help interpretting 12-pole generator winding configuration 3

[electricpete]

I am trying to interpret the following stator winding description for a syncronous generator stator:

KVA - 6875
Poles: 12
coils per slot: 2
Slots: 144
Connect 1 and: 4
Coils in Slot 1 and: 11
No. Circuits: 6 at 4160 Volts
Connection: 120-degrees Phase B Star: 4160
Grouping: 888 - repeated 6 times
Coils per group: 8

I know 12-poles is correct... it is a 600rpm machine (60HZ system). If I ignore the last two items, I can piece together the following:
- we have 144/(12*3) = 4 coils per pole phase group
- Connect 1 and 4: defines pole-phase group connections for first pole phase group.
- Coils is Slot 1 and 11. Reasonable fractional pitch. Full pole pitch would be 144/12=12 i.e. 1 and 13 . This gives 2 coils overlap between pole-phase groups (right?).
- With 6 circuits, that must mean that each phase has 6 parallels, two pole-phase groups in each parallel.

Now the last two items throw me a curve. Why do they say 8 coils in a group? I could understand if they said 8 coils in a circuit or parallel, but this is not normal interpretation of the word group, is it? If not then what do they mean by 8 coils in a group?

I get to look at this machine tomorrow. Any quick reply would be appreciated. Thx.

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[edison123]

pete,

Since the winding has 6 parallel ckts out of 12 groups per phase, each parallel ckt in first phase has 2 groups of 4 coils each connected in series (1&4, 7&10, 13&16, 19&22 and 25&28). They probably meant coils per circuit (not group) as 8. This series grouping of two groups is repeated 6 times in each phase and 18 times in total winding covering all the 144 coils.

You are right about pitching. The coil overlap over phases is the no. of slots by which full pitch is short chorded. In this case, a pitch of 10/12 will have, in two slots (per phase per pole) coils belonging to belonging to different phases in each layer.

 

[electricpete]

Thanks edison, that confirms what I was thinking.

Their use of the term "group" threw me off. I would have called this 4 coils per group, 2 groups per circuit, 6 circuits per phase.

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[aolalde]

Electricpete:

This winding is called “consequent groups” or 120°E groups. It has one half of the groups (18) as compared to a regular 60°E grouping (36). The polarity of all groups is the same. First group is phase “A”, as second group is 120°E apart, it is phase “B” and third group is phase “C”. All groups have the same polarity ( eg in +, exit - ). Jumper is 1 – 4 to make a series with the same phase.

For 6 circuits and 18 total groups, you have one group per circuit.

Similar connection is used for two speed single winding motors in the low speed connection.

 

[electricpete]

Aha. Thanks aolalde. Great comment as usual.

I can begin to picture what you say:

Normal motor:
(ab'c a'bc')^6 = 36 groups 60 degrees apart.
36*(60/360)=6 electrical cycles per mechanical revolutions (600rpm)
coils/group = 142/36 = 4

Consequent pole motor:
(a b c)^6 = 18 groups 120 degrees apart.
18*(120/360)=6 electrical cycles per mechanical revolutions (600rpm)
coils/group = 142/18 = 8
Jumper 1-4 means same polarity of groups 1 and 4.

How would normal motor pole jumper be identified?
Jumper 1-4'?

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[electricpete]

Also, why would a designer choose consequent pole winding? (for one speed machine)

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[edison123]

aolalde,

As pete says, I do not see any reason to use consequent pole winding in single speed machine and that too in generators, where harmonics will be a big problem when consequent pole winding is used. As you say, it is typically used in single winding two speed low voltage motors.


Also, a 120 deg phase band does not mean automatically consequent pole winding. It defines only the phase spread of the winding and not the pole to pole connections.

Again a more common 60 deg phase spread gives about 15% more fundamental distribution factor (0.955/0.827) as compared to a 120 deg phase spread. Since this gives a 15% more output for a given current, a 60 deg spread is preferrred by winding designers.


pete,

You mentioned about that you will get to look at the actual winding. May be you can post here what sort of winding is actually there.

 

[aolalde]

Hi; Electricpete & Edison123.

I’ll wish to answer your questions but I never designed a Generator winding this fashion, I have found a few (2 on Electric Products Generators with this winding).

What I found is that connecting the winding is simplified since the amount of jumpers is reduced. If the question about 1 – 4 jumper as compared to length for standard 60°Grouping, the length of the phase coils terminal lead is like that for a std 1 – 7 jumper coil. For this winding the simplification is great since all your groups are lines or neutral (4, 5&6) for 6 circuits. Probably this winding has six terminal leads (1 to 6) around the winding with six connection points to each lead and no jumpers.

Edison, remember that at a given instant, the fem induced on each conductor has amplitude and angle related to the position (slot) it keeps between each North and South Pole, then when connected in series with other conductors the resultant voltage will be the vectorial addition of all the fems in the series conductors. That is true for the fundamental and any harmonic. The designer should optimize the resultant voltage for the Fundamental and minimize total voltage result for harmonics. I think that this winding eliminates totally the 3rd harmonic (I have read that wye connection does too, in regular windings). You could try to find a distribution factor by the books and rules or better, make the analysis of this particular array. There are some few generators outside with non conventional windings.

 

[electricpete]

My thought, like edison, is that this design would produce higher space harmonics.

aolalde has correctly decuded this is in fact an Electric Products Generator. Based on that and his other comments, something tells me he knows a lot more about electric machines than me.

We will be rewedging this generator and I will have a change to take a look at the connections.

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[edison123]

aolalde,

Pete posted that this m/c has 6 circuits and also "connect 1 & 4". If it had been a consequent pole winding, then question of connecting 1 & 4 does not arise since all 8 coils are serially connected to produce N (or S) poles.

So, my bet would still be it is a normal pole connected winding with 60 deg phase spread with 6 jumpers/phase and with 36 pole-phase groups having 4 coils each. May be pete will be kind enough to post his findings.

Reg, your last paragraph, while I agree what you've said, I still don't undertsand what you are really trying to say. If you disgaree with my earlier post, I will be glad to correct myself.

 

[aolalde]

Edison
Please analyze my comments to your post:

"I do not see any reason to use consequent pole winding in single speed machine and that too in generators, where harmonics will be a big problem when consequent pole winding is used”.

I calculated the distribution factor for the fundamental and harmonics up to the 13TH with the following results:

1st 3rd 5th 7th 11th 13th
60° 0.9577 0.653 0.205 0.1575 0.126 0.126
120° 0.8294 0.0 0.1778 0.1365 0.1091 0.1091
Kp 0.9239 0.3827 0.3827 0.9239 0.3827 0.3827

All the low range harmonics will be reduced with actual winding, as compared to the conventional 60°E group belt.

I think this winding has a premium performance regarding the 3rd harmonic for line to neutral loads. It is totally eliminated.

“Also, a 120 deg phase band does not mean automatically consequent pole winding. It defines only the phase spread of the winding and not the pole to pole connections.”

If the electrical spacing of each group of coils is 120°E, the fourth group has 360 °E out of phase, is not this consequent? The salient poles polarity is still N,S,N,S, etc
and should have 12.

I agree that for the same current the power output could be up to 15.5% higher with a conventional 36 groups winding as the fundamental voltage increases, but that should be considered at the original design evaluation, the output against quality of the generated wave. My best advice is leaving it with the original design (if it is as I assumed).

Thanks both of you for your interest.

 

[edison123]

aolalde,

I have worked distibution factors for various harmonics as below. (correct me if I am wrong)

Spread 1st 3rd 5th 7th 9th harmonic
60° 0.955 0.637 0.191 - 0.136 -0.212
120° 0.827 0.0 -0.165 0.118 0.0

With a star connection, the 3rd harmonic is eliminated across line terminals and with 5/6th chording used here, the spread factors for 5th and 7th are reduced to 0.259, which gives a reasonably clean waveform with a 60 deg spread. (Unless there is a line to neutral circuit in use that requires a very clean waveform, which pete can confirm).

Why I am puzzled in this case is that "connect 1 & 4" which does not arise in a 6 ckt in a 120 deg spread.

As you rightly said that the phase spread advantage is taken care of in the design stage, which is exactly why a designer would choose a 60 deg spread to avail the increased output benefit which results in a smaller machine.

Anyway, thx for making this thread interesting. Rest is now in pete's court.

 

[jbartos]

Comment on electricpete (Electrical) Jan 19, 2004 marked ///\\I am trying to interpret the following stator winding description for a syncronous generator stator:
///Windig described by words only without winding figures to follow often leave some ambiguities.\\KVA - 6875
Poles: 12
///implies 6 pole-pairs\\coils per slot: 2
///1 side of two coils\\Slots: 144
///144 slots / 2 coils per slot = 72 coils per pole pair
72 coils per pole pair / 12 poles = 6 pole pairs
\\Connect 1 and: 4
Coils in Slot 1 and: 11
No. Circuits: 6 at 4160 Volts
Connection: 120-degrees Phase B Star: 4160
Grouping: 888 - repeated 6 times
/// 8 in 8 slots + 8 in the next appropriate 8 slots + 8 in the next appropriate 8 slots gives 24 slots. Repeated 6 times give 6 x 24 = 144 slots.\\Coils per group: 8
///8 coils per 8 slots. This gives 144 coils occupying 144 slots.\\I know 12-poles is correct... it is a 600rpm machine (60HZ system). If I ignore the last two items, I can piece together the following:
- we have 144/(12*3) = 4 coils per pole phase group
///Agree\\- Connect 1 and 4: defines pole-phase group connections for first pole phase group.
- Coils is Slot 1 and 11. Reasonable fractional pitch. Full pole pitch would be 144/12=12 i.e. 1 and 13 . This gives 2 coils overlap between pole-phase groups (right?).
///There are 144 slots and 144 coils\\- With 6 circuits, that must mean that each phase has 6 parallels, two pole-phase groups in each parallel.
///6 circuit x 6 parallels x 2 group = 72 slots instead of 144 slots.\\Now the last two items throw me a curve. Why do they say 8 coils in a group?
///To cover one phase. Notice 888 taken 6 times.\\ I could understand if they said 8 coils in a circuit or parallel, but this is not normal interpretation of the word group, is it? If not then what do they mean by 8 coils in a group?
///See above\\\

 

[electricpete]

Thx kumar (edison) and aolalde.

I spent awhile studying pitch and distribution factors last night and still have some more studying to do.

I can see right off the bat that the pitch factor is unchanged as aolalde says.

The distribution factor as I understand it describes behavior of harmonics for a single pole-phase group.

Now there remains the question of adding the effects of the groups together. The harmonics of the sum (as fraction of fundamental) cannot be any higher, but it can be lower if there is full or partial cancellation of harmonics among groups. For example triplen harmonics as edison said are completely cancelled. Although I can't prove it my intuition tells me that there is better cancellation of harmonics when we add the 60-degree groups together than when we add the 120 degree groups together.

Here is some unscientific reasoning that leads me to suspect the 120 degree winding has higher content of low-order harmonics (5,7,11,13). Let's say had a single-layer full-pitch winding with very very large number of slots so that the steps of stator slotting become negligible... instead within a group the mmf distribution curve looks like a straight line. The mmf of that winding for 60-degree winding at given snapshot in time will look like a sin-wave constructed out of 6 straight straight lines (over one period of fundamental... two pole pitches). In contrast, the mmf of that winding for 120 degree winding will look like sin wave constructed out of 3 straight lines over the same fundamental distance. Clearly much higher harmonics for the 120-degree winding in that case.

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[aolalde]

Edison123

How did you calculated the distribution factor?

Distribution factor is defined as:

Kd = (magnitude of resultant voltage)/(sum of magnitudes of individual coil voltages)

after some algebraic simplification;

Kd= sin(q*a/2) / (q*sin(a/2))

Were q = number of slots per group
a= slot pitch angle in electric degrees

For this generator fundamental frequency:
q=8
a=360*6 (pair of poles)/144 (slots) = 15°E

Kd= sin(8*7.5)/(8*sin7.5)=0.8660254/1.044209

Kd= 0.829359787 is’nt it?

you got Kd= 0.827 ¿?


if q=4
Kd= sin(4*7.5)/(4*sin7.5) = 0.957662197

you got Kd=0.955 ¿? and so on.

 

[edison123]

aolalde,

I have reworked distibution factors for various harmonics as below. Sorry about that.

Spread 1st 3rd 5th 7th 9th harmonic
60° 0.958 0.653 0.205 - 0.158 -0.271
120° 0.837 0.0 -0.224 0.224 0.0

 

[aolalde]

Electricpete I do not agree with your last statement:


“The harmonics of the sum (as fraction of fundamental) cannot be any higher, but it can be lower if there is full or partial cancellation of harmonics among groups.”

The harmonics cancellation in each group is given by the distribution factor and the pitch factor Kd*Kp for each frequency.

For example for the 5th

60° group --- Kp*Kd = 0.205*0.3827 = 0.07845, this induced harmonic is reduced to 7.84%

120° group --- Kp*Kd = 0.1778*0.3827 = 0.068044, this induced harmonic is reduced to 6.8%

The harmonics that remain in a group cannot be reduced with the connection of the groups except for the 3rd in a wye connection and only from line to line.

For 60°E or 120°E groups, the next groups have identical harmonic content and out of phase in whole multiples of 360°E, then there is no possible elimination.

As I mentioned the 3rd harmonic with 60°E groups is the exception since 3* 60°E = 180 °E so if two adjacent groups are connected together, the 3rd harmonic content of that group cancels that in the first group because is identical in magnitude and with reversed polarity ( 180°E offset) .

 

[jbartos]

Clarification: 2 coils per slot also lead to a double layer machine. Double layer windings usually lead to simpler end connections, and to a machine which is more economical to manufacture. These machines are found in all machines except some small motors below 10kW.

 

[electricpete]

I agree as aolalde has pointed out I was wrong: there is not cancellation among 5, 7, 11, 13 etc space harmonics of different groups. Rather, these space harmonics 5,7,11,13 all in-phase among groups. Thanks very much for identifying that misconception to me. I didn’t believe it until I worked it out (below).

One thing I disagree on the minor point that the non-existence of 3rd space harmonics of mmf is dependent on the connection wye or delta. As shown in the same analysis below, the 3rd space harmonics among adjacent groups are a total phase difference of 240, therefore any group of three will sum to zero. I understand that 3rd time harmonic currents (a different type of harmonic) are zero-sequence and cannot flow in ungrounded wye winding. That is a slightly different subject.

Here is my discussion.

The mmf space harmonics are given by Ak*cos(w*t + k * theta*p/2 + Phi_k)

Where
w = 2*Pi*Fline
p’ = number of pole pairs = 2*p (=6 for our example).
theta = mechanical angle
k = order of mmf the space harmonic of interest
k<0 means reverse rotation
(k = 1 = main/working p-pole mmf wave )
Ak = magnitude of the kth space harmonic
Phi_k = phase angle of the kth space harmonic
N (below) is index for counting groups.

Assume we have a normal 60-degree spread machine (not consequent pole).

D1 = “Wavelength” of the main (working) mmf is 360 / (p/2) = 720/p DegreesMechanical
(I apologize for terminology – “wavelength” here is intended to mean twice pole pitch, the spatial analogy of to “period” for time variation).

Dk = “Wavelength” of the kth space harmonic = Wavelenth of main mmf / k = 720/(p*k) DegMech

PP = Pole Pitch = Wavelendth/2 = 360/p DegMech
Dpg = Spatial Distance between adjacent pole-phase groups = PolePitch / 3 = 120 / P DegreesMechanical.

Dpgk = Spatial Distance between adjacent pole-phase groups expressed relative to wavelength of kth harmonic = Dpg/Dk = [120/p] / [720/(p*k)] = k/6 = k*360/6 = k*60 degrees expressed on kth spatial harmonic basis

DeltaT = Time difference between adjacent groups = 60 degrees.

Total angle difference between adjacent groups for kth harmonic is Dpgk+DeltaT = 60+k*60 = (K+1)*60

For k=3, the pole phase groups are separated by (3+1)*60 = 240 degrees.
These are equal magnitude but angle separated 240 degrees => any adjacent group of 3 cancel out.

For k=5, the pole phase groups are separated by (5+1)*60 = 360
All in-phase as aolalde has said.

For k= -7: the pole phase groups are separated by (-7+1)*60 = 0, -360, -720 etc.
All in-phase as aolalde has said.

Now I have some questions on the big picture of kd and kp for the harmnonics.
Do you agree:
We use kd and kp to predict the magnitude of stator space mmf harmonics (in presence of stator slotting), and that magnitude (relative to fundamental) is given by (kd*kp / nu) where nu is the order of the harmonic?
- The same numerical kd and kp are also used to predict voltage (and exciation current) harmonics arising from non-sinusoidal air-gap mmf. This would not include mmf harmonics caused by stator slotting itself (these occur in standing wave forward/reverse paris and therefore are stationary with respect to stator coils), and so would be limited to harmonics associated with the rotor or eccentricity. There is no factor nu (space order) here as was used above.
What are other uses of kd and kp (other than relating fundamental voltage to flux, turns etc).

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[aolalde]

Electripete.

Congratulations, you have made a great homework.
I have one last comment that I hope will help to center your thoughts.

If the magnetic flux distribution in the air-gap produced by the field poles were following a perfect sinus distribution and no distortion due to slots, saturation etc should exist; then you will induce a perfect fundamental voltage in the stator winding. (No harmonics).

As this ideal condition will not exist, the harmonic voltage induced will be proportional to the type of distortion on each particular generator.

A properly designed winding will get rid or at least will reduce to a minimum the remaining harmonic voltage induced. This could be achieved with the coil span, grouping, skewing, etc.