Discussion at Winter convention: The M. M. F. wave of polyphase windings
2
948 DISCUSSION AT WINTER CONVENTION Journal Α. I. Ε. E. and rise, usually attributed to gaseous ionization. Above 10 cm. pressure rising power-factor curves appear, reaching the typical ionization shape at 25 cm. pressure. 8. Typical gaseous ionization curves have been obtained and controlled by variations in the tightness of the lead sheath or test electrodes. It appears that the rising power-factor curves found in cables are in all probability due either to loose fitting sheaths or to imperfect impregnation, causing extended layers of air rather than to original entrained air as dependent on the evacuation pressure. 9. Power factor and dielectric absorption follow similar curves and the latter is suggested as a promising method for the predetermination of the properties of cable insulation. Discussion at Winter Convention THE Μ. M. F. WAVE OF POLYPHASE WINDINGS 1 (GRAHAM) NEW YORK, Ν . Y . , FEBRUARY 7, 1927 P. L. Alger: This paper raises questions whose discussion might be carried to great lengths, since the ramifications of the effects of harmonics on various characteristics of the motor are very extensive. I will confine myself, however, to making two comments on this paper and then giving a few things from my own experience. In the first place, Mr. Graham develops a formula for the magnitude of any particular harmonic, w r hich contains the coefficient y/ 1 - cos η Β. That, to my mind, is very hard to visualize, and it is much better to replace it by the exactly - η Β equivalent expression y/2 sin —^—. When this is done, the magnitude of each harmonic is seen to be proportional to the pitch factor for that particular harmonic. As the pitch factor is a very familiar thing to all designers, this expression tells the relative magnitudes of different harmonics almost by inspection. In the second place, it appears obvious to me from physical considerations that with a perfectly balanced winding, every phase being like every other phase, the other phases can only introduce purely reactive voltages in the first phase, similar to the voltages induced by that phase in itself. That is, if you have a perfectly balanced arrangement, the currents in each phase being displaced in time by the same angle as they are in space position, there cannot be produced any two harmonic waves of the same order but opposite directions of rotation. So the nth pulsating harmonic made by phase 1 alone will either be con- verted into a revolving field of amplitude 3/2, due to the three phases, or else will be cancelled out altogether. For that reason, it is clear that Graham's equations showing a phase difference between the various harmonic voltages in a single phase must be wrong. There is no phase difference because all of them are purely reactive voltages. Once we have admitted the existence of these harmonics and shown they are present and undesirable, the really interesting thing is how to avoid them. That Mr. Graham did not touch upon at all. By rearranging the windings in various groupings, a great many effects can be produced. There are a number of arrange- ments possible for any particular winding, all of which give balanced phase voltages, but which have different characteristics. Systems of distribution can be worked out to give minimum vibration, minimum reactance or minimum load losses, or to meet other conditions, and some of those other arrangements have distribution factors so little different from the one that we ordinarily use, that they are more desirable than the ordinary arrangement. An interesting case illustrating these possibilities is that of a 1000-h. p. induction motor, with 14 poles and 4 2/7 slots per pole per phase, which I had the opportunity of observing in 1923. When the motor was tested the first time, it developed a very severe load vibration, similar to that Mr. Graham observed on his motor. We determined the vibration to be of twice line frequency, and due to the 10-pole field produced by the irreg- ular winding arrangement. By reconnecting the winding to the arrangement giving a minimum 10-pole field, the trouble was remedied without any mechanical change. In general, unbalanced magnetic pull occurs whenever two fields of nearly the same numbers of poles exist together, and so the way to avoid vibration is to arrange the winding to minimize that particular harmonic whose number of poles is nearest the fundamental. The study of the best winding arrangement, taking into account all the factors, is very fascinating, but it is quite difficult to make a complete analysis of the problem. I have been working on this matter for some time, and I hope ultimately to be able to say for any given number of fractional slots per pole per phase what arrangement gives the best combined charac- teristics, taking into account noise, fundamental distribution factor, reactance and losses. C. A. Nickle: I agree with Mr. Alger that in a rotor with uniform permeance, reactive voltages other than 90 deg. out of phase with the currents cannot be obtained. When such voltages exist, we must have reluctance torques in the machine, we must have consumption of power, and we cannot have reluctance torques in a uniform-permeance machine. The author has made calculations of the leakage reactance introduced by sub-harmonics and he gets a value of approxi- mately 1 per cent. Of course, we add reactance voltages vectorially, we shall get a much smaller voltage than if we add them arithmetically. If all these reactance voltages were added in time phase, the total reactance voltage might be considerably greater, and I think might be worth investigating. W. V. Lyon: Mr. Graham has applied the principles of harmonic analysis to an interesting and not uncommon problem, the most important aspects of which I believe are the extra losses and vibration which may occur when these irregular windings are employed. He has clearly shown how the problem may be attacked. In the spring of 1926, apparently at about the time when Mr. Graham was preparing this paper, I analyzed the same problem with a class of graduate engineers at the General Electric Works at Lynn. Curiously enough the illustrative problem that we worked through was the same that Mr. Graham has chosen, viz., one in which there are 6% slots per pole. Also the winding arrangement was the same in both cases. The only difference was that ours was a stator having 54 slots and wound for 8 poles. We found no particular difficulty in obtaining a resultant nth harmonic reduction factor for this winding which was a combination of the ordinary pitch and breadth factors. We did not, however, determine the criteria for the existance of the nth harmonic nor for its direction of rotation. One point that Mr. Graham has made is well worth emphasiz- 1. Α . I . Ε . E . JOURNAL, February, 1927, p. 118.
Transcript of Discussion at Winter convention: The M. M. F. wave of polyphase windings
948 D I S C U S S I O N A T W I N T E R C O N V E N T I O N Journal Α . I. Ε . E .
and rise, usually attributed to gaseous ionization. Above 10 cm. pressure rising power-factor curves appear, reaching the typical ionization shape at 25 cm. pressure.
8. Typical gaseous ionization curves have been obtained and controlled by variations in the tightness of the lead sheath or test electrodes. It appears that the rising power-factor curves found in cables are in all
probability due either to loose fitting sheaths or to imperfect impregnation, causing extended layers of air rather than to original entrained air as dependent on the evacuation pressure.
9. Power factor and dielectric absorption follow similar curves and the latter is suggested as a promising method for the predetermination of the properties of cable insulation.
Discussion at Winter Convention T H E Μ . M . F. W A V E OF P O L Y P H A S E W I N D I N G S 1
( G R A H A M )
N E W Y O R K , Ν . Y . , F E B R U A R Y 7, 1927
P. L. Alger: This paper raises questions whose discussion might be carried to great lengths, since the ramifications of the effects of harmonics on various characteristics of the motor are very extensive. I will confine myself, however, to making two comments on this paper and then giving a few things from m y own experience.
In the first place, M r . Graham develops a formula for the magnitude of any particular harmonic, w rhich contains the coefficient y/ 1 - cos η Β. That, to m y mind, is very hard to visualize, and it is much better to replace it b y the exactly
- η Β equivalent expression y/2 sin —^—. W h e n this is done, the
magnitude of each harmonic is seen to be proportional to the pitch factor for that particular harmonic. As the pitch factor is a very familiar thing to all designers, this expression tells the relative magnitudes of different harmonics almost b y inspection.
In the second place, it appears obvious to me from physical considerations that with a perfectly balanced winding, every phase being like every other phase, the other phases can only introduce purely reactive voltages in the first phase, similar to the voltages induced b y that phase in itself. That is, if you have a perfectly balanced arrangement, the currents in each phase being displaced in time b y the same angle as they are in space position, there cannot be produced any two harmonic waves of the same order but opposite directions of rotation. So the nth pulsating harmonic made b y phase 1 alone will either be converted into a revolving field of amplitude 3 / 2 , due to the three phases, or else will be cancelled out altogether. For that reason, it is clear that Graham's equations showing a phase difference between the various harmonic voltages in a single phase must be wrong. There is no phase difference because all of them are purely reactive voltages.
Once we have admitted the existence of these harmonics and shown they are present and undesirable, the really interesting thing is how to avoid them. That M r . Graham did not touch upon at all.
B y rearranging the windings in various groupings, a great many effects can be produced. There are a number of arrangements possible for any particular winding, all of which give balanced phase voltages, but which have different characteristics. Systems of distribution can be worked out to give minimum vibration, minimum reactance or minimum load losses, or to meet other conditions, and some of those other arrangements have distribution factors so little different from the one that we ordinarily use, that they are more desirable than the ordinary arrangement.
A n interesting case illustrating these possibilities is that of a 1000-h. p . induction motor , with 14 poles and 4 2 / 7 slots
per pole per phase, which I had the opportunity of observing in 1923. When the motor was tested the first time, it developed a very severe load vibration, similar to that M r . Graham observed on his motor . W e determined the vibration to be of twice line frequency, and due to the 10-pole field produced by the irregular winding arrangement. B y reconnecting the winding to the arrangement giving a minimum 10-pole field, the trouble was remedied without any mechanical change. In general, unbalanced magnetic pull occurs whenever two fields of nearly the same numbers of poles exist together, and so the way to avoid vibration is to arrange the winding to minimize that particular harmonic whose number of poles is nearest the fundamental.
The study of the best winding arrangement, taking into account all the factors, is very fascinating, but it is quite difficult to make a complete analysis of the problem. I have been working on this matter for some time, and I hope ultimately to be able to say for any given number of fractional slots per pole per phase what arrangement gives the best combined characteristics, taking into account noise, fundamental distribution factor, reactance and losses.
C . A . Nickle: I agree with M r . Alger that in a rotor with uniform permeance, reactive voltages other than 90 deg. out of phase with the currents cannot be obtained. When such voltages exist, we must have reluctance torques in the machine, we must have consumption of power, and we cannot have reluctance torques in a uniform-permeance machine.
The author has made calculations of the leakage reactance introduced b y sub-harmonics and he gets a value of approximately 1 per cent. Of course, we add reactance voltages vectorially, we shall get a much smaller voltage than if we add them arithmetically. If all these reactance voltages were added in time phase, the total reactance voltage might be considerably greater, and I think might be worth investigating.
W . V. Lyon: M r . Graham has applied the principles of harmonic analysis to an interesting and not uncommon problem, the most important aspects of which I believe are the extra losses and vibration which may occur when these irregular windings are employed. He has clearly shown how the problem may be attacked.
In the spring of 1926, apparently at about the time when M r . Graham was preparing this paper, I analyzed the same problem with a class of graduate engineers at the General Electric Works at Lynn. Curiously enough the illustrative problem that we worked through was the same that M r . Graham has chosen, viz., one in which there are 6 % slots per pole. Also the winding arrangement was the same in both cases. The only difference was that ours was a stator having 54 slots and wound for 8 poles. W e found no particular difficulty in obtaining a resultant nth harmonic reduction factor for this winding which was a combination of the ordinary pitch and breadth factors. W e did not, however, determine the criteria for the existance of the nth harmonic nor for its direction of rotation.
One point that M r . Graham has made is well worth emphasiz-1 . Α . I . Ε . E . JOURNAL, February, 1 9 2 7 , p. 1 1 8 .
Sept. 1927 D I S C U S S I O N A T W I N T E R C O N V E N T I O N 949
ing. When a uniform air-gap is acted upon by a magnetizing winding there will in general be produced component sinusoidal flux distributions which have two poles, four poles, six poles, eight poles, etc. B y properly arranging the winding, certain of these distributions can be completely or partially eliminated. If, for example, a symmetrical three-phase winding having an integral number of slots per pole per phase and wound for 4 poles is used there will be no components except the 4-polar, 20-polar, 28-polar, 44-polar, 52-polar, etc. Again in the 20-pole winding that M r . Graham cites there will be 10-polar, 20-polar, 30-polar, 40-polar, 50-polar, 70-polar, etc., distributions.
I should like to add a little to what M r . Graham has said about vibration. If the stator and rotor were perfectly rigid the internal stresses between them due to the magnetic field could cause no vibration. Actually, however, both the stator and rotor have a certain amount of flexibility and thus these internal stresses may produce serious vibration. There are two distinct types of internal stress. One is due to the action of a single sinusoidal flux distribution and the other is due to the joint of two sinusoidal distributions of different wave lengths. If there is a single sinusoidal component of flux in the gap, the rotor will be acted upon b y balanced radial forces which can cause no vibration in the rotor if its laminations are rigidly connected to the shaft. On the other hand the rotation of the flux distribution will produce a harmonic variation in the magnetic force b e tween the stator and rotor in any fixed radial direction of such a frequency that it will go through one cycle while the magnetic field is moving one pole pitch. If the stator frame is flexible in a radial direction this harmonically varying force may set up serious vibration. This is apparently the case that M r . Graham cites.
The other cause of vibration may, I believe, be equally important. If there are in the gap two component distributions of different wave lengths the radial forces acting on the rotor may be unbalanced. T w o polar distributions that differ b y a single pair of poles will produce this effect. This unbalanced force on the rotor may be either constant or variable. If the distributions are moving properly with respect to each other the unbalanced force acting on the rotor will vary harmonically and serious vibrations may result.
Quentin G r a h a m : M r . Alger has suggested the substi-
ηβ tution of V 2 sin — — for the expression V 1 — cos η β which
Δ
I have used. I agree that this change would aid in visualizing the magnitude of the harmonics.
M r . Alger and M r . Nickle have bo th pointed out the error contained in the last paragraph of Appendix Β and also in the b o d y of the paper where it is stated that the reactance voltages of the various harmonics are not in phase. I am giving below a number of corrections in the mathematics, changing the final equation on which this false conclusion was based. I am indebted to M r . Nickle for having pointed out the particular points which were in error. The corrections are as fol lows:
Equation (6) should read
η θη = — tan
which can be simplified to
_j sin η β
1 — cos η β
η θ η -ηβ 7Γ
~ 2 2 ~
Using this value for η θη equation (30) may be simplified so
that the quantity in the parenthesis becomes | ω ί — η ψ —
The statement following equation (31) should give the displacement angle as — η ψ instead of η ψ.
With this correction the quantity in the parenthesis in equa
tions (32), (33) and (34) will be, t - ^j. I t is clear then
that the final paragraph, following equation (34), is in error and that the reactance vol tage components of the various harmonics must be in phase.
I have experimented to some extent with the rearrangement of windings, as M r . Alger suggests, for the purpose of reducing some particular harmonic. This is usually accomplished at the expense of increasing some other harmonic but, as he says, the total result may be beneficial.
M r . Lyon ' s discussion of the vibration problem is very interesting and his conclusions appear to agree with M r . Alger's experience.
C O M B I N E D L I G H T A N D P O W E R S Y S T E M S FOR A - C . S E C O N D A R Y N E T W O R K S
( R I C H T E R )
N E W Y O R K , Ν . Y . , F E B R U A R Y 9, 1927
D . K . Blake: M r . Richter 's paper does not attempt to take sides. He tried very hard to avoid that. Some years ago, together with others, I made a similar study and obtained similar results, showing that the 115/199-volt system had the lowest cost, the 120/208 next, and then the two-phase system.
Of course this problem will not be settled in this meeting. It will have to be settled b y the Ν . E. L. Α. , the Power Club and the Ν . Ε. Μ . Α . , but I would like to state m y positive convictions along these lines.
I believe, based upon my discussion with various operating engineers and knowing the manufacturers' conditions, that the 115/199-volt system will be the solution to our problem. I am just going to make three statements, without attempting to prove them as to why I believe so. They are b y no means all of the reasons.
The first is because of the lower cost. The second is because of the large number of consumers unaffected b y retaining the 115-volt standard. When I stop and think of the data that were given in the Electrical World showing that we have somewhere around 14,000,000 domestic customers, about 2,000,000 commercial lighting customers, and about a half-million power customers, I think that in view of our attempts at good public relations, it is b y far better to change things that affect the least number of consumers even though they may have more kilowatt' demand and about an equivalent revenue.
The third thing is that I recognize the work that has already been done b y the Ν . E. L. A . in attempting to make the 115-volt system a standard. N o w of course if that is the answer, if the committee 's work proves that 115/199-volt system is preferable, it means two lines of polyphase induction motors. I know positively that no manufacturer recommends the use of 220-volt motors on systems rated nominally 199 volts.
N o w I want to say a word about the practise of using 220-volt motors on 208-volt systems. Suppose you decide on a 120/208-vol t system, and use the old arguments of lower power factor and over-motoring, etc., to justify utilizing the 220-volt motor. Y o u then have a system that 110-volt single-phase devices do not fit. I think those arguments are perfectly valid for existing conditions, and during the period of change-over, but I think it is wrong to continue to grow throughout the years without having a system supplying devices that do not fit the system voltage.
Therefore I can see no other answer than two lines of motors. N o w the manufacturers in the past have always, to the best of
m y knowledge, built additional lines of devices whenever there was a sufficient demand. I have no doubt in m y own mind that they will do so in case it is the general opinion that two lines of motors would be desirable.
1. Α. I . Ε . E . JOURNAL, July 1927, page 7 2 4 .
