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This paper presents an alternate approach for modeling of steady state performance of large turboalternators including the effects of magnetic saturation. To avoid the superposition limitations of the conventional d-q approach, a sectoral model of a pole of the machine is developed and solved iteratively. The computational effort is orders of magnitude less than for a finite element solution. Results from the proposed model are compared with those from a conventional d-q model and with measurements made for a wide range of load conditions on a 588-MVA turbogenerator.

This paper presents alternative equivalent circuits for modeling the steady state frequency response (SSFR) data measured for turboalternator synchronous machines. These models provide direct representation of the frequency-dependent skin-effect properties of the dampers and rotor iron. The parameters are determined by matching the measured data to the model frequency response using standard optimization methods. The accuracy of matching is comparable to that of conventional third-order d-q models but the required number of parameters is reduced.

The adjusted synchronous reactance method has traditionally been used for prediction of field current and load angle steady state operation of turboalternators particularly those with negligible saliency. In this method saturation is associated with the air gap reactance. This paper notes that saturation in the stator is dependent on the total stator flux while that in the rotor is dependent on net rotor flux. An alternate equivalent circuit model is proposed in which these effects are represented separately. The results for these two models are compared with load measurements. For most load conditions, both models give good results with a small advantage in angle accuracy for the proposed model. For highly inductive and capacitive loads there is however a considerable difference.

This paper elaborates on a new approach introduced in an earlier paper for the steady-state and transient analysis of synchronous machines and demonstrates the validity and accuracy of this model for system studies. The approach is based on developing an equivalent flux linkage circuit model from the dimensions and material properties of the machine. The model provides inherent flexibility for representation of magnetic saturation, deep bar effects, and saliency. The paper includes a number of example applications in which the analytical results are compared with lest results and with those obtained from conventional analysis based on Park's two axes machine model. >

A method of reducing ripple torque, i.e., the sum of cogging and commutation torques, in permanent-magnet motors without skewing is proposed. The ripple torque for a given range of stator current can be substantially reduced by shifting the pole pairs by half a slot pitch and by choosing the value of magnet width so as to minimize the second-order component of the cogging torque. The method is confirmed by the finite-element analysis of permanent-magnet motors with both radially magnetized and parallel-magnetized magnets. The optimal magnet width of the experimental motor is 6.18 slot pitches for the radially magnetized magnets and 5.80 slot pitches for parallel-magnetized magnets. >

Variable-speed permanent (PM) magnet motors are being used in an ever-increasing range of industrial and commercial applications. The objective of this paper is to provide a basis for optimizing the design of such permanent magnet motors and, through this, to provide insight into a comparison of PM motors with other types of drive motor. First, design models are presented for the approximate analysis of torque capability, losses, thermal characteristics, magnet protection and power factor control. These models are then used in an optimization program using sequential unconstrained minimization techniques to produce designs for a wide range of motor torque ratings. In order to examine the potential for large PM motor drives, the design criterion chosen for emphasis in optimization is the minimum total lifetime cost, including the cost of losses. The high efficiency and good power-to-weight ratio of the optimized PM motors leads to a total present value cost which is expected to be significantly lo...

Methods of optimizing the design of electrical machines are discussed. The augmented Lagrangian multiplier method is described, and an algorithm for this method is introduced. The method is compared with the more familiar exterior penalty function method using, as an example, the cost optimization of permanent magnetic variable-speed drive motors. The improved method is shown to be superior, both in its ability to reach an optimum consistently and in the number of required iterations. >

An equivalent circuit approach is presented for synchronous machine analysis. The approach provides a detailed treatment of magnetic nonlinearity without excessive computational complexity. The number of parameters is typically in the range of 30 to 100, in contrast with 13 to 19 in conventional linear models and with 2000 to 10000 for finite-element analysis. The models developed are intended for use with digital simulation software in the solution of transient, asynchronous, and synchronous steady-state situations. >

Permanent magnet (PM) motors offer potential energy savings as compared with induction motors because of the virtual elimination of rotor loss and the reduction of stator loss from operation near unity power factor. In PM machines, iron losses form a significant fraction of the total loss partly due to the nonsinusoidal flux density distribution. Design optimization therefore requires good means of predicting these iron losses. Finite element analysis can be employed but this approach is cumbersome and costly when used in the many iterations needed in optimizing the design. This paper presents a set of improved approximate models for the prediction of iron loss. They can be used in design optimization programs and, since they are directly related to machine dimensions and material properties, they also provide quick insight into the effects of design changes. A time-stepped finite element method is employed to evaluate the iron losses in a range of typical PM machines and the results are used to evaluate the adequacy of the models. The predictions of overall iron losses are then compared with measurements made on two PM motors.

It is pointed out that the conventional approach to core loss prediction using the Fourier series of the space wave of air gap flux density is not applicable to surface mounted permanent magnet (PM) motors. An alternative approach based on the concept that eddy current losses are proportional to the square of the time rate of change of the flux density is presented. Expressions are derived for predicting hysteresis and eddy current losses in the stator teeth and yoke. Prediction of core losses is compared with measurement of losses on a four-pole PM motor, confirming the applicability of the proposed approach. >

For many years, induction machines operating in the balanced steady state have been represented for analysis by the conventional “T” form of equivalent circuit. Simplification of this circuit to expedite analysis has normally involved approximation This paper presents a number oE simplified equivalent circuits which preserve the accuracy of the “T” circuit and to some extent improve on it by more appropriate representation of saturation and core loss. Experimental confirmation of this improvement is included. The new circuits are denoted as “T” and “inverse-T” because of their inductance configuration.

This paper reports on design and experimental studies, currently being conducted in Canada, of an electrodynamically-levitated passenger vehicle system. Using a flat-topped guideway, the vehicle is levitated by superconducting magnets interacting with aluminum strips. It is propelled by an inverter-driven, track-powered linear synchronous motor. Control, guidance and damping systems are discussed. Propulsion concepts have been tested in full scale on a wheel test facility.

This paper presents an analysis and experimental verification of the operating point stability of a synchronous motor supplied from a current source inverter with simple frequency control of motor speed. The effects of magnetic saturation in the motor and of inverter imperfection are included in the analysis. In contrast with earlier analyses based on an ideal inverter, it is shown that the inverter parameters have a dominant effect on stability.

This paper explores the use of linear synchronous motor control to provide active damping for magnetically-levitated vehicles. Using a single LSM, only heave and surge damping can be provided, but, with a dual LSM, roll and yaw damping can also be achieved. The paper gives design data applicable to the reference design of theCanadian 500 km/h Maglev system.

This note presents some experimental results relating to the effect of applied voltage waveform on the complex fundamental permeability of a ferromagnetic-cored inductor and on the phase angles of the harmonic complex permeabilities. These results may be useful in interpretation of subharmonic and other effects in circuits containing nonlinear cores.

This paper describes a single-phase single-winding induction motor which is self-starting without the use of a shading winding. Starting torque is produced by a combination of several stator asymmetries: an airgap under the main pole which is-tapered down in the direction of rotation, poles without windings in the quadrature axis with solid iron flux bridges to the lagging sides of the main poles, and yoke sections which are larger on the leading than on the lagging sides of the main poles. A qualitative explanation of the action of these asymmetries is presented using equivalent circuits.

This paper presents some experimental results obtained from a small homo-polar linear synchronous motor which has been tested on the two-metre test wheel facility at the University of Toronto. The primary of the motor has both armature and field windings while the secondary consists of alternately-placed solid iron poles on the wheel rim. A short three-pole primary has been used so that end effects are accentuated. Test results are presented over a wide range of operating speed, load angle and winding currents. These results indicate that the motor is a promising contender for urban transit propulsion.

This paper examines the possibilities of designing large, integral-horsepower hysteresis motors to have efficiency and power factor comparable with that of induction motors. Scaling techniques are used, together with a previously published analytical method, to scale up an existing laboratory hysteresis motor of 3 kW rating. The resulting design for a 200 kW hysteresis motor is predicted to have an efficiency in excess of 90% and a power factor in excess of 70%.

This paper develops steady-state time harmonic expressions for synchronous motors. Using these expressions, the current harmonics and waveforms for motors supplied by variable-frequency solid-state power converters can be predicted. Such waveforms are particularly useful in the design of inverter commutation circuits. The models include the effects of saliency and dampers. Experimental results are included to confirm the analysis and show its limitations.

Design of inverters for use with induction motors requires a knowledge of the impedances of the machine to harmonics of the supply frequency. This paper presents an harmonic equivalent circuit and describes how its parameters may be obtained. It shows that, when the harmonic current magnitudes and relative phase angles are such as to produce phase modulation of the rotating field, the harmonic magnetizing inductance is equal to the fundamental saturated magnetizing inductance. When the current harmonics produce amplitude modulation of the rotating field, the harmonic magnetizing inductance is equal to the incremental slope of the fundamental magnetization curve at the point of operation. Measurements made with phase currents having controllable harmonic content are presented to corroborate the theory.

This paper describes a linear synchronous motor which has been designed to propel a 500 km/hr electrodynamically-levitated vehicle. Superconducting magnets on the vehicle interact with an aluminum-cable winding built into the guideway. Following a description of the motor, a coupled-circuit model is derived and used to optimize the winding Configuration and to predict the performance of the motor. An inverter which acts as a controllable current source is used with the motor.

This paper investigates some of the potentialities and limitations of the technique of scale modelling as it applies to magnetic field problems. Simple relations for modelling static and dynamic linear devices are presented first. Particular attention is then given to the problem of scale modelling of nonlinear ferromagnetic devices. While static nonlinear fields can usually be modelled with good accuracy, time-varying fields in nonlinear ferromagnetic materials have severe modelling limitations.

An adaptation of Parseval's theorem is used to compute the pitch torque produced in an arc-type single-sided linear induction motor, directly from the Fourier transforms of the air gap magnetic field components. Results predicted through this approach are shown to agree favourably with measurements made on a 2-m diameter test wheel facility.

This paper presents an analysis and experimental verification of the operating point stability of a synchronous motor when supplied from a current source inverter provided with power factor control. The control system acts to inject the stator current at a controlled angle related to the stator voltage. The effects of magnetic saturation and inverter imperfections are included.

Magnetic fields produced by superconducting magnets on high speed guided vehicles may produce intolerably large eddy losses in armature and stabilization windings as well as in structural Steel components unless proper precautions are taken. This paper describes an approximate method of calculating the eddy losses and illustrates the method by calculating the losses for a proposed linear synchronous motor.

This paper examines a number of the assumptions which are frequently made in the analysis of linear induction motors. Thrust and attractive force measurements made on a 2-m diameter test wheel fitted with an iron-backed aluminum sheet secondary and an arc-type primary are compared with results from three-dimensional field analyses. Among the effects which are examined in the paper are the curvature of the machine, the winding overhang, the finite permeability, conductivity and thickness of the backing iron.

We have tested a large superconducting linear synchronous motor designed for high-speed magnetically levitated vehicles. A single superconducting magnet, from the array of 45 carried by the proposed vehicle, interacts with guideway windings mounted on the rim of a 7.6 m diameter rotating wheel. The split 3-phase "stator" windings are energized from a variable-frequency 40 kVA current-source inverter power supply. All forces and torques developed on the magnet have been monitored over the complete 360° cycle of force angle for a range of suspension heights, lateral displacements, and pitch, roll and yaw angles, at speeds up to 100 km/h. Controlled starting, stopping and section entry have been demonstrated. The results are in excellent agreement with analysis based on mutual inductance computations and on a coupled circuit model of the machine. Highlights of the results are discussed.

This paper describes a drive in which a wound-rotor induction motor is supplied through a static-magnetic power modulator. The drive provides accurate, continuously variable control of speed at any setting up to synchronous speed in either direction of rotation. Other features of the drive are its low-speed regulation, its provision for acceleration and braking at controlled torque, with nearly linear transient response, low cost, and high reliability.

A magnetic frequency tripler is a nonlinear magnetic system which is used for the production of triple-frequency output from a 3-phase fundamental frequency source. Although triplers have been used extensively for certain applications, the design of these devices has until now been largely empirical. Earlier papers1,2 have presented limited analyses of magnetic frequency-tripling devices and the authors have previously reported on an equivalent-circuit approach to the analysis and design of these devices.3 This latter approach was still partly empirical in that the parameters from which the equivalent circuit was derived had to be determined experimentally.

Most equivalent circuit models for synchronous machines have either neglected saturation or used only one saturable reactance which was made a function of one or more machine variables. The approach of this paper is, first, to determine the regions of magnetic saturation and to identify the magnetic flux variable on which each depends. Analytical models are then developed in which each saturable region of the machine is represented by a nonlinear parameter, the value of which is dependent on only one node voltage.

A simply constructed device, combining the benefits of static switching and static power modulation, which may be employed to control a standard 3-phase induction motor is described. Inherent reduced voltage starting and reversal without switching of the main supply lines are features of the device. Methods of performance prediction sufficiently accurate for system design requirements are given. Such divergencies as exist between predicted and realized performance for an experimental system consisting of device and standard motor are explained.

Experimental work is described which indicates the feasibility of making minor loop loss predictions in devices which use permanent magnet materials. The methods of making these loss predictions and some general conclusions about losses are discussed. Minor loop loss predictions are important in any device in which the material undergoes high-frequency operation along recoil or incremental permeability lines. However, little has been published about minor loops in permanent magnet materials. In Alnico 5, the hysteresis (zero frequency) component of the minor loop is found under certain conditions to exhibit a small secondary B/H loop superimposed upon the major loop. The behavior of this secondary B/H loop with variation of temperature gives insight into the behavior of one of the phases of the material and shows that improper metallurgical heat treatment can degrade the over-all permanent magnet characteristics.

A major constraint on the performance prediction of a hysteresis machine arises from the parasitic losses associated with the rotor magnetic material. These losses can be high enough to absorb much of the developed torque, particularly for small sizes and large numbers of poles. In this paper the phenomena which cause parasitic losses are examined in detail. Analytical expressions are developed to predict these losses in terms of the air-gap field and the stator current.

This paper describes a controllable direct-current supply in which the current is essentially independent of the load and in which very low ripple is achieved at essentially all values of controlled current output. The system consists of a 3-phase saturable reactor with a high-impedance control circuit used in conjunction with uncontrolled rectifiers. An analysis of the system is presented and experimental results are given.

A method of analysis for three-phase inverters is described. The method is based on Park vectors [1], [2] and predicts the waveforms of inverter quantities under various load conditions. The procedure discussed can be used to determine the commutation sequence of a pulsewidth modulated inverter. The current distribution of the inverter can be obtained from the current vector. The vectors of the inverter voltage and currents are determined for passive R-L and R-C loads. Oscillograms of the current vectors are shown for different loads.

Part I of this paper presented an analysis of an idealized polyphase hysteresis machine having a radial-flux type of rotor. In this Part II, a hysteresis machine with a circumferential-flux type of rotor is analyzed. Using a rectangular loop approximation to the B-H characteristic of the hysteresis material, the flux density distribution in the machine is found and an equivalent circuit is developed. An improved model of the B-H loop is then used, and two approximate analyses are developed for this improved representation of the machine.

A variable-speed drive is described in which a 2-phase induction motor is energized by power modulators of the frequency-doubler type. The system provides continuous and reversible control of motor torque. In comparison with similar drives using conventional magnetic amplifiers this system has the advantages of simplicity, high efficiency, inherent zero stability, and reasonably flat torque-speed characteristics. Both steady-state and transient characteristics of the drive are described and analyzed.

Keen interest in the design of Permanent Magnet (P.M.) synchronous motors is being fuelled by continuing developments in permanent magnet material technology. The most recent of these developments has been in the introduction of Neodymium-Boron-Iron (N d BF e ) with residual flux density of 1.23 T and energy product (BH max ) of 320 kJ/m3. However a continuing difficulty with the analysis of permanent magnet motors, irrespective of their magnet composition, is the prediction of the direct and quadrature axis reactances. This is particularly the case with motors having permanent magnets imbedded in the rotor iron below the cage winding. The purpose of this paper is to present equivalent circuit models for such interior-type P.M. motors and develop simple analytical expressions for the calculation of axis reactances. Computed reactances including saturation effects are presented along with experimental values for verification.

Cogging torque in a permanent magnet motor, which arises from the interaction of the rotor magnets with the steel teeth on the stator, can be reduced by skewing the stator teeth, but only at the expense of added complexity in stator construction and some loss of output torque. It is shown that by appropriate choice of the angular width of the magnet relative to the tooth-plus-slot dimension, the cogging torque can be reduced to about 1% of rated torque. A further reduction to about 0.3% resulted from a rotational shift of one pair of poles with respect to the other pair in a four-pole motor. The analysis of cogging torques with both surface mounted and inset magnet rotors as well as experimental confirmation are reported. >

Effects of samarium cobalt permanent magnet on the steady-state performance of hysteresis-reluctance motors are presented. Based on the parallelogram approximation of the B-H loop for the semi-hard hysteresis materials of 36% colbalt-steel and Alnico 5, analytical expressions to predict the motor terminal characteristics are given. Experimental verification of the theoretical analysis is also provided. It leads to some useful conclusions, enabling the designers to choose between the types of permanent magnet materials for different drive requirements.

A permanent magnet motor with power semiconductor supply and shaft position sensing can be constructed using radially- directed high energy magnets on its rotor. This paper presents equivalent circuit models for such motors. The model parameters are related to the motor structure and dimensions. Computed values of parameters are compared with those measured from two experimental motors with different rotor construction.

A linear synchronous motor has been designed to propel a 480 km/h magnetically levitated passenger vehicle. The paper describes the motor and presents results of tests which have been performed on essentially full-scale components of the motor using a 7.6 m-diameter test-wheel facility. Controlled starting, acceleration, cruising, deceleration and transient operation have been demonstrated. A 6-component force balance has been used to measure the three forces and three moments acting on a single stationary superconducting magnet due to its interaction with the split 3-phase windings mounted on the rim of the test wheel and energized by a variable-frequency current-controlled inverter power supply. Measured forces and terminal characteristics over complete cycles of force angle are claimed to be in agreement with analysis based on a coupled circuit model of the machine and mutual inductance computations. Moments were measured to be small under all operating conditions. Two modes of control have been demonstrated. The alpha -scheme, proposed for a full-scale system, maintains the angle between induced voltage and phase current at a value which optimizes the motor characteristics, i.e. inverter Mva rating, etc. beta- control, which may be required for starting, uses vehicle position detectors to fire the inverter thyristors at appropriate times.