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.

Le nombre d’appareils électroniques et de systèmes de communication sans fil a considérablement augmenté au cours des 20 dernières années. Les boîtiers de blindage utilisés pour protéger les appareils électroniques contre les radiations externes, mais aussi pour limiter leurs émissions sont généralement conçus en alliages d’aluminium. Mais la nécessité de réduire le poids des aéronefs incite l’industrie aéronautique à l’utilisation de matériaux composites.La modélisation de boîtiers de blindage composés de matériaux homogènes est possible par l’utilisation d’outils numériques tels que la méthode des éléments finis. Mais la discrétisation de boîtiers constitués de matériaux composites impliquerait un nombre d’éléments trop important rendant impossible toute modélisation numérique. Le recours à l’homogénéisation semi-analytique est une possibilité pour s’affranchir de cette restriction. Les milieux homogènes équivalents obtenus avec ces méthodes peuvent être insérés dans des outils numériques pour simuler le comportement électromagnétique de boîtiers de blindage complexes. Les modèles d’homogénéisation existants, tel que le modèle de Maxwell-Garnett, sont toutefois limités a des applications quasi-statiques.La définition des propriétés effectives de matériaux composites illuminés par des ondes électromagnétiques est l’objectif principal de ce travail. Il en résulte deux méthodes d’homogénéisation dynamiques. La première introduit un effet de taille entre les fibres et la longueur d'onde. Elle permet ainsi d’étendre une méthode basée sur des problèmes d'inclusion aux micro-ondes. Mais elle reste limitée par l’apparition de l’effet de peau dans les renforts conducteurs. La seconde est basée sur la définition des pertes par effet Joule dans les fibres, permettant ainsi d’étendre la première méthode après l’apparition de l’effet de peau. Cette dernière est enfin utilisée pour modéliser le comportement électromagnétique d’un boîtier de blindage réaliste. / The number of electronic devices and wireless communication systems has significantly increased over the past 20 years. Shielding enclosures used to protect electronic devices against radiated waves and to limit their emissions are usually designed in aluminum alloys. But the need to reduce the weight of aircraft incites the aerospace industry to the use of composite materials.Modeling shielding enclosures composed of homogeneous materials is possible by the use of numerical tools such as the finite element method. But considering every details of the microstructure would involve a excessive number of unknowns preventing numerical modelings. The use of semi-analytical homogenization methods is a possibility to overcome this restriction. The equivalent homogeneous mediums obtained with these methods can be inserted into numerical tools to simulate the electromagnetic behavior of complex shielding enclosures. But classical homogenization models such as Maxwell-Garnett model, are limited to quasi-static applications.Calculating the effective properties of composite materials illuminated by electromagnetic waves is the main objective of this work. This leads to two dynamic homogenization methods. The first one introduces a size effect between the fibers and the wavelength. It allows to extend a method based on inclusion problems to microwave frequencies. However it is limited by the occurrence of the skin effect in conductive inclusions. The second consider Joule losses and extends the first method after the occurrence of the skin effect. This second homogenization method is finally used to model the behavior of a realistic shielding enclosure.

Práce se zabývá výpočty magnetických a tepelných vlastností servomotoru s permanentními magnety (motor M718 I vyráběný firmou VUES s.r.o. v Brně). Všechny uvedené výpočty jsou založené na numerických metodách konečných prvků a konečných objemů. 2D magnetická analýza motoru byla řešena s pomocí programu FEMM, zatímco pro 3D analýzu byl využit software ANSOFT. Magnetické analýzy umožnily stanovit rozložení magnetického pole v motoru a ve vzduchové mezeře. Ztráty způsobené vířivými proudy byly počítány v závislosti na rozměrech permanentních magnetů a velikosti toku magnetické indukce ve vzduchové mezeře. U 3D modelu v programu ANSOFT byly vypočítány i Joulovy ztráty. Pro daný servomotor byly navrženy dva způsoby chlazení. V prvním případě se jedná o vnitřní chladicí systém. K původnímu modelu motoru byly přidány některé modifikace (otvory v rámu motoru a radiální ventilátor na hřídeli uvnitř rámu motoru). U druhého způsobu chlazení bylo navrženo vnější chlazení. K původnímu rámu byly přidána chladicí žebra a radiální ventilátor na hřídeli vně rámu motoru. Výpočty proudění a tepelná analýza byly provedeny jak pro původní model motoru, tak i pro modifikovaný návrh (vnitřní a vnější chlazení) pomocí software ANSYS Workbench. Teplotní charakteristiky původního motoru byly měřeny různými senzory. Bylo provedeno porovnání experimentálně získaných výsledků s vypočteným teplotním modelem. Práce byla vytvořena v rámci doktorského studijního programu Elektrotechnika a komunikační technologie, obor Silnoproudá elektrotechnika a elektroenergetika. Podstatná část práce vznikla za podpory Centra výzkumu a využití obnovitelných zdrojů energie a výzkumných projektů CZ.1.05/2.1.00/01.0014 and FEKT S-11-9.

This Master Thesis deals with the study of analytical and finite-element (FE) models for calculation of losses in traction induction motors. Motors are fed through inverters for this type of application. Therefore, both fundamental and harmonic losses are considered. The study is done with one particular motor and one initial analytical model. In order to validate the model and improve it, a FE model is developed with the tool FLUX 2D. Several chosen operating points with different modulation patterns are simulated both with FE and analytical models and results are compared. Stator and rotor Joule losses are studied first. A model to calculate stator Joule losses at strand level is proposed as an improvement to the current analytical model. Then iron losses, both in stator and rotor, are calculated. Two different computations methods with data extraction from FE are studied: the Bertotti model and a recently developed method called MVPRS in the report. It is based on a mathematical model for curve fitting of the core loss material data. Results with the two methods are compared with the ones from ana-lytical model. Finally total fundamental and harmonic losses are compared with measurements and conclusions are drawn on the quality and accuracy of the analytical model. / Detta examensarbete handlar om analytiska och Finita Element (FE) modeller för beräkning av förluster i asynkronmotorer för traktion. Motorer matas genom växelriktare för denna typ av applikation. Därför är det nödvändigt att både grundläggande och harmoniska förluster beaktas. Studien görs för en särskild motor och en redan existerande analytisk modell. För att validera modellen och förbättra den, utvecklats en FE modell med verktyget FLUX 2D. Flera arbetspunkter med olika moduleringsmönster simuleras både med FE och analytiska modeller och resultaten jämförs. Först studeras stator och rotor Joule förluster. En modell för att beräkna stator Joule förluster i varje ledare föreslås som en förbättring av den nuvarande analytiska modellen. Sedan beräknas järnförluster, både i stator och rotor, beräknas. Två olika metoder baserad på flödestäthet variationer i tid och rum från FE simuleringar studeras med Bertottis modell och en nyutvecklad metod som kallas MVPRS. Den är baserat på en matematisk modell för kurvanpassning av materialet förlust data. Resultaten med de två metoderna jämförs med de från analytiska modellen. Slutligen jämförs totala fundamentala och harmoniska förluster med mätningar och slutsatser dras om kvalitet och noggrannhet av analytiska modellen.

This thesis explores the losses occurring in a specific region located in the southern part of Eskilstuna, where ESEM serves as the network owner. The study places particular emphasis on power factor and load factor as key factors. Its objective is to analyze and comprehend the extent of losses in the network and their implications. The results demonstrate that losses in the chosen area of the Eskilstuna network align with prior research and theoretical expectations. Based on calculations, the losses in this network segment amount to approximately 483 MWh per year, corresponding to a cost of approximately 272,000 Swedish Kronor for ESEM in 2022. The method of studies is based on calculations, analyzer, and literature studies to achieve a reliable result. The results show that losses within the selected area of the Eskilstuna network are consistent with previous research and theoretical expectations. Of the total loss, there are some customers who show larger losses compared to the average case. These customers were identified, and a summary analysis was made of their power factor and load factor standard deviation. These losses depend on various factors, such as the existence of reactive power, technical and non-technical losses. Measures to deal with these problems are suggested based on previous research and literature studies. Optimization of transformers, phase compensation and monitoring are some of these measures. This study provides significant insights into power grid losses and proposes potential strategies to mitigate these losses in the examined region. By minimizing such losses, ESEM has the potential to enhance the efficiency of the electrical grid, lower carbon dioxide emissions, and enhance economic outcomes for energy producers, the electricity grid operator, and consumers. For continued progress in the field, further research, and implementation of the proposed measures to streamline the power grid and reduce losses in the future is recommended. / Elnätförluster har konsekvenser för miljön, energisystemet och slutanvändarna. När energi går förlorad i elnätet minskar den totala effektiviteten i systemet och ökar belastningen på kraftgenereringen. Detta kan leda till ökade kostnader för energiproducenter och potentiellt högre priser för konsumenterna. Dessutom kan ökade elnätförluster bidra till en ökning av koldioxidutsläppen från kraftverken och därmed ha en negativ miljöpåverkan. Syftet med studien är att undersöka det befintliga elnätet i det utvalda området genom analys av data från mät-elnätavdelningen i ESEM. Metoden för studien är baserad på beräkningar, analyser och litteraturstudier för att uppnå ett pålitligt resultat. Resultaten visar att förluster inom det valda området av Eskilstunanätverket överensstämmer med tidigare forskning och teoretiska förväntningar. Baserat på beräkningar uppgår förlusterna i detta nätsegment till cirka 483 MWh, vilket motsvarar en kostnad på cirka 272 000 svenska kronor för ESEM 2022. Av den totala förlusten finns det vissa kunder som uppvisar större förluster jämfört med genomsnittsfallet. Dessa kunder identifierades, och en översiktsanalys gjordes av deras effektfaktor och standardavvikelse för belastningsfaktorn. Dessa förluster beror på olika faktorer, såsom existensen av reaktiv effekt, tekniska och icke-tekniska förluster. Åtgärder för att hantera dessa problem föreslås baserat på tidigare forskning och litteraturstudier. Optimering av transformatorer, faskompensering och övervakning är några av dessa åtgärder. Denna studie bidrar med viktig kunskap om elnätförluster och identifierar potentiella åtgärder för att minska förlusterna i det studerade området. Genom att minska förlusterna kan man öka elnätets effektivitet, minska koldioxidutsläppen och förbättra ekonomiska aspekter för energiproducenter, elnätägaren och konsumenter. För fortsatta framsteg inom området rekommenderas ytterligare forskning och implementering av de föreslagna åtgärderna för att effektivisera elnätet och minska förlusterna i framtiden.