A paper to be presented at the 25th annual conven­tion of the American Institute of Electrical Engineers, Atlantic City, N. / . , June 29— July 2, 1908.

Copyright 1908. By Α. I. Ε. Ε.

(Subject to final revision for the Transactions.)

A P P L I C A T I O N OF F R A C T I O N A L PITCH W I N D I N G S TO A L T E R N A T I N G - C U R R E N T G E N E R A T O R S

BY J E N S B A C H E - W I I G

Fractional pitch windings have been treated by various authors in the past , especially with regard to the influence they have upon the self-induction of the armature winding. The object of this paper is to deal briefly with the points leading to the use of a chorded winding for alternating-current generators from the standpoint of manufacture and design, and to indicate the influence this winding has on the performance of a machine.

Reasons for chording the winding. In general, the chorded winding has been adopted to facilitate the manufacture of arma­ture windings. As generators are manufactured, there are certain standard frames used for a number of ratings at different speeds and voltages. Group windings, with the number of slots per pole per phase equal to an integer, are generally preferred, and the number of conductors is fixed within a limited range for a given voltage. This often necessitates the use of a chorded winding in order to get the proper effective number of con­ductors. This is especially the case for low-voltage machines of large size. Further, a winding often works out in such a way that a better arrangement of conductors in the slot can be ob­tained through chording. A two- or a four-pole high-speed gen­erator is another example where the chorded winding facilitates manufacture. Such a machine will naturally have a com­paratively small bore, and if open slots and form-wound coils are used, it is impossible with a coil-throw equal to the pole pitch to bring the coil through the bore of the armature without bend­ing it entirely out of shape. The only solution, therefore, is to chord the winding a sufficient amount to allow it to pass through

657

6 5 8 BACHE-WIIG: PITCH WINDINGS [ J u n e 29

the bore. In this case, therefore, the chorded winding is of great advantage, as it permits the use of form-wound coils. This may not hold in cases where the coils are made in halves.

With regard to the construction of the end-connections of form-wound armature coils for large alternating-current gen­erators, especially for a generator with a small number of poles, the space occupied by the end-connections is considerably smaller for a chorded winding than it is for pitch, even taking ri to account the increased number of armature conductors made necessary by the chord. The effect of chording upon the num­ber of armature conductors is to increase the number in the ratio of the sine of half the electrical angle between the two sides of the coil, whereas the length of the end-connection and the distance the coils build out decreases directly in proportion to the electrical angle. The result is a saving in space. This is of particular benefit to all two-pole machines, but applies also to four- and six-pole machines above 500 kw. It may also be of advantage to chord the winding for these reasons for smaller machines when wound for high voltage.

Take, for example, a 300-kw. 11,000-volt three-phase 500-rev. per min. 25-cycle generator. This machine has six poles, and with six slots per pole per phase will have 108 slots total. Having form-wound coils with the coil-ends extending in a parallel plane to the shaft, one coil per slot, and a pitch winding (1 and 18) the distance between the armature iron and the extreme end of the coils is approximately 16.5 in. Between adjacent coils 0.25 in. air space is provided. Chording this winding down to 1 and 14, or 130 electrical degrees, reduces the above distance to approximately 14.9 in. or decreases the width of the machine 3.2 in. The same winding arranged for two coils per slot, builds out approximately 20.5 in. for pitch winding and 16.75 in. for throw 1 and 14. This means a 7.5 in. reduction in all-over width of the machine. The width of the armature iron being 8 in., it can readily be seen that this insures relatively large saving in space. As indicated by the above dimensions, the winding with two coils per slot extends farther beyond the armature core than does the winding with one coil per slot, and, accordingly, chording the winding is more ad­vantageous for a two-coil-per-slot winding.

As stated above, space can be saved in the way the coils build out even for a six-pole, 300-kw. machine. As space is saved,

1908] BACHE-WIIG: PITCH WINDINGS 6 5 9

the mean length of one armature turn is reduced. On the other hand, the number of conductors on the armature is increased, and thus a certain throw will give the most efficient winding in regard to copper loss and amount of copper. Taking the above mentioned 300-kw. generator and working it out on the basis of equal iron losses, with one coil per slot there is practically no difference in the weight of copper with different throws— the decrease in length of mean turn is balanced by the increase in the number of turns. With two coils per slot there is a saving of approximately 2 5 % in the weight of copper and of copper loss in favor of the chorded winding having coils lying in slots 1 and 14 over the pitch winding having coils lying in slots 1 and 19. The gain by reducing the throw, therefore, amounts to gaining space for the one-coil-per-slot winding only, and means a saving in space and a reduction in copper loss and weight of copper as well for the two-coil-per-slot winding.

As mentioned above, the winding with two coils per slot builds out farther than does the winding with one coil per slot, and the comparison between the pitch winding and the chorded winding will, therefore, show up more in favor of the winding with two coils per slot.

As the six-pole 300 kw. generator here referred to is a com­paratively small machine, it is evident that for large generators, or generators with a smaller number of poles, the above figures will show up still more favorably for the chorded winding; the example indicates that even down to this size of machine it is advantageous to chord the winding.

One may say that chording the winding is to take the copper out of the end-connections and put it in the slots, wrhich is another point in favor of the chorded winding, for it is easier to get rid of the heat in that part of the coil which is imbedded in iron than it is to cool the end-connections of the winding. The ventilating conditions, therefore, are often improved by chording. As above stated, this applies particularly to large machines and windings having a comparatively large throw.

It is stated above that the length of the end-connections de­creases in proportion to the chord and that, even if the weight of the copper is not decreased, the chording has the effect of decreasing the amount that the coil-ends build out. As the question of bracing the coil-ends of a generator with a small number of poles and a large throw is of great importance, it will readily be seen that shortening the end-connections is a great

6 6 0 BACHE-WIIG: PITCH WINDINGS [ J u n e 29

benefit in this respect; it makes them stiffer, so that even if coil supports are used, both in the case of pitch winding and chording, the chorded winding is superior in mechanical strength.

It may be argued in connection with the above that a chorded winding requires heavier insulation of the end-connections than does a pitch winding as the phases are intermixed and points of higher potential are brought together. As a rule it is true that a chorded winding, will have more points of higher poten­tial between adjacent coils than will a pitch winding, but con­sidering that the coil-ends for larger generators always should be arranged with an air-space between adjacent coils, and further that they are braced and prevented from touching one another, in only extreme cases will it be necessary to pro­vide for any extra heavy insulation. In an ordinary pitch wind­ing, points of high potential are brought together at the beginning of the phases. As a rule no extra heavy insulation is provided for at such points. Considering the part of the coil lying in the slot, even if the full-line voltage exists between two coils in one slot, it should not cause any trouble as each coil is already in­sulated against ground.

The effect of chorded winding upon armature reaction. As, for a given voltage, the effective number of turns 'must be the same whether the winding is pitch or chorded, the effective number of armature ampere-turns is also the same in both cases; conse­quently the demagnetizing effect will remain practically un­changed. The chord, however, has an influence upon the self-induction of the machine. This effect is very much the same as in the case of an induction motor, a subject considered at length in a paper read before the Institute.* The reducing in-leakage, and the coil-end leakage, a s pointed out in that paper, could be applied to similarly wound alternating-current gener­ators. In many cases, however, the self-induction does not have much influence upon the short-circuit ratio, as it is small com­pared with the demagnetizing ampere-turns, and, consequently, a change in self-induction will not change the short-circuit ratio to any extent, so that in ordinary cases the self-induction can be figured without considering the chord. There are cases, however, where the decrease of the self-induction due to the chording of the winding has to be carefully considered. One

* F r a c t i o n a l P i t c h W i n d i n g s for I n d u c t i o n M o t o r s , b y C . A . A d a m s , W. K . C a b o t a n d G . A . I r v i n g , J r . , N i a g a r a F a l l s , J u n e 28 , 1907. fluence of the chording upon the slot leakage, the tooth-tip

1908] BACHE-WIIG: PITCH WINDINGS 6 6 1

such case is when a delta connection is used for a three-phase generator with chorded winding with two coils per slot. It is a well known fact that when the wave-form is not a sine, the higher harmonics present in such a winding cause currents to flow round the delta. In most cases these currents are small and the loss due to them is negligible. This, however, does not hold in the case referred to ; for as the same current flows in the

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three legs of the delta through all the coils in succession the slot and the tooth-tip leakage is eliminated for those slots in which the current flows in opposite directions, thus reducing the self-induction of the circuit. The self-induction, however, is the main thing that opposes the flow of this current, and thus it can easily be seen that when the chording of a delta-connected winding is carried too far excessive internal currents may be

6 6 2 BACHE-W11G: PITCH WINDINGS [ J u n e 29

induced in the winding, and, consequently, losses will arise. A one-coil-per-slot winding with the same chording will have far less influence upon the local currents flowing, as in this case the sides of the coils opposing each other do not lie in the same slots. Chording the two-coil-per-slot delta-connected winding down to 120 electrical degrees, cuts out the part of the self-induction due to slot and tooth-tip leakage so far as the internal circulating-currents are concerned, and thus the only reactance left to

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oppose these currents is that of the coil-ends. This is the worst condition for a delta-connected winding.

It may be added that the chording of a two-coil-per-slot winding has also some influence upon the eddy-current losses set up in the armature conductors. As is well known, eddy-current losses are set up in the conductors, and, in cases of large copper section are considerable. The chording has the effect of bringing conductors belonging to different phases into the same slots, and thus the currents flowing in these conductors are not

1908] BACHE-WIIG: PITCH WINDINGS 663

in phase, which again tends to reduce the eddy-current losses. The effect of the chorded winding upon the wave-form. If the

field form of the generator follows a sine wave, the chording of the armature winding will not change the form of the electro­motive force wave; the wave-form will remain a sine wave. The more the field form departs from the true sine wave, the more will the influence of the chord show up in the shape of the wave­form. In the case of high-speed generators with a small num­ber of poles, it is often, for mechanical reasons, not possible

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to bevel the poles at all, or else it is not possible to bevel the poles in such a way as to give a smooth field form approximating a sine curve. At the same time a generator having a small number of poles will usually have a large number of slots per pole per phase, so that this will tend to smooth out the wave-form and make it approximately a sine wave.

Considering a generator having a cylindrical field construc­tion, as in the case of a two-pole turbo-generator, the field form will be approximately as shown in Fig. 1, curve 1. For this held form the electrorriotive force wave-forms are plotted in

6 6 4 BACHE-WIIG: PITCH WINDINGS [ J u n e 29

Fig. 1 for a three-phase Y-connected winding having four slots per pole per phase ; the wave forms are plotted for pitch winding and for chord winding: 1 and 10, 1 and 8, and 1 and 6. It will be seen that the chord 1 and 10 improves the wave-form, but that 1 and 8, and 1 and 6, are distorted.

For the same winding and the same throws, the wave-forms of each leg are plotted in Fig. 2; these wave-forms would also be obtained when connecting the winding in delta. As is to be expected, these wave-forms are in all cases considerably more

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distorted than those shown in Fig. 1 and indicate the influence of the higher harmonics.

Figs. 3 and 4 show the wave-forms for the same field forms and same number of slots per pole per phase when the winding is con­nected in Y and delta, but with two coils per slot. As the phases by these combinations are more distributed over the pole face,

v the wave-forms are less distorted than for the one-coil-per-slot winding; in the case of the Y connection the shape of the wave approximates as nearly a sine for the chord 1 and 6 as it does

1908] BACHE-WIIG: PITCH WINDINGS 6 6 5

for the pitch winding. The wave-forms in Fig. 4, however, show evidence of higher harmonics of similar nature, but less pronounced than the one-coil-per-slot winding, Fig. 2.

As noted above, these wave-forms are plotted for a nearly rectangular field-form. The more the field-form approximates a sine curve, the less will the chord distort the shape of the wave. However, it is evident that the chord does have an influence upon the wave-form, and when chorded windings are used the wave­form should, therefore, be considered.

Conclusion. In determining the most efficient amount of chording, so many ppints are to be considered in each case that no general rules can be formulated. In cases where the chord is not made necessary solely for mechanical reasons, the most efficient chord will depend upon the number of poles, the ratio of pole-pitch to pole-length, the voltage, and the size of machine. These must be worked out in each individual case. The reasons then for chording the winding are:

1. To obtain the proper number of effective turns. 2. To enable form-wound coils to be used in generators of

small bore and few poles. 3. To reduce the space occupied by the end-connections. 4. To improve ventilation. 5. To save copper and insulation.