# Excessive odd harmonics in motor current

A set of odd harmonics of excessive magnitude ( in particular 3xLF ) has been recorded in a 250 HP motor. Winding connection - star.
Unfortunately no phase current unbalance data, voltage unbalance or THD, offline winding unbalance data is available.

What would potentially cause this?

Thanks
Dave

DGluzman

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Original Post
Tough to say.

The magnetizing component of current can be distorted due to non-linear magnetization characteristics of the iron. This could be accentuated by:
1 - operating at low load where magnetizing current is a large portion of the total
2 - elevated voltage - causing increased saturation
3 - unbalanced voltage - causing localized saturation

The wye connection should supress any third harmonics that are balanced among phases because they are "zero sequence". i.e. if the current waveform on all three phases are identical, then the first harmonics are 120 degrees apart (positive sequence)... the 2nd harmonics are 240 degrees apart (negative sequence), 3rd harmonics = 360 degrees apart (zero sequence).... 360 degrees apart means "in phase"... and if you have three identical in-phase currents feeding the neutral, they must sum to zero, they must all be zero.

Based on the above, I would be inclined to suspect volage imbalance. You cannot have balanced 3rd harmonic components in a wye winding. Of course gathering the data you listed would be important to getting a better answer.
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The attachment gives a full picture of current and voltage harmonic content for each phase.

The 3rd current harmonic is obviously standing out making up about 24% of the fundamental. It is well balanced though.

Voltage higher harmonic content, as it appears, is not a matter of concern. Because of that, apparently current distortion is not caused by voltage distortion. In general, current distortion could be caused by a non-linear characteristic/saturation of the magnetic core, but how this effect can be applied to the 3rd harmonic?

How in a 'Y' wound stator circuit, a zero sequenced 3rd current harmonic could exist all together?
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Sorry, here is a good one.

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I just found out that this motor is being switched from Y to Delta on startup. It is a Delta curcuit when running. The current is measured in each phase. It is the PHASE current as oppose to LINE current.

If so, it becomes clear as to why the 3rd zero sequence current harmonic does exist in there: it is circultaing in a complete Delta circuit.

However, the fact that 3rd current harmonic is 24% of the fundamental magnitude indicates that likely the magnetic core is oversaturated, possibly due to excessive line voltage.

The apllied voltage is 490 V, although well balanced and just little distorted. This is possibly above the tolerance.

Questions:
1. What is permitted current distortion in %%per IEEE standard?
2. What is RMS voltage tolerance band in %% for new motors (150 HP - 250 HP )?

Dave
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So it is a delta motor (while running) and you are measuring the currents of the delta legs themselves (rather than phase current).

I would say that explains very well the high 3rd harmonic content.

Looking at the time waveform and trying to explain it:
• If we start with a simple model like a stationary magnetic coil to explain the behavior of the magnetizing current, we cannot explain this time waveform. We expect in the magnetizing current to have high "spikes" precisely at the positive and negative peaks of the otherwise sinusoidal waveform. And the magnetizing current lags the load compoentn of current... so we expect the spikes to lag the sinusoidal peak. Review of your time waveform shows it is not the case. So this model is lacking and we need something more...
• The better model considers the effect of spatial harmonics. Draw the spatial flux around the airgap. It is flattened at the peaks due to saturation. That flattening corresponds to a 3rd SPATIAL harmonic component of flux. Since the entire flattened wave rotates at the speed of the main flux wave, the third spatial harmonic must rotate at the same speed as the flux wave, but since it has a spatial variation 3 times as high as the main flux wave, the associated induced voltages will be at a frequency corresponding to the third TIME harmonic in each winding. For wye winding, that 3rd time harmonic induced voltage does not cause any current (the impedance to that zero sequence is infinite). For delta winding, the induced voltages in all three legs are additive around the loop. We get a very high 3rd time harmonic current in response to the induced 3rd time harmonic voltage which was created by flattened tops of the spatial flux wave due to saturation.

The effects of that extra 3rd harmonic current will certainly create extra I^2*R heating and other losses. The 3rd time harmonic current actually does help to restore the spatial shape of the main flux wave toward sinusoidal, which has some benefits. But the disadvantages apparently outweigh the benefits, because virtually all large motors are designed for wye connections, unless there are starting considerations (wye delta) or dual-voltage considerations that dictate otherwise.

You asked about limits for harmonics – those are generally complicated because the harmonic content can depend on the whole system,not just one part, and each may have own requirements for what it expects and what it creates. In this case we presume the motor non-linearity is the source of the 3rd harmonics. I am 99% sure that NEMA does not specify any limit for circulating 3rd harmonic within a delta winding (because it does not affect anything outside the motor). The important performance requirement for the motor is to operate within its temperature ratings.

I am sure if you look you can find various limits of voltage THD of the power system to which you connect a motor... in order to avoid the power system creating excessive heating of the the motor. But again that does not apply when the motor is the source of the harmonics such as appears to be the case here.

That's my thoughts anyway. Maybe others can add.
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quote:
Originally posted by electricpete:

So it is a delta motor (while running) and you are measuring the currents of the delta legs themselves (rather than phase current).

That is correct and I'll show the electrical diagram tomorrow as to how this could occur. It is specific to the way of the amp clamp location and Wye to Delta switching. The 3rd harmonic is internal to the motor due to Delta connection and therefore has no effect on the grid. I agree it only affects motor heating.

I just wonder where the 3rd current harmonic is coming from. Likely, from the voltage, although having low THD but being on the high side in magnitude.
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This is a complicated topic. Here are my thoughts about it.
On the David’s attachment we are seeing current as it changes in time. It does not really have anything to do with spatial distribution of the induction in the airgap which is indeed flattened on the top. This is a strictly time dependent wave. Just imagine for a moment that we are looking at no load current. The motor behaves as a passive impedance, but passive impedance with an IRON core.
Let’s look at equation: V=4.44 B.S.f.N. It shows direct proportionality between the voltage and the induction B. We bring sinusoidal voltage on the terminals of the motor (sinusoidal in time), so we have to expect sinusoidal flux density B (sinusoidal in time again). We cannot expect sinusoidal current in time, because the impedance is nonlinear, it contains iron. To support this way of thinking, think about a transformer. The flux density is sinusoidal even when we reach the saturation. Otherwise the sinusoidal voltage would not appear on the secondary.
Going back to the motor, the SPATIAL distribution in the airgap will not be sinusoidal, but will be flattened on the top. The flux density close to zero SPATIAL points will grow faster due to the steepness of the hysteresis curve. In the spatial points close SPATIAL maximum the hysteresis curve is not as steep (saturation) hence it causes flattening of the top of the SPATIAL distribution of the flux density in the airgap.
To make it clearer, imagine that we feed the motor single-phase while the wound rotor winding is an open circuit. It is clearly just passive impedance with nonlinear iron. Every phase is sitting in one place only, produces the fluctuating flux and does not care about spatial distribution. It just goes up and down in time.
The concern about the third harmonic is only valid for the spatial harmonics. The third TIME harmonic is a different animal; it can flow in delta or Y, no problem. I can post dozens of current signatures with 3rd, 5th, 7th, 9th … harmonics. The “triple” harmonics are always there regardless of the connection.
The derivation of the magnetizing current from the sinusoidal voltage is shown in the attached file. Since some readers may not be able to read Check, here is a rough translation:
“Exercise 120. Derive graphically the magnetizing current in time when the input flux density is sinusoidal with maximum Bm with the hysteresis curve valid for the magnetic material, AC magnetization and the frequency according to Fig. 77.”
The derived curve is awfully close to what was posted. Of course in the David’s case there is a mixture of the nonlinear magnetizing current and linear working current.
jank

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Glad you joined the conversation, Jan. I agree it is a complicated topic, and I certainly don't claim to understand it all.
quote:
The concern about the third harmonic is only valid for the spatial harmonics. The third TIME harmonic is a different animal

They are certainly different entities, but in the particular case of saturation, the third time harmonic current can arise from the third spatial harmonic. As you said, the 3rd spatial harmonic arises from the flattened waveform. The very important thing about this particular 3rd harmonic is that it travels at the same speed as the main wave because the whole flattened wave travels at the same speed ....the flat spot is always at the peak. (this is completely different than the slot harmonics which do not travel at the same speed as the main wave.... the sharp edge associated with a given slot current is not always at the same position in the main wave because it travels at a different speed than the main wave). Now, do the math: 1st spatial harmonic traveling at the main wave speed creates emf induced in a given stationary coil at a frequency of 1*LF... so 3rd spatial harmonic traveling at the same speed will create emf induced in a given stationary coil at three times as high frequency... or 3*LF. So, for this particular scenario of saturation creating rotating flattened wave, the 3rd spatial harmonic does create a 3rd time harmonic. (again if it were a 3rd harmonic due to stator slotting, it would be a different animal... it would not travel at a 1/3 the speed of the main wave and create an emf at a time frequency of 1*LF).

I also agree we get a 3rd time harmonic by applying voltage to a simple lump of iron. That is the model I discussed in the first of two bullets of my post 19 February 2010 07:34 PM. I thought that the mechanism must a little more complicated than that in order to explain the posted waveform, but I could be wrong.
quote:
The third TIME harmonic...in delta or Y, no problem

There is a huge difference in how much 3rd time harmonic can flow in a wye vs in a delta.

In fact, if three non-sinusoidal three phase currents flowing in a wye connection are identical except for time shift of of one-third of the fundamental period (the normal time shift between phases in a balanced 3phase system), then the 3rd harmonic component of the current MUST be zero. It can be proven.
Symbols:
• T = fundamental period.
• w1 = 2*Pi/T
• w3 = 3*w1
• i1 = magnitude of first harmonic current in all 3 phases
• i3 = magnitude of third harmonic current in all 3 phases
• ia(t) = total current flowing in a phase
• ib(t) = total current flowing in b phase
• ic(t) = total current flowing in c phase
• ia3(t) = third harmonic component flowing in a phase
• ib3(t) = third harmonic component flowing in b phase
• ic3(t) = third harmonic component flowing in c phase

==========Proof:========
ia(t) = i1*sin(w1*t) + i3*sin(w3*t)
ib(t) = i1*sin(w1*<t+T/3> ) + i3*sin(w3*<t+T/3> )
ic(t) = i1*sin(w1*<t+2*T/3> ) + i3*sin(w3<t+2*T/3> )

Look at the third harmonic term of ib. Call it ib3(t):
ib3(t) = i3*sin(w3*<t+T/3> )

multiply out the term in brackets < >:
ib3(t)= i3*sin(w3*t+w3*T/3)

Substitute T = 2*pi/w1:
ib3(t)= i3*sin(w3*t+w3*(2*pi/w1)/3)

Substitute w3 = 3*w1 in denominator of phase:
ib3(t)= i3*sin(w3*t+w3*(2*pi/w3)

Cancel out w3:
ib3(t)= i3*sin(w3*t+2*pi)

Remove 2*pi since adding 2*pi does not affect result of sin function:
ib3(t)= i3*sin(w3*t)

Similar logic will show:
ic3(t) = i3*sin(w3(t)).

The total currents must sum to zero at the wye neutral point. That means each frequency component must sum to zero at the neutral, including the third harmonic:
ia3(t) + ib3(t) + ic3(t) = 0
(i3+i3+i3) * sin(w3*t) = 0
i3 = 0
========== END OF PROOF ===========
That proves we cannot have "symmetric" (same magnitude and shifted by time interval one third of fundamental period) 3rd harmonic currents flowing in a wye winding.

If 3rd harmonic currents exist, they must show up in an asymmetric pattern (phase shift differing than time period corresponding to 1/3 of fundamental... or different magnitudes in each phase), but the impedance to induced 3rd harmonic emf will clearly be much higher in wye than in delta and therefore the current magnitudes much smaller since the driving 3RD harmonic emf tends to be balanced and phase shifted by 1/3 of fundamental.

If you connected the same motor in wye and delta and adjusted the voltage by sqrt(3) to keep flux density the same, I am positive that you will see dramatically higher 3rd harmonic current inside the legs of the delta winding (where David measured) than you would see in the wye winding.

In the attached article first page, I think you will see he describes how saturation harmonics travel at the same speed as the main wave. In the last paragraph of the first page he describes how 5th and 7th harmonic stator currents will flow to "dampen" (reduce) these 5th and 7th spatial harmonics, but 3rd harmonic cannot flow due to the wye connection.

By the way, do you have any other suggestion why large motors are always wound in wye (except when needed for starting considerations or dual voltage application).
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Here is the electrical diagram showing how amps are measured in the PHASE. The 3rd current harmonic is confined within the motor due to Delta connection.

I'll measure LINE current as well and likely the above will be proven.

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Yes I agree if you measured where Ammeters are shown during run, you are measuring inside the delta and should see very high 3rd harmonics.

It is a very safe prediction that the 3rd harmonic will be much lower when measured in the line current than when measured inside the delta. I don't have any hesitation in predicting that.

To clarify, there are three cases we can talk about in order from highest measured 3rd harmonic fraction to lowest:
Case 1 - delta winding, measuring currents inside the delta leg.
Case 2 - delta winding, measuring line currents
Case 3 - wye winding (at voltage sqrt3 higher than case 1 and 2 for fair comparison with same flux density).

That Case 1 will have much higher 3rd harmonics than either case 2 or case 3 should be obvious from previous discussion. Case 2 compared to 3 is tricky, but I tend to think case 2 can have a little higher 3rd harmonics than case 3, because Case 2 winding connection encourages large 3rd harmonic flow within the delta and the small portion of it that is unbalanced can escape from the the delta.
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quote:
Originally posted by David_G:
How in a 'Y' wound stator circuit, a zero sequenced 3rd current harmonic could exist all together?

Saying that the 3rd harmonic can flow in Y or delta, I was reacting to the above. And indeed, any time harmonic can flow in delta or star. Nonlinearity of the circuit is enough to deform the current causing harmonics.
But inducing the current into Y is a different story. You certainly cannot induce 3rd harmonic from rotor into the Y connected stator. You can induce it to the Delta and the current can circulate in the Delta. The question is how much? I did not have a clue what is the zero sequence impedance. Luckily I have a 20 hp Delta connected motor in my garage. So I broke the Delta connection and measured the zero impedance. To my surprise it was 10 Ohms at 60 Hz, it means it is 30 Ohms at 180 Hz (3rd harmonic). The locked rotor impedance is about 1.45 Ohm, so the zero sequence is much, much larger. In order to push any significant current (such as 24% FL) through this impedance would require the 3rd harmonic voltage to be huge. Does not seem realistic to me.
The Delta connection is routinely used even on medium voltage machines (2300/ 4160 Volts). Never have I heard about necessity to de-rate the motor when ran in Delta. Yet the flattening of the spatial flux density is an absolutely normal and very well known fact and it is present in every motor.
The paper is an interesting new look at the torque due to 3rd harmonic. As I have indicated above, the deformation of the spatial flux density has been known and accounted for differently than thinking about 3rd harmonic. One way (I am familiar with) increases the calculated flux by an empirical formula. The increase is larger for small motors and smaller for large motors.
The fact is that most of the large motors are connected in Y. As I have said I am not aware of necessity to de-rate due to the 3rd harmonic (due to saturation). I do know that the delta connection may support “secondary armature reaction”. It is a very complicated thing. The rotor harmonics can induce frequencies other than the 60 Hz in the stator. Those currents can freely circulate in Delta and create parasitic torques during the acceleration. On the top of it the parallel branches in the stator can contribute to the problem. But I have to admit, I have never looked into the details.

I have just realized that some time ago I have taken current signature on the Delta connected motor. I took the signature inside the delta and on the input line. I am attaching the spectra and waveforms. It was taken on 150 hp motor, 575 Volts. The nameplate current is roughly 150 Amps. You can see that the third harmonics inside Delta is indeed larger (2.89 Amps) compared to the 3rd harmonic in the input line (0.89 Amps). The increase seems to be significant until you take into account the full load current (the signature was taken at no load). Hence, the 3rd harmonics will drown in the full load current once the motor is loaded.
jank

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Thanks for your comments Jan. I certainly respect your opinion and your insight on these things. And it's always great to have real measurements to discuss and compare with the theory.

My thoughts on your two sets of measuements fwiw:

quote:
Luckily I have a 20 hp Delta connected motor in my garage. So I broke the Delta connection and measured the zero impedance. To my surprise it was 10 Ohms at 60 Hz, it means it is 30 Ohms at 180 Hz (3rd harmonic). The locked rotor impedance is about 1.45 Ohm, so the zero sequence is much, much larger. In order to push any significant current (such as 24% FL) through this impedance would require the 3rd harmonic voltage to be huge. Does not seem realistic to me.

Two comments on this experiment fwiw:
• 1 – A simplistic linear analysis - let's say the main wave spatial harmonic pattern has 3rd spatial harmonic which is 8% of the fundamental space harmonic. Since induced voltage is proportional to frequency, the induced 3rd harmonic voltage will be a factor of 3 higher, or 24% relative the the fundamental induced voltage (and fundamental induced voltage approximately matches the applied voltage). Now we connect them in a delta loop and the induced voltage around that loop is 3x as high... or 72% of fundamental applied phase-to-phase voltage. If 100% voltage with 1.5 ohms produces 700% of FLA (fundamental), then 74% voltage with 30 ohms produces 0.72 * 700%FLA * (1.5/30) = 25% FLA (third harmonic). So this linear model suggests that a 3rd time harmonic which is 25% of fundamental FLA equates to a 3rd harmonic spatial 3rd harmonic flux of approx 8% of the fundamental. That 8% sounds credible to me. [caveat – the 3rd time harmonic current reduces 3rd spatial harmonic flux, so we can't really say one causes the other... they are interrelated in a more complicated manner than what I suggested]
• 2 – The key word in my last paragraph was linear. It is all based on an impedance measurement presumably conducted at low voltage far from saturation. When you apply fundamental voltage to force the core into saturation, the effective impedance seen by 3rd harmonic will be much lower. The 3rd time harmonic currents will be much higher than predicted by this type of linear analysis.
quote:
I have just realized that some time ago I have taken current signature on the Delta connected motor. I took the signature inside the delta and on the input line. I am attaching the spectra and waveforms. It was taken on 150 hp motor, 575 Volts. The nameplate current is roughly 150 Amps. You can see that the third harmonics inside Delta is indeed larger (2.89 Amps) compared to the 3rd harmonic in the input line (0.89 Amps). The increase seems to be significant until you take into account the full load current (the signature was taken at no load). Hence, the 3rd harmonics will drown in the full load current once the motor is loaded.

Here are the ratios of 3rd/1st current harmonics:
Line side of Delta: 3rd / 1st = 0.89 / 30.75 = 2.9%
Inside of delta: 3rd/1st = 2.86 / 18.53 = 15.4%

The fraction is more than a factor of 5 higher inside the delta (as we expected). Whatever
current is flowing on the line side is just the result of some kind of imbalance.

[Note also - The line side fundamental is sqrt3 higher than inside delta fundamental as expected]

What you point out is that the 3rd harmonic flowing is very low compared to the FLA. In my mind it means we have found a motor that operates below saturation during the measurement conditions. It does not mean all motors act that way under all conditions.

======================

Now, I gathered somewhere in your tone that there is still some disagreements and I'm having a hard time putting my finger on what they are. So here is some discussion to try to narrow it down - maybe I can learn something.

Looking back over everything said, I will acknowledge two corrections or clarifications:
• 1 – When describing MV motors that have wye windings, I should have said "most" rather than "all except".
• 2 - The complicated model considering saturation spatial harmonics for our purposes gives qualitatively the same results as the simple model where we apply voltage to a coil wrapped on a stationary lump of iron such as a toroidal gapped core. So I did not need to discuss the spatial harmonics (even though I believe everything I said about spatial harmonics is correct).

With those clarifications/corrections, I believe everything I said above is correct, although I am interested to hear if something I said still sounds wrong.

Several times you mentioned derating in a tone as if it is something I suggested (my interpretation of your tone). I never suggested derating at all. I said the opposite... I said that the important performance requirements are temperature, not current harmonics inside the delta. So I presume that a manufacturer who provides a motor with nameplate permitting delta connection operated near saturation will take the heating from 3rd harmonics into account when establishing nameplate parameters. That is why I suggested that the 24% 3rd harmonic that David measured inside the delta is not a problem (it is expected). On the other hand, I get the feeling you are not comfortable with the 24% (?)
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Or maybe when you use the term "derate", you are talking about a thought process that the motor designer would go through (rather than the user?). In that case my belief is yes: the designer must incorporate some factor to account for the 3rd harmonics flowing in the delta. How much a factor is it? In this case knowing the acutal data (3rd harmonic are 24% of FLA.... assuming the data was taken near FLA, which I didn't check), a simple calculation is that stator I^2*R losses would increase by about 3% = sqrt(1^2+0.24^2)-1.

And as you know better than me, the I^2*R may not tell the whole story... there is also effects on stray losses, core losses, spatial flux distribution, etc.

At any rate, I believe this circulating current is why the vast majority of large motors are designed to be connected in wye (unless there is special need for delta connection such as wye-delta start or dual-voltage nameplate).
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quote:
Originally posted by electricpete:
....How much a factor is it? In this case knowing the acutal data (3rd harmonic are 24% of FLA.... assuming the data was taken near FLA, which I didn't check), a simple calculation is that stator I^2*R losses would increase by about 3% = sqrt(1^2+0.24^2)-1.

...the I^2*R may not tell the whole story... there is also effects on stray losses, core losses, spatial flux distribution, etc.

That is correct and added together they may account for up to 8-10% of name plate energy and that is a lot. As you mentioned, Delta is a less preferred scheme for that reason. Note, the plot shows a percentage of fundamental and not FLA.

Agreeing on the cause of the 3rd current harmonic I plan on reducing it by utilizing more linear section of the magnetizing curve and reducing the power voltage from 490 VAC to around 475 VAC. Any suggestions on that?

Just to show LINE current 3rd harmonic, an updated file is attached. LINE current 3rd harmonic makes up only 0.3% of fundamental and therefore won't have an effect on the grid.

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460 vac is typical nameplate voltage.
NEMA allows range +/- 10%, so 506 would be max voltage. 490vac is certainly near the top of the band.

I agree you should see reduction in 3rd harmonic content if you decrease voltage. I'm not sure if it's necessary. Are there stator winding temperature sensors on the motor? You'll have to talk to plant people on how to change the voltage... perhaps transformer taps can be changed by someone who knows what they're doing, but you also have to look what happens when grid voltage droops low and you try to start a motor etc.

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Attached I did some simulations of a similar model to what Jan posted - it is the exciting current using the simple model of a series resistor and non-linear inductor (*) fed by a single phase sinusoidal voltage source. Slide 2 gives the characteristics of the non-linear inductor... with a knee current corresponding to approx 10 amps. On slide 4 thru 9 the source voltage magnitude is gradually increased and you can see the distortion of time waveform, as well as harmonic content tabulated on right side of each slide.

An interesting comparison between slides 9 and 10: we get twice as much 180hz current when we excite the circuit with 240volt 60hz as with 240volt 180hz. At first it sounds backwards... how can we get more 180 hz using 240volt 60hz source than using 240volt 180hz source (same voltage magnitude)? The answer of course lies in volts per hz... the 240 volt 60hz is much higher volts per hz and pushes the core much further into saturation than the 240 volt 180hz.

We have already seen the 3-phase connections have an effect on what shows up in our waveforms compared to the single phase simulation.

(*) - By the way it would be like a gapped toroidal transformer. The lower portion of the flux vs current curve is purely linear because it is dominated by the airgap... the upper portion follows constant slope because iron is in saturtion.

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Attached is the spreadsheet used to generate the last powerpoint. There are instructions there if anyone is interested to play around with it.

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When I came to work today there was sitting a 500 Hp, 3600 rpm delta connected motor on the test bed. What a strike a good luck! Since the highest vibration was 0.04 in/sec I had time to do some tests.
The locked rotor impedance: 0.08 Ohm
The zero sequence impedance for the 3rd harmonic: 0.51 Ohm.
I cannot accept the 3rd harmonic being 24%, because I simply do not see it in real life. I have already posted the ppt file where the 3rd harmonic is way away from the 24%. The motor was 150 hp @575V, hence the full load current is roughly 150 Amps or 150/1.73=87 Amps inside the Delta. The 2.86 amps is just 3.3%, way away from 24 %.
The fact is, that the motor may not have been saturated as much as the others. I will make sure that this doubt will disappear in today’s measurement.
In the ppt file attached to this post, there is comparison of the current signature taken on a 500 Hp motor at 460 Volts (the nameplate voltage). Then the voltage was increased to 577 V and the current signature was taken again. The voltage was hence increased by 25 %. The NO LOAD current increased from 97 to 137 Amps (41%). No doubt, the saturation was present. Yet the 3rd harmonic of 3.80 Amps has increased to only 4.05 Amps (6.5%). Further, one must consider that the full load current on this motor is 542 Amps. The current of 3rd harmonics is just a tiny fraction, miles away from 24%.

There was a calculation of the losses due to 24% 3rd harmonic. Somehow the “sqrt” got in front of the formula. The sqrt is not supposed to be there. Hence, the loss increase is not 3%, but it is probably very close to 6%. The 6% increase would have to trigger de-rating in my opinion. However I do not believe that de-rating is necessary because the impact of the 3rd harmonic is never close to 24%. I do believe that the 24% was correctly found by David. But the real reason for the huge number must be elsewhere. I did not realize, that the motor works on variable speed drive. If feeding from the normal power, the numbers simply do not seem to add up.
In the ppt file the red spectra are from the inside of the Delta, the black spectra are from the line.
jank

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That is some fantastic data. A controlled experiment to see the effect of change of voltage upon harmonic current at no-load, including line-side and inside-the-delta.

I have to admit I would have bet a beer that you would see MUCH larger increase in 3rd harmonic inside the delta upon increasing voltage to 125% of nameplate. I guess I would end up buying the next round!

First some rambling attempt at analysis on the question: how far are we into saturation at 125%:
• For 125% increase in voltage, there was 130% increase in fundamental current inside the delta, 140% increase in current in line side. (They should be the same.) The ratio of increase in fundamental to increase in voltage was 1.04 inside the detla and 1.11 outside the delta.
• Ratio of Line/Delta fundamental is 1.73 at 100% voltage, 1.86 at 125% voltage. They should both be 1.73.
• Both of the above make me wonder if the line-side fundamental reading at 125% is 10% too high for some reason. Don’t know why.
• In the single-phase model powerpoint, the increase in fundamental going from 140vac to 180 vac (a 128% increase in voltage) was 132.6%. The ratio of increase in fundamental to increase in voltage is 1.03
• In the single-phase model powerpoint, the increase in fundamental going from 160vac to 200 vac (a 125% increase in voltage) was 145.2%. The ratio of increase in fundamental to increase in voltage is 1.16
• Based on all the above using the parameter “ratio increase in fundamental to increase in voltage”, if we tried to map the where the 460vac machine lies compared to single phase simulation, we guess that 125% voltage on 460 vac machine must correspond to somewhere between 180vac and 200vac (peak) on the single phase simulation.

Does the above really mean anything? IF we took it at face value (and that’s a big if... it's a tenous string), it suggests we are still not very far into saturation at 125% voltage. And we might certainly think the harmonic harmonic content seems to paint the same picture. Maybe knowing that the motor is nameplated for delta, the manufacturer intentionally designs very low flux density? It’s a stretch, but I don’t know the answer. If anything I think 2-pole motors tend to be designed to have slightly higher flux density than lower speed because there is such a lower magnetizing current requirement to achieve a given flux level, due to smaller airgpap circumference.

I agree the sqrt did not belong there discussing losses the way I did. It would belong there if discussing RMS current.... the calculation gives 3% increase in RMS current, so derating factor -3% on line current would be appropriate if we were inclined to apply a derating factor (I’m still not convinced this is not normal... inside-delta harmonics is certainly something that is not normally measured... although Jan has certainly made a good case).
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It appears that EP's simulation clearly shows increase in 3rd current harmonic (up to 27% of fundamental) at a higher voltage due to non-linearity between magnetic density and magnetizing current.

I believe that in Jan's example insignificant increase in 3rd current harmonic as voltage increased from 460 to 575 VAC can be explained by the fact that the motor is designed with 575 VAC in mind ( to be within the linear portion in the magnetizing curve), so that 460 VAC automatically fell within the linear portion.

The motor is NOT on VFD!

I still believe reducing the voltage to 475 VAC will reduce 3rd harmonic from monstrous 24%. I think it is worthwhile doing as power savings could be around 8% and the motor temperature reduced.

I'll take IR readings (just out of curiosity, since I have no similar motor running with Wye connection to compare with.)

If there are different solutions I'll be interested in hearing them.
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Attached is another datapoint. Shows published no-load current test results on 15hp, 208vac, 4-pole Delta-conn motor at no-load. Voltage is varies similar to what Jan did.

The 3rd harmonics are a higher fraction of fundamental than Jan's results. The variation with voltage is much higher than Jan's results.

Safe to say not all motors act the same. What are the relevant variables that predict the differences? Beats me. One would think large form wound motors with generally open slots act different than small random wound with closed slots... but Jan's and David's example motors are both large motors.

The article doesn't shed any light on the harmonic variation with load (it provides an algorithm for simulating that, but I don't have the time).

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In my case it is a big 250 HP motor, almost fully loaded. Voltage ratio is 490/460=1.065 or exceeds the nameplate only by 6.5%. But the 3rd current harmonic inside the Delta is hugh - 24%.

I think it is an original design deficiency of magnetic system for this particular motor type. The negative effect - additional losses in the copper and iron which is roughly 20% of total losses - will lower motor efficiency by additional 2% of total HP. These numbers are just a quick estimation.

If correct, then just energy saving per motor per year is substantial ( assuming 2% consumption reduction):

200 kw * 0.02 * 8,000 hr * 0.07 \$/kw*hr = \$2,200

Higher insulation temperature is another negative effect.

Unfortunately, still can not find any information on the issue....
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