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Le contrôle non destructif électromagnétique (CNDE) est appliqué dans des domaines variés pour l'exploration de défauts cachés affectant des structures. De façon générale, le principe peut se poser en ces termes : un objet inconnu perturbe un milieu hôte donné et illuminé par un signal électromagnétique connu, et la réponse est mesurée sur un ou plusieurs récepteurs de positions connues. Cette réponse contient des informations sur les paramètres électromagnétiques et géométriques des objets recherchés et toute la difficulté du problème traité ici consiste à extraire ces informations du signal obtenu. Plus connu sous le nom de « problèmes inverses », ces travaux s'appuient sur une résolution appropriée des équations de Maxwell. Au « problème inverse » est souvent associé le « problème direct » complémentaire, qui consiste à déterminer le champ électromagnétique perturbé connaissant l'ensemble des paramètres géométriques et électromagnétiques de la configuration, défaut inclus. En pratique, cela est effectué via une modélisation mathématique et des méthodes numériques permettant la résolution numérique de tels problèmes. Les simulateurs correspondants sont capables de fournir une grande précision sur les résultats mais à un coût numérique important. Sachant que la résolution d'un problème inverse exige souvent un grand nombre de résolution de problèmes directs successifs, cela rend l'inversion très exigeante en termes de temps de calcul et de ressources informatiques. Pour surmonter ces challenges, les « modèles de substitution » qui imitent le modèle exact peuvent être une solution alternative intéressante. Une manière de construire de tels modèles de substitution est d'effectuer un certain nombre de simulations exactes et puis d'approximer le modèle en se basant sur les données obtenues. Le choix des simulations (« prototypes ») est normalement contrôlé par une stratégie tirée des outils de méthodes de « plans d'expérience numérique ». Dans cette thèse, l'utilisation des techniques de modélisation de substitution et de plans d'expérience numérique dans le cadre d'applications en CNDE est examinée. Trois approches indépendantes sont présentées en détail : une méthode d'inversion basée sur l'optimisation d'une fonction objectif et deux approches plus générales pour construire des modèles de substitution en utilisant des échantillonnages adaptatifs. Les approches proposées dans le cadre de cette thèse sont appliquées sur des exemples en CNDE par courants de Foucault / Electromagnetic Nondestructive Evaluation (ENDE) is applied in various industrial domains for the exploration of hidden in-material defects of structural components. The principal task of ENDE can generally be formalized as follows: an unknown defect affects a given host structure, interacting with a known electromagnetic field, and the response (derived from the electromagnetic field distorted by the defect) is measured using one or more receivers at known positions. This response contains some information on the electromagnetic constitutive parameters and the geometry of the defect to be retrieved. ENDE aims at extracting this information for the characterization of the defect, i.e., at the solution of the arising “inverse problem”. To this end, one has to be able to determine the electromagnetic field distorted by a defect with known parameters affecting a given host structure, i.e., to solve the “forward problem”. Practically, this is performed via the mathematical modeling (based on the Maxwell's equations) and the numerical simulation of the studied ENDE configuration. Such simulators can provide fine precision, but at a price of computational cost. However, the solution of an inverse problem often requires several runs of these “expensive-to-evaluate” simulators, making the inversion procedure firmly demanding in terms of runtime and computational resources. To overcome this challenge, “surrogate modeling” offers an interesting alternative solution. A surrogate model imitates the true model, but as a rule, it is much less complex than the latter. A way to construct such surrogates is to perform a couple of simulations and then to approximate the model based on the obtained data. The choice of the “prototype” simulations is usually controlled by a sophisticated strategy, drawn from the tools of “design-of-experiments”. The goal of the research work presented in this Dissertation is the improvement of ENDE methods by using surrogate modeling and design-of-experiments techniques. Three self-sufficient approaches are discussed in detail: an inversion algorithm based on the optimization of an objective function and two methods for the generation of generic surrogate models, both involving a sequential sampling strategy. All approaches presented in this Dissertation are illustrated by examples drawn from eddy-current nondestructive testing.

<p>Electromagnetic transients impinging on electromagnetic power devices - such as electric machines, transformers and reactors - can stress the design severely. Thus the magnitudes of the transients are often decisive for the design of the devices. Further, the operation of a device can be transient in itself. This is the case for the explosive magnetic flux compression generator (EMG) and a ferromagnetic actuator. </p><p>Models are presented that are mainly intended for transients in the millisecond range and faster. Hence, eddy currents and the related skin and proximity effect become significant in windings, magnetic cores and in the armatures of the devices. These effects are important for, e.g., the damping of the transients. Further, the displacement current in the insulation of the winding is significant. It changes the response of the windings dramatically, as it manifests the finite velocity of propagation of the electromagnetic fields. Under such circumstances, reflections and excited resonances can make the transient voltage and current distribution highly irregular. </p><p>Induced voltages are modelled with self and mutual inductances or reluctances combined with winding templates. The displacement currents are modelled with capacitances or coefficients of potential. Cauer circuits and their dual form are used to model eddy currents in laminated cores and in conductors. The Cauer circuit enables one to consider hysteresis and the non-linear response of a magnetic core. It is also used to model the eddy currents in the moving armature of an EMG. </p><p>A set-up is presented that can be used to study the transient voltage and the current distribution along a coil. </p><p>The transient response of coaxially insulated windings is analysed and modelled in detail. A lumped circuit model is developed for a coil, Dryformer^TM - the new high-voltage transformer - and Powerformer^TM, the new high-voltage generator. An alternative model, a combined lumped circuit and FEM model, is presented for a coaxially insulated winding in two slot cores.</p>

Electromagnetic transients impinging on electromagnetic power devices - such as electric machines, transformers and reactors - can stress the design severely. Thus the magnitudes of the transients are often decisive for the design of the devices. Further, the operation of a device can be transient in itself. This is the case for the explosive magnetic flux compression generator (EMG) and a ferromagnetic actuator. Models are presented that are mainly intended for transients in the millisecond range and faster. Hence, eddy currents and the related skin and proximity effect become significant in windings, magnetic cores and in the armatures of the devices. These effects are important for, e.g., the damping of the transients. Further, the displacement current in the insulation of the winding is significant. It changes the response of the windings dramatically, as it manifests the finite velocity of propagation of the electromagnetic fields. Under such circumstances, reflections and excited resonances can make the transient voltage and current distribution highly irregular. Induced voltages are modelled with self and mutual inductances or reluctances combined with winding templates. The displacement currents are modelled with capacitances or coefficients of potential. Cauer circuits and their dual form are used to model eddy currents in laminated cores and in conductors. The Cauer circuit enables one to consider hysteresis and the non-linear response of a magnetic core. It is also used to model the eddy currents in the moving armature of an EMG. A set-up is presented that can be used to study the transient voltage and the current distribution along a coil. The transient response of coaxially insulated windings is analysed and modelled in detail. A lumped circuit model is developed for a coil, DryformerTM - the new high-voltage transformer - and PowerformerTM, the new high-voltage generator. An alternative model, a combined lumped circuit and FEM model, is presented for a coaxially insulated winding in two slot cores.

In order to design a power transformer it is important to understand its internal electromagnetic behaviour. That can be obtained by measurements on physical transformers, analytical expressions and computer simulations. One benefit with simulations is that the transformer can be studied before it is built physically and that the consequences of changing dimensions and parameters easily can be assessed. In this thesis a time-domain transformer model is presented. The model includes core phenomena as magnetic static hysteresis, eddy current and excess losses. Moreover, the model comprises winding phenomena as eddy currents, capacitive effects and leakage flux. The core and windings are first modelled separately and then connected together in a composite transformer model. This results in a detailed transformer model. One important result of the thesis is the feasibility to simulate dynamic magnetization including the inhomogeneous field distribution due to eddy currents in the magnetic core material. This is achieved by using a Cauer circuit combined with models for static and dynamic magnetization. Thereby, all magnetic loss components in the material can be simulated accurately. This composite dynamic magnetization model is verified through experiments showing very good correspondence with measurements. Furthermore, the composite transformer model is verified through measurements. The model is shown to yield good correspondence with measurements in normal operation and non-normal operations like no-load, inrush current and DC-magnetization. / QC20100708

Hydropower research is often perceived to be an old and exhausted field of study but with ageing equipment and the need for more intermittent operation caused by an increased share of other renewable energy sources new challenges lie ahead. The main focus of this dissertation are the electromagnetic forces resulting from nonuniform air gap flux, whether it be caused by rotor eccentricity or a faulty field winding. Results are predominantly obtained from measurements on an experimental generator and numerical simulations. With the computational capacity available today it is possible to numerically analyse physical phenomena that previously could only be studied with analytical tools. Numerical models can also be expanded to encompass more than one aspect of generator operation in coupled field-circuit models without model complexity surpassing computer capability. Three studies of unbalanced magnetic pull, UMP, in synchronous salient pole generators constitute the main part of this thesis. The first is a study of how parallel stator circuits affect the unbalanced magnetic pull caused by rotor eccentricity. Depending on the relationship between the geometry of the separate circuits and the direction of the eccentricity it was found that parallel circuits could reduce the UMP substantially. Secondly, an investigation of the effect of damper winding configuration on UMP was performed. The results showed that damper winding resistivity and the distance between the damper bars in a pole determine the effectiveness of the damper winding in reducing the UMP. Simulations of a production machine indicate that the reduction can be substantial from damper windings with low resistivity. The third study analyses the consequences of field winding interturn short circuits. Apart from a resulting rotating unbalanced magnetic pull it is found that the unaffected poles with the same polarity as the affected pole experience an increase in flux density. In a fourth article a new stand still frequency response, SSFR, test method including measurements of damper winding voltage and current is presented. It is found that the identified models are capable of predicting the stator to damper transfer function both with and without the damper winding measurements included.

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.

Στις ηλεκτρικές μηχανές ο υπολογισμός των απωλειών και οι μηχανισμοί που τις προκαλούν αποτελούν ένα πολύ απαιτητικό αντικείμενο μελέτης. Τα τελευταία χρόνια καθώς αυξάνεται η ανάγκη για ολοένα και πιο αποδοτικές μηχανές μεγάλο κομμάτι της έρευνας έχει επικεντρωθεί στον υπολογισμό των απωλειών τους και πιο συγκεκριμένα στον υπολογισμό των απωλειών σιδήρου. Οι απώλειες σιδήρου ή αλλιώς απώλειες πυρήνα αποτελούν σημαντικό μέρος των απωλειών μια μηχανής, ταυτόχρονα όμως ο υπολογισμός τους εμφανίζει ιδιαίτερη δυσκολία. Στην παρόυσα διπλωματική εργασία η προσπάθεια επικεντρωνεται στον υπολογισμό αυτών των απωλειών σε μια ασύγχρονη μηχανή με διάφορες μεθόδους. Πιο συγκεκριμένα, στο πρώτο κεφάλαιο γίνεται μια εισαγωγή στα σιδηρομαγνητικά υλικά και στις ιδιότητες τους. Αρχικά παρουσιάζεται το φαινόμενο της μαγνήτισης και του κορεσμού. Στη συνέχεια μελετάται το φαινόμενο της υστέρησης και οι ιδιότητες της που παίζουν καθοριστικό ρόλο στις απώλειες του πυρήνα της μηχανής, αλλά και το φαινόμενο των δινορευμάτων. Στο δεύτερο κεφάλαιο μελετώνται οι απώλειες της μηχανής. Με ποιό τρόπο δηλαδή το φαινόμενο της υστέρησης και των δινορευμάτων πρoκαλούν απώλειες στη μηχανή και με ποια μορφή εμφανίζονται. Παρουσιάζονται ακόμα οι μηχανισμοί που συνδέονται με τις απώλειες χαλκού, επιδερμικό φαινόμενο και φαινόμενο γειτνίασης και ο ρόλος τους. Παρουσιάζεται επίσης μια βιβλιογραφική έρευνα σχετικά με τις διάφορες μεθόδους που χρησιμοποιούνται για τον υπολογισμό των απωλειών σιδήρου. Το τρίτο κεφάλαιο αποτελεί ουσιαστικά μια εισαγωγή στα ηλεκτρονικά ισχύος και πιο συγκεκριμένα στον αντιστροφέα τάσης με τεχνική PWM. Σημαντικός θεωρείται ο τρόπος με τον οποίο διαμορφώνεται η τάση εισόδου στη μηχανή, αλλά και η μορφή της, καθώς επηρεάζει άμεσα τις απώλειες σιδήρου της μηχανής. Στο τέταρτο και τελευταίο κεφάλαιο βρίσκουν εφαρμογή όλα τα παραπάνω. Η εργασία γίνεται με τη βοήθεια ενός μοντέλου πεπερασμένων στοιχείων, δύο διαστάσεων, μιας ασύγχρονης μηχανής βραχυκυκλωμένου κλωβού. Αρχικά η μηχανή τροφοδοτείται από μια ημιτονοειδή τάση είσόδου. Υπολογίζονται οι απώλειες χαλκού και στη συνέχεια οι απώλειες σιδήρου με τη βοήθεια υπολογιστικών μεθόδων ανάλυσης του μαγνητικού πεδίου σε σειρές Fourier. Τέλος μελετάται η μορφή του μαγνητικού πεδίου σε διάφορα σημεία της μηχανής και οι απώλειες που εμφανίζεται σε κάθε στοιχείο του μοντέλου ανά περίπτωση. Τα βήματα αυτά επαναλαμβανονται τροφοδοτώντας αυτή τη φορά τη μηχανή μέσω αντιστροφέα τάσης με τεχνική PWM. Συγκρίνοντας τα αποτελέσματα από κάθε περίπτωση εξάγονται σημαντικά συμπεράσματα για τις απώλειες της μηχανής και τη συμπεριφορά των μηχανισμών που τις προκαλούν. / In electrical machines the calculation of loss and the mechanisms that cause them are a very demanding subject of study. Recently, the increasing need for ever more efficient machines has made the research focus on the calculation of their losses and more specifically the calculation of the iron losses. The iron losses or core losses, constitute an important part of the total machine losses, but also their calculation is particularly difficult. In this thesis we focus on the calculation of these losses in an asynchronous machine using various methods. More specifically, the first chapter is an introduction to the properties of ferromagnetic materials. First, we study the phenomenon of magnetization and saturation and then we examine the phenomenon of hysteresis and its properties which play a crucial role in the core losses of the machine. Finally we study eddy current phenomenon. In the second chapter we discuss the losses of the machine. In which way the phenomenon of hysteresis and eddy currents generate losses in the machine and the form in which they appear. Also presented are the mechanisms associated with the copper losses, skin effect and proximity effect. Also shown is a literature survey on various methods used to calculate the iron losses. The third chapter is essentially an introduction to power electronics, and more particularly to the PWM technique. Important in this chapter is the way in which the input voltage to the machine affects the iron losses. In the fourth and final chapter we produce results of the above theory using simulation methods. The work is done using a finite element model in two dimensions of a squirrel cage asynchronous machine. Initially the machine is fed by a sinusoidal input voltage. Firstly copper losses are calculated and then the iron losses with the help of computational methods which analyze the magnetic induction in Fourier series. Finally, we study the shape of the magnetic field in different parts of the machine and the losses occurring in each element of the model in each case. These additional losses are known as rotational core losses. These steps are repeated, this time powering the machine via inverter supply using the PWM technique.

La découverte de nombreuses planètes extrasolaires depuis 1995 est une source d’inspiration pour les modèles de formation et évolution des systèmes solaires. Une fraction de ces planètes ont un demi-grand axe inférieur à 0.1 UA; une planète qui migre à proximité de son étoile subit donc d’abord un fort vent solaire et, après son entrée dans la magnétosphère stellaire, un fort champ magnétique. Nous étudions séparemment l’interaction entre ces planètes et la composante périodique et indépendente du temps du champ magnétique dipolaire stellaire. L’interaction périodique est associée à des courants induits confinés dans la planète. Nous étudions deux effets qui pourraient augmenter le moment angulaire d’une planète gaseuse géante qui migre vers son étoile: un torque de Lorentz qui transferre du moment angulaire de la rotation de l’étoile vers l’orbite de la planète et une perte de masse induite par la dissipation ohmique dans la planète qui peut donner du moment angulaire à la planète lorsque cette masse est accrétée sur l’étoile. Nous modellisons l’interaction indépendente du temps comme un modèle d’inducteur unipolaire, dans lequel le courant induit circule dans une boucle fermée formée par la planète, le flux de tube, et le pied du flux de tube dans l’atmosphère stellaire. Nous calculons de fa con cohérente la dissipation ohmique dans la planète et le pied du flux de tube ainsi que le couple de Lorentz. Nous utilisons alors ce modèle pour expliquer l’aspect enflé de certaines planètes géantes. Finalement, nous suggérons que ce modèle permettrait également d’estimer la conductivité électrique des super-Terres qui interagissent magnétiquement avec leur étoile. / The numerous and diverse extrasolar planets detected since 1995 provide much inspiration for planetary astrophysics. A fraction of these extrasolar planets orbit their host stars at semi-major axes less than 0.1 AU; a planet which has migrated toward its host star would thus first encounter a strong magnetized wind and, as it enters the stellar magnetosphere, strong magnetic fields. We model the interaction of such a close-in extrasolar planet with the dipolar magnetic field of its host star and study separately the time-dependent and independent components. The time-dependent interaction gives rise to Eddy currents confined in the planet. We investigate two effects that may transfer angular momentum to a planet approaching its host TTauri star through type II migration: a Lorentz torque that transfers angular momentum from the stellar spin to the planetary orbit and a mass loss induced by the ohmic dissipation in the planet, which may transfer angular momentum to the planet as the gas is accreted onto the star. We model the time-independent interaction with the unipolar inductor model, which allows the current induced in the planet to flow along a closed loop constituted by the planet, the flux tube, and its footprint on the stellar atmosphere. We self-consistently calculate the ohmic dissipation in the planet and the star and the associated Lorentz torque. We then suggest that the ohmic dissipation may provide the extra energy needed to explain some planets with inflated radii. Finally, we propose that the model may also be used to remotely infer the electric conductivity of the outer layers of super-Earths interacting magnetically with their host stars.