Instantaneous 3-phase power:

[steve66]

Re: Instantaneous 3-phase power:

Steve, v(t)^2/R is instantaneous power. This is fundamental. Where do you get this notion that it is average power?

I say you started with average power due to your post on Jan 22:

3) Pavg = 120V x 120V/14 .14 Ohms = 1018 W (V^2/R)

Which you then used to justify:

Note that in eqn 3, there is no need to know anything about the current or the reactive elements of the load. In other words, I have recognized a difficulty and avoided it. The only angles we need consider are the phase angles of the 3-phase voltages

You used an equation for average power to justify ignoring all reactances in your equation for instantenous power.

Steve

 

[steve66]

Re: Instantaneous 3-phase power:

rattus:

You posted:

That current does not flow through the resistance, therefore it has absolutely no effect on power! Apparent power in KVA yes, but no effect on real power in KW

That it "affects the apparent power " was exactly the point I was trying to make.

If you are only concerned with the instantenous value of "real power" (if there is such a thing - see Crossman's discussion) is constant, then I agree you can ignore the value of reactance.

I have been arguing the more general case that the instantenous "total" power flow (real and reactive) is constant.

Steve

 

[steve66]

Re: Instantaneous 3-phase power:

Crossman:

I think there is more to power flow than the current and voltage at one instant and one point. Power can flow to and from the source. And I will agree that a current and voltage reading at a single point will not tell which way the power is flowing.

Power might actually be carried by the Electro-Magnetic wave surrounding a wire rather than just in the current and voltage (I'm not sure about that one, just consider it food for thought.)

Steve

 

[physis]

Re: Instantaneous 3-phase power:

I keep watching this thread get bigger.

 

[rattus]

Re: Instantaneous 3-phase power:

Steve, the equations for Pavg are not part of the proof. That is from an example showing various ways to compute power. I used RMS values because all are so comfortable with them.

Now you may be right that the energy flow in a balanced 3-phase system is constant, but this proof considers only power in KW, not KVA and not VARs.

Charlie B., I don't recall using Z in my proof. I would not know how.

 

[crossman]

Re: Instantaneous 3-phase power:

This thread has been fun and certainly has caused my gray matter to think deeper than it usually does.

I think that the question I proposed gets right at the heart of the matter: If you have a theoretically perfect wattmeter (capable of producing a graph of instantaneous values) connected to a theoretically perfect sinusoidal AC source connected to a theoretically perfect capacitor with theoretically perfect conductors, will the wattmeter give a wattage curve greater than zero at any point in the first quadrant of the sine wave?

I am going to say that it does. I would love to hear some comments on this. Is this just a matter of definition of the Watt? Wattage is only consumed in a resistor by definition? I don't believe that there is any scientifically valid proof of this. Certainly it is a rule of thumb used when averaging power over time but is it really true for less than one full cyle of the sine wave? Doesn't a source have to perform real work when charging a capacitor?

How is a Watt defined? Does this definition automatically exclude reactance?

Now, I like the simplicity of Rattus' proof. At first I was thinking "this is cool, why can't these other guys see the simple elegance in this?" But then Steve66 made a comment something like "you can't ignore the reactive current when speaking of instantaneous values".

That is what got me to thinking. You really can't. The fact that we have always been taught that inductors and capacitors do not consume power is causing my confusion. When the statement is made that reactance does not consume power, in other words, zero watts, it really means that the reactances do not consume power when averaged over time. But I am of the notion that they DO consume power in the various quadrants of the cycle.

Having said that, and realizing that the reactive power really doesn't affect the true power OVER TIME, then Rattus is essentially safe in ignoring it when "proving" that the power is constant over time.

Still, to truely "prove" that the power in our three-phase circuit is a constant over time, we need to account for ignoring the instantaneous values of...

ARRRRGGGHHHH!!!! My brain is frying. I think I will sit back and let y'all finish this one! I surrender!

I really would like to hear something about the wattmeter/capacitor issue though.

 

[rattus]

Re: Instantaneous 3-phase power:

Originally posted by charlie b:
You did not ignore the reactive current. You expressed VI as V^2/Z, and started your proof from there. It takes calculus to prove that I = V^2/Z, but once you have that, you can use that. You are no longer treating current in the mathematical steps. Any actual values of R, X, Z, PF, Vp, and Ip were swallowed up by your method of just proving that power is constant, without caring about the value of that constant.

I think we are not all on the same page, with regard to the phrase ?time domain.? My view is that any expression that has time as a variable, such as v(t) = Vp cos (wt), is being handled in the time domain. Is there another meaning of this phrase?

Charlie, I did not use V^2/Z in my proof, maybe in an example, but not in the proof. Just pretend that the concept of RMS, reactance, etc. have not been invented. One can still solve problems in the time domain with calculus and no mention of X or Z. Yes, you are on the right page with time domain.

I maintain that reactance and impedance per se cannot be used in time domain calculations. Does it make sense to say,

i(t) = v(t)/Z?

I challenge anyone to show me a valid example of impedance used in a time domain equation!

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!

Charlie B. insists that the values of X, Z, etc, were swallowed up by my method. No Charlie, they were never considered.

Now Vp was used in the definition of v1, v2, and v3, and that is perfectly valid, but it is not RMS.

Charlie, in your proof, you converted the peak values to RMS after you had proved your point, but you did not use RMS in the proof itself.

Now, however this thing ends, it has been a lively discussion, and that is good.

[ January 25, 2005, 02:37 PM: Message edited by: rattus ]

 

[steve66]

Re: Instantaneous 3-phase power:

Don't worry Physis, this thread is no threat to your "infinite thread"

By Rattus:

I challenge anyone to show me a valid example of impedance used in a time domain equation!

You did that yourself with:

i(t) = v(t)/Z

Of course this would only hold true for sinusoidal waves, but that's what this entire discussion has been about. And if we wern't talking about a sine wave, we wouldn't have a "Z" anyway. On the other hand, any waveform can be written as a sum of sine waves, so technically, we can use this equation for any waveform.

Steve

 

[rattus]

Re: Instantaneous 3-phase power:

Steve, you will have to show me where I used Z in a VALID time domain equation. I was making the point that the expression was INVALID! We must be speaking a different language.

In an inductor,

i(t) = int[e(t)dt]/L

but this is not impedance!

In a capacitor,

i(t) = C(dv/dt),

but that is not impedance.

You use impedance with RMS values which are NOT functions of time.

You have not met the challenge.

[ January 25, 2005, 01:52 PM: Message edited by: rattus ]

 

[physis]

Re: Instantaneous 3-phase power:

It's not that Steve, I want to play too, but I'll have to do work to get up to speed.

Edit: And as an added barrier, I'm not that familiar with three phase.

[ January 25, 2005, 02:02 PM: Message edited by: physis ]

 

[steve66]

Re: Instantaneous 3-phase power:

Rattus:

Are you implying that impedence can not be used to find instantenous values of current, voltage, or power????

You asked for a vaild time domain equation and I gave you one.

Edited because I misread your last post.

[ January 25, 2005, 04:12 PM: Message edited by: steve66 ]

 

[crossman]

Re: Instantaneous 3-phase power:

I can't help but throw my uneducated thoughts into this thread.

Sorry!

But when you say impedance, if you are talking about the impedance that equals the square root of the sum of resistance squared plus reactance squared, then I am going to say NO you cannot use impedance for instantaneous calculations.

 

[physis]

Re: Instantaneous 3-phase power:

Alright, I'm in.

How do you figure?

An instantanious value excludes reactance?

 

[wirenut1980]

Re: Instantaneous 3-phase power:

I challenge anyone to show me a valid example of impedance used in a time domain equation!

I may be in over my head here, but impedance is used all the time in time domain equations, but it is not the impedance itself that is time dependent. It is current or voltage or power. I want to read all of this thread to catch up

 

[crossman]

Re: Instantaneous 3-phase power:

Let's say I give you an instant in time. I tell you that the voltage is 78 volts. I tell you that the impedance of the circuit is 20 ohms.

Can you tell me the current flowing at that instant?

Uh-oh... I think I see what is coming next...

 

[physis]

Re: Instantaneous 3-phase power:

Then you know I'm going to ask what the difference would be if it were impedence or resistance or both.

I wont bother posting an equation.

But I figure you're prepared for that.

 

[steve66]

Re: Instantaneous 3-phase power:

Crossman:

Is that 78 volts just real voltage, or does it include reactive voltage. Just kidding

If you told me you had 78 volts at a 0 deg phase angle applied to a reactance of 20 ohms at a -40 degree angle, here is the math to find the current as a function of time.

i(t)=v(t)/Z.

We can also write this as I=V/Z where I, V, and Z are all phasors. (And phasors are functions of time by definition. The Z phasor just happens to be a constant phasor that doesn't rotate. I and V are rotating phasors at the applied freq, and the 0 deg angle is the phase with respect to some reference phase).

So I=78@0 / 20@-40 where 78@0 is 78 at angle 0.

Then I= (78/20) @ (0-(-40)) = 3.9@40.

3.9@40 is just shorthand for:

i(t) = 3.9 sin (wt+40)

If you want to find the current at .1 sec, just substitute .1 on the right hand side. So we have found current as a function of time using impedence.

Steve

 

[crossman]

Re: Instantaneous 3-phase power:

Steve66, I think I see where I was going wrong.

Sometimes all the discussion boils down to definitions and differences in definitions which are assumed or vague.

When I think of "instantaneous" I am thinking of the most strict definition in that all you know is what can be measured at that precise instant. For all we know, the voltage could be DC or a square wave or anywhere on a sine wave AC voltage.

This is what is behind every one of my posts in this thread. I was viewing every instant as being disconnected and unrelated to every other instant and thinking that the proof had to reflect this, that every point on the graph would have to be examined separately.

Now, I am seeing that my view of "instantaneous" doesn't really fall into line with this thread because of the given parameters of "three phase power" which tells us sine waves, 120 degrees out of phase, phase relationships, etc etc...

Thanks to everyone who has contributed to this thread! I am enjoying it.

But I still think that watts are produced in the first quadrant of the voltage applied to a capacitor....

[ January 25, 2005, 06:04 PM: Message edited by: crossman ]

 

[steve66]

Re: Instantaneous 3-phase power:

I know what you mean about definitions. I saw that too when Rattus kept throwing out the reactance, and I kept saying you can't do that. Turns out he was trying to calculate something different than I had in mind.

The thing I was trying to show with impedance mixed with time varrying waves, is that if we take Rattus' equation:

P(t)=V(t)^2/R

we can substitute Z for R IF we meet a lot of caveats like:

1. Were only dealing with sine waves.
2. Everything is steady state.
3. We have written permission from the AHJ.

So we get P(t) =V(t)^2/Z. Now its pretty easy to show that instantaneous power (real, reactive, or all) is constant.

Again, my appology to Charlie B., its not a mathematical proof, but somewhat convincing.

 

[rattus]

Re: Instantaneous 3-phase power:

Steve, you are not in left field, you are not even in the cheap seats. You are out of the ball park!

Consider a simple example, say a capacitor with reactance, Xc. Current in this capacitor is:

i(t) = (dv/dt)*C

Say v(t) = 78V and that is all, OK? We do not know dv/dt, therefore we cannot compute the current in the cap.

If Vp = 78V, then dv/dt = 0 and

i(t) = (0)*C = 0, not 78/Xc

You can contrive all these examples you wish, but you are wrong, wrong, wrong. Give me something from a textbook or reference book.

Until you can provide a solid example, you are not proving your argument.