Question for experienced rewinders 5

[zlatkodo]

I would like to know how often exist in practice (on the U.S. market and in other areas outside Europe), three-phase low voltage induction motors with 96 slots and for which number of poles , power and purpose ?
Thanks in advance.
Zlatkodo

 

[electricpete]

Attached spreadsheet adds a new tab - we now have one for the 6-pole 42-slot and one for the 6-pole 96 slot. Both match Wolf's results.


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[edison123]

Hi Wolf - could you possibly expand on this a bit with some example ?

"For such units there is a design prerequisite that fractional slot windings with a denominator (devider) devisible by 3 must be avoided."

When you say denominator, do you mean no. of poles like 6, 12, 18 etc. (even multiples of 3) ?


Hi pete - I have downloaded your spreadsheet. Thanks. Let me see if I'm capable of learning something from it.

Muthu

http://www.edison.co.in

 

[electricpete]

I think he was talking about the C number where
q = Q/(m*p) = A + B/C
Q = Slots
m = phases
p = poles
q = slots per pole phase group
B/C is the fractional part of q expressed as a lowest fraction.

The quoted references suggest C=3 is to be avoided to preserve balance. Although the degree of unbalance can be quite small as in Wolf's 6-pole 96 slot example.
======================
The spreadsheet requires the analysis tookpak. I think the calculation is pretty simple, but my explanation and spreadsheet made it look more complicated than it really is. It can all be summarized in one equation:
Vk = exp(I*k*[p/2]*2*pi/Q)
where
Vk is voltage in kth coil
I=sqrt(-1) is used to give complex representation of the vector in the complex plane based on Euler's identity (exp(I*x) = cos(x) + I*sin(x))

After that you just add up the vectors of voltages of coils in each series leg and compare them.

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[edison123]

Thanks pete. Do you see any reason why 3 is such a taboo ?

Muthu

http://www.edison.co.in

 

[electricpete]

When n is not 3, we can create a fractional slot winding that has geometric symmetry and therefore textbook symmetry (balance). Ray's example of 96 slot 10-pole machine demonstrated this. B phase is a carbon copy of A phase which is a carbon copy of C phase, all just shifted.

When n is equal to 3, we cannot create a fractional slot winding that has geometric symmetry and therefore we can expect some degree of unbalance. Ray's 12 pole 96 slot example and Wolf's 6 pole 42-slot and 6-pole 96 slot are exmples of this.

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[starkopete]

Hi,
I am attaching excerpts out of WINDING ALTERNATING-CURRENT MACHINES (A Book for Winders, Repairmen, and Designers of Electric Machines) By Michael Liwschitz-Garik & Assisted By Celso Gentilini, I hope that they will help the discussion and verify some of the exceptional work that appears on this thread. This book is by far my favorite as a re-winder, the fact that it is dated helps out when I come across some old 2 phase water turbine generators. It has all of the charts, tables and formulas for most of what is being discussed here (although most is over my head).

Thank You

 

[starkopete]

I'll try it again.

 

[rhatcher]

Pete,

The case where the denominator (C or n) equals the number of phases seems to be problematic. The problem appears to be that since the section pattern is equal to the number of phases that this results in unbalance. I agree at this point that this (C=3 for 3 phase or C-2 for two phase, etc.) is a 'special case'. However, I am not convinced of the reason why this is imbalanced.

Since you appear to be posting based on 'google book' references, perhaps you can show us the reference that explains your ideas and that derives the equations:

The kth slot is at mechanical angle k*2*pi/Q.
The kth slot electrical angle is k*p*2*pi/Q = k*alpha
The kth slot voltage vector is therefore represented as exp(I*k*alpha)

Are you sure that this equation applies to the general case (any number of poels) and not specifically to a two pole winding ( 2 * PI)?

Also, your reference to the EASA Technical Manual is interesting since you said that; "Also the 6 and 12 pole 96 slot options are shown in the EASA Technical Manual section 3 "Coil Groupings for 3-phase Windings" without any precautions/warnings." Are you implying that the 'Easa Technical Manual' is wrong or are you saying that the Easa Tech. Manual correctly contradicts your point?

 

[electricpete]

Are you sure that this equation applies to the general case (any number of poels) and not specifically to a two pole winding ( 2 * PI)?

It's right if you stick with one message at a time. I am aware I am not always consistent in my notation between messages (sorry) but if you stick withone message it is correct.

The excerpt quoted is correct as written but I think the shifting of p into the definition of alpha (alpha is electrical angle here) could be misleading:

The kth slot is at mechanical angle k*2*pi/Q.
The kth slot electrical angle is k*p*2*pi/Q = k*alpha
The kth slot voltage vector is therefore represented as exp(I*k*alpha)

where in this case p was defined as pole pairs

We can deduce from the statement "k*p*2*pi/Q = k*alpha" that alpha = p*2*pi/Q. So the angle of the kth slot voltage vector is the same as the slot electrical angle.... k*p*2*pi/Q. If p=1 (2-pole motor), then the angle is 2*pi/Q = 360deg/Q.... same as mechanical angle... as expected for 2-pole. For more poles pairs, the factor of p included in electrical angle alpha increases electrical angle for the same mechanical angle.

What is tricky is that in the spreadsheet alpha was strictly the mechanical angle... no p included there.... but I multiplied alpha by p before I plugged it into the argument so it still works. Same results, sloppy notation. Sorry.

Also in some places I used p = poles and some places (like this message) p = pole pairs. I try to define it each time.

The method of the spreadsheet is based on the same principle that is used for developing distribution factor (see Fitzgerald or other books). Again, once you have an expression for voltage in a coil like exp(I*k*p*2*pi/Q) , just add up the voltages. Starkopete had a reference... but we can't see it. (Did you click the "insert link" button?)

Also, your reference to the EASA Technical Manual is interesting since you said that; "Also the 6 and 12 pole 96 slot options are shown in the EASA Technical Manual section 3 "Coil Groupings for 3-phase Windings" without any precautions/warnings." Are you implying that the 'Easa Technical Manual' is wrong or are you saying that the Easa Tech. Manual correctly contradicts your point?

EASA isn't specific, but the fact they include it with no warning I interpret to mean the results will definitely not be catastrophic and probably be "acceptable". But there will be an unbalance and I suspect an OEM would not design one this way.

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[wolf39]

Muthu:

Pete explained your denominator question perfectly well. Every fractional slot winding with a denominator devisible by 3 is unsymmetrical.

q = A + B/C

The lower the A number the higher the imbalance.

The higher the C number (still devisible by 3) the lower the imbalance.

Also, for a 60 pole 420 slot winding it may be possible to minimize voltage imbalances by re-grouping stator coils or stator bars.

Regards

Wolf

http://www.hydropower-consult.com

 

[wolf39]

Pete:

Yes, I was wrong to say that adding 5 + 5 + 6 or 5 + 6 + 5 or 6 + 5 + 5 voltage vectors lead to identical phase voltages. This I found out when further investigating on this topic (see my post dated 3 Jan 10 7:06). I'm sorry to have shaken you by shifting gear from forward to reverse. But what you mean by saying

"It leaves me wondering exactly where the heck you are coming from".

This remark somehow tells me that I irritated you with my views. This was not my intention, I assure you. As a generator designer I'm familiar with stator windings but must admit that I'm not a winding specialist.

Regards

Wolf

http://www.hydropower-consult.com

 

[electricpete]

No, not at all irritated. I was just looking for something resembling a turn signal, which you now provided.

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[starkopete]

Hi

 

[wolf39]

Pete:

You've quoted a definition of a symmetrical winding from a publication as follows:

"A winding is said to be symmetrical if when fed from symmetrical supply it creates a rotating field".

I'm also sceptical about this statement. We all agree now that the 96 slot 6 pole winding is unsymmetrical. Nevertheless a symmetrical supply obviously creates a rotating field in this unsymmetrical stator winding and the motor works as expected.

An internet source confirmed my suspicion that the inversely rotating magnetic field causes a negative (breaking) torque, thus reducing the motor output. The motor bearings may suffer mechanical damage because of the induced torque components at double system frequency and the rotor is heated up which may lead to faster thermal ageing. We therefore agree with each other that no competent OEM would choose fractional slot windings with a denominator devisible by 3. Instead of a 96 slot winding for a 6 pole motor it would be advisable to select 5 1/2 slots per pole and phase to obtain a symmetrical 99 slot winding. An additional way to fine-tune a multiple-turn coil winding would be to modify the number of turns per coil.

When I previously mentioned that the 96 slots 6 pole winding is physically balanced (symmetrical) I had in mind the winding appearance. Looking from the non-connection side you couldn't tell which coil numbers (slot numbers) belong to a group of 2 or 3. And there are no empty slots.

I may have been wrong to treat as equivalent the terms "balanced" and "symmetrical". The term "balanced" can be expressed as

reasonably balanced
nearly/almost balanced
balanced
well balanced
perfectly balanced

whereas the term "symmetrical" to me implies that something is perfect. But I may be wrong here. English is not my native language.

In this context I found in the internet a definition as follows:

"A three-phase power system is called balanced if the three-phase voltages and currents have the same amplitude and are phase shifted by 120 degrees with respect to each other. It is assumed that the waveforms are sinusoidal". This definition may satisfy all of us.

It is possible to quantify an imbalance in voltage or current of a three-phase system. European standard EN 50160 gives limits for the unbalance ratio of less than 2% for LV and MV systems and less than 1% for HV systems, measured as 10-minutes values, with an instantaneous maximum of 4%. As we can see certain standards even specify an allowance for the term "balanced". The only problem I see is this one: A phase voltage related imbalance of 1% may be permissible by the EN 50160 standard. With an inverse reactance of X2 = 0.20 p.u. this leads to a current imbalance of 5% which doesn't seem to be acceptable standard-wise nor may this be acceptable loss-wise for stator and rotor.

Regards

Wolf

http://www.hydropower-consult.com

 

[starkopete]

Hi,
The book Winding Alternating-Current Machines (Liwschitz-Garik) refers to balanced & unbalanced fractional-slot windings. From the book:

"Conditions of Balance. It has been mentioned that in this chapter only the balanced fractional-slot windings will be considered. These are the windings for which

No.of poles/d = an integer

d/No. of phases = fractional number

When these 2 conditions are satisfied, the winding is balanced, i.e., the voltages generated in the phases have the same magnitude and are displaced from each other by the same angle."

Thanks

 

[zlatkodo]

Hi, Starkopete,
If you read my earlier post from 21. Dec. 09. 3:46:

“But if q is fractional number then symmetrical THREE-PHASE winding MUST meet two
additional requirements:
1/ - Number of poles must be divisible with "c" and
2/ - Number "c" should not be divisible by 3 .”

then you can see, this is the same thing.
Zlatkodo

 

[starkopete]

zlatkodo,
You are correct, they are the exactly the same thing.

Thanks

 

[electricpete]

Wolf - To me there is logic in the book definition of symmetrical in the following sense:. If you have balanced voltage applied to a symmetrical winding, and you plot the resulting "instantaneous flux vector" (the space fundamental component of flux distribution at a given point in time), then the tip of the vector would travel along a circle of uniform radius at uniform velocity. But if the winding is unbalanced/assymetrical (or if the voltage is unbalanced for that matter), THEN we don't have a perfect circle traversed at uniform velocity. For example if B phase has a lower distribution factor as in our examples, then the radius of the circle is a little higher (yes higher, not lower) when the flux peak is centered on a B-phase group. Perhaps it would be beneficial for the author to clarify it is a perfect rotating field (in the sense described above), rather than any field that has any rotating component as I think you're interpretting... but seems obvious becsue it would be a challenge to create a winding with no rotating component.

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