PWM AC Drive torque ripples 4

[thinker]

When selecting AC induction motor to be fed from PWM inverter, what is the difference between usage of delta
or wye connected motor winding from the point of view
to get a minimum of torque ripples?

 

[rhatcher]

Please give more info on the nature of the torque ripples that you expect to see. In general, when comparing a wye to a delta for designs with the same rating, the motors will be equivalent when viewed from the terminals (electrically) or from the shaft (mechanically).

 

[jbartos]

Suggestion: Delta motor winding connection will create a path for the tripplen harmonics to cancel. Star motor winding connection does not provide this. Therefore, the star motor connection harmonics will impact the torque speed curve more than delta motor connection harmonics. After all, the motor is a special kind of the transformer.

 

[rhatcher]

Please explain what a tripplen harmonic is and how/why they can be cancelled in a wye connection but not in a delta.

 

[redtrumpet]

Triplen harmonics are zero-sequence harmonics that are multiples of third harmonic. The fundamental (60 Hz) is positive-sequence, second harmonic (120 Hz) is negative-sequence, and third harmonic (180 Hz) is zero-sequence. This pattern repeats for higher order harmonics.

Harmonics with positive sequence have a forward rotation and will increase motor heating due to skin effect and eddy currents.

Harmonics with negative sequence produce a reverse rotation or torque that causes excess heating in the motor winding as it works against the fundamental current.

Zero-sequence harmonics have no effect on rotation, and thus it should not matter one whit whether the motor is connected wye or delta as far as torque pulsation is concerned.

Even-numbered harmonics cancel and have no effect on the power system connected to the motor.

Zero-sequence harmonics require a zero-sequence path to flow. If a neutral of a wye winding is present and connected to ground, then triplens are additive in the neutral and can overload the neutral conductor if the currents are large enough. In a delta winding, there is no zero-sequence path outside the winding and triplen harmonics are trapped in the delta winding. They circulate in the delta winding and do not flow in the rest of the system. Perhaps this is what jbartos is referring to, as the zero-sequence currents do not actually cancel. This is good for the rest of the system, bad for the motor as the circulating current is a source of heat.

 

[electricpete]

I vote Redtrumpet a star for a good response to rhatcher's question.

Can you clarify your statement:

"Even-numbered harmonics cancel and have no effect on the power system connected to the motor". What about the effects you noted for 2nd harmonic?

 

[electricpete]

The period of the k'th harmonic is T/k (where T is 1/60 sec).

The fraction of a period which the kth harmonic due to the normal T/3 fundamental period phase shift (120 degrees) would be (T/3)/(T/k) = k/3. = 1/3,2/3,1,4/3,5/3 etc 6/3 etc.

So 1st, 4th, 7th etc should act alike in producing positive sequence (forward torque).

2nd, 5th, 8th etc should act alike in producing negative sequence - reverse torque.

3,6,9 etc are all zero sequence.

What is unique about even harmonics? I think perhaps they are not produced by most electronic loads which draw symmetrical currents on positive and negative half-cycle.

 

[electricpete]

Before someone corrects me... I'll clarify that my last statement about 2nd harmonics applies to current drawn from 60hz power mains (on input to electronic device). It probably doesn't have any meaning in the context of our discussion of motor current (on output of pwm drive).

 

[redtrumpet]

The particular statement concerning cancellation of even-numbered harmonics comes from Chapter 6 of "Variable Speed Drive Fundamentals" by Clarence A. Phipps. I didn't think too much about it because it agrees with my own observations that I have never seen 4th, 6th, 8th, 10th harmonic, etc. in a power system. 5th, 11th, 17th harmonics, etc., which are negative-sequence like 2nd harmonic, are seen in power systems. However, negative-sequence currents of double the power system frequency are the major cause of overheating in unbalanced systems, so they obviously are not canceled.

I think what is happening, and if I do the Fourier transform hopefully it will prove out, is that commutating devices like rectifiers produce a harmonic spectrum where the even-numbered harmonics cancel out, and that statement applies to those devices only. It would make sense, as I read it in a VSD book. And, every time I have looked at harmonics with a meter, it has been upstream of a drive with a rectifier front end. That would explain my field observations.

To my rescue - the IEEE Red Book (old 1986 version) states in 3.10.3 that full-wave rectifiers tend to eliminate the even-numbered harmonics.

Then more confusion, in 8.13.2 of the Red Book, where they state "in a symmetrical three-phase system, even-multiple harmonics of the fundamental are absent."

Aha, the key words - "symmetrical three-phase system". In a balanced system there are no negative-sequence currents.

On the other hand, the 2nd harmonic always involves some sort of unbalance, whether it is voltage unbalance, unbalanced impedances/loads, etc. So the 2nd harmonic arises from a different set of causes and is present. The same thing happens with 3rd harmonic, which doesn't arise in balanced systems but is present in unbalanced systems.

So, I know the 2nd harmonic arises in an unbalanced system, thanks to Mr. Fortescue of long ago. Whether the higher-ordered, even-numbered harmonics still cancel in the unbalanced system, I don't have the brainpower to say.

To further throw a wrench into things, I also checked in "Analysis of Faulted Power Systems" by Paul M. Anderson, and in Section 6.12, Induction Motor Equivalent Circuit, Anderson states "Since induction motors are usually wound either for delta or ungrounded wye connection, the zero sequence currents in the motor are always zero and there is no need for a zero sequence equivalent circuit." I thought there would be zero-sequence currents in the motor from asymmetry in the windings, rotor, or stator core. So now I am more confused than ever.

I think the original question has been answered - a delta versus wye connection would only trap zero-sequence currents from getting into the system, but no zero-sequence currents are being produced and if they were, they have no effect on the motor rotation anyway.

On other issues relating to harmonics and symmetrical components, I could still use some learning. Anyone know of good reference material I can study?

 

[redtrumpet]

Maybe not so confused on the issue of zero-sequence currents in the motor - there is still no zero-sequence path to the system neutral, so the zero-sequence currents won't arise. Consider a delta-wye transformer, where the zero-sequence currents arise on the wye side only if a path to neutral exists and there are unbalanced loads. The zero-sequence currents are transformed to the delta primary, where no zero-sequence path to the system neutral exists, so the currents circulate in the delta. These currents would never arise if the zero-sequence path didn't exist, say if the transformer neutral on the wye side was not grounded. This is what is happening in the motor winding - no zero-sequence path, no zero-sequence currents, regardless of asymmetry, which will cause negative-sequence currents only to flow.

 

[redtrumpet]

I apologise in advance for three consecutive posts - just trying to make sure I've got everything sorted in my head. Thanks, electricpete, for the post explaining the harmonic period and for noting that the 2nd harmonic in the mains supply was probably unrelated to the PWM - got me thinking. A star for you.

As I understand it, there are two separate mechanisms giving rise to harmonic currents. The first is non-linear devices on a three-phase symmetrical system. These harmonics are (theoretically) odd-numbered only, and positive- and negative-sequence only, due to the full-wave rectification that takes place. (Still don't know if zero-sequence harmonics would flow if a zero-sequence path existed - need to do the Fourier transform).

The other mechanism giving rise to harmonics occurs only when the symmetrical system becomes unbalanced. Then negative-sequence 2nd harmonic current will flow, and zero-sequence 3rd harmonic will flow only if there is a zero-sequence connection to the source neutral.

To answer thinker's original question, the torque ripples in a motor driven by a PWM VFD are caused because the output waveform to the motor is non-sinusoidal. The positive- and negative-sequence harmonic components of the output work with and against the fundamental component to cause a ripple in the motor torque. Zero-sequence currents are unable to flow because there is no zero-sequence path (the wye winding has ungrounded neutral, the delta winding has no neutral). Even if the zero-sequence path existed, the PWM waveform may still not have any zero-sequence component.

A delta or wye motor winding connection has no effect on positive- or negative-sequence harmonic currents. A delta winding can trap zero-sequence currents induced in it; however, zero-sequence harmonics are not a consequence as explained above. Thus, the motor winding connection has no effect on the torque ripple, as pointed out by rhatcher.

If a symmetrical system with harmonics becomes unbalanced, a 2nd harmonic negative-sequence current will flow independent of the existing harmonics. A 3rd harmonic zero-sequence current will flow if a zero-sequence path to the system neutral exists. Higher-order harmonics will not be generated by an unbalanced system. Even-numbered harmonics of 4th order and higher will (theoretically) continue to cancel due to the nature of the non-linear devices that exist on the system.

This is how I see it. If I have gone wrong somewhere, please let me know.

 

[electricpete]

redtrumpet - good post. I didn't understand all of it. There were some places where I think you may have been looking at it wrong (although possibly only because I don't understand your point). Here's your stuff in bold, followed by my comments:

As I understand it, there are two separate mechanisms giving rise to harmonic currents. The first is non-linear devices on a three-phase symmetrical system. These harmonics are (theoretically) odd-numbered only, and positive- and negative-sequence only, due to the full-wave rectification that takes place. (Still don't know if zero-sequence harmonics would flow if a zero-sequence path existed - need to do the Fourier transform).

The other mechanism giving rise to harmonics occurs only when the symmetrical system becomes unbalanced. Then negative-sequence 2nd harmonic current will flow, and zero-sequence 3rd harmonic will flow only if there is a zero-sequence connection to the source neutral.

I would say:
#1 - There is only on mechanism by which harmonic currents are introduced into an otherwise sinusoidal system... by non-linear devices (usually electronics, and magnetics in saturation)

#2 - An unbalanced set of three phase voltages or currents in a perfectly sinusoidal system (no harmonics) can always be decomposed into positive, negative and zero sequence single-frequency components for purposes of analysis. Balanced system has only positive sequence.... unbalanced system also has one or more of negative and zero sequence.

#3 - The 3,6,9 harmonics described in #1ne often have a zero sequence nature... meaning all three phase 3rd harmonics are in phase with each other. Likewise 2,5,8 harmonics have negative sequence nature, meaning their phase sequence is opposite the fundamental.

#4 - The negative sequence fundamental described in item #2 (unbalanced sinusoidal system) is a diffferent animal than the negative sequence 2nd harmonic described in item #3. They are at different frequencies. The first can be analysed in terms of symmetrical components at the fundamental frequency. The second might be analysed in terms of symmetrical components at the 2nd harmonic frequency. But symmetrical component analysis can't combine items of different frequencies. The use of symmetric current analysis (positive, negative, zero sequence) describes phasors which inherently have a single assumed frequencies. Just like we can't combine phasors from different frequencies, we can't combine sequence components from different frequencies. We can only solve each frequency separately (often by method of symmetrical components) and then combine the results.

So I would disagree with your statement that an unbalanced system automatically creates harmonics. There is one possible scenario where this could occur... that is when the unbalanced system creates an overvoltage on one phase which forces a transformer or motor into saturation. The transfomrer or motor is then acting nonlinear and will create harmonics.

A delta or wye motor winding connection has no effect on positive- or negative-sequence harmonic currents. A delta winding can trap zero-sequence currents induced in it; however, zero-sequence harmonics are not a consequence as explained above. Thus, the motor winding connection has no effect on the torque ripple, as pointed out by rhatcher.

I'm not sure I agree. You guys let me know if I'm wrong on this one...

When a core is exposed to fundamental voltage exceeding a certain level, it will draw non-linear excitation current. In the ungrounded wye configuration, that excitation current can contain no 3rd harmonic since there is no path for three in-phase 3rd harmonic currents to flow. In the delta winding there is a path... circulating around the delta. I don't know all the ramifications of a change in harmonic content of excitation current, but it is easy for me to believe that it might affect harmonic content of flux, rotor current, and possible torque oscillations. (I can't prove it or disprove it).

Of course the above discussion applies to harmonics arising from within the motor itself.... so would not be unique to PWM. That still doesn't rule out the fact in my mind that there may be much more complex interactions for PWM than what we have discussed, and I never have understood the nature of the oscillations that were mentioned to begin with. I have heard of "cusps" in the torque speed characteristic of induciton motor arising from spatial harmonics.... I have heard of torque oscillations on syncrounous motors during starting.

Thinker - is this a syncrounous or induction motor? Can you define a little better the type of oscillations?

 

[redtrumpet]

Excellent comments, electricpete. I think you cleared up some of my confusion between harmonic sequences and symmetrical component analysis of balanced systems at fundamental frequency. Another star for you. However, I still have some questions.

1. As I understand your comments, the positive, negative, and zero-sequence vector systems derived from a set of balanced phasors are all at fundamental frequency. Why, then, are negative sequence currents arising from unbalanced loads, unbalanced faults, open conductors, etc. at double the fundamental frequency instead of at fundamental frequency? Or am I wrong here? I base my comments on 11.4.5 of IEEE Buff Book, Generator Protection - Phase Balance Current Relay - Device 46, which states "the resulting unbalanced (negative sequence) currents induce double system frequency currents in the rotor that quickly cause rotor overheating." Is this not 2nd harmonic?

2. As I further understand your comments regarding zero-sequence harmonics in a delta winding, are you saying that zero-sequence in this sense simply means the harmonic currents are in phase, and that unlike the zero-sequence component arising in an unbalanced system, no zero-sequence (ground) path is required for those harmonic currents to flow?

 

[redtrumpet]

electricpete - you said in your previous post you weren't familiar with the nature of the oscillations or torque pulsations in question - I think these were originally a problem on the original "six-step" or variable-voltage inverter (VVI) drives which basically had a six-step square wave output. At low frequencies the stepped nature of the stator rotating field caused the torque to be applied in pulsations. This was called "cogging" of the drive and was a limitation of this design as the cogging created stress on the shaft and driven equipment.

On PWM the problem of torque pulsations is greatly reduced, because the output wave is near-sinusoidal, even at low speeds. Still, since the output waveform is composed of a train of on-off pulses, there may be a very small torque pulsation at the motor. Generally, I haven't heard of any torque pulsation problems with current-design PWM drives.

 

[electricpete]

redtrumpet - I give a star to your most recent post. It sounds like it's getting closer to the heart of the original question. It makes fairly good sense to me that the PWM method provides relatively harmonic free current due to the inherent filtering by the inductive load. Off-hand I'm having a hard time remembering the exact nature of the old six-step monster. I don't remember whether it might be worse becauase #1 - it is richer in lower-order voltage harmonics (2,3,4) which are not as well filtered as the high-order harmonics in PWM or #2 - it uses some principle of switching of inductive current amohng output phases which forces a stepped current output.


Some more comments to your previous posts (your's in bold, mine in plain)

1. As I understand your comments, the positive, negative, and zero-sequence vector systems derived from a set of balanced phasors are all at fundamental frequency. Why, then, are negative sequence currents arising from unbalanced loads, unbalanced faults, open conductors, etc. at double the fundamental frequency instead of at fundamental frequency? Or am I wrong here? I base my comments on 11.4.5 of IEEE Buff Book, Generator Protection - Phase Balance Current Relay - Device 46, which states "the resulting unbalanced (negative sequence) currents induce double system frequency currents in the rotor that quickly cause rotor overheating." Is this not 2nd harmonic?

An unbalanced sinusoidal voltage produces no harmonic voltages anywhere in the power system or motor stator (excluding saturation effects). It does cause a negative sequence fundamental current to flow in the stator of the motor. This causes a stator field component which flows at fundamental frequency but in the reverse direction. In relation to the rotor which is traveling at [almost] fundamental frequency in the forward direction, the relative speed between forward rotor and reverse-rotating field is [almost] 2 times the fundamental. The rotor will have induced in it some [almost] 2nd harmonic current, which due to very high frequency (compared to normal rotor current which is only slip frequency) flows only on surface of the rotor (skin effect) and causes heating rotor heating problems. None of this 2nd harmonic behavior is seen by the stator or the power system.

2. As I further understand your comments regarding zero-sequence harmonics in a delta winding, are you saying that zero-sequence in this sense simply means the harmonic currents are in phase, and that unlike the zero-sequence component arising in an unbalanced system, no zero-sequence (ground) path is required for those harmonic currents to flow?

Zero sequence by definition means that all three phase currents are in phase. This applies whether we're talking about the fundamental component or the third harmonic component.

Zero sequence currents require a special type of path to flow (whether they are fundamental resulting from imbalance or 3rd harmonic resulting from nonlinear load). Specifically the current that flows in one phase conductor CANNOT return in the two phase conductors because those other phase conductors are carrying current which is identical (in-phase) to the first phase condcutor. Thre result is that the zero sequence current path generally involves a return path from center of a wye or a circulating path within a delta. These factors play a central role in determing the zero-sequence models for various transformer connections.

 

[busbar]

Question-- Do even-order harmonics and DC offset/components always occur together?

 

[redtrumpet]

Thank you, electricpete, for answering my two questions. My knowledge of symmetrical components was somewhat limited prior to this discussion, mainly involving positive-sequence impedances for doing three-phase fault calcs, and zero sequence impedances when determining ground faults in substations. I bought "Analysis of Faulted Power Systems" by Paul M. Anderson a few weeks ago to learn more about the theory behind symmetrical components, but haven't had time to delve into it yet.

I dug myself a bit of a hole on this discussion, but you helped pull me out, which is why I really like this forum. Thanks again.

 

[electricpete]

Redtrumpet - glad I could help. It helps me to walk through those discussions every once in awhile to dust off the cobwebs. I think you gave a good focus on the difference in behavior of different drives.

I should mention that from my perspective, rhatcher may have been right when he asked whether delta or wye connection might make no difference in practical terms... I've never heard of it in real-life for motors but have heard about delta windings used intentionally on transformers for control of 3rd harmonic currents.

busbar - you are correct that the magnetic saturation induced by a dc offset voltage will have even harmonic components in the excitation current (as well as odd).

We mentioned that electronic devices draw current symmetrically on the two half-cycles which precludes even harmonics. But we forgot to mention that dc offset causes "assymetrical" (different in positive and negative half cycle) non-linear excitation currents which will have even harmonics in addition to the normally expected odd.

So if you have a transformer inrush, a motor starting, a transformer through-fault application, there will be even harmonics (along with odd) during the transient. Likewise dc voltage due to geomagnetic currents would cause even harmonics in transformer. (but not for another 10 years or so when we the cycle peaks again!).

over-excitation due to simple overvoltage (no dc component) would give only odd harmonics.

 

[electricpete]

I think I need to correct one statement from my last message. For the case of transformer inrush, there definitely is a dc offset in the excitation current which will cause even harmonics. It is fairly easy to model this as suddently applying a voltage to the magnetizing inductance. Even if it were linear the excitation current would have a peak making it go to twice normal. Saturation will make the excitation current rise even higher, possibly peaking at 10 times normal excitation peak current.

I've also seen a waveform for motor energization and if I subtract the decaying dc component and focus on the remaining ac, I think I can see a second harmonic (different in the positive half cycle than the negative half cycle). It's a little tougher to model because in addition to excitation current there is a load current present at the time of energzation.

I'm not as sure about the case of transformer thru-fault.
There may not be even harmonics present. Certainly we use harmonic restraint to distinguish inrush from thru-fault, so harmonic content of thru-fault must be lower overall.

 

[rhatcher]

I have been away for a while and return to be greeted by many informative posts. Thanks to all for the good info. I am still digesting the info presented on harmonics. I do seem to remember that for a balanced 3 phase system that mathematically the even harmonics have a magnitude of zero (cancel out) and the odd harmonics have magnitudes that reduce in value as the order increases.

With respect to VF drives, the older six pulse systems may produce measurable torque pulses, but I would imagine that the PWM systems would not based on the switching frequency being between 2khz and 8khz. However, for a square wave PWM, it seems that the output would be rich in harmonic content, but for some reason I have it in my mind that harmonics do not produce torque, only additional heating.

Anyway, I will quit for now as I have a lot of reviewing to do to catch up on this topic before I can post anything useful. Thanks again to all who posted.