VFD spikes in multiple motor installation
VFD spikes in multiple motor installation
(OP)
Hi guys,
I did additional measurements and wanted to share with everybody.
the original topic is:
http://www .eng-tips. com/viewth read.cfm?q id=298784& amp;page=1
to sum up:
- there are several fans supplied from a VFD, they appear strong voltage spike ringing at farthest motor terminals.
- several solutions and a model was suggested, I did additional measurements and give it a try to a filter first "tested" in spice model. Unfortunately not luck
.
I would like to understand what is wrong with the model (apart of my uncompetence) if anybody have any idea please contribute..
In anycase, for solution fan supplier has said that we MUST use a sinewave filter and we are buying that.
Regards
I did additional measurements and wanted to share with everybody.
the original topic is:
http://www
to sum up:
- there are several fans supplied from a VFD, they appear strong voltage spike ringing at farthest motor terminals.
- several solutions and a model was suggested, I did additional measurements and give it a try to a filter first "tested" in spice model. Unfortunately not luck
I would like to understand what is wrong with the model (apart of my uncompetence) if anybody have any idea please contribute..
In anycase, for solution fan supplier has said that we MUST use a sinewave filter and we are buying that.
Regards





RE: VFD spikes in multiple motor installation
I'm not sure about the source inductor... I'll take a look at that.
From this computer I cannot access your LTspice file. But what I saw in a previous file was that you had two transmission lines connected in series with the motor, as if one was a supply and one was a return. I don't think that is right.
A single four-terminal transmission line element in LTspice represents a single pair of conductors (of which one may be ground). As far as I can imagine, there is no circumstance when one pair is connected in series with the motor which is in turn connected in series with another pair in that fashion.
For medium voltage motors with shielded cable, there is no coupling between phases and using a single transmission line to represent a phase-to-ground pulse on a single phase is a very straightforward and logical model imo. That is the model I had used for your motor, even though your motor cable is not shielded..... So my model was not a great match for your configuration in that respect. Nevertheless I think you will find a majority of authors and literature use simple single TL to represnt a cable even for unshielded configuration and in some circumstances (limited phase to phase coupling) it is a reasonable guess. To the best of my knowledge, the next more accurate solution method would represent a large increase in complexity when you try to solve a multi-conductor transmission line model. Specifically, the general multi-conductor transmission line solution involves solving an eigenvalue problem to develop the transformation matrix to transform the coupled physical system into a decoupled modal system. Then the decoupled modal system could easily be solved in LTspice as a several separate single-transmission lines. The results would be transformed from modal domain back to physical domain using the inverse of the modal transformation matrix. There may be some intermediate approach which is not as complicated as the modal transformation, but I am not familiar with it. The only way I would know how to solve the system better woudl be to use modal analysis.
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RE: VFD spikes in multiple motor installation
Keith Cress
kcress - http://www.flaminsystems.com
RE: VFD spikes in multiple motor installation
I tend to think the kink in the rising wavefront was a clue to the physcial behavior. I'm trying to picture whether adding another mode could create this. I know the phase mode and ground modes can travel at different speeds, so at first glance it seems plausible that we're seeing a single pulse at the source travelling two different speeds to give the two-part slope at the load. Just a thought, subject to more thinking...
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I used both TL for + and return because in your first circuit with just one TL inserting the 0.5uH MCB coil caused that all the ringing was filtered out and that had no sense.
I think that I saw other post relating to some discussion about "cable screen should be connected to earth or not in both sides" and there, there was a circuit using these two TL scheme, I took the idea from there and maybe I understood it wrong.
VFD source is 220V one phase, input filter inductor (not known value) rectifier and dc bus capacitor (i think that it is some hundreds of uF, I will check in specification).
RE: VFD spikes in multiple motor installation
interesting that you are seeing turn-on & turn-off transients at the motor and not at the vfd.
good luck
RE: VFD spikes in multiple motor installation
On slides 4 and 5, the fans that are not working, are they disconnected at the motor end of the cable or the supply end of the cable?
When you said "Added 3 serial phase inductors at VFD output of 4.7mH (0.9A)", does that mean one 4.7mH in each phase of vfd output (upstream of the branch point where the cables split to multiple motors) ?
By the way, thanks for sharing your data. I agree with you simulation is not worth much without measurements. Hopefully in some cases, the combination of the two together can work well together. For me it is interesting to try to figure out and it sounds like you are also interested. I have just recently started studying from books/papers various ways to model surges, but I haven't had any chances to do measurements, and probably won't (the applications I'm interested in are medium voltage).
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RE: VFD spikes in multiple motor installation
The reason that you do not see transients at the VFD end is - and this is part of the physical description of a transmission line with zero source impedance - that the IGBTs have a very low impedance so there's no way for the transients to do anything at the VFD end.
At the motor end, it something entirely different. There, it is a business between cable impedance and terminal impedance. In this case the motor winding.
Also, the 'turn off' transient isn't really a turn off but a turn on of the opposite polarity switch in that phase.
Gunnar Englund
www.gke.org
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Half full - Half empty? I don't mind. It's what in it that counts.
RE: VFD spikes in multiple motor installation
guys I just realised that in the mess of testing arrangement I put the inductors in supply side UPSTREAM VFD ),
so it is very undesrtandable that we didn´t see any effect
I will try to repeat the measurements and tell you how it works,
RE: VFD spikes in multiple motor installation
your description does not explain the lack of transients at the other loads...
RE: VFD spikes in multiple motor installation
There is a free program called ATP which is supposed to solve Electromagnetic Transients (EMTP type program). Does anyone know if it solves multiconductor (multi-pair) transmission line problems?
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RE: VFD spikes in multiple motor installation
suspect there there may be a ground loop issue with the with motor #7, a ground loop in the sense that the return path is not the one intended.
Back in the day we had some multiconductor 13kv power cables that failed continuity tests. TDR was used to locate the offending section, when the cable was opened up, one of the phases, the red wire, were laying past each other with no electrical connection. The other phases were and neutral were continuous. The entire cable replaced. Amazing that a reel could have such a manufacturing defect...
RE: VFD spikes in multiple motor installation
The lengths of the cables are approx 1/7*20m, 2/7*20m, 3/7*20, ....7/7*20m according to OP.
What would you expect to see different in the traces that would suggest reflection issues?
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RE: VFD spikes in multiple motor installation
A lot of interesting stuff seen, see pdf.
RE: VFD spikes in multiple motor installation
With the TL basis and with a low impedence source, the first negative swing at the load would take place about 0.66 microsec after the initial rise, and without loss could would at most be double the incident wave height (25-30 in the scope trace). The numbers just don't match
RE: VFD spikes in multiple motor installation
Right. More load lowers the Q-factor of your resonant circuit so it isn't as 'peaky'.
-In general and specifically in case of two fans load it seems to be a resonance-like effect and voltage is amplified up to 1.6kVpp. ¿Could be resonance of filter inductor with cable and motor capacitance?. PWM source pulse period is about 28us.
Your pulse period is 28 uS giving a fundamental of 35 KHz, but your 100 nS rise time shows you have harmonic content out past 3 MHz (1/PI*tr is a good approximation).
Is your 220V measurement 220VAC? If so it is Vrms (root mean square). Once you start talking about peak voltages you have to multiply your rms by 2.828, so 220Vrms is 622Vpp. With multiple transmission lines it seems probably that you can get multiple reflections that will add up to more than a 2x factor (1.6kv / 622 = 2.6).
- Don´t know why but leaving in open circuit the point of measurement (fan7 connector) changes things quite a lot as helps to limit this amplification effect (slides 10 and 12) or worsens it very badly (slide 6).
As you open or close different switches the transmission line length to #7 changes. With your open at varying lengths from the source, it can look like an open (90 degree) or a short (0 degree) depending upon the phase delay from your source.
At 20m and a velocity factor of 0.6 you have the wavelength of 9 MHz (if I did the math correctly). I use the rule of thumb that I have to consider transmission line effects once the length of the transmission line approaches 10% of the wavelength; your rise time is at about 30% so you do need to treat this as a transmission line.
In the RF world I'd add source impedance to keep the reflections from reflecting at the source; that costs half the voltage but optimizes the power so it seems applicable here too.
I hope that helps.
Z
RE: VFD spikes in multiple motor installation
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Slide 1 shows example duty cycle from previous post. 10usec on, 18 usec off (the 28usec period referred to above).
Slide 2 just shows an Ltspice trick for easy changing multiple values at once using parameter statement. The transmission line delays are controlled by the parameter Tval near lower left corner (dot statement). The cables are assigned lengths 1*Tval, 2*Tval, 3*Tval.... 7*Tval. Changing Tval changes all proportionalely at once.
Note I have set the motor resistance very high and capacitance very small... representing idealized condition where motor acts like open circuit (See Note 1).
Slides 3 through 10 show the result of sweeping the paramter Tval from 10 through 17nsec, which sweeps the longest cable from 70nsec thru 118nsec. It is clear that a resonant type peak response (for this particular system) occurs near Tval = 15 (longest cable 104 nsec).
Slides 11 thru 18 show a simpler version with only a single line. The line length is swept 60 through 130nsec. The Peak again occurs around 110nsec.
The longest cable you have is 20m = 67feet. Travel time would be 67nsec at speed of light. If speed in cable is 0.6, then the longest cable travel time would be 110nsec, and this would match the resonant condition of the simulations above.
This obviously is not a perfect model (motor modeled as open circuit for simplicity, source assumed perfectly periodic, etc). Just something to consider.
Note 1 - My intent in choosing simple idealized values was that it might be easier to analyse the system mentally (without computer) that way to figure out the logic for the particular resonant length/frequency combination that popped out of the simulation. That did not happen. The resonant behavior popped out but there is no obvious mental model to explain why this particular frequency ./ length combination as far as I can see.... it happens that the resonant length (for this source frequency) turned out to be in the neighborhood 4* the period of the source pulse. You'll recall the last post identified a resonant frequency of the cable which was 4 times the travel time of the cable. Those two factors of 4 sound similar, but they are not... they are inverse and do not match each other. Using the conclusion of previous post we would have suspected resonant length of 1/4 the source period, rather than 4 times the source period.
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it is a remarkable problem being considered.
the majority of my experience is mostly learned in the field and am just amazed that TL effects have become an issue in power wiring within a plant. The point of solid wire vs signal cable etc, involved testing armored cables. Unless you had stranded center conductors and copper shielding, the eddy current losses drastically limited the high frequency response (<100 khz) for the cables of 1000ft or longer.
RE: VFD spikes in multiple motor installation
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RE: VFD spikes in multiple motor installation
zappedagain, your quality factor argumentation convices me quite a lot,
about voltages, it is 220VAC but I think that your guess of voltage add up is not correct. Pulses are 310Vpp value for each semiperiod, so we should have two fudamental components exciting the circuit here, 35kHz pulses of +/-310Vpp (change sign each some ms) and 40Hz components of 610Vpp.
The 40Hz component you can consider that goes 620Vpeak to peak, but 35kHz pulses, that is what it seems to excite the resonant mode, are really just 310Vpp, and their response gets almost to 1kV peak to peak in first measurement.
I see it as an RLC circuit where I am measuring voltage at C and it goes out of control due to resonance. Changing lenghts changes impedance value of terminal point as TL theory explains, so this can explain the strong variations (as you can imagine my knowledge about TL field is very limited, so maybe this is not very comparable).
As told, we are installing a sinewave filter. We are now discussig with fan manufacturer if it should be just "normal" LC sinewave or sinewave+common mode filter, filter supplier say us that "common mode" option is not frequently used.
Regarding velocity factor, we are using 2.5mm2 separate unipolar cables for each phase, I read somewhere that 300 Ohms characteristic impedance and 0.95c for speed should be a reasonable guess for this setup as TL parameters, you guys know quite a lot about this stuff ¿is it right?
Regards!
RE: VFD spikes in multiple motor installation
fwiw, I attempted to "validate" the results of my single-cable simulation using transmission line theory (i.e. just do the same calculation by hand, not validate the assumptions). It was just a textbook excercize. The results are attached:
Slides 1 and 2 simply show the input voltage waveform and spectrum. As expected it has frequencies of 36khz, 2*36khz, 3*36khz, etc
Slide 3 shows simulation results: When excited with square wave at 35,700, the complete system with longest cable of approx 104nsec experiences resonance.
Slide 4 shows simulation results: When excited with square wave of 35,700, the single-cable system shows a "resonance" (max response) when cable length is approx 104nsec.
Slide 5 shows Analytical Solution of single cable
Slide 6 plots the analytical solution of single cable to find the "resonant length" when powered by sinusoidal excitation of 36khz. The length of 104nsec does NOT show as a resonant frequency, instead the length of 420nsec shows up. At first glance this suggests disagreement between simulation and analytical solution (we will later show they agree).
Slide 7 plots the same analytical solution of single cable to find the "resonant frequency" when cable length is assumed to be 104nsec. The result is a maximum at 72khz. That is the 2nd harmonic of the exciting square wave. Suggests the resonance that we saw on the simulation was not excited by the fundamental, but the second harmonic.
Slide 8 is review of the simulation output. It confirms that there are two cycles of response per one cycle of input (contrast to 1 cycle of response per cycle of input on slide 3).. The response is twice as fast as the fundamental of the input. The response is 72khz, and is responding to the 2nd harmonic of the input.
Slide 9 is the conclusions:
When excited with 36khz square wave, the simulation showed:
* Complete system resonant when longest cable was 104nsec. Resonant response frequency was 36khz (fundamental freq of square wave)
* Single cable resonant when cable length was 104nsec. Resonant response frequency was 72khz (2nd harmonic of the square wave).
This single-cable resonant frequency of 72khz for 104nsec-length single-cable system was validated by analytical calculations.
The fact that both systems (complete system and single cable system) powered by 35.7khz square wave experienced some kind of resonance resonant at same length (104nsec) was probably a coincidence. They were different types of resonances (responding to different frequencies of the input).
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is V2 at the motor terminals?
shouldn't the phasors in the ppt file show the propagation delays ?
RE: VFD spikes in multiple motor installation
The TL behavior is properly modeled in slide 5. V2 and Vs are at same side of TL, so no propagation delay between those. V1 is related to V2 through ABCD matrix which completely represents TL response to sinusoidal excitation (note that transmission delay tau is used to compute the A, B, C, D).
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In my analysis of single cable with sinusoidal excitation to find resonant frequency, I used ABCD model which is appropriate/required for a long cable. A long cable does not meet the short cable definition of Tau <<1/f. This cable assumed 104nsec for my analysis would be long considering the rise-times.... but it is a short cable when considering the fundamental switching frequency and first few harmonics. Therefore since it's a short cable, ABCD was overkill, and a simpler lumped circuit analysis is possible as atached. The results are the same, but a lot simpler with short cable approximation.
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RE: VFD spikes in multiple motor installation
Changing VFD freq. helps, but not much really.
I did a similar circuit model like ElectricPete`s, but the value of the end capacitor must be changed quite much to match real results in case with/without 4.7mH filter (don´t understand why)
Comments are welcomed
Regards!
RE: VFD spikes in multiple motor installation
if it is a solid wire pair #12's you get about 0.4 db/100m at 2 mhz
if in conduit its a bit higher.
RE: VFD spikes in multiple motor installation
In the most recent attachment, we have the motor running on the 20m cable.....
What is the configuration of the remainder of the circuit? (Are the other motor cables attached?
Are the other motors running?)
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RE: VFD spikes in multiple motor installation
so 3 phase single wires from VFD to motor end.
RE: VFD spikes in multiple motor installation
wiring is with #12 wires no conduit, only single phase modeled just to get my head around vfd's
RE: VFD spikes in multiple motor installation
if not you get a lot of resoance effect that cover a broad frequency range
RE: VFD spikes in multiple motor installation
I am by no means an expert on vfds, but on the last post or so an inductor was added in series with the hot leg of the 20m cable to the motor. This is a single-phase system with one side grounded, the neutral, is it not?
Why not consider parallelling a capacitor with an inductor, thereby forming a parallel resonant circuit (calculate this) tuned to the switching frequency of the vfd (36Khz ?)forming a high impedance for the carrier frequency and a negligable impedance for the power frequencies used. This parallel resonant device in series with the hot leg. Then the length of the cable to the motor would not matter as no HF would get into the cable from the beginning.
Maybe such a device has to be put into both legs to be effective depending where or if the neutral is grounded.
Just an idea, from a non-vfd outsider...
rasevskii
RE: VFD spikes in multiple motor installation
3-phase is described in the original problem, I had worked in electrical through the mid-eightys about the time vfd came out, and familiar with induction, dc variable speeds, etc, what surprised me is that the power cables are exhibiting transmission line effects.
as the previous responders indicate, however, it is a very real problem
I only modeled a single sphase equivalent circuit with an a-c source (not pulsed) to see what various filter combinations produced.
a parallel resonant circuit as you discribe, would block a specific harmonic no more, but the really negative outcome is that the resonant circuit would develop extremely high voltages, higher that was being measured by the original post. The latter would be dangerous...
amazing what you learn on this site...
RE: VFD spikes in multiple motor installation
R may get a little big due to power disipation.
It puzzles me that just an inductor, as seems to be the usual practice, seems that will not be enough in any case for this kind of circuit, as overshoot will be in any case at least x2Vp no matter the L value for reasonable figures (1-20mH).
With same R parallel value (500), the results are similar for a wide range of L1 filter inductor values. Additionally, the result gets less "chaotic", as it repeats each cycle in a very similar way (in contrast with pure L filter in which it can changes quite a lot from a cycle to next).
RE: VFD spikes in multiple motor installation
with that much harmonic content getting rid of the heat is a toughy
good luck
RE: VFD spikes in multiple motor installation
1 - a series R-C filter connected in parallel with the motor
2 - a parallel R-L filter connected in series with the source.
The second type is of course identical in form to the one you guys were just talking about.
"Damping circuit to suppress motor terminal overvoltage and ringing in PWM inverter-fed AC motor drive systems with long motor leads" BY Aoki, N.; Satoh, K.; Nabae, A.; Industry Applications Conference, 1998. Thirty-Third IAS Annual Meeting. The 1998 IEEE Volume: 1 Digital Object Identifier: 10.1109/IAS.1998.732413
Publication Year: 1998 , Page(s): 767 - 772 vol.1
This is a peer-reviewed publication. And 2 of the authors are "Fellows" in IEEE, which I think is about as high an honor as IEEE gives (maybe there is one higher, but Fellow is pretty darned good). So, we expect this should be a pretty good reference.
An excerpt from this article is attached. I found it to be a fairly well-written and easy to understand article. After reading it 5 times, I think I understand exactly what the authors did (that's better than most articles, where I never get the feeling that I understood what they did). Most of it can be explained simply by viewing the diagrams.
The system model (without filter) is shown in Figure 6. It uses simply the lumped L-C model of a cable (the same one I used 12 Jun 11 1:47, valid only for relatively short line relative to frequency of interest). The model of the motor is simply assumed to be an open circuit (we have made that assumption at times). The source is simply assumed to have ZERO impedance (I find that assumption will probably be ok for the L-R filter in series with source since L-R filter will probably have a larger impedance, but probably lacking for the R-C filter in front of motor).
You'll also notice the system model of Figure 6 represents all three phases as they would exist between switching. For example one phase is connected to the positive bus and the other phases are connected to the negative bus. Obviously, we'd like to simplify it to a single-phase circuit, which is done in Figure 7 (they call this single phase equivalent circuit a "synthetic circuit"). The translation between Figure 6 (3 phase physical circuit) and Figure 7 (single phase equivalent/synthetic circuit) is mapped by Table II, where lower case l0 and c0 refer to figure 6 and upper case L0 and C0 refer to figure 7 and is derived from simple series/parallel combinations of the elements.
When we add the filter, we get the more complete single-phase equivalent/synthetic circuits of Figure 2 (for motor-end RC filter, where Rd and Cd are the filter elements) and Figure 4 (for supply end RL filter, where Rx and Lx are the filter elements).
Now we have a very simple circuit that can be anslysed by Laplace transfer function analysis to determine regions of stability. The details of that analysis constitute the bulk of the paper, very straightforward (textbook) but slightly tedious. The results of that analysis are shown in dimensionless form in Figure 2 (for RC filter) and Figure 4 (for LC filter), where the shaded region represents the combination of parameters for RC filter/system (Rd, Cd, L0, C0) and for LR filter/ system (Lx, Cx, L0, C0). We recall L0 and C0 are single-phase equivalents of the physical three-phase system parameters l0 and c0 as mapped by Table II, and likewise Rd, Cd, Lx, Rx are the single-phase equivalents of the physical 3-phase filter parameters rd, cd, lx, rx as mapped by the same table.
Experimental/Simulation results of application of this approach is shown in figures 10/11 for the motor-side RC filter and 12/13 for the source-side RL filter. They show good agreement.
Section V shows calculation of power dissipated by the resistor – this is the only part of the paper that I didn't understand, although I didn't spend too much time on it. If someone can explain it to me, please do.
That is my summary of the paper....
It should be fairly straightforward to apply to your system. The only inputs that are required are the values of L0 and C0. Since we already know the resonant frequency (w = 1/sqrt(L0*C0)), and we know the length, we would only need one more piece of information or assumption to determine L0 and C0. I think it may be reasonable to assume c=0.9 * (3E8m/sec), which would allow to compute L0, C0. I'll post some more this weekend.
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RE: VFD spikes in multiple motor installation
The results of that analysis are shown in dimensionless form in Figure 2 (for RC filter) and Figure 4 (for LC filter), where the shaded region represents the combination of parameters for RC filter/system (Rd, Cd, L0, C0) and for LR filter/ system (Lx, Cx, L0, C0).
should have been:
The results of that analysis are shown in dimensionless form in Figure 2 (for RC filter) and Figure 4 (for LC filter), where the shaded region represents the desired combination of parameters for RC filter/system (Rd, Cd, L0, C0) and for LR filter/ system (Lx, Cx, L0, C0). which best elminate oscillation
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great reference,
RE: VFD spikes in multiple motor installation
The results do not seem to be critically dependent on the motor load parameters (RLC).
RE: VFD spikes in multiple motor installation
I include a excel sheet to calculate paper RL filter parameters. From paper you get a range of R to use, but I found that it must be selected the low resistor values to get a good damping (if you get the higher limit the oscillations don´t dissappear in this example).
Now simulation behaves quite similar to real results. I tried 3 models,
1) Ideal TL model that lacks damping but shows good results in frequency response. I had to increase delay to 145ns to match real ringing freq. and keep all results coherent. That would mean that propagation speed is 0.63c (final real distance is near 27m). I don´t know if 0.63c is reasonable for separate unipolar cables but it is the progation speed which better adapts to real measurements.
2) "synthetic" equivalent circuit like shown in referenced paper. I had to add a 1k damping resistor to match real damping. It shows similar results than real case in all the options.
3) "Lossy line" equivalent circuit based on "synthetic" circuit values. The results are similar but I had to tweak a little the C value to match results. Resistance/unit lenght it is a little bit high to match damping. Could it be due to skin effect?
RE: VFD spikes in multiple motor installation
RE: VFD spikes in multiple motor installation
2-wire model(27 m) Cable spec:
L0 2.63E-05H 1.7608E-05H L0 III 1.75E-05H
C0 3.00E-09F 1.2024E-09F C0 III 4.50E-09F(total)
This gives you (two wire) velocity factor of 61.8% with the internal inductance of the wire, but 67.2% at higher frequencies. You might be on to something. The vfd cable specs seem to be predicting a much lower velocity factor of 44%. Once you have a filter and damping in-place, the actual velocity factor has very little effect.
You really need an external shunt capacitance at the motor terminals, not just distributed cable capacitance, for the filter (RL) to work. The 4 nF is about right. This shunt capacitance insures that the high freq at the motor is taken to ground. The filter does not work without it. This really puts a burden on the field electrical tech to wire it right.
it is not clear to me what the filter shunt resistance dissipation will be, since you are really designing a matching network of sorts. When everthing is matched i.e. voltage peak i s close to unity at the 35khz point, the line is basically flat & the power disappation will be set by the frequency components of the vfd wave form.
RE: VFD spikes in multiple motor installation
I think that I got lost somewhere in your explanation
, from my assumed IEEE paper "synthetic circuit" parameters, it is true that speed is about 0.65c (I just choose them to match real measurements, so it makes sense that it gives same speed factor than ideal TL model included in same circuit, as both models give very similar results).
The 4nF capacitor just represents the cable equivalent, it is not an additional capacitor to add. If I remove it, just improves the ringing and RL filter continue working well¿?.
About damping resistor dissipation, from simulation I see about 10W mean power, from paper formulae (included in excel) it gives about 45W so someting don´t make sense there (or simuation or applicability of the formulae to this specific situation).
RE: VFD spikes in multiple motor installation
the IEEE paper goes beyond a simple two distributed element wire model and should govern parameter selection for 3ph circuits like this.
okay finally read over the paper, it covers it all, my ravings are just that...the guys worked out the resistance and the dissapation given the over-shoots encountered...piece of cake.
RE: VFD spikes in multiple motor installation
in going through the Aoki model calculations, the spreadsheet has
Three phase line parameters
L0 III 1.75E-05 H
C0 III 4.50E-09 F
Filter inductor parameters
Lx III 4.73E-03 H
Aoki uses the conductor-to-conductor capacitance in the calc.
CO III (above) appears to be the cap between the ph and all other conductors tied together. Should be about 2.23E-9 F.
Pretty neat model, but it is only useful for cables 100m or so. It gradually breaks down for increasing cable length. It also does not deal with what happens with possible higher harmonics.
If you get too much interference above a few hundred khz, then you heed a shunt cap across each phase.
RE: VFD spikes in multiple motor installation
I agree.
I agree on that also, and I think it can be a pretty big shortcoming.
If you put the two observations together, the more correct (less-simplified) model has the following features:
1 - system response which has a fundamental (first) "natural frequency", and a series of higher order "natural frequencies".
2 - forcing function (source) with a fundamental "forcing frequency" plus harmonically related series of higher "forcing frequencies".
Note my terminology:
* "natural frequency" is characteristic of the system
* "forcing frequency" is characteristic of the source
* "resonance" corresponds to the condition when a low-order harmonic (**) "forcing frequency" of the sourc eis relatively close to a "natural frequency" of the system. (**I say we say low order harmonic forcing frequency, because the fourier transform of the square wave pulse has components that tend to decrease as the harmonic order increases).
The best way to avoid any resonance in such situation is to place the first system natural frequency very high, above even the majority of the forcing function harmonics. The original system (before filter) resembled that best-case scenario in theory (first natural frequency up around 1Mhz, switching fundamental around 35khz I think, source harmonics dieing roughly as 1/f should be pretty small by the time you get up near 1 Mhz). But still we had the high peaks in the original system, which were never fully explained, and not explainable by considering resonance. Adding the huge (compared to cable) filter inductor significantly drops the first resonant frequency of the (w = 1/sqrt(LC)) down somewhere in the ballpark of the switching frequency, and makes resonance between a low-order harmonic of the forcing function and a fundamental or low-order system responace natural frequency more likely. I think that may explain somewhat why changing the switching frequency was not a great strategy. The resistor adds damping which narrows the width of the natural frequencies which makes likelihood and severity of resonance less likely. The effect on first natural frequency was carefully studied in the paper. Although it wasn't studied, I believe by physcial resoning that the resistor represents damping for all harmonics and will also decrease the width of the higher order natural frequencies, which may help to some extnet... the extent wasn't quantified in the paper.
Also I will admit that while harmonic analysis of individual frequencies is good at predicting resonances, it may not be great for predicting the true peak of the time waveform. It does not take into account the relative phase relationships of the individual harmonic terms of the response.... if they all tend to align "in-phase" (such that when the fundamental hits its peak, the harmonics are all hitting their peaks), it results in the higher time waveform peaks than a comparable frequency content where the individual frequencies are not in phase.
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(2B)+(2B)' ?
RE: VFD spikes in multiple motor installation
the Aoki paper is pretty good, in fact outstanding. they did a remarkable amount of work for a publication! Took me a while to sort out the 2/3, 3/2 equivalent circuit but the old handbook proved to sort that out.
had to export to word and move the figures to the last pages in order to read it through.
when you model a detached phase of the wiring, you can play around with the cable length and see where the wave effects start to get important (sans all the coupling). The higher order system modes are there (for swept freq excitation), as you say but likely not excited by the vfd, at least we hope.
still sorting through the resistor dissipation estimate
RE: VFD spikes in multiple motor installation
The voltage measured at the motor terminal included the spectral content of the excitation at the source end.