## Power apparatus and electric machines

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Polyphase symmetrisation is a new geometrical process for obtaining balanced fractional-slot (irregularly distributed) windings. Practical polyphase windings cannot always comply exactly with the ideal geometry. The paper shows how to calculate the very small residual unbalance, where any exists, with particular reference to 2-speed p.a.m. windings.

Multispeed p.a.m. windings are now well established in electrical engineering practice, particularly for close pole ratios, such as 4/6 poles, 6/8 poles etc. Manufacture of these windings is simple, though the theory is very difficult. One of the key techniques for generalising this theory is a ‘clock diagram’ of a novel type. The paper therefore gives a short analysis and explanation of the clock diagram for p.a.m. windings, as a guide to a more general understanding of the principles involved.

In several respects, the design and performance of 4/6-pole p.a.m. windings present features which are contrary to the earlier and more usual forms of close-ratio pole-amplitude modulation (p.a.m.), and also to certain orthodox concepts relating to the harmonic m.m.f. content of the waveform of an induction motor. A very careful examination has therefore been given, in general terms, to the special features of 4/6-pole windings and to the effects both of subharmonics and of higher-order harmonics on the operation of an induction motor. (This latter part of the paper is of importance in relation to single-speed machines also.) Taking a 4/6-pole winding in 36 slots as an important example, the paper uses it to consolidate earlier p.a.m. windings with a number of later p.a.m. design methods. The differences between ‘sum’ and ‘difference’ modulation are also very fully considered. The whole paper serves to emphasise that pole-amplitude modulation is a general philosophy for polyphase windings, and not a specific design method. In principle, there is no limit to the number of design methods which may be evolved for embodying this philosophy in particular windings.

An alternative method of operation for the well known moving-coil voltage regulator is discussed, and its theory is treated on classical lines. In the new régime, the short-circuited coil is fixed, and the output is drawn from the moving coil, instead of vice versa. A comparison is drawn between this moving-secondary regulator, the moving-coil regulator and the induction-type voltage regulator, which serves to clarify certain basic points in transformer theory. Tests were made on a small laboratory regulator, specially devised for experimental purposes, and some discussion of these tests is included. The same regulator also enables a variety of other educational tests to be performed, the regulator being, in effect, a generalised transformer.

It has already been shown how to obtain 2-speed single-winding squirrel-cage induction motors, using a normal stator with all coils identical, and with only six terminals to the winding. The earlier methods showed how an integral-slot winding may be modulated to give a 2-speed winding for any pole combination, and also how to design a fractional-slot 2-speed winding for pole combinations which do not include a multiple of 6. The fractional-slot windings are the best, and this paper completes the record of close-ratio pole-amplitude modulation in its basic form by showing how to design a fractional-slot winding for any close-ratio pole combination.The performance of machines with such fractional-slot windings very nearly approaches that of a single-speed motor, for both speeds; and it is thought that, for most applications, these fractional-slot windings will supersede the earlier integral-slot ones. Tables of finished winding designs for one pole combination are given in full, together with details of the design methods, which are illustrated by the complete working of one particular design. The basic part of the task of converting the single-winding squirrel-cage induction motor into a close-ratio 2-speed machine has therefore been completed and recorded in full. The application of the same principles to wide-ratio 2-speed machines has been separately described, as will also be certain further developments of the work already recorded.

Previous work on 2-speed single-winding squirrel-cage induction motors, using the principle of pole-amplitude modulation, has now been extended to synchronous machines, and really simple and satisfactory 2-speed salient-pole synchronous motors have been designed, constructed and tested. This paper records the basic principles involved and illustrates these by reference to an industrial 10/8-pole motor of this type, for which test results are given. Such motors can equally well be used as generators, either to give a choice of output frequency for a given speed of prime mover or to maintain the output frequency constant in spite of a change of driving speed.

A 2-speed single-winding squirrel-cage induction motor, with only six terminals and of excellent rating and performance, has been described in several previous papers. The same principles have now been extended to give a 3-speed motor of comparable quality. Only twelve terminals and reasonably simple control gear are required for three speeds. Almost any speed combination can be obtained, the example given in the paper being a motor for 6/8/10 poles, particularly suitable for fan or pump drives.

It has already been shown how an induction motor with a single winding of normal type can be made to give efficient and economic operation at two alternative speeds, using the new method of polyphase pole-amplitude modulation. Various detailed improvements in this method have been devised since it was first developed; but both the original method and the modifications hitherto disclosed are only directly applicable to pole-combinations in which neither pole-number is a multiple of three, or to multiple repetitions of such pole-combinations.The paper discusses further theoretical developments which enable the same principles to be applied for any speed and pole ratio between unity and 1.5; and it describes theory and design methods for 6/8-pole and 6/4-pole machines, as typical examples. For all speed ratios, the winding can be made of coils which are all identical, undivided and of standard type. Six control leads and six terminals only are required in every case, and the control gear is therefore extremely simple, and can be standardized for all speed ratios.The method is so general that, 70 years after its invention, the standard squirrel-cage induction motor has, in effect, ceased to be a single-speed machine, and has become a 2-speed machine at a trivial extra manufacturing cost.

Previous papers on pole-amplitude modulation have described methods of increasing the pole number and reducing the speed, by modulation. The reciprocal possibility has already been pointed out; and it has now been found that, under some conditions, it is better to use modulation to reduce the pole number and increase the speed.The particular form of modulation used in the examples described here gives exceptionally good performance. By way of example, test results are recorded for a small laboratory machine, and for a very large machine made by an industrial company, both for 10/8 poles, and both being very successful. The general conclusions are drawn that, for very many purposes, a 10/8-pole motor is to be preferred to an 8/10-pole one; and that modulation to reduce the pole number of an electrical machine has important industrial possibilities.

An earlier paper has described the basic steps which led to a practical form of 8/10-pole induction motor, of good performance, having only one stator winding. The principle on which this speed-changing motor was based has been given the name of ‘pole-amplitude modulation’. Since the publication of the original account of it, the principle has been further developed, and a number of improvements in the method have been devised and tested in practice on several new forms of 8/10-pole motor. This paper discusses the theory and tests on these new machines, which are of interest both in themselves and for the further light which they throw on the principles of pole-amplitude modulation. The tests were completely successful, and this type of machine is now in the repertory of several manufacturers as an established industrial product.

An original method of changing the speed of squirrel-cage induction motors has recently been developed which enables efficient and economic operation to be obtained at either of two chosen speeds, using a single winding of standard type.The method has considerable generality, but is particularly applicable to speed ratios not very different from unity. The initial tests have therefore been performed on a motor for two speeds in the ratio 5:4, but a variety of ratios can be obtained by using the same principle. The control gear needed is extremely simple.

The paper describes two further and improved 3:1 pole-changing windings which both have only nine control leads, and in which a 60° spread has been used, instead of the 120° spread which was used in a machine previously described. A particular feature of these windings is that the coil pitch is critical, and can have only one value. Full-pitched coils cause very bad crawling effects.

The paper explains a very simple method of much improving the performance of 2:1 pole-changing induction motors. In spite of the extensive use of such machines for a very long time past, windings of standard type, as described in most advanced textbooks, seem always to have been used. The new winding discussed in the paper has given excellent results on test.

A particular type of moving-coil regulator, of exceptional ingenuity, has found wide application over the last fifteen to twenty years, but it is believed that no rigorous analysis of it has previously been carried out. Besides being rigorous, it is thought that the theory here given also facilitates calculations on the performance of the regulator, and test results have shown that the theory is fully and closely supported by practical performance.

An earlier paper has described a very successful pole-changing winding for 3:1 speed ratio; which, however, had the disadvantage of needing eleven control leads and a slightly complicated controller. A new winding is here described^{1} which needs only six control leads and a very simple controller, and which gives greater flexibility in the relative ratings at the two speeds. In addition, this winding can be made to operate efficiently at a third speed, using only nine control leads altogether, giving three speeds in the ratio 6:3:1, and at a fourth speed using thirteen control leads, giving four speeds in the ratios 6:3:2:1. The methods of obtaining the third and fourth speeds are described in the latter part of the paper.Besides being very successful in operation, this asymmetrical winding has a number of unusual theoretical features of very great interest. It is a working testimony to the possibility of permitting various forms of asymmetry and unbalance in electrical machinery without detriment to its operation.

The paper describes the development of a new 3:1 pole-changing induction motor with one 3-phase winding only, in which the performance and rating of a given machine frame for each speed are in all respects nearly equal to the best values that could be obtained from the same frame if it were wound in a normal manner for that speed only. The comparison is equally favourable both for torque ratings and for continuous horse-power ratings, and the machine is free from the crawling torques common in pole-changing motors. The number of control leads (eleven) is not unduly large, and the switch controller required is relatively simple.A simple pole-changing winding which gives a high performance for a 2 : 1 speed ratio is well known and widely used, and it seems probable that the development of a winding giving even better performance for a 3 : 1 speed ratio will find many applications, once its existence is generally known. It is believed that this is the first time a satisfactory winding of this type has been devised, although several comparable but unsatisfactory variants have previously been proposed.

The paper first digests existing information about 3rd-harmonic fields, mainly published previously in piecemeal fashion, and then adapts and extends it into modern form for use in symmetrical-component theory as applied to machines. This theory has provided the basis for a very successful 3:1 pole-changing machine which is described in another paper,^{8} and the present paper includes a number of test results which verify that the theory of 3rd-harmonic fields given here is essentially sound.