 rad = 90 deg.

So you are approaching my question here. IS IT IMPLIED THAT THE VALUE OF wt IS CONVERTED TO AN ANGLE?

 

[physis]

Re: Instantaneous 3-phase power:

I've edited the post containing my solution of the equation to remove the calulation error.

 

[physis]

Re: Instantaneous 3-phase power:

Rattus,

I thought I'd post this with the hope that, having an angle to radians conversion graph right here, you might beleive that I know what a radian is.

 

[rattus]

Re: Instantaneous 3-phase power:

Sam, your calculator apparently is taking the sine of 1.57 degrees. You should convert back to degrees for the calculator.

And wt is an angle in radians.

BTW, back in 1971 I worked with the hp guys in Palo Alto on the development of the hp-35 scientific calculator.

[ January 29, 2005, 01:35 PM: Message edited by: rattus ]