## Power apparatus and electric machines

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In the design of synchronous salient-pole generators and motors, current formulas for the output coefficient express this constant in terms either of the apparent power, speed, length of stator core and gap diameter or of the magnetic and electric loading. The paper develops an analysis in which the output coefficient is expressed as a function of the dimensions of the stator core, the magnetic loading and the electric loading related to the temperature rise of the stator winding, in terms of the thickness of insulation and slot dimensions. The output of the rotor is derived as a function of the pole pitch and height of pole. It is shown that there are two optimum values of the mean flux density in the air gap, and that there is also an optimum value of the electric loading, defined as a function of the width of slot. It is also shown that, for a stator designed in accordance with this analysis, there is one value of the height of rotor pole required to accommodate a field coil to establish the m.m.f. required to balance the armature reaction. The theory is illustrated by a series of curves calculated from the parameters of an existing large hydroelectric generator. It is further shown that the overall dimensions and cost could possibly have been reduced by the application of the principles established in this paper.

The paper shows that the capacitance and inductance distributions within a power transformer can be so synthetised that an acceptable transient surge-voltage distribution can be obtained without necessarily requiring the reinforcement of end turns. This process can furthermore be carried out without contravening practical requirements, in particular without increasing a given transformer frame size. Linear, exponential and hyperbolic-sine distributions are considered in the paper, although the method, in fact, extends to any arbitrarily chosen function of voltage distribution. The effect of a particular distribution on the main geometric parameters of the transformer windings is then established in such a way that they can be incorporated in the transformer design. It is shown that arrangements giving initial and final voltage distributions of exponential and hyperbolic-sine form, respectively, are likely to be satisfactory to the designer.

It is shown that the nonquadrature, tapped-quadrature and shaded-pole forms of single-phase induction motor can be equivalent to a conventional quadrature motor having a common line impedance. It follows that a single equivalent circuit can be used to determine the performance of each form of motor, provided that appropriate values are employed for the circuit elements in each case. In consequence, the same arrangement of a given type of analogue computer can be used to predict the performance of all three special forms of single-phase motor, as well as the conventional quadrature motor. Further, in contrast to some existing equivalent circuits, the presented circuit has the advantage of direct representation of the actual supply currents taken by each form of motor without any transformation of the supply voltage.

The paper analyses the behaviour of induction motors in control systems in response to sinusoidally varying torque distrurbances by using a 2-coil rotor model. It is found that induction motors exhibit resonance and possibilities of instability in response to torque disturbances, and transient torques substantially greater than the steady-state peak torque of the motor may be generated in the region of resonance. It is also observed that, in certain frequency ranges, the speed may be considered as leading the torque disturbances. Extension of previous frequency-response analysis in response to excitation-frequency variations and applicability of the present analysis to constant-net-flux operation are also given.

The problem of travelling electromagnetic waves in multiregion induction machines at power frequencies is examined. Using the concept of surface impedance, a method is derived whereby equivalent circuits can be established in a systematic manner. A method of determining levitation force from a knowledge of the equivalent circuit is developed. Calculation of input and output power is simplified using the approach outlined. The ferromagnetic portions of the multiregion system are assumed to have constant permeability.

The paper is devoted to the development of mathematical models for the analysis of the behaviour of h.v.d.c. convertors during unbalanced a.c. faults. A current-source simulation is used for the convertor in either 3-phase or sequence components representation. The analysis using these models can be adapted for digital/analogue simulation. Using the digital approach, results were obtained for systems with varying degrees of unbalance, and limits of normal operation were established. For normal operation, the degrees of unbalance of the convertor currents were determined. This provides both the pattern and the limits of variation of these currents, which form a valuable basis for the assessment of overall performance of a.c./d.c. interconnected systems.

Earlier papers have discussed the air-gap flux-density distribution in inductor alternators and have verified the theory by measurement. It is the aim of this paper to show that, with a knowledge of flux-density distribution, it is possible to predict the load performance of these machines from the open-circuit curve—an easily calculable starting point.First, the measured open-circuit voltages are compared with those calculated from previous knowledge of the flux-density wave, which in turn has earlier been compared with that calculated from air-gap geometry. By taking the correct components of armature reaction, it is shown that the voltage at any load point can be obtained by combining these with the open-circuit flux distribution, to obtain a resultant flux distribution, and hence voltage. This involves the intersection of generalised curves, expressing the vector-diagram geometry, with the special curve for the particular machine, expressing the open-circuit-voltage/field-current relation. Examples of this method are given both for the experimental machine and for a much larger commercial alternator, and are shown to predict the load curves under widely varying conditions.

The paper presents an analytical and experimental study of the additional losses which occur in induction motors supplied with nonsinusoidal waveforms. Measurements on an inverted induction motor are used to show the importance of losses due to skew-leakage and end-leakage fluxes, and to verify the methods developed for calculating these components. Computed losses are compared with test results obtained on a variety of machines and supply waveforms, and the agreement is shown to be consistently good. The manner in which the losses are related to the machine design and to the supply harmonic content is described.

Depending on the choice of design parameters, an induction machine can produce a cogging torque sufficiently high to give rise to locking at standstill. It is noted that the commonly used method of analysis of these torques, involving permeance waves, is strictly incorrect, and its use in conjunction with the ‘overlap’ method is inaccurate. The way in which cogging torques arise is discussed in terms of the energy associated with the magnetic field in the machine. A new method is described by which this torque variation can be determined from simple equations. Experiments on machines confirm the results of the analysis.

Simultaneous recovery of grading grids has been observed in a multigrid mercury-arc valve without the appearance of grid discharges in the recovery period. From this work it is concluded that a compact valve exhibiting rapid deionisation and recovery to potentials in excess of 250kV may be feasible. Such a valve could readily find applications for h.v.d.c. power transmission and for high-power modulators.

The letter gives details of a method of using a high-power two-phase induction motor as a servomotor in a positional servomechanism. The method utilises a constant-frequency power source and does not have the disadvantage of a permanently excited winding.

In an earlier paper, it was established that a major mechanism of flashover involved the generation of a series of intersegmental arcs, and further relevant work has been carried out on the properties and characteristics of such arcs and on means by which they may be extinguished. The dependence of the flashover voltage (per gap) on gap width, the velocity of sliding and the brush grade have been investigated. This voltage increases markedly with increasing gap width; but, except at low speeds, it is independent of the velocity for a given gap width. The flashover voltage was found to be only marginally dependent on the brush grade when brushes selected from the main types were tried. Sequences of ciné photographs showed a phenomenon known as ‘jetting’, in which molten copper, formed at an upper edge of a segment, is thrown outwards by the pressure of vaporising copper. The method considered whereby short arcs could be extinguished was based on a transverse magnetic field. Under the earlier conditions, the arcs accelerated uniformly; but it was suggested that a terminal velocity should be reached, which has been shown to be correct using additional apparatus. A formula describing the dependence of this terminal velocity on basic parameters has been derived. Further work has been carried out on the practical aspects of extinguishing short arcs by means of an air blast.

The paper includes a survey of the very sparse literature on copper drag and gives a general outline of the metallurgy of commutator bars and copper drag from various sources. Laboratory experiments are described which simulate the production of copper drag, and typical specimens obtained are shown to be very similar to practical examples. The basic cause of copper drag appears to be a vibration and hammering action of the brushes predominantly occurring under low-load conditions. This produces a flowed surface layer on the commutator of heavily cold-worked material. The effects of temperature, time, bar material and sparking or arcing are discussed. Several recommendations are given for reducing or preventing the occurrence of copper drag on bothnew and existing machines.

The paper describes a new measuring technique in which synchro resolvers are used to generate the transformed 2-axis variables from the armature phase quantities. It is applicable to any a.c. machine under dynamic conditions, and the technique has particular significance in the analysis of synchronous machines, enabling much information to be obtained from a single starting test. Frequency-response loci of the axis impedances are readily obtained from an oscillogram of the 2-axis quantities, and in certain cases the loci may be extrapolated to yield the usual machine reactances. The technique also enables the instantaneous electromagnetic torque to be determined and analysed with the aid of the complex admittance loci into components associated with the direct and quadrature axes.

The possibilities of using magnetic, instead of electric, equivalent circuits for eddy-current devices, which have recently been pointed out by Laithwaite, are here explored further. Couplings between distributed flux paths and windings can be expressed in terms of a generalised linkage parameter *N*, which is associated with flux linkage in electric circuits, and with an analogous current linkage in the magnetic equivalent. The magnetic-circuit treatment extends to rotating, as well as to static, devices, and leads to a view of induction machines as nonpassive magnetic elements.The relationships between the energy flow through the terminals, the mechanical forces and the magnetic terminal parameters are examined, and an alternative equivalent circuit, in which the analogue of current is not the flux but its rate of change, is shown to be in many respects a more useful one. The force equations are applicable, in particular, to devices in which induced currents are important.

The asynchronous performance of a synchronous motor, at a given slip, may be estimated from the 2-axis operational-admittance frequency functions *Y _{d}*(

*js*ω

_{0}),

*Y*(

_{q}*js*ω

_{0}). The functions are commonly depicted as frequency-response loci. The frequency-response loci of a laminated-pole motor are shown to be analogous to the traditional induction-motor circle diagram. An accurate theoretical method is given to determine the asynchronous performance from the 2-axis loci, allowing for the effect of armature resistance. In addition, an approximate graphical method is given for the simplified condition when armature resistance is neglected.New equivalent circuits for the solid-pole motor are derived. The new circuits allow for the distribution of flux entering the rotor surface, and for the possibility of complete pole-tip saturation. Impedances, representing the parts of the magnetic circuit containing solid iron, are based on the rectangular magnetisation characteristic, and therefore have a magnitude, determined by the voltage across them, and a constant angle of 26.6°. The impedances are inserted into the equivalent circuits and the operational admittances are calculated by an iterative method. It is shown that the angle of the single effective ‘solid iron’ rotor impedance is found to lie between 26.6° and 45°, depending on the rotor frequency and flux. The method is also applicable to machines in which adjacent pole shoes are connected by end rings.Comparisons are shown between calculated and measured operational-admittance loci and between calculated and measured starting-performance characteristics for the solid-salient-pole micromachine at Imperial College, London, and for ten large solid-salient-pole machines of widely different dimensions and numbers of poles.A method of measuring, without attenuation, the component of oscillating starting torque of a synchronous motor, by measuring the total instantaneous input power, is demonstrated.