Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Exact analytical solutions for the quasistationary electromagnetic fields in the presence of conducting objects require the field solutions both internal and external to the conductors. Such solutions are limited for certain canonically shaped objects but are useful in testing the accuracy of various approximate models and numerical methods developed to solve complex problems related to real world conducting objects and in calibrating instruments designed to measure various field quantities. Theoretical investigations of quasistationary electromagnetic fields also aid in improving the understanding of the physical phenomena of electromagnetic induction. This thesis presents rigorous analytical expressions derived as benchmark solutions for the quasistationary field quantities both inside and outside, Joule losses and the electromagnetic forces acting upon a conducting spheroid placed in the proximity of a non-uniform field produced by current-carrying turns. These expressions are used to generate numerous numerical results of specified accuracy and selected results are presented in a normalized form for extended ranges of the spheroid axial ratio, the ratio of the depth of penetration to the semi-minor axis and the position of the inducing turns relative to the spheroids. They are intended to constitute reference data to be employed for comprehensive comparisons of results from approximate numerical methods or from boundary impedance models used for real world conductors. Approximate boundary conditions such as the simpler perfect electric conductor model or the Leontovich surface impedance boundary condition model can be used to obtain approximate solutions by only analyzing the field external to the conducting object. The range of validity of these impedance boundary condition models for the analysis of axisymmetric eddy-current problems is thoroughly investigated. While the simpler PEC model can be employed only when the electromagnetic depth of penetration is much smaller than the smallest local radius of curvature, the results obtained using the surface impedance boundary condition model for conducting prolate and oblate spheroids of various axial ratios are in good agreement with the exact results for skin depths of about 1/5 of the semi-minor axis when calculating electromagnetic forces and for skin depths less than 1/20 of the semi-minor axis when calculating Joule losses.

Σκοπός της διπλωματικής αυτής εργασίας ήταν η μελέτη των ηλεκτρομαγνητικών δυνάμεων που δημιουργούνται μέσα σε μια ασύγχρονη ηλεκτρική μηχανή, ειδικότερα των ακτινικών δυνάμεων, καθώς και η μηχανική συμπεριφορά της μηχανής λόγω των δυνάμεων αυτών. Χρησιμοποιήθηκε ένας τριφασικός ασύγχρονος κινητήρας βραχυκυκλωμένου δρομέα, ισχύος 4 kW, συνδεσμολογίας τριγώνου. Η προσομοίωση και η μελέτη έγινε με τη χρήση του προγράμματος Opera 2-D της εταιρείας Vector Fields, το οποίο χρησιμοποιεί τη μέθοδο των πεπερασμένων στοιχείων για την επίλυση των μερικών διαφορικών εξισώσεων που περιγράφουν τη ηλεκτρομαγνητική λειτουργία της μηχανής. Πρώτα γίνεται η ηλεκτρομαγνητική ανάλυση των μοντέλων της μηχανής στη μόνιμη κατάσταση. Μετά χρησιμοποιώντας τα μοντέλα αυτά, υπολογίστηκαν οι ηλεκτρομαγνητικές πιέσεις που ασκούνται σε δόντια του δρομέα και του στάτη και η συνολική ακτινική και εφαπτομενική δύναμη που ασκείται πάνω στον δρομέα. Όταν οι ιδιοσυχνότητες ταλάντωσης της μηχανής είναι κοντά στις συχνότητες που υπάρχουν στο φάσμα συχνοτήτων της ακτινικής δύναμης, δημιουργείται συντονισμός και προκαλεί θορύβους και ταλαντώσεις στη μηχανή. Για να αποφευχθούν τέτοιου είδους θόρυβοι και ταλαντώσεις υπολογίζονται τα πλάτη και οι συχνότητες της ακτινικής δύναμης καθώς και οι ιδιοσυχνότητες της μηχανής. Οι ίδιες μετρήσεις έγιναν και σε μοντέλο μηχανής με μια σπασμένη μπάρα του κλωβού. Απεικονίσθηκαν οι ακτινικές δυνάμεις και συγκρίθηκαν με αυτές του υγιούς μοντέλου στο πεδίο του χώρου, του χρόνου και της συχνότητας. Επίσης παρουσιάζεται μια μέθοδος για την ανίχνευση «υπογραφών» ηλεκτρικών σφαλμάτων, μέσω ανάλυσης Fourier της ακτινικής ηλεκτρομαγνητικής δύναμης και πίεσης. Τα αποτελέσματα δείχνουν πως η ηλεκτρομαγνητική δύναμη είναι μια καλή παράμετρος με τη χρήση της οποίας μπορεί να ανιχνευτεί το σφάλμα της σπασμένης μπάρας. / The aim of this thesis was to study the electromagnetic forces generated in an asynchronous electric machine, especially the radial forces and the mechanical behavior of the machine due to these forces. A three-phase squirrel cage asynchronous motor, 4 kW power, was used. The simulation and the study was performed using the program Opera 2-D of Vector Fields, which uses the finite element method to solve partial differential equations describing the operation of the electromagnetic machine. First of all, the electromagnetic analysis of models of the machine in steady state was performed. Using these models, the electromagnetic pressure on teeth of the rotor and stator was calculated and the total radial and tangential force exerted on the rotor was estimated. When the natural frequencies of oscillation of the machine are close to the frequencies of the radial force, coordination is generated and causes noise and vibrations in the machine. To avoid such noises and vibrations, the amplitudes and frequencies of the radial force and the natural frequencies of the machine must be calculated. The same measurements were made on a model engine with a broken bar. The radial forces were plotted and compared with those of the healthy model, in the field of space, time and frequency. Also, a method for the detection of "signatures" electrical fault, through Fourier analysis of the radial electromagnetic force and pressure is disclosed. The results showed that the electromagnetic force is a good parameter to use for the detection of the broken bar fault.

Cette thèse aborde la problématique de la modélisation multiphysique en génie électrique, avec une application à l’étude des vibrations d’origine électromagnétique des cages de développantes. Cette étude comporte quatre parties : la construction de la densité de courant, le calcul des forces locales, le transfert de solutions entre maillages et la résolution des problèmes couplés. Un premier enjeu est de correctement représenter les courants, cette opération est effectuée en deux étapes : la construction de la densité de courant et l’annulation de la divergence. Si des structures complexes sont utilisées, l’imposition du courant ne peut pas toujours être réalisée à l’aide de méthodes analytiques. Une méthode basée sur une résolution électrocinétique ainsi qu’une méthode purement géométrique sont testées. Cette dernière donne des résultats plus proches de la densité de courant réelle. Parmi les nombreuses méthodes de calcul de forces, les méthodes des travaux virtuels et des forces de Laplace, considérées par la littérature comme les plus adaptées au calcul des forces locales, ont été étudiées. Nos travaux ont montré que bien que les forces de Laplace sont particulièrement précises, elles ne sont pas valables si la perméabilité n’est plus homogène. Ainsi, la méthode des travaux virtuels, applicable de manière universelle, est préférée. Afin de modéliser des problèmes multi-physiques complexes à l’aide de plusieurs codes de calculs dédiés, des méthodes de transferts entre maillages non conformes ont été développées. Les procédures d’interpolations, les méthodes localement conservatives et les projections orthogonales sont comparées. Les méthodes d’interpolations sont réputées rapides mais très diffusives tandis que les méthodes de projections sont considérées comme les plus précises. La méthode localement conservative peut être vue comme produisant des résultats comparables aux méthodes de projections, mais évite l’assemblage et la résolution de systèmes linéaires. La modélisation des problèmes multi-physiques est abordée à l’aide des méthodes de transferts de solutions. Pour une classe de problème donnée, l’assemblage d’un schéma de couplage n’est pas unique. Des tests sur des cas analytiques sont réalisés afin de déterminer, pour plusieurs types de couplages, les stratégies les plus appropriées.Ces travaux ont permis une application à la modélisation magnéto-mécanique des cages de développantes est présentée. / The modeling of multi-phycics problems in electrical engineering is presented, with an application to the numerical computation of vibrations within the end windings of large turbo-generators. This study is divided into four parts: the impositions of current density, the computation of local forces, the transfer of data between disconnected meshes, and the computation of multi-physics problems using weak coupling, Firstly, the representation of current density within numerical models is presented. The process is decomposed into two stages: the construction of the initial current density, and the determination of a divergence-free field. The representation of complex geometries makes the use of analytical methods impossible. A method based on an electrokinetical problem is used and a fully geometrical method are tested. The geometrical method produces results closer to the real current density than the electrokinetical problem. Methods to compute forces are numerous, and this study focuses on the virtual work principle and the Laplace force considering the recommendations of the literature. Laplace force is highly accurate but is applicable only if the permeability is uniform. The virtual work principle is finally preferred as it appears as the most general way to compute local forces. Mesh-to-mesh data transfer methods are developed to compute multi-physics models using multiples meshes adapted to the subproblems and multiple computational software. The interpolation method, a locally conservative projection, and an orthogonal projection are compared. Interpolation method is said to be fast but highly diffusive, and the orthogonal projections are highly accurate. The locally conservative method produces results similar to the orthogonal projection but avoid the assembly of linear systems. The numerical computation of multi-physical problems using multiple meshes and projections is then presented. However for a given class of problems, there is not an unique coupling scheme possible. Analytical tests are used to determine, for different class of problems, the most accurate scheme. Finally, numerical computations applied to the structure of end-windings is presented.

The continuously increasing demand for clean renewable energy has rekindled interest in multi-terminal high voltage direct current (HVDC) grids. Although such grids have several advantages and a great potential, their materialization has been thwarted due to the absence of HVDC breakers. In comparison with traditional alternating current (AC) breakers, they should operate and interrupt fault currents in a time frame of a few milliseconds. The aim of this thesis is focused on the design of ultra-fast electro-mechanical actuator systems suitable for such HVDC breakers.Initially, holistic multi-physics and hybrid models with different levels of complexity and computation time were developed to simulate the entire switch. These models were validated by laboratory experiments. Following a generalized analysis, in depth investigations involving simulations complemented with experiments were carried out on two of the sub-components of the switch: the ultra-fast actuator and the damper. The actuator efficiency, final speed, peak current, and maximum force were explored for different design data.The results show that models with different levels of complexity should be used to model the entire switch based on the magnitude of the impulsive forces. Deformations in the form of bending or elongation may deteriorate the efficiency of the actuator losing as much as 35%. If that cannot be avoided, then the developed first order hybrid model should be used since it can simulate the behavior of the mechanical switch with a very good accuracy. Otherwise, a model comprising of an electric circuit coupled to an electromagnetic FEM model with a simple mechanics model, is sufficient.It has been shown that using a housing made of magnetic material such as Permedyn, can boost the efficiency of an actuator by as much as 80%. In light of further optimizing the ultra-fast actuator, a robust optimization algorithm was developed and parallelized. In total, 20520 FEM models were computed successfully for a total simulation time of 7 weeks. One output from this optimization was that a capacitance of 2 mF, a charging voltage of 1100 V and 40 turns yields the highest efficiency (15%) if the desired velocity is between 10 m/s and 12 m/s.The performed studies on the passive magnetic damper showed that the Halbach arrangement gives a damping force that is two and a half times larger than oppositely oriented axially magnetized magnets. Furthermore, the 2D optimization model showed that a copper thickness of 1.5 mm and an iron tube that is 2 mm thick is the optimum damper configuration. / <p>QC 20150422</p>

In a synchronous machine, radial, tangential, and axial forces are generated. In this thesis, three different technologies to control them are proposed. The first one, involves the utilization of the radial forces that arise between the rotor and the stator. This is achieved by segmenting the rotor field winding into groups of poles and controlling their corresponding magnetization individually. This technology is particularly useful to achieve magnetic balance and to create controllable radial forces. The second technology, involves the control of the rotor field in order to influence the tangential forces that produce torque. This is achieved by inverting the rotor field winding polarity with respect to the stator field. With this technique, breaking and accelerating torques can be created. It is particularly useful to start a synchronous machine. Finally, the application of axial forces with a magnetic thrust bearing is discussed. The main benefits of this technology are higher efficiency and increased reliability. The work presented in this thesis was carried out within the Division of Electricity in the Department of Engineering Sciences at Uppsala University. It is based on original research supported by analytical calculations, computational simulations and extensive experimental work.