A Spline-Based Partial Element Equivalent Circuit Method for Electrostatics

This contribution investigates the connection between Isogeometric Analysis (IgA) and the Partial Element Equivalent Circuit (PEEC) method for electrostatic problems. We demonstrate that using the spline-based geometry concepts from IgA allows for extracting circuit elements without an explicit meshing step. Moreover, the proposed IgA-PEEC method converges for complex geometries up to three times faster than the conventional PEEC approach and, in turn, it requires a significantly lower number of degrees of freedom to solve a problem with comparable accuracy. The resulting method is closely related to the isogeometric boundary element method. However, it uses lowest-order basis functions to allow for straightforward physical and circuit interpretations. The findings are validated by an analytical example with complex geometry, i.e., significant curvature, and by a realistic model of a surge arrester

Mixed Proper Orthogonal Decomposition with Harmonic Approximation for Parameterized Order Reduction of Electromagnetic Models

This paper presents some preliminary investigations on a hybrid Model Order Reduction approach for parameter-dependent electromagnetic systems. Starting from an integral equation formulation of the field problem, we introduce a first level of compression based on the well-established Proper Orthogonal Decomposition (POD). The result is a small-scale approximation of the full-order discrete field formulation, which retains an explicit dependence on the set of free parameters defining the geometry. The evaluation of the reduced model for arbitrary parameter configurations remains very expensive, as it requires the construction of the full system equations before its projection onto a lower-dimensional space. This problem is solved by constructing a surrogate macromodel of the parameterized reduced-order system through a multivariate Fourier approximation. Numerical results applied to a moving coil over a finite ground plane show model compression above 99% while preserving accuracy on currents and fields within 1%

Do Wind Turbines Amplify the Effects of Lightning Strikes A Full-Maxwell Modelling Approach

Wind turbines (WTs) can be seriously damaged by lightning strikes and they can be struck by a significant number of flashes. This should be taken into account when the WT lightning protection system is designed. Moreover, WTs represent a path for the lightning current that can modify the well-known effects of the lightning discharge in terms of radiated electromagnetic fields, which are a source of damage and interference for nearby structures and systems. In this paper, a WT struck by a lightning discharge is analyzed with a full-wave modelling approach, taking into account the details of the WT and its interactions with the lightning channel. The effects of first and subsequent return strokes are analyzed as well as that of the rotation angle of the struck blade. Results show that the lightning current along the WT is mainly affected by the ground reflection and by the reflection between the struck blade and the channel. The computed electromagnetic fields show that, for subsequent return strokes, the presence of a WT almost doubles their magnitude with respect to a lightning striking the ground. Such enhancement is emphasized when the inclined struck blade is considere

Fast Solver for Implicit Continuous Set Model Predictive Control of Electric Drives

This paper proposes a fast and accurate solver for implicit Continuous Set Model Predictive Control for the current control loop of synchronous motor drives with input constraints, allowing for reaching the maximum voltage feasible set. The related control problem requires an iterative solver to find the optimal solution. The real-time certification of the algorithm is of paramount importance to move the technology toward industrial-scale applications. A relevant feature of the proposed solver is that the total number of operations can be computed in the worst-case scenario. Thus, the maximum computational time is known a priori. The solver is deeply illustrated, showing its feasibility for real-time applications in the microseconds range by means of experimental tests. The proposed method outperforms general-purpose algorithms in terms of computation time, while keeping the same accuracy

Inhalation therapy in the next decade : Determinants of adherence to treatment in asthma and COPD

Peer reviewedPublisher PD

Une extension de la méthode PEEC non structurée aux problèmes magnétiques, temporels et stochastiques

The main focus of this thesis is to extend and improve the applicability and the accuracy of the Unstructured Partial Element Equivalent Circuit (PEEC) method. The interest on this argument is spurred by the growing need of fast and efficient numerical methods, which may help engineers during the design and other stages of the production of new generation electric components.First, the PEEC method in its unstructured form is extended to magnetic media. In this regard, two formulations are developed and compared: the first, based on the Amperian interpretation of the magnetization phenomena, is derived from the existing literature concerning the standard (structured) version of PEEC; the second, based on the Coulombian interpretation of the magnetization phenomena, is proposed by the author with the aim of collocating PEEC in the context of Volume Integral Equation methods.Then, the coupling of PEEC with low-rank compression techniques is investigated. Two different methods are applied: the first is based on hierarchical matrices (H and H2 matrices) while the second is based on hierarchical-semi-separable (HSS) matrices. The two methods are compared and the main numerical issues which emerge by applying low-rank techniques to PEEC are analyzed.Finally, the developed unstructured PEEC method is combined withthe Marching On-in-Time scheme for the study of fast transient phenomena with a rich harmonic content. Moreover, two different stochastic PEEC methods are developed for uncertainty quantification analysis. The first is based on the Polynomial Chaos expansion while the second is based on the Parametric Model Order Reduction technique coupled with spectral expansion.L'objectif principal de cette thèse est d'étendre et d'améliorer la précision de la méthode des circuits équivalents à éléments partiels non structurés (Unstructured PEEC). L'intérêt pour ce sujet est stimulé par le besoin croissant de méthodes numériques rapides et efficaces, qui peuvent aider les ingénieurs pendant la conception et les autres phases de la production de composants électriques et électroniques de nouvelle génération.Dans un premier temps, la méthode PEEC sous sa forme non structurée est étendue aux supports magnétiques. Deux formulations sont développées et comparées: la première, basée sur l'interprétation ampérienne des phénomènes d’aimantation, provient de la littérature relative à la version standard (structurée) de la méthode PEEC. La seconde, basée sur l'interprétation Coulombienne des phénomènes d’aimantation, est proposée par l'auteur dans le but de recentrer la méthode PEEC dans le contexte des méthodes d'intégrale de volume (Volume Integral Equation).Dans un deuxième temps, les travaux portent sur l’utilisation de techniques de compression de bas rang afin de résoudre efficacement les problèmes de PEEC et de préserver le temps et la mémoire de calcul. Deux méthodes différentes sont appliquées: la première est basée sur des matrices hiérarchiques (matrices H et H2), tandis que la seconde repose sur des matrices hiérarchiques semi-séparables (HSS). Les deux méthodes sont comparées et les principaux problèmes numériques qui se posent en appliquant ces techniques de compression de bas rang à la méthode PEEC sont analysés.La méthode PEEC non structurée est ensuite combinée à l’approche Marching On-In Time (MOT) pour l’étude des phénomènes transitoires rapides avec un contenu harmonique riche.Enfin, deux méthodes PEEC stochastiques différentes ont été développées pour la quantification des incertitudes. La première est basée sur l'expansion Polynomial Chaos, tandis que la seconde repose sur la technique de réduction de l'ordre du modèle paramétrique (Parametric Model Order Reduction) combinée à une expansion spectrale

Extending the Unstructured PEEC Method to Magnetic, Transient, and Stochastic Electromagnetic Problems

L'objectif principal de cette thèse est d'étendre et d'améliorer la précision de la méthode des circuits équivalents à éléments partiels non structurés (Unstructured PEEC). L'intérêt pour ce sujet est stimulé par le besoin croissant de méthodes numériques rapides et efficaces, qui peuvent aider les ingénieurs pendant la conception et les autres phases de la production de composants électriques et électroniques de nouvelle génération.Dans un premier temps, la méthode PEEC sous sa forme non structurée est étendue aux supports magnétiques. Deux formulations sont développées et comparées: la première, basée sur l'interprétation ampérienne des phénomènes d’aimantation, provient de la littérature relative à la version standard (structurée) de la méthode PEEC. La seconde, basée sur l'interprétation Coulombienne des phénomènes d’aimantation, est proposée par l'auteur dans le but de recentrer la méthode PEEC dans le contexte des méthodes d'intégrale de volume (Volume Integral Equation).Dans un deuxième temps, les travaux portent sur l’utilisation de techniques de compression de bas rang afin de résoudre efficacement les problèmes de PEEC et de préserver le temps et la mémoire de calcul. Deux méthodes différentes sont appliquées: la première est basée sur des matrices hiérarchiques (matrices H et H2), tandis que la seconde repose sur des matrices hiérarchiques semi-séparables (HSS). Les deux méthodes sont comparées et les principaux problèmes numériques qui se posent en appliquant ces techniques de compression de bas rang à la méthode PEEC sont analysés.La méthode PEEC non structurée est ensuite combinée à l’approche Marching On-In Time (MOT) pour l’étude des phénomènes transitoires rapides avec un contenu harmonique riche.Enfin, deux méthodes PEEC stochastiques différentes ont été développées pour la quantification des incertitudes. La première est basée sur l'expansion Polynomial Chaos, tandis que la seconde repose sur la technique de réduction de l'ordre du modèle paramétrique (Parametric Model Order Reduction) combinée à une expansion spectrale.The main focus of this thesis is to extend and improve the applicability and the accuracy of the Unstructured Partial Element Equivalent Circuit (PEEC) method. The interest on this argument is spurred by the growing need of fast and efficient numerical methods, which may help engineers during the design and other stages of the production of new generation electric components.First, the PEEC method in its unstructured form is extended to magnetic media. In this regard, two formulations are developed and compared: the first, based on the Amperian interpretation of the magnetization phenomena, is derived from the existing literature concerning the standard (structured) version of PEEC; the second, based on the Coulombian interpretation of the magnetization phenomena, is proposed by the author with the aim of collocating PEEC in the context of Volume Integral Equation methods.Then, the coupling of PEEC with low-rank compression techniques is investigated. Two different methods are applied: the first is based on hierarchical matrices (H and H2 matrices) while the second is based on hierarchical-semi-separable (HSS) matrices. The two methods are compared and the main numerical issues which emerge by applying low-rank techniques to PEEC are analyzed.Finally, the developed unstructured PEEC method is combined withthe Marching On-in-Time scheme for the study of fast transient phenomena with a rich harmonic content. Moreover, two different stochastic PEEC methods are developed for uncertainty quantification analysis. The first is based on the Polynomial Chaos expansion while the second is based on the Parametric Model Order Reduction technique coupled with spectral expansion

Extending the Unstructured PEEC Method to Magnetic, Transient, and Stochastic Electromagnetic Problems

The main focus of this thesis is to extend and improve the applicability and the accuracy of the Unstructured Partial Element Equivalent Circuit (PEEC) method. The interest on this subject is spurred by the growing need of fast and efficient numerical methods, which may help engineers during the design and other stages of the production of new generation electric components. First, the PEEC method in its unstructured form is extended to magnetic media. In this regard, two formulations are developed and compared: the first one, based on the Amperian interpretation of the magnetization phenomena, is derived from the existing literature concerning the standard (structured) version of PEEC; the second one, based on the Coulombian interpretation of the magnetization phenomena, is proposed by the author with the aim of collocating PEEC in the context of Volume Integral Equation methods. Then, the application of low-rank compression techniques to PEEC is investigated. Two different methods are applied: the first is based on hierarchical matrices (H and H2 matrices) whereas the second is based on hierarchical-semi-separable (HSS) matrices. The two methods are compared and the main numerical issues which emerge by applying low-rank techniques to PEEC are analyzed. Finally, the developed unstructured PEEC method is combined with the Marching On-in Time scheme for the study of fast transient phenomena with wide range of harmonics. Moreover, two different stochastic PEEC methods are developed for uncertainty quantification analysis. The first is based on the Polynomial Chaos expansion while the second is based on the Parametric Model Order Reduction technique coupled with spectral expansion