parasytic capacitance formula

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charlie b

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Re: parasytic capacitance formula

I have never heard of capacitance being described as parasitic, so I'm not sure what you are asking. I will say, however, that the property of capacitance can only be spoken of in terms of two objects. There is capacitance between two wires, or between one wire and the Earth, or between two parallel plates. The formula for capacitance between two identical wires is bit messy, and I don't think it is really what you are looking for. But here it is anyway:
C = (pi) times (k) divided by the natural log of (D/r),
Where "k" is the relative permeability of the medium between the two wires (and is 8.85 E-12 farads/meter for free space),
"D" is the distance between the two wires, and
"r" is the radius of the wires.

Can you let us know where the question came from, and what it is that you are trying to find?
 

rattus

Senior Member
Re: parasytic capacitance formula

Yes Charlie, there is such a thing as parasitic capacitance. Generally speaking, it is the capacitance you had rather not have.

In coaxial and twin line cables, the capacitance is not parasitic, it is a necessary element in the computation of characteristic impedance.

For most any cable configuration, formulas do exist, but one must know the cross sectional geometry of the cable as well as the permittivity of the insulating material.
 

steve66

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Illinois
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Re: parasytic capacitance formula

I agree with Rattus with one addition. If you are at a high enough frequency to worry about the capacitance of a cable, then you are probably in the transmission line realm. In other words, the capacitance is no longer "lumped". It is distributed along the cable with distributed inductance. That gives the cable its characteristic impedance Rattus mentioned.

Also, the cable is probably not a small fraction of the wavelength of the voltage (or current). As a result, the capacitance your voltage sees will depend on how long the transmission line is, and how it's terminated.

For example, a 1/2 wave line terminated in a short circuit might look like an open circuit. A 1/2 wave line terminated in a open circuit might look like a short circuit. (I say might because I'm not sure I remember these right).

Match the source, load and line impedence, and the the line will look resistive.

Steve
 

charlie b

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Re: parasytic capacitance formula

Originally posted by rattus: Yes Charlie, there is such a thing as parasitic capacitance. Generally speaking, it is the capacitance you had rather not have.
I understand the meaning of the word "parasitic." I just had not seen the phrase "parasitic capacitance" before.

Back to Richard T: What type of cable are you talking about? Also, what type of power system?
 

Richard T

Member
Re: parasytic capacitance formula

we are putting a vfd nearly 800 feet from a 30 hp 3phase motor. from the manufactures literature i can see that this will require a filter if we are to use a freq. that is above 60hz for sure. an email to the design team said that it need not be considered in this application. however it has me wondering. i would like to be able to figure this stuff out my self. there was something else.overvoltage at the motor leads all of this would be really awesome to me to figure out but i want to start with the amounts of capacitance in the cable over various distances, voltages, amperages and frequencies. This realy has me stumped and my journeyman and design are looking for the formula but haven't had any luck.
 

Richard T

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Re: parasytic capacitance formula

some vfd's can run up to 8ooo hz. if i am correct the frequency is directly proportional to the capacitance between the wires.
 

Richard T

Member
Re: parasytic capacitance formula

charlie b.
we use alot of vfd's and some of them are connected to the motor via tray cable and others by wire in conduit. the voltages are anywhere from 208 to 480 with an occasional 240v. and from 1/2 hp to 200hp
 

rattus

Senior Member
Re: parasytic capacitance formula

Richard T.,

Do I understand this right? The VFD changes the frequency of the motor supply, and this frequency could be as high as 8KHz, right?

I believe the frequency of the VFD is set by the speed requirements of the motor and has nothing to do with stray capacitance.

I also think that stray capacitance would have no effect on the power cables to the motor.

Now, is there any control wiring between the VFD and motor?

This is merely my opinion not based on first hand experience.
 

steve66

Senior Member
Location
Illinois
Occupation
Engineer
Re: parasytic capacitance formula

Do I understand this right? The VFD changes the frequency of the motor supply, and this frequency could be as high as 8KHz, right?
I don't think that's quite right. The VFD output is usually a Pulse Width Modulated output. I think the carrier frequency is usually around the 15-40KHz wave. But a lower frequency signal is used to modulate the carrier (usually in the 10 to 60Hz range). But the motor only responds to the lower 10 -60Hz signal.

The filter is used to filter out the carrier, so the signal isn't distorted before it reaches the motor.

STeve

P.S. Not that I know what youre application is, the transmission line stuff doesn't apply.

[ September 22, 2005, 09:15 AM: Message edited by: steve66 ]
 

tony_psuee

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Location
PA/MD
Re: parasytic capacitance formula

The carrier frequency of VFD's that I have seen are from 8-15kHz. The issue with filters on the output for long cable lengths is more to deal with the induced voltages. The longer the cable run, the higher the spikes at the motor. We did testing with a 460V VFD running a 680Vdc bus and measured spikes of almost 1200Vrms at the motor with about 220ft of cable. The majority of motor manufactures that I have used all state their inverter duty motors have 1700V insulation. The output filters reduce the rise time of the output wave form to reduce the magnitude of the spikes that the motor sees and thus prevent burning the motor winding insulation. You are correct that the capacitance of the cable does contribute to this factor. However, I have yet to deal with a VFD app engineer that will actually calculate those values. They start with cookie cutter figures for output reactors and if that doesn't work, recommend a full sine wave filter. Just MHO.

Tony

edit for spelling

[ September 22, 2005, 09:40 AM: Message edited by: tony_psuee ]
 

rattus

Senior Member
Re: parasytic capacitance formula

OK, now I see I think.

The VFD is a switching amplifier which changes a low power sine wave into a high power sine wave and controls frequency and amplitude as well.

I did an engineering report on switching amplifiers many years ago, but I don't claim to know anything about them now.
 

Richard T

Member
Re: parasytic capacitance formula

Toney is right on the money as far as application however i am really interested in finding out, in theory at least, how much capacitance i will see not only with this app. but with others as we use alot of vfd's and motors. This way I am able to see more of what is happening with the systems we are putting in. I really appreciate everyones time and comments, I've only been in this trade for a little over 2 yrs so i have a lot to learn and forgive me if my terminology is a little wierd
 

Richard T

Member
Re: parasytic capacitance formula

www.abb-drives.com


wow i was able to find alot of information in the product documents part of this site in a document called "effects of ac drives on motor insulation" after reading all of this i wonder if knowing a formula for the capacitance will help much with vfd's. however if anyone can find this formula i would still appreciate it. It is a good starting point
 

tony_psuee

Senior Member
Location
PA/MD
Re: parasytic capacitance formula

rattus,

A VFD does not change a low power sine wave into a high power sine wave. As simply as I can put it, it is a full wave rectifier with power output, current technology is IGBT's. The VFD uses pulse width modulation of the IGBT's to switch the DC bus voltage, positive and negative, to provide power to the motors. If you average the area under the curve of the PWM DC output you get the value of the sine wave the motor thinks it is receiving.

Tony
 

rattus

Senior Member
Re: parasytic capacitance formula

Tony,

I am suggesting that in essence a VFD is a switching amplifier because that is what switching amplifiers do. They switch the output between the positive and negative rails or leave it open; the output is clamped to the rails to maintain current if the output is open. This is done with pulse width modulation. The VFD would also contain an oscillator which determines the waveshape, frequency, and amplitude although this may be done with a computer these days.

A low-pass filter is then used to remove the undesirable frequencies.

A matter of wording, I think.
 

steve66

Senior Member
Location
Illinois
Occupation
Engineer
Re: parasytic capacitance formula

I think the bottom line is that it would be very difficult to calculate the voltage spikes at the motor given the capacitance of the line. Probably easier to just hook up the VFD and measure the spikes with different frequencies and drive speeds.

But given 800' to the motor, I find it hard to believe that you don't need a filter. I wonder what their reasoning was.

Steve
 

bob

Senior Member
Location
Alabama
Re: parasytic capacitance formula

The following site will answer most of your questions.
http://www.mtecorp.com/techpaper.html

The IGBT transistors perform the switching of the frequency which is variable from low to about 20kc. From this is derived what I think is a "dirty square wave" that simulates the sine wave. Due to the carrier frequency being high the fact that the impedance of the cable and motor do not match, causes a reflected wave that can be equal and of oposite polarity resulting in a peak to peak value of about 1600 volts at 480 supply. Generally you will see a 5% reactor in series to reduce this peak value. To me a cable run of 800 ft is way out of line. Ask the MFG for suggestions as to the Max cable run.
 

rattus

Senior Member
Re: parasytic capacitance formula

It is my understanding that the switching frequency (or carrier) frequency is constant and is in the order of 10-20kHz. The pulse widths are then modulated to synthesize a sine wave with frequency in the 60Hz range.

Indeed, the output is dirty. It is not the carrier frequency per se, but the short rise times of the switched output which generate extraneous signals in the MHz range. These signals can be reflected by the mismatched load at the end of the cable.

Since the cable impedance cannot be matched, a filter is in order, and it seems that these filters can be rudimentary--not unlike the RF filters found in light dimmers.

It would seem prudent to twist the cables between the VFD and load and perhpas shield it as well.
 
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