The Maxwell equations of electromagnetism form the foundation of classical electromagnetism, and are of interest to mathematicians, physicists, and engineers alike. The first part of this thesis concerns boundary value problems for the anisotropic Maxwell equations in Lipschitz domains. In this case, the material parameters that arise in the Maxwell system are matrix valued functions. Using methods from functional analysis, global in time solutions to initial boundary value problems with general nonzero boundary data and nonzero current density are obtained, only assuming the material parameters are bounded and measurable. This problem is motivated by an electromagnetic inverse problem, similar to the classical Calder\'on inverse problem in Electrical Impedance Tomography. The second part of this thesis deals with materials having negative refractive index. Materials which possess a negative refractive index were postulated by Veselago in 1968, and since 2001 physicists were able to construct these materials in the laboratory. The research on the behavior of these materials, called metamaterials, has been extremely active in recent years. We study here refraction problems in the setting of Negative Refractive Index Materials (NIMs). In particular, it is shown how to obtain weak solutions (defined similarly to Brenier solutions for the Monge-Amp\`ere equation) to these problems, both in the near and the far field. The far field problem can be treated using Optimal Transport techniques; as such, a fully nonlinear PDE of Monge-Amp\`ere type arises here. / Mathematics

[pt] O presente trabalho propõe técnicas numéricas para a síntese de antenas refletoras que utilizando seções de cônicas ou superfícies quádricas confocais. Para tal, utilizando os princípios da Óptica Geométrica, foram desenvolvidos algoritmos capazes de sintetizar as superfícies refletoras desejadas. São analisadas duas geometrias distintas: a antena duplo-refletora com cobertura omnidirecional e a antena refletora offset com um único refletor. No primeiro problema, é apresentado um método alternativo para a síntese geométrica de antenas duplo-refletoras com cobertura omnidirecional e diagrama de radiação arbitrário no plano de elevação. O subrefletor é um corpo de revolução gerado por uma única seção cônica e o refletor principal modelado é gerado por uma série de seções cônicas locais sequencialmente concatenadas. Para ilustrar o método, duas configurações axialmente simétrica são sintetizadas para proporcionar diagramas de radiação uniforme ou cossecante ao quadrado no plano de elevação. Os resultados são validados por uma técnica híbrida baseada em Casamento de Modos e o Método de Momentos. No segundo problema, é investigado um procedimento numérico alternativo para a síntese geométrica de antenas refletoras offset com diagrama de radiação arbitrário na região de campo distante. O método usa superfícies quádricas confocais com eixos deslocados para representar localmente a superfície modelada. Nesta abordagem, um operador não linear deve ser resolvido como um problema de contorno. Para ilustrar o método, são apresentadas antenas modeladas para prover diagrama de radiação Gaussiano em contornos de cobertura circular, elíptico e super-elíptico. / [en] This work proposes numerical techniques for synthesis of reflector antennas, using conic sections or confocal quadric surfaces. Under Geometrical Optics principles, algorithms to shape desired reflective surfaces have been developed. Two different geometries have been considered: omnidirectional dual-reflector antenna and single offset reflector antennas. In the first problem, it was presented an alternative method for synthesis of omnidirectional dual-reflector antennas with an arbitrary radiation pattern in elevation plane. The body-of-revolution subreflector is generated by a single conic section, while the shaped main reflector is generated by a series of local conic sections, sequentially consecutively concatenated. In order to illustrate the method, omnidirectional axisdisplaced ellipse (OADE) and Cassegrain (OADC) configurations are synthesized to provide uniform or cosecant squared radiation pattern in the elevation plane. The GO shaping results are validated by a hybrid technique based on Mode Matching and Method of Moments. In the second problem, an alternative numerical procedure was investigated for the geometrical synthesis of offset reflector antennas with an arbitrary radiation pattern in the far-field region, according to geometrical optics. The method uses local axis-displaced confocal quadric surfaces to describe the shaped reflector. In this approach, a nonlinear operator must be solved as a boundary value problem. To illustrate the method, we have chosen several offset configurations with circular, elliptical and super-elliptical contour coverage and Gaussian power density. The results were validated by the physical optics approximation.

Recently, permanent magnet assisted (PMa)-synchronous reluctance motors (SynRM) have been considered as a possible alternative motor drive for high performance applications. In order to have an efficient motor drive, performing of three steps in design of the overall drive is not avoidable. These steps are design optimization of the motor, identification of the motor parameter and implementation of an advanced control system to ensure optimum operation. Therefore, this dissertation first deals with the design optimization of the Permanent Magnet Assisted Synchronous Reluctance Motor (PMa-SynRM). Various key points in the rotor design of a low cost PMa-SynRM are introduced and their effects are studied. Finite element approach has been utilized to show the effects of these parameters on the developed average electromagnetic torque and the total d-q inductances. As it can be inferred from the name of the motor, there are some permanent magnets mounted in the rotor core. One of the features considered in the design of this motor is the magnetization of the permanent magnets mounted in the rotor core using the stator windings to reduce the manufacturing cost. At the next step, identification of the motor parameters is discussed. Variation of motor parameters due to temperature and airgap flux has been reported in the literatures. Use of off-line models for estimating the motor parameters is known as a computationally intensive method, especially when the models include the effect of cross saturation. Therefore in practical applications, on-line parameter estimation is favored to achieve a high performance control system. In this dissertation, a simple practical method for parameter estimation of the PMa-SynRM is introduced. Last part of the dissertation presents one advanced control strategy which utilized the introduced parameter estimator. A practical Maximum Torque Per Ampere (MTPA) control scheme along with a simple parameter estimator for PMa-SynRM is introduced. This method is capable of maintaining the MTPA condition and stays robust against the variations of motor parameters. Effectiveness of the motor design procedure and the control strategy is validated by presenting simulation and experimental results of a 1.5 kW prototype PMa-SynRM, designed and manufactured through the introduced design method.

The Master's thesis discusses the design and realization of electronic meter of volt-ampere characteristics using Wifi module ESP32. The device is designed to be able to measure the characteristic in the voltage range of +/- 20 V and current range of +/- 200 mA. The device is controlled by web interface. The user is able to connect to it with for example his or her smartphone. This interface enables the user to configure various parameters, including the range of measurement and the power restriction. Furthermore, it is possible to graphically display the measured characteristic and export the data. To be independent on the outer network, the ESP32 is operated as an access point, which is creating a new simple network without the internet connection. In the Master's thesis, the principle of voltage and current measurement is explained theoretically, the circuit connection of device and the printed circuit board are designed and the cover of the device is modeled. Also the process of creating the device according to the design is described and the cover of the device is printed on 3D printer. After that, the control program is designed, described and uploaded into the resulting device. Finally, the functionality of the device is tested by measuring the volt-ampere characteristics of a few components.

Lithium-ion (Li-ion) batteries have become a crucial factor in the recent electro-mobility trend. People's increased interest in electric vehicles (EVs) has motivated several automotive manufacturers and research organizations to develop suitable drivetrain designs involving batteries. Especially the development of the 48V Li-ion battery has been of great importance to reduce CO2 emissions and meet emission standards. However, accurately modeling Li-ion batteries is a difficult task since multiple factors have to be considered. Conservative Methods are using pyhsico-chemical models or electrical circuits in order to mimic the battery behavior. This thesis deals with developing a Li-ion battery model using artificial neural network (ANN) algorithms to predict the state of charge (SOC) as one of the key battery management system states. Due to the rising power of GPUs and the amount of available data, ANNs became popular in recent years. ANNs are also applicable to different areas of battery technology. Using battery data like the battery voltage, temperature, and current as input features, a neural network is trained that predicts battery SOC. A novel approach based on ANNs and one of the most commonly used SOC estimation methods are presented in this thesis to model the battery behavior. Furthermore, an approach for dealing with the highly unbalanced data by creating multidimensional bins and compare different neural network architectures for time series forecasting is introduced. By creating the model, our main priority is to reduce the model's errors in extreme operating areas of the battery. According to our results, long short-term memory (LSTM) architectures appear to be the best fit for this task. Finally, the developed ANN model can successfully learn battery behavior, however the model's accuracy under harsh operating circumstances is highly dependent on the data quality gathered.

This work develops a new mathematical model to the salient pole synchronous machines (SPSM), based on the abc reference system. The model considers the distribution and coil pitch factors of windings and develops a new function for the variable air gap, generated by the curvature of the polar mass. As a result, the development of the modeling takes into account the spatial harmonic components of: magneto motive force MMF(θ)h, electromagnetic ux density B(θ)h and variation function of the air gap g(θ)h. It is also proposed a new and simplied methodology using the locked rotor tests, volt-ampere method, to obtain the constants of the synchronous machine design, which allow the calculation of the modeling parameters and the terminals magnitudes determination. It presents also contributions to traditional methods of obtaining experimental inductances, using the locked rotor test. Yet it develops procedures and makes the simulation of the main temporal magnitudes at the generator terminals connected to the utility grid, electrical torque, speed, voltage and current. The model is validated through the theoretical and experimental confrontation of inductances, and also of the voltages and currents at the generator terminals connected to the utility grid. / Este trabalho desenvolve uma nova modelagem matemática para as máquinas síncronas de polos salientes (MSPS), baseada no sistema abc de referência. A modelagem considera os fatores de distribuição e de passo de bobina dos enrolamentos e desenvolve uma nova função para o entreferro variável, gerado pela curvatura da sapata polar. Como conseqüência o desenvolvimento da modelagem leva em consideração os componentes harmônicos espaciais de: força magneto motriz FMM(θ)h, densidade de uxo eletromagnético B(θ)h e da função de variação do entreferro g(θ)h. É também proposto uma nova e simplificada metodologia a partir dos testes de rotor bloqueado, método volt-ampere, para a obtenção das constantes de projeto da máquina síncrona que possibilitam os cálculos dos parâmetros da modelagem, bem como a determinação das grandezas terminais. Também apresenta contribuições aos métodos tradicionais de obtenção de indutâncias experimentais, a partir dos testes de rotor bloqueado. Ainda desenvolve os procedimentos e faz a simulação das principais grandezas temporais nos terminais do gerador conectado à rede da concessionária: torque elétrico, velocidade, corrente e tensão. A modelagem é convalidada através das confrontações teórico-experimental das indutâncias, e também dos resultados de correntes e tensões nos terminais do gerador conetado à rede da concessionária. / Doutor em Ciências

Kondenzátor na bázi oxidu niobu je novým typem pasívní součástky, jehož vývoj byl motivován snahou vyřešit hlavní nedostatky tantalového kondenzátoru – omezený zdroj tantalové suroviny a nebezpečí hoření při průrazu. Chování kondenzátoru na bázi oxidu niobu lze stejně jako u tantalového kondenzátoru popsat prostřednictvím reverzní MIS struktury. Pro studium mechanismu transportu nosičů nábojů v dielektriku Nb2O5 a pro stanovení fyzikálních parametrů, které řídí zbytkový proud, bylo využito měření V-A charakteristik v normálním a reverzním módu při 77 a 300K, dále závislosti kapacity ochuzené vrstvy na napětí a frekvenci, teplotní a časové závislosti zbytkového proudu a spektrální hustoty šumu ve frekvenční a časové doméně při různých napětích. Experimentální data potvrdila platnost navrženého pásového diagramu MIS struktury a poskytla jeho klíčové parametry. Bylo ověřeno, že transport nosičů náboje v NbO kondenzátorech je určen ohmickou, Poole-Frenkelovou a tunelovou složkou v normálním módu, a Schottkyho emisí v reverzním módu. V rozsahu standardních aplikačních napětí dominují v normálním módu Poole-Frenkelova emise a v reverzním módu Schottkyho emise. Při vyšších napětích v normálním módu určuje průrazné napětí kondenzátoru tunelový mechanismus. V reverzním módu rozhoduje o odolnosti vůči tepelnému průrazu kondenzátoru výška bariéry mezi dielektrikem a anodou. Bylo zjištěno, že NbO a Tantalové kondenzátory mají stejný mechanismus vodivosti. Specifika NbO anody se projevují pouze v rozdílných hodnotách parametrů pásového diagramu, nikoliv v principech mechanismu transportu nosičů náboje. To vysvětluje základní rozdíl mezi oběma kondenzátory, který je v kvalitě dielektrické vrstvy na přechodu anody a dielektrika. Nižší potenciálové bariéry a vyšší počet defektů v dielektriku, který je způsoben dalším stabilním oxidem, má za následek vyšší zbytkový proud NbO kondenzátoru. Tento jev však nemá žádný vliv na spolehlivost součástky. Teoretické modely a vybrané testovací metody byly použity k volbě vhodných materiálů anody, ke stanovení vhodných dopantů a k optimalizaci technologie anodické oxidace. Byla nalezena korelace mezi parametry transportu nosičů náboje a spolehlivostí, a na základě experimentálních dat byly navrženy optimalizace výrobního procesu kondenzátorů. Lepší porozumění transportním mechanismům v NbO kondenzátorech umožnilo úplný popis nové součástky na bázi oxidu niobu. Byly zdůrazněny silné a slabé stránky této nové technologie a nalezeny nástroje pro optimalizaci procesů, které umožní vyšší spolehlivost a efektivitu NbO kondenzátorů.

Ce travail de thèse porte sur différentes caractérisations des modèles multivariés de stables-Tweedie multiples dans le cadre des familles exponentielles naturelles sous la propriété de "steepness". Ces modèles parus en 2014 dans la littérature ont été d’abord introduits et décrits sous une forme restreinte des stables-Tweedie normaux avant les extensions aux cas multiples. Ils sont composés d’un mélange d’une loi unidimensionnelle stable-Tweedie de variable réelle positive fixée, et des lois stables-Tweedie de variables réelles indépendantes conditionnées par la première fixée, de même variance égale à la valeur de la variable fixée. Les modèles stables-Tweedie normaux correspondants sont ceux du mélange d’une loi unidimensionnelle stable-Tweedie positive fixé et les autres toutes gaussiennes indépendantes. A travers des cas particuliers tels que normal, Poisson, gamma, inverse gaussienne, les modèles stables-Tweedie multiples sont très fréquents dans les études de statistique et probabilités appliquées. D’abord, nous avons caractérisé les modèles stables-Tweedie normaux à travers leurs fonctions variances ou matrices de covariance exprimées en fonction de leurs vecteurs moyens. La nature des polynômes associés à ces modèles est déduite selon les valeurs de la puissance variance à l’aide des propriétés de quasi orthogonalité, des systèmes de Lévy-Sheffer, et des relations de récurrence polynomiale. Ensuite, ces premiers résultats nous ont permis de caractériser à l’aide de la fonction variance la plus grande classe des stables-Tweedie multiples. Ce qui a conduit à une nouvelle classification laquelle rend la famille beaucoup plus compréhensible. Enfin, une extension de caractérisation des stables-Tweedie normaux par fonction variance généralisée ou déterminant de la fonction variance a été établie via leur propriété d’indéfinie divisibilité et en passant par les équations de Monge-Ampère correspondantes. Exprimées sous la forme de produit des composantes du vecteur moyen aux puissances multiples, la caractérisationde tous les modèles multivariés stables-Tweedie multiples par fonction variance généralisée reste un problème ouvert. / In the framework of natural exponential families, this thesis proposes differents characterizations of multivariate multiple stables-Tweedie under "steepness" property. These models appeared in 2014 in the literature were first introduced and described in a restricted form of the normal stables-Tweedie models before extensions to multiple cases. They are composed by a fixed univariate stable-Tweedie variable having a positive domain, and the remaining random variables given the fixed one are reals independent stables-Tweedie variables, possibly different, with the same dispersion parameter equal to the fixed component. The corresponding normal stables-Tweedie models have a fixed univariate stable-Tweedie and all the others are reals Gaussian variables. Through special cases such that normal, Poisson, gamma, inverse Gaussian, multiple stables-Tweedie models are very common in applied probability and statistical studies. We first characterized the normal stable-Tweedie through their variances function or covariance matrices expressed in terms of their means vector. According to the power variance parameter values, the nature of polynomials associated with these models is deduced with the properties of the quasi orthogonal, Levy-Sheffer systems, and polynomial recurrence relations. Then, these results allowed us to characterize by function variance the largest class of multiple stables-Tweedie. Which led to a new classification, which makes more understandable the family. Finally, a extension characterization of normal stable-Tweedie by generalized variance function or determinant of variance function have been established via their infinite divisibility property and through the corresponding Monge-Ampere equations. Expressed as product of the components of the mean vector with multiple powers parameters reals, the characterization of all multivariate multiple stable- Tweedie models by generalized variance function remains an open problem.

Diploma thesis is focused on the study of optoelectric properties of thin layers of organic materials based on phthalocyanines, which can be used as an active layer of photovoltaic cells. Especially are studied the properties of the thin active layers of PdPc and PdPc + IL on the glass or ceramic substrates with aluminium contact, which are prepared by material printing here. On the prepared samples were first measured current-voltage characteristics in the dark and in the light and then were measured impedance spectrums in the dark. The received results will be used to improve the properties and structures of photovoltaic cells.

Cette thèse est consacré à l’évaluation et l’amélioration de la performance de la machine synchrone à réluctance variable pour des applications à vitesse variable en général et pour les applications automobiles en particulier. Les deux axes de développement sont la conception de la machine et l’injection des harmoniques de courants de phase. Le rotor est un élément important dans la conception de la machine, et un intérêt particulier est dédié à la conception et l’évaluation du rotor pour améliorer la performance de la machine. Une méthode analytique est proposée dans la thèse pour concevoir le rotor. Plusieurs éléments tels que les ponts qui maintiennent le rotor mécaniquement résistant, ainsi que le rapport d’isolation d’axe q (rapport air-acier) sont étudiés. Une étude de conception assistée par ordinateur basé sur un problème d’optimisation paramétrique est présentée aussi. Les trois familles des algorithmes d’optimisation sont évaluées pour la procédure d’optimisation: un algorithme à base de gradient (algorithme de Newton Quasi), un algorithme non-évolutionnaire sur la base de non-gradient (Nelder Mead Simplex) et un algorithme évolutif sur la base non-gradient (algorithme génétique). Les designs de machines basées sur la procédure analytique et la procédure d’optimisation sont testés sur un banc d’essai. Le deuxième axe d’études de la thèse est l’injection d’harmoniques dans les courants de phase de la machine à réluctance variable synchrone. L’interaction des harmoniques de courant avec les harmoniques spatiales des inductances est étudiée et formalisée pour une machine à m-phases. Ensuite, le concept d’injection d’harmoniques est évalué dans le cas particulier d’une machine à deux phases. Cette étude montre l’avantage de l’injection d’harmoniques dans la réduction de l’ondulation de couple de la machine. Un design d’une machine est finalement développé pour une application automobile sur la base de l’optimisation paramétrique du stator et du rotor. Cette conception est évaluée pour les spécifications imposées électromagnétiques par une application de traction à puissance moyenne / This thesis is dedicated to the evaluation and the improvement of the synchronous reluctance machine’s performance for variable speed drive applications in general and for automotive applications in particular. The two axes of development are machine design and phase current harmonics injection. The rotor is an important element in the machine design and particular emphasis is placed to the design and evaluation of the rotor for enhancing the machine performance. An analytical procedure is proposed for the rotor design. The rotor elements like the ribs and the bridges that maintain the rotor mechanically strong as well as the q-axis insulation ratio (air-to-steel ratio) are studied. A computer-aided design study based on a parametric optimization problem is presented as well. The main three families of the optimization algorithms are evaluated for the optimization procedure: a gradient-based algorithm (Quasi Newton Algorithm), a non-gradient based non-evolutionary algorithm (Nelder Mead Simplex) and a non-gradient based evolutionary algorithm (Genetic Algorithm). The machine designs based on the analytical procedure and the optimization procedure are both manufactured and tested on a bench. The second axis of study of the thesis is the injection of harmonics in the phase currents of the synchronous reluctance machine. The interaction of current harmonics with the spatial inductance harmonics is studied and formalized for an m-phase machine. Then, the harmonics injection concept is evaluated in the particular case of a 2-phase machine. This study shows the benefi t of harmonics injection in the reduction of the machine torque ripple. A synchronous reluctance machine design is fi nally developed for an automotive application based on parametric optimization of the stator and rotor. This design is evaluated for the electromagnetic specifi cations imposed by a mid-power electric vehicle traction application