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No description available.

No description available.

No description available.

Due to unique characteristics, current-mode control architectures with different implementation approaches have been widely used in power converter design to achieve current sharing, AVP control, and light-load efficiency improvement. Therefore, an accurate model for current-mode control is indispensable to system design due to the existence of subharmonic oscillations. The fundamental difference between current-mode control and voltage-mode control is the PWM modulation. The inductor current, one of state variables, is used in the modulator in current-mode control while an external ramp is used in voltage-mode control. The dynamic nonlinearity of current-mode control results in the difficulty of obtaining the small-signal model for current-mode control in the frequency domain. There has been a long history of the current-mode control modeling. Many previous attempts have been made especially for constant-frequency peak current-mode control. However, few models are available for variable-frequency constant on-time control and V2 current-mode control. It's hard to directly extend the model of peak current-mode control to those controls. Furthermore, there is no simple way of modeling the effects of the capacitor ripple which may result in subharmonic oscillations in V2 current-mode control. In this dissertation, the primary objective to investigate a new and general modeling approach for current-mode control with different implementation methods. First, the fundamental limitation of average models for current-mode control is identified. The sideband components are generated and coupled with the fundamental component through the PWM modulator in the current loop. Moreover, the switching frequency harmonics cannot be ignored in the current loop since the current ripple is used for the PWM modulation. Available average models failed to consider the sideband effects and high frequency harmonics. Due to the complexity of the current loop, it is difficult to analyze current loop in the frequency domain. A new modeling approach for current-mode control is proposed based on the time-domain analysis. The inductor, the switches and the PWM modulator are treated as a single entity to model instead of breaking them into parts to do it. Describing function method is used. Proposed approach can be applied not only to constant-frequency modulation but also to variable-frequency modulation. The fundamental difference between different current-mode controls is elaborated based on the models obtained from the new modeling approach. Then, an equivalent circuit representation of current-mode control is presented for the sake of easy understanding. The effect of the current loop is equivalent to controlling the inductor current as a current source with certain impedance. The circuit representation provides both the simplicity of the circuit model and the accuracy of the proposed model. Next, the new modeling approach is extended to V2 current-mode control based on similar concept. The model for V2 current-mode control can accurately predict subharmonic oscillations due to the influence of the capacitor ripple. Two solutions are discussed to solve the instability issue. After that, a digital application of current-mode control is introduced. High-resolution digital pulse-width modulator (DPWM) is considered to be indispensable for minimizing the possibility of unpredicted limit-cycle oscillations, but results in high cost, especially in the application of voltage regulators for microprocessors. In order to solve this issue, a fully digital current-mode control architecture which can effectively limit the oscillation amplitude is presented, thereby greatly reducing the design challenge for digital controllers by eliminating the need for the high-resolution DPWM. The new modeling strategy is also used to model the proposed digital current-mode control to help system design. As a conclusion, a new modeling approach for current-mode control is fully investigated. Describing function method is utilized as a tool in this dissertation. Proposed approach is quite general and not limit by implementation methods. All the modeling results are verified through simulation and experiments. / Ph. D.

In comparison with PWM converters, resonant converters are gaining increasing popularity for cases in which efficiency and power density are at a premium. However, the lack of an accurate small-signal model has become an impediment to performance optimization. Many modeling attempts have been made to date. Besides the discrete time-domain modeling, most continuous-time modeling approaches are based on fundamental approximation, and are thus unable to provide sufficient accuracy for practical use. An equivalent circuit model was proposed by Yang, which works well for series resonant converters (SRCs) with high Q (quality factor), but which is inadequate for LLC resonant converters. Furthermore, the model is rather complicated, with system orders that are as high as five and seven for the SRC and LLC converter, respectively. The crux of the modeling difficulty is due to the underlying assumption based on the use of a band-pass filter for the resonant tank in conjunction with a low-pass output filter, which is not the case for most practical applications. The matter is further complicated by the presence of a rectifier, which is a nonlinearity that mixes and matches the original modulation frequency. Thus, the modulation signal becomes intractable when using a frequency-domain modeling approach. This dissertation proposes an extended describing function modeling that is based on a Fourier analysis on the continuous-time-domain waveforms. Therefore, all important contributions from harmonics are taken into account. This modeling approach is demonstrated on the frequency-controlled SRC and LLC converters. The modeling is further extended to, with great accuracy, a charge-controlled LLC converter. In the case of frequency control, a simple third-order equivalent circuit model is provided with high accuracy up to half of the switching frequency. The simplified low-frequency model consists of a double pole and a pair of right-half-plane (RHP) zeros. The double pole, when operated at a high switching frequency, manifests the property of a well-known beat frequency between the switching frequency and the resonant frequency. As the switching frequency approaches the resonant frequency of the tank, a new pair of poles is formed, representing the interaction of the resonant tank and the output filter. The pair of RHP zeros, which contributes to additional phase delay, was not recognized in earlier modeling attempts. In the case of charge control, a simple second-order equivalent circuit model is provided. With capacitor voltage feedback, the order of the system is reduced. Consequently, the resonant tank behaves as an equivalent current source and the tank property is characterized by a single pole. The other low-frequency pole represents the output capacitor and the load. However, the capacitor voltage feedback cannot eliminate the high-frequency poles and the RHP zeros. These RHP zeros may be an impediment for high-bandwidth design if not properly treated. Based on the proposed model, these unwanted RHP zeros can be mitigated by either changing the resonant tank design or by proper feedback compensation. The accurate model is essential for a high-performance high-bandwidth LLC converter. / Doctor of Philosophy / For high-frequency power conversion, resonant converters are increasingly popular. However, the lack of an accurate small-signal model has become an impediment to performance optimization. The existing equivalent circuit model and its simplified circuit were based on fundamental approximation, where the resonant tank was deemed a good band-pass filter. These models work well for series resonant converters (SRCs) with high Q (quality factor), but are inadequate for LLC resonant converters. The crux of the modeling difficulty is due to the fact that the operation of this type of resonant converter is based on the use of a band-pass filter in conjunction with a low-pass filter. The matter is further complicated by the presence of a rectifier, which is a nonlinearity that mixes and matches the original modulation frequency. Thus, the modulation signal becomes intractable when using a frequency-domain modeling approach. This dissertation proposes an extended describing function modeling that is based on a Fourier analysis on the continuous-time-domain waveforms. Therefore, all important contributions from harmonics are taken into account. This modeling approach is demonstrated on the frequency-controlled SRC, frequency-controlled LLC converter, and charge-controlled LLC converter, and the resulting models are proven to be accurate at all frequencies. A simple equivalent circuit model is provided that targets the frequency range below the switching frequency. This simple, accurate model is able to predict the small-signal behaviors of the LLC converter with high accuracy at half of the switching frequency. At high modulation frequencies, the resonant converter behaves like a non-minimum phase system, which was neither recognized nor characterized before. This property can be represented by RHP zeros, and these RHP zeros may be an impediment for high-bandwidth design if not properly treated. Based on the proposed model, these unwanted RHP zeros can be mitigated by either changing the resonant tank design or by proper feedback compensation. Accurate modeling is essential for a high-performance high-bandwidth LLC converter.

Lithium-ion batteries are critical components in electric vehicles, portable electronics, and grid energy storage systems, necessitating advanced modeling techniques to enhance their safety, performance, and lifespan. This thesis presents the development and validation of a coupled electrical and lumped thermal model for cylindrical lithium-ion batteries along with a finite difference thermal model for spatial temperature prediction of cylindrical cell These models address key challenges in simulating real-world battery behavior. The electrical model utilizes a 2 R-C pair equivalent circuit framework integrated with a busbar model to account for current imbalances in parallel-connected cells. This model is a common equivalent circuit model used to represent a Li-ion cell using a voltage source, series resistor, and two resistor-capacitor pair connected in parallel. A lumped thermal model coupled with the electrical framework dynamically adjusts parameters based on temperature variations, achieving a voltage prediction error of less than 200 mV. Additionally, the thermal model employs a finite difference method (FDM) to solve the 3D transient heat conduction equation, providing spatial temperature distribution within cells and capturing critical gradients between core and surface temperatures. The vectorization of the thermal solver reduced simulation time by half, and its validation against Ansys™ simulations and module-level data demonstrated temperature prediction accuracy within a 2–3°C margin. The developed tool is scalable for any number of cylindrical cells arranged in a rectangular grid, addressing key gaps identified in the literature, including the need to simulate spatial and temporal non-uniformities in state-of-charge (SOC), state-of-health (SOH), and temperature, which significantly affect battery performance and lifespan. It provides a scalable, efficient tool for predicting thermal and electrical behavior across cell and module levels. This work contributes to the development of a tool that will, enable informed design decisions for next-generation energy storage systems. Future research could focus on extending the model to incorporate aging effects, enhanced thermal management configurations, and real-time simulations for battery management systems. / Master of Science / Lithium-ion batteries play a crucial role in powering electric vehicles, smartphones, and renewable energy storage systems. As demand for these technologies grows, ensuring that batteries operate safely and efficiently becomes increasingly important. This research focuses on developing computer models that simulate how lithium-ion batteries behave under different conditions, helping engineers design better and longer-lasting batteries. The project introduces two main models: an electrical model that predicts how energy flows through a battery and a thermal model that estimates how the battery heats up during use. The electrical model simplifies complex battery behavior by representing it with basic circuit components, while the thermal model uses advanced calculations to simulate how heat spreads within the battery. By combining these models, the research creates a tool that can predict how batteries perform over time and how temperature changes affect their efficiency and lifespan. One of the key achievements of this work is improving the speed and accuracy of these simulations. The thermal model was enhanced to calculate heat distribution more efficiently, cutting simulation times in half. The model was also validated against industry-standard tools like Ansys™, with results showing temperature predictions within a 2-3°C margin of error. This tool can simulate battery packs of any size, making it valuable for designing electric vehicle batteries and large-scale energy storage systems. By identifying potential issues like overheating or uneven energy distribution, the model helps engineers develop safer and more reliable battery technologies. Ultimately, this research contributes to the advancement of energy storage systems, supporting the transition to cleaner and more sustainable energy solutions for the future.

Electromagnetic coupling phenomena between overhead power transmission lines and other nearby structures are inevitable, especially in densely populated areas. The undesired effects resulting from this proximity are manifold and range from the establishment of hazardous potentials to the outbreak of alternate current corrosion phenomena. The study of this class of problems is necessary for ensuring security in the vicinities of the interaction zone and also to preserve the integrity of the equipment and of the devices there present. However, the complete modeling of this type of application requires the three- -dimensional representation of the region of interest and needs specific numerical methods for field computation. In this work, the modeling of problems arising from the flow of electrical currents in the ground (the so-called conductive coupling) will be addressed with the finite element method. Those resulting from the time variation of the electromagnetic fields (the so-called inductive coupling) will be considered as well, and they will be treated with the generalized PEEC (Partial Element Equivalent Circuit) method. More specifically, a special boundary condition on the electric potential is proposed for truncating the computational domain in the finite element analysis of conductive coupling problems, and a complete PEEC formulation for modeling inductive coupling problems is presented. Test configurations of increasing complexities are considered for validating the foregoing approaches. These works aim to provide a contribution to the modeling of this class of problems, which tend to become common with the expansion of power grids. / Les phénomènes de couplage électromagnétique entre les lignes aé- riennes de transmission d\'énergie et des structures voisines sont inévitables, surtout dans les zones densément peuplées. Les effets indésirables découlants de cette proximité sont variés, allant de l\'établissement des tensions dangereuses à l\'apparition de phénomènes de corrosion dus au courant alternatif. L\'étude de cette classe de problèmes est nécessaire pour assurer la sécurité dans les alentours de la zone d\'interaction et aussi pour préserver l\'intégrité des équipements et des dispositifs présents. Cependant, la modélisation compl ète de ce type d\'application implique la représentation tridimensionnelle de la région d\'intérêt et nécessite des méthodes numériques de calcul de champs spécifiques. Dans ces travaux, des problèmes liés à la circulation de courants électriques dans le sol (ou de couplage dit conductif) seront abordés avec la méthode des éléments finis. D\'autres problèmes résultants de la variation temporelle des champs électromagnétiques (ou de couplage dit inductif) seront aussi considérés et traités avec la méthode PEEC (Partial Element Equivalent Circuit) généralisée. Plus précisément, une condition limite particulière sur le potentiel électrique est proposée pour tronquer le domaine de calcul dans l\'analyse par éléments finis des problèmes de couplage conductif et une formulation PEEC complète pour la modélisation de problèmes de couplage inductif est présentée. Des con gurations tests de complexités croissantes sont considérées pour valider les approches précédentes. Ces travaux visent ainsi à apporter une contribution à la modélisation de cette classe de problèmes, qui tendent à devenir communs avec l\'expansion des réseaux électriques.

L’émergence du concept d’un avion plus électrique implique une refonte en profondeur des réseaux embarqués. L’axe principalement développé repose sur une augmentation de la tension du réseau et un passage au bus continu. Le contrôle des actionneurs électriques embarqués passe alors par l’utilisation massive de convertisseurs électroniques qui vont imposer des fronts de tension très raides et des contraintes particulières aux enroulements des machines. Les oscillations pseudopériodiques qui suivent ces fronts raides sont à l’origine de champs électriques intenses qui peuvent dépasser le seuil d’apparition des décharges partielles (PDIV) et de ce fait provoquer une dégradation rapide des isolants classiques qui sont à base de polymères. Le travail effectué dans cette thèse est centré sur l’étude d’une nouvelle méthode de conception des bobinages permettant la réduction des problèmes de décharges partielles. Un dispositif expérimental mis au point dans ce cadre reproduit les contraintes imposées par des convertisseurs modernes et permet de mesurer les tensions inter-spires d’une bobine. L’étude expérimentale met en évidence les phénomènes àprendre en compte avec ce type d’alimentation et donne une première idée des axes d’optimisation envisageables. Un modèle prédictif capable de donner la distribution des tensions inter-spires, en réponse à un front raide de tension, aide à identifier les points critiques. Les paramètres constitutifs de ce modèle ont été déterminés en utilisant des méthodes analytiques, expérimentales et numériques. Compte tenu de la complexité du modèle, un outil numérique automatisé a été élaboré afin de simuler le modèle des bobines étudiées. Plusieurs types de bobinage ont été analysés et optimisés avec succès. Cette optimisation consiste à diminuer la tension inter-spires en agissant sur l’arrangement des fils dans les encoches. L’utilisation des bobines optimisées avec cette méthode permet d’envisager une nette amélioration de la fiabilité des machines électriques. / The emergence of the concept of a more electric aircraft requires a major overhaul of onboard grid. The main developed axis is based on an increase in the grid voltage and a switch to DC bus. In this context, the onboard electric actuators are supplied through power electronic converters that will impose very fast voltage fronts and particular constraints in the windings of the machines. The transient over-voltages that follow the steep-fronted pulses are the source of intense electric fields which may exceed the partial discharge inception voltage (PDIV) and cause a rapid deterioration of polymer based insulators. This thesis focuses on the study of a new design method of the windings in order to reduce problems of partial discharges. An experimental device developed in this framework reproduces the constraints of modern converters and allows measuring the turn-to-turn voltages of a coil. The experimental study shows the phenomena to be considered with this type of power supply and gives an idea of possible areas for optimization. A predictive model able to give the distribution of turn-to-turn voltages, in response to a steep-fronted voltage, helps to identify critical points. The constitutive parameters of this model were determined using analytical, experimental and numerical methods. Given the complexity of the model, an automated numerical tool has been developed in order to simulate the model of studied coils. Several types of coil have been analyzed and optimized successfully. This optimization consists in reducing the turn-to-turn voltages by acting on the arrangement of the wires in the slots. The use of optimized coils with this method allows envisaging a significantimprovement in the reliability of electrical machines.

Les phénomènes de couplage électromagnétique entre les lignes aé- riennes de transmission d\'énergie et des structures voisines sont inévitables, surtout dans les zones densément peuplées. Les effets indésirables découlants de cette proximité sont variés, allant de l\'établissement des tensions dangereuses à l\'apparition de phénomènes de corrosion dus au courant alternatif. L\'étude de cette classe de problèmes est nécessaire pour assurer la sécurité dans les alentours de la zone d\'interaction et aussi pour préserver l\'intégrité des équipements et des dispositifs présents. Cependant, la modélisation compl ète de ce type d\'application implique la représentation tridimensionnelle de la région d\'intérêt et nécessite des méthodes numériques de calcul de champs spécifiques. Dans ces travaux, des problèmes liés à la circulation de courants électriques dans le sol (ou de couplage dit conductif) seront abordés avec la méthode des éléments finis. D\'autres problèmes résultants de la variation temporelle des champs électromagnétiques (ou de couplage dit inductif) seront aussi considérés et traités avec la méthode PEEC (Partial Element Equivalent Circuit) généralisée. Plus précisément, une condition limite particulière sur le potentiel électrique est proposée pour tronquer le domaine de calcul dans l\'analyse par éléments finis des problèmes de couplage conductif et une formulation PEEC complète pour la modélisation de problèmes de couplage inductif est présentée. Des con gurations tests de complexités croissantes sont considérées pour valider les approches précédentes. Ces travaux visent ainsi à apporter une contribution à la modélisation de cette classe de problèmes, qui tendent à devenir communs avec l\'expansion des réseaux électriques. / Electromagnetic coupling phenomena between overhead power transmission lines and other nearby structures are inevitable, especially in densely populated areas. The undesired effects resulting from this proximity are manifold and range from the establishment of hazardous potentials to the outbreak of alternate current corrosion phenomena. The study of this class of problems is necessary for ensuring security in the vicinities of the interaction zone and also to preserve the integrity of the equipment and of the devices there present. However, the complete modeling of this type of application requires the three- -dimensional representation of the region of interest and needs specific numerical methods for field computation. In this work, the modeling of problems arising from the flow of electrical currents in the ground (the so-called conductive coupling) will be addressed with the finite element method. Those resulting from the time variation of the electromagnetic fields (the so-called inductive coupling) will be considered as well, and they will be treated with the generalized PEEC (Partial Element Equivalent Circuit) method. More specifically, a special boundary condition on the electric potential is proposed for truncating the computational domain in the finite element analysis of conductive coupling problems, and a complete PEEC formulation for modeling inductive coupling problems is presented. Test configurations of increasing complexities are considered for validating the foregoing approaches. These works aim to provide a contribution to the modeling of this class of problems, which tend to become common with the expansion of power grids.