thingmaker3,

Nope. It's there.

I don't think so.

About phasors being vectors. Havn't you been reading this thread? Silly Ratch!

Of course, I have been part of building this thread.

You catch on quick. Only took two threads.

I think you misunderstood me. I said it sarcastically. I was not agreeing with you.

Okay, enough of me having fun at your expense. I'll go back to it again, of course. But for right now I want to make a clear point:

I am having as much fun as you are. Come back any time. Let's see what you have now.

Ratch

 

Ratch, although I have seen you do complicated electrical calculations in other threads, you have consistently avoided displaying even simple ones in this thread.

I have displayed several calculations, now it is your turn (with or without Mr Kosow) to put up or shut up.

You mean a arbitrary periodic function whose values are continuous, but not sinusoidal, and repeat at the same frequency as the sine? As I said before, you can the add the real projections and orthogonal projections to get a resultant. Same as you do for two phasors.

If what you say is true then you should be able to display a phasor diagram showing current and voltage phasors for the following situation. (I have not asked for one for my magnetising current as I know that would require an infinite number of calculations so I have made it easy and provided a formula for a different current waveform)

A voltage V = 100sin(wt) + 50sin(2wt+60) + 5sin(4wt-10) volts

is applied to a circuit resulting in a current

I = 2.685sin(wt-57.1) +0.758sin(2wt-12.34) + 0.039sin(4wt-90.95) amps

All angles are in degrees,
Both the current and voltage are non sinusoidal periodic continuous functions as you prescribed.

Further, if what you say is true, you should be able to calculate the power in the circuit, from your voltage and current phasors.

 

studiot,

Further, if what you say is true, you should be able to calculate the power in the circuit, from your voltage and current phasors.

OK, I made a polar plot the voltage, current, and the product, which is power. There was a learning curve for the plotting routine I used, and that took time to get up to speed. It was time well spent, however. I still have to check over what I did for mistakes, and make the plots pretty. Then I have to figure out how to post it. Maybe my scanner will work for that. I will try to complete it tomorrow. Stay tuned.

Ratch

 

The power is 77.85 watts and the power factor 0.499

Since the fundamental rotating arm will only be half way round when the second harmonic has finished its cycle and a quarter way round when the fourth harmonic has finished its cycle, I will be interested to see how you represent this on a single phasor diagram.

 

studiot,

I will probably post the graphs tonight. They will show the instantaneous voltage, current, and power in polar format. I will also graphed those quantities in rectangular format so that we can keep our sanity when looking at the polar plots. It appears, unless I made a mistake, that the fundamental of the voltage and current are about 0.8 radians apart. That makes the displacement power factor (DSP) cos(0.8) = 0.7 . For power, I took the average of all the instantaneous values over a 0 to 360 range and got 78.69. Look at this article for different power factor definitions like DSP. http://www.splatco.com/tips/pwrfact/pfarticl.htm .

Ratch

 

I'm just about to watch a film, but perhaps I should save you extra work.

There are not one but three phasor diagrams associated with this question, it cannot be done in one.

The whole point is that the powers are additive, i.e. the total power is the sum of each harmonic voltage times its respective current times the respective phase angle for that harmonic divided by 2 (for peak to RMS conversion).

Power factor is total power divided by total VI.

 

studiot,

There are not one but three phasor diagrams associated with this question, it cannot be done in

That is true, but I believe also that a composite voltage, current, and power graph can also be made.

The whole point is that the powers are additive, i.e. the total power is the sum of each harmonic voltage times its respective current times the respective phase angle for that harmonic divided by 2 (for peak to RMS conversion).

Yes, powers are additive. I added all the instantaneous powers and found the average. It agree quite closely with you value.

Power factor is total power divided by total VI.

I show a 1 radian phase difference between the fundamentals of voltage and current. That corresponds to cos(1) = 0.54 power factor. Not too far from your value either.

I hope you can read a Rich Text File (RTF).

Ratch

 

Cor blimey, you really worked hard here.

A numerical solution. The only way if you have a very difficult waveform.

But you can't call any of your loops phasors. Why were they not circular as all the functions are sine functions?
Perhaps the next step along this route is to go for full complex variables and allocate winding numbers to the harmonics?

I see you plotted the waveforms. Did you notice that they are not symmetrical about the time axis? This is a characteristic of even order harmonics. And why even order harmonics are not good in magnetic applications as they lead to magnetic polarisation of core media.

If you take the general sine series expansion to N terms for current and voltage and multiply you will find all terms where Nv ≠Ni drop out to zero, leaving only products of corresponding current and voltage harmonics, for the power sum.

All of this is guaranteed by the fact that an infinite sine series forms a basis for the linear space of all finite continuous functions. You might like to look this up in your linear analysis book.

Anyway here is a shorter analytical solution, including the three phasors needed.

 

studiot,

Cor blimey, you really worked hard here.

There was a learning and trial period to get up to speed on the software package I used. It was time well spent, however. The computer did all the hard work once I got the hang of it.

But you can't call any of your loops phasors. Why were they not circular as all the functions are sine functions?
Perhaps the next step along this route is to go for full complex variables and allocate winding numbers to the harmonics?

Well, the polar plots show magnitude and phase of the composite waveform. Isn't that what a phasor is? I knew the magnitudes would not be circular as a single frequency sinusoid is.

I see you plotted the waveforms. Did you notice that they are not symmetrical about the time axis? This is a characteristic of even order harmonics. And why even order harmonics are not good in magnetic applications as they lead to magnetic polarisation of core media.

That makes sense.

If you take the general sine series expansion to N terms for current and voltage and multiply you will find all terms where Nv ≠Ni drop out to zero, leaving only products of corresponding current and voltage harmonics, for the power sum.

Yes, I used a brute force method. I was trying to show that a phasor diagram could be drawn. I would not do what I did if I only had a calculator.

All of this is guaranteed by the fact that an infinite sine series forms a basis for the linear space of all finite continuous functions. You might like to look this up in your linear analysis book.

Yes, infinite series expansions are good for a lot of things.

Anyway here is a shorter analytical solution, including the three phasors needed.

Yes, that is the way to go if a computer and software package is not available. I have trouble reading your solution because it is so light and the lines break up a bit. However, I know that superposition of each component is the way to go without massive amounts of computer resources.

Ratrch

 

The whole idea of phase is that it is measured against some reference waveform. It is the t axis distance between a given point on one waveform and "the corresponding point" on another.

This should be the same for all corresponding points in both the wave forms.

So we can ask the question: what is meant by corresponding point?

Well if we just measure the time t from a zero crossing on one waveform and take the same value along the t axis from a zero of the other wave form we run into problems if they are not of the same frequency.

We could try to generate a number by dividing the the integral of the waveform from zero to t by the integral of the waveform over two half cycles.

This would give us a fraction or % of the total achieved at any point t, and could be compared to the point on the second waveform of the same %

 

studiot,

The whole idea of phase is that it is measured against some reference waveform. It is the t axis distance between a given point on one waveform and "the corresponding point" on another.

Everything I read about phasors say they are in the frequency domain, and do not reference themselves to time. That is the way I plotted them. I referenced the composite waves of current and voltage to each other. You referenced the component waves of the same frequency to themselves. Either way is legitimate as far as I can see. As far as I am concerned, a phasor is only a visual aid for problem solving anyway. I know of no one who plots out the voltage/current and graphically measures the length of the resultant to obtain the answer. Everything is done by calculator or computer these days.

Ratch

 

Everything I read about phasors say they are in the frequency domain, and do not reference themselves to time.

How does one divorce frequency from time?

 

thingmaker3,

How does one divorce frequency from time?

Express the magnitude of the periodic voltage/current/whatever in terms of its angle of rotation. This is what I and studiot did for our postings to make a phasor. A phasor is not interested in time, only its magnitude at given angle. As a small sidetrack, the Laplace transform also converts a time domain function into the "s" or complex domain.

Ratch

 

I'm still not following. How does one divorce angle of rotation from time?

 

thingmaker3,

I'm still not following. How does one divorce angle of rotation from time?

Well, suppose we have a periodic wave form expressed as wt, where w is the angular velocity. Then the wave can be expressed as a magnitude at time T1, T2, etc. Now instead of time, suppose we express the magnitude at angle A1, A2, etc. So now we are not interested in how long it took the wave to get to Ax. In this domain, time is irrelevant. Only the difference in angles between two waves is of interest.

Ratch

 

How does changing the name of something change it's nature?

 

I am interested in an explanation of the polar plots in your numeric solution.

In particular what does a polar plot of power represent?

Power and energy are not vectors ( or phasors if you will) but scalars, albeit signed ones.

 

thingmaker3,

How does changing the name of something change it's nature?

It doesn't. Who said it did?

Ratch

 

studiot,

I am interested in an explanation of the polar plots in your numeric solution.

In particular what does a polar plot of power represent?

Power and energy are not vectors ( or phasors if you will) but scalars, albeit signed ones.

For voltage and current, the magnitude of each at a phase within its period, i.e., 45 deg, 90 deg, etc.

For power, the same thing, the instantaneous power at each value of its phase. The vertical distance represents the instantaneous reactive power and the horizontal distance represents the instantaneous real power.

As I said before, phasors are a visual aid rather than a method of doing computations with periodic waveforms.

Ratch

 

So why are there multiple loops?

Your program specified 0 to 2pi so each 'phase' value appears only once and your waveforms are single valued.