## Power apparatus and electric machines

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- Electrical and electronic engineering [61]
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With the usual methods of connecting static capacitors as a reactive-power source on the primary or tertiary of a convertor transformer, their latent ability to produce a rapid discharge current, which will directly assist the commutation process and so reduce commutation angle, is not utilised. By connecting the capacitors to the secondary winding (valve winding) of the convertor transformer, appreciable reduction of commutation angle can be obtained, resulting in a saving in reactive-power consumption, which is particularly important in the case of invertor operation.Investigation shows that the connection of capacitors alone on the valve winding produces transient overvoltages, and that these can be eliminated by incorporating the capacitors in a suitable filter configuration. This also results in improved filtering of current harmonics compared with primary- or tertiary-connected filters. Other advantages and disadvantages have been assessed, and theoretical calculations have been experimentally confirmed. Provision of capacitive filter circuits on the transformer secondary is particularly commendable for convertors using semiconductor rectifiers.

A solution is presented for the eddy-current loss occurring in a solid steel cylinder surrounded by an air gap, owing to the application of a uniform pulsating m.m.f. This approximates to the practical condition of a steel clamping bolt inserted in a laminated machine core. It is shown that the demagnetising effect of the eddy currents is important within the region of practical interest. Curves are drawn which illustrate the relative importance of the various parameters in determining the loss. The presence of even a small gap is a dominating influence.

In the paper it is shown that a reluctance-machine rotor of the conventional salient-pole type can be successfully operated, not only with a stator winding developing the same number of magnetic poles as the rotor has salient poles, but also with a winding developing twice this number. The mode of operation at the lower speed is explained in the light of a recently described machine,^{1} in which salient poles are replaced by peripheral segments. The theory of low-speed operation is developed, and calculated results of performance are shown to be in good agreement with experimentally obtained values for a number of different machines. It is concluded that, for a single-winding two-speed machine, it is possible to design for either equal torques or, with mesh connection, equal powers at both speeds. Good efficiencies and approximately equal power factors are possible at both speeds.

The theory presented in the paper attempts to explain the origins of load losses in detail. It includes an analysis of the losses produced, at any given value of slip, by current flow through the rotor iron between two adjacent bars, owing to the imperfect insulation of the squirrel cage. The theory also includes a calculation of the eddy-current and hysteresis losses in the rotor teeth, caused by the high-frequency harmonic fluxes that penetrate them. It shows how eddy currents in the iron surface can reduce the value of the differential harmonic leakage of a bar, thus allowing more harmonic bar current to flow, and hence more *I*^{2}*R* losses to be produced. It discusses how the effective skew differs from its geometrical value, depending upon the width of the rotor bars. The theoretical formulas developed are used to predict the torque/slip characteristics of three 7½hp squirrel-cage induction motors, and the results show good agreement with the experimental curves, thus verifying the validity of the theoretical argument. A simplified theory of interbar currents is finally given, and the effect of skew and slot combination on the magnitude of the load losses, under normal operating conditions, is discussed.

Transformer-core vibrations, which are caused by magnetic and magnetostrictive forces, are responsible for the noise radiated by the tank. Since the core is a structure consisting of distributed mass and stiffness, it has an infinite number of natural frequencies, one of which may coincide with one of the harmonics of the above forces, resulting in increased noise level. Because of the nonuniformity of the core steel, vibrations may be excited, both in the plane of the core and normal to it. The paper sets out to show how these natural frequencies can be calculated for both directions, taking longitudinal vibrations, shear deformation and rotational inertia into account. A distinction is made between cores having a large overlap at the joints and those having mitred joints with small overlap. The correctness of the mathematical model and the validity of the assumptions made for the calculations were checked on two models and two transformer cores. Satisfactory correlation was achieved between the experimentally determined natural frequencies and those calculated with the help of a computer programme.

The paper discusses the relationship between the eddy currents flowing inside a conducting material and the magnetic field outside. The particular problem of a current sheet carrying a sinusoidally distributed current parallel to a conducting magnetic slab is examined in detail. It is shown that this mathematical model is relevant to the calculation of eddy-current losses in many types of rotating machine.The investigation shows that the eddy-current loss in any conducting surface can be simply related to the tangential component of the field at the surface, if the problem fulfils certain conditions. These conditions are set out in the paper.As far as the calculation of the tangential field is concerned, it is shown that electromagnetic images (zero permeability) can be used to represent plane surfaces approximately for a surprisingly wide range of materials, even if these are magnetic. For more accurate representation, modified images are introduced. These may be difficult to formulate, but, where the analytical solution is known, modified images can shorten the labour of computation. Some experimental verification of the method of modified images is included in the paper.

In conventional machines, the assumption of cylindrical symmetry simplifies theoretical considerations considerably and leads to the belief that there is no essential difference between the operation of an a.c. machine in which all the coils of each phase of the primary winding are connected in series and one in which they are in parallel. The paper shows that such an assumption is not valid for machines with asymmetric magnetic circuits.Linear motors are used to emphasise the phenomena discussed, since the degree of asymmetry in such machines is very large. Methods of end-grading of windings are derived.

Recently, a number of single-winding multispeed induction motors have been devised in which some unbalance of the windings has been inevitable. This paper sets out to analyse such windings using the balanced applied voltage as the reference. The criteria necessary to form asymmetrical windings which will draw balanced currents are obtained. Particular attention is directed towards the pole-amplitude-modulated type of winding, in which two phases are alike and placed symmetrically about the third. Experimental verification of the theoretical results obtained is given for this type of winding.

The effect of supply frequency on the speed transients of an induction motor due to small voltage and torque disturbances is discussed. The transients which depend on four nondimensional parameters are obtained by a graphical (root-locus) method which could well be followed at the design stage.The transfer functions between speed and small changes in input voltage and torque are given. It is shown that in low-frequency motors a lightly damped transient speed oscillation will occur at a frequency just below the supply frequency, which is influenced only slightly by the machine parameters.

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.