Calculation of machine winding electrical parameters at highfrequencies for switching transient studies

This paper describes a multiconductor transmission line approach for calculating the machine winding electrical parameters for switching transient studies. The technique is based upon the solution of the one dimension diffusion equation in the slot of electrical machines. The coil electrical parameters are calculated considering both the magnetic flux in the iron and in the air. Several practical formulations for calculating the winding electrical parameter are proposed which take into account the machine winding design characteristics. The computer models are validated by a comparison of measured and calculated results in two high voltage induction motors     

Transient model of a doubly excited reluctance motor

A transient machine model of a doubly fed reluctance motor is derived by means of winding function and d-q transformation theory. The machine consists of a double-wound stator with four and eight pole sets. The rotor is equipped with six poles. The machine, related to the Hunt motor, has the synchronous speed of a twelve-pole machine. Comparison of simulated results to test results indicates that the higher harmonics in the motor inductances are important for predicting the current waveform     

Characterization of coil faults in an axial flux variable reluctance PM motor

Variable-reluctance (VR) and switch-reluctance (SR) motors have been proposed for use in applications requiring a degree of fault tolerance. A range of topologies, of brushless SR and VR permanent-magnet (PM) motors are not susceptible to some types of faults, such as phase-to-phase shorts, and can often continue to function in the presence of other faults. In particular, coil-winding faults in a single stator coil may have relatively little effect on motor performance but may affect overall motor reliability, availability, and longevity. It is important to distinguish between and characterize various winding faults for maintenance and diagnostic purposes. These fault characterization and analysis results are a necessary first step in the process of motor fault detection and diagnosis for this motor topology. This paper examines rotor velocity damping due to stator winding turn-to-turn short faults in a fault-tolerant axial flux VR PM motor. In this type of motor, turn-to-turn shorts, due to insulation failures, have similar I-V characteristics as coil faults resulting from other problems, such as faulty maintenance or damage due to impact. In order to investigate the effects of these coil faults, a prototype axial flux VR PM motor was constructed. The motor was equipped with experimental fault simulation stator windings capable of simulating these and other types of stator winding faults. This paper focuses on two common types of winding faults and their effects on rotor velocity in this type of motor.     

Standstill frequency-response methods and salient-pole synchronousmachines

Standstill frequency-response (SSFR) literature to date has primarily focused on turbo-alternators, which have a double-cylindrical topology. Synchronous machines driven by hydraulic turbines or internal combustion engines are salient-pole machines whose electrical constants are somewhat different due to construction differences: (1) the salient-pole topology produces a ratio of L_q/L_d of approximately 0.5 as opposed to unity for cylindrical-rotor machines; (2) the salient poles are constructed of steel-sheet stampings rather than forged steel; (3) salient-pole field windings are concentric whereas those of cylindrical rotor machines are distributed; (4) salient-pole generators often have amortisseur windings embedded in the pole faces; and (5) fractional slot/pole/phase (SPPP) stator windings are commonly employed in salient-pole machines whereas turbo-alternators are more apt to be limited to integral SPPP windings. These differences alter time constants, inductances, and transfer functions. This paper provides needed information for the modeling of salient-pole machines for use in simulation studies using a theoretical approach     

Preliminary Evaluation of a Megawatt-Class Low-Speed Axial Flux PMSM With Self-Magnetization Function of the Armature Coils

This paper presents an axial flux permanent magnet synchronous machine (PMSM) with a disk rotor between two stators, which are wound in a tooth-coil technology (a concentrate winding type with subunitary number of slots/pole/phase). This type of winding facilitates the magnetizing inductor function of stator coils. A potential magnetizing system can be envisioned by taking into account that the coil span and the slot pitch are practically identical, the number of tooth-coils and poles are almost the same, and that there are two rotor poles between four tooth-coils (two adjacent tooth-coils on each stator). Thus, a special magnetizing inductor is not required in order to magnetize, pair by pair, the permanent magnet (PM) rotor poles. The number of tooth-coils exceeds the number of rotor poles by one (Ns = 2p + 1). Some aspects of the average performance obtained in both modes of operation-machine and magnetizing inductor-are highlighted by digital simulation. A scale-down demonstrating model also confirmed the feasibility of the magnetizing inductor function of the stator.     

Detection of rotor slot and other eccentricity related harmonics ina three phase induction motor with different rotor cages

Detection of rotor slot and other eccentricity related harmonics in the line current of a three phase induction motor is important both from the viewpoint of sensorless speed estimation as well as eccentricity related fault detection. However, it is now clear that not all three phase induction motors are capable of generating such harmonics in the line current. Recent research has shown that the presence of these harmonics is primarily dependent on the number of rotor slots and the number of fundamental pole pairs of the machine. While the number of fundamental pole pairs of a three phase induction motor usually is within one to four (higher pole pairs are generally avoided due to increased magnetizing current), the number of rotor slots can vary widely. The present paper investigates this phenomenon further and obtains a hitherto nebulous theoretical basis for the experimentally verified results. Detailed coupled magnetic circuit simulation results are presented for a four pole, three phase induction motor with 44, 43, and 42 rotor slots under healthy, static, dynamic and mixed eccentricity conditions. The simulation is flexible enough to accommodate other pole numbers also. These simulations are helpful in quantifying the predicted harmonics under different combinations of load, pole pair numbers, rotor slots and eccentricity conditions, thus making the problem easier for drive designers or diagnostic tools' developers. Data from three different induction machines, namely, a 4 pole, 44 bar, 3 hp, a 4 pole, 28 bar, 3 hp and a 2 pole, 39 bar, 100 hp motor have been used to verify the results experimentally. The simulation and the experimental results clearly validate the theoretical findings put forward in this paper     

Standstill frequency response testing and modeling of salient-polesynchronous machines

Standstill frequency response (SSFR) testing and modeling of salient-pole synchronous machines are presented for two machines with integral and nonintegral numbers of stator slots per pole per phase. Frequency responses at different rotor positions have been investigated to explore the effects of rotor position in a machine with a fractional slot winding, as the electromagnetic fields and the armature magnetomotive forces do not precisely repeat every pole. The test results do not show any significant differences for various direct and quadrature axes rotor positions. The authors obtained a negative value of differential leakage inductance as theoretically postulated in the literature. The pertinent features of testing and modeling of salient-pole synchronous machines are described to point out the differences with SSFR testing of round rotor turbogenerators extensively published in the literature     

Experimental Verification of Critical-Speed Increase of Single-Phase Induction Machines via Winding Reconfiguration With Solid-State Switches

The concept of online electronic switching of windings will be applied to a single-phase induction motor with two separate windings with different pole numbers p₁ = 4 and p₂ = 6 and an auxiliary winding required for starting. During switchover from the low-speed winding to the high-speed winding, and vice versa, lasting less than a few milliseconds, small electrical torque and speed transients occur. Relying on closed-loop speed control, a smooth speed response is measured. This concept is, therefore, applicable to variable-speed drives, where a large speed range is desirable. Test data indicate that a speed-control range from 600 to 4000 r/min is obtainable with a single-phase induction motor.     

Transient Analysis of Partial Armature Short Circuit in an Electronically Commutated Permanent Magnet Motor System using an Integrated Nonlinear Magnetic Field-Network Model

The simulation of the dynamic performance characteristics of an electronically commutated brushless dc machine system with radially oriented permanent magnets, which is experiencing a partial short in one of its phases, is reported in this paper. The newly introduced integrated field network (IFN) method was used throughout this work. The IFN method, which is detailed in a companion paper, is based on simultaneously solving the dynamic equations of the machine system network, using machine winding parameters (inductances and emfs) which are determined from numerical solutions of the nonlinear magnetic field prevailing in the machine cores for the corresponding winding currents. These field solutions and corresponding machine parameters are updated at every time step of the solution of the dynamic equations. The results presented here document effects of the shorting of a portion of an armature phase winding on the dynamic performance of a 15 hp (11.2 kw), 120 volts samarium-cobalt permanent magnet brushless dc motor. A comparison of the current, inductance, enf, torque and power time profiles of the motor system with and without partial armature winding failure (short) is given here. These studies are of importance in motor system security and redundancy considerations. The dramatic change of the values of machine parameters upon occurrence of the partial short circuits demonstrate that conventional solution methods would have left much to be desired.     

A machine winding model for switching transient studies using network synthesis

This paper describes a computer model for calculating the surge propagation in the winding of electrical machines. The model considers the winding as a combination of a multiconductor transmission line and a network of lumped parameters. The frequency dependence of the winding electrical parameters is calculated and incorporated into the analysis by means of Foster and Cauer circuits. The multiconductor transmission line provides the surge propagation characteristics for the winding model and its parameters are calculated from machine design characteristics. Finally, this hybrid model is validated by a comparison of calculated and measured results inside a high-voltage machine winding.     

Design and Experimental Verification of a Linear Permanent Magnet Generator for a Free-Piston Energy Converter

This paper discusses issues that are pertinent to the design of a linear permanent magnet generator for application in a free-piston energy converter. To achieve the required high power density, high efficiency, and low moving mass, a tubular machine equipped with a modular stator winding and a quasi-Halbach magnetized armature is employed. It is shown that the machine design can be optimized with respect to three key dimensional ratios while satisfying other performance requirements. It is also shown that, when the generator is interfaced to an electrical system via a power electronic converter, both the converter volt-amps rating and the converter loss should be taken into account when optimizing the machine design. The performance of such a tubular generator is demonstrated by measurements on a 10-pole/9-slot prototype machine.     

A three-phase model for surge distribution studies in electricalmachines

This paper describes a computer model for surge distribution studies in the windings of electrical machines. The computer model takes the coil as the basis for the analysis and uses multiconductor transmission line theory to obtain the transference matrix for the winding. Several practical formulations based on machine design characteristics are used for calculating electrical parameters. Flux penetration into the iron core and mutual coupling between coils in different phase windings are incorporated into the analysis. The model was validated by a comparison of predicted and calculated results in a high voltage motor     

A brushless, exciterless, single-phase, sinusoidal wave synchronousmachine having an auxiliary stator winding

Analytical and experimental studies of a brushless, exciterless, single-phase, sinusoidal-wave synchronous machine operating as a generator or a motor, derived from a three-phase machine, are reported. One phase armature winding of the three-phase machine is used as an auxiliary stator winding of the single-phase machine and is used to supply the exciting power for the other two-phase armature windings acting as the load winding of the single-phase machine. A 1.5 kW, 200 V, 60 Hz, four-pole synchronous machine was used the experiments. It is shown that the waveforms of the armature terminal voltage and the load current are nearly sinusoidal. The advantages of the single-phase machine as a portable generator or small-load motor are discussed     

Integrated Nonlinear Magnetic Field-Network Simulation of an Electronically Commutated Permanent Magnet Motor System under Normal Operation

An integrated magnetic field-network computer-aided method is presented, and is verified here by applying it in the determination of the performance of an electronically commutated permanent magnet motor system, and comparing the results with test results at rated operating conditions. Test results were found to be in very good agreement with numerical simulation data. At the core of this method are the instantaneous calculation of the magnetic field distribution within the machine, using the finite element method, and the determination of the winding inductances from these field solutions with the aid of an energy perturbation technique. The armature induced emfs are also obtained from these field solutions. These winding parameters, which are load dependent, are used in a nonlinear time domain network model of first order differential equations governing the dynamic performance of the motor to solve for the instantaneous phase currents. These new currents are then used at every time instant to determine the corresponding machine winding parameters, and the above process is repeated at successive time instants until the complete analysis period is covered. Though the validity of this method of analysis is verified in this paper by applying it to a 15 hp (11.2kw), 120 volt electronically commutated brushless dc motor system operating under normal and balanced conditions, the real utility of the method lies in its ability to analyze these motor systems under unbalanced partial or total component failure (fault) in the windings and associated conditioners. This type of application is given in a companion paper.     

Experimental determination of the forward and backward-field torquein shaded-pole motors

An experimental method for determining the forward- and backward-field torque and the amplitude of a pulsating torque at twice the line frequency in shaded-pole motors is developed on the basis of revolving-field theory. These parameters are determined from the induced voltage in a measured winding by segregating a forward and backward fundamental component using a spectrum analyzer. This torque-measuring method has been tested for a shaded-pole motor with one shading coil, and a shaded-pole motor with two shading coils per pole. The forward-field torque minus the backward-field torque, as measured by the measuring winding, agreed with that measured by a Prony-brake torque meter with sufficient accuracy. The amplitude of the pulsating torque also agreed approximately with that measured with an accelerometer. Each torque can be determined more precisely in this experimental technique than in existing calculation techniques     

Skew and linear rise of MMF across slot modelling-winding functionapproach

A method of calculation of the inductances of an induction machine is proposed. The skewing of the rotor bars of the machine and the resultant linear rise of MMF across the slot, together with the nonsinusoidal distribution of the stator winding are taken into account. The method is based on the winding function approach, which allows for all harmonics of the MMF to be taken into account. The results obtained by the proposed method have been compared with those obtained by a conventional manner, which take into account the above phenomena by means of scale factors applied to the harmonics. A very good agreement between them is demonstrated     

Analysis and design of a two-speed single-phase induction motor with 2 and 18 pole special windings

The motor presented employs multiple independent windings for operation with two very different pole numbers. The 18-pole field is produced with a symmetrical three-phase winding connected in a Steinmetz arrangement to a single-phase supply. A unified analysis method has been developed and used to demonstrate the equivalence of a Steinmetz delta or star connection with a main and auxiliary winding of a single-phase motor. The method has been experimentally validated and also included are some specific motor design considerations.     

Electromagnetic design and optimization of dual‐stator brushless doubly‐fed wind power generator with cage‐barrier rotor

This paper explores the feasibility of an intuitive solution torque density for the existing brushless doubly‐fed generator by dual‐stator and cage‐barrier rotor structure, so as to better adapt to the offshore wind power generation. The torque density of electrical machine is related to the key design parameters, such as the machine main dimensions, slot‐pole combinations, coupling between stator and rotor, and nonmagnetic ring thickness. According to working principles and design requirements of electrical machine, the dual‐stator brushless doubly‐fed wind power generator (DSBDFWPG) with cage‐barrier rotor is designed, and the key parameters relating to torque density are analyzed and discussed. Meanwhile, the main parameters of electrical machine are optimized by Taguchi method, such as air‐gap length and nonmagnetic ring thickness. On this basis, the performance parameters of DSBDFWPG are analyzed by finite element method, which is verified by experimental tests. Through analysis of the results, not only the design requirements are satisfied by the DSBDFWPG, but also the correctness and rationality of machine design method can also be verified. Finally, the torque density and other aspects of designed DSBDFWPG are compared with dual‐stator brushless doubly‐fed induction generator, doubly‐fed induction generator, asynchronous machine, and brushless doubly‐fed generator; it demonstrates the torque density improvement of the studied machine with its significance and value.     

Peaked-MMF smooth-torque reluctance motors

The authors investigate the steady-state torque characteristics of reluctance motors with nonsalient stator punchings, but with peaked rotating magnetomotive forces (MMFs). The torque calculation includes the effects of saturation and fringing and groove fluxes. The peaked rotating MMF is produced by properly coordinated current waveforms and winding. Peaked-MMF reluctance motors have tow major advantages: the torque is smooth and the flux per pole required to produce a given torque is lower than that of conventional reluctance motors. This property is most beneficial to two-pole reluctance motors, for a given frame whose bore diameters and slot areas can be increased significantly for higher ratings or better performance. Unlike switched reluctance motors, shaft encoders are not required for peaked-MMF motors     

The effects of laminations on steep fronted surge propagation inlarge AC motor coils

To date, the modeling of machine windings for steep fronted surge propagation has been based on an assumption that the slot walls act as flux barriers at the frequencies of interest (1 to 10 MHz). This assumption led to the use of a line end coil structure embedded in a solid slot core for experiments, and excellent agreement between measured and computed waveforms has been reported by P.G. McLaren et al. (1988). The assumption is valid for a solid slot environment as the magnetic flux cannot penetrate beyond the skin depth, δ, which is on the order of 10^-6 m for the frequencies concerned. However, this is not the case for a laminated slot environment as it can allow magnetic flux penetration deeper into the core that the skin depth, δ. In the present study, the effects of such a flux penetration on steep fronted surge propagation in large AC motor coils are studied. The results obtained demonstrate that the solid slot models cannot accurately replace the actual laminated environments in the study of steep fronted surge propagation in machine windings. Maximum interturn voltages observed for the solid slot model are smaller (by a factor of about 2/3) than those for the laminated slot environment