The widespread integration of power converters in applications such as microgrids and data centers has introduced significant stability challenges. This dissertation presents a novel approach to modeling and comprehensive stability analysis for both single-phase and three-phase converters, addressing vital gaps in the existing literature. The first part of the dissertation (Chapters 2 to 4) focuses on single-phase power supply units, proposing an impedance model and a loop gain model based on dq-frame analysis. These models have been validated through extensive experimental testing, demonstrating their effectiveness in stability analysis across a range of system configurations, including single-phase, three-phase three-wire, and three-phase four-wire systems. The second part (Chapters 5 and 6) examines three-phase converters used for integrating renewable energy into microgrids. It introduces a grid-forming control, followed by a detailed investigation into its impedance modeling and stability assessment. This part specifically tackles the challenges posed by the appearance of right-half-plane poles in stability analysis, proposing a new stability margin index to address these issues. The efficacy of these research findings is further substantiated by the development and implementation of a Power-Hardware-in-the-Loop testbed, providing practical validation. Overall, this dissertation has enhanced the modeling, understanding, and management of stability issues in power electronics systems, offering valuable insights and methodologies that are likely to influence future research and development in the field. / Doctor of Philosophy / Power electronics play a crucial role in many of today's advanced technologies, including Renewable Energy (like wind and solar power), Electric Vehicles, Cloud Computing, and Artificial Intelligence. In renewable energy, power electronics are key for converting energy sources for efficient grid integration. Electric vehicles rely on power converter systems for charging their batteries and driving their motors. Similarly, in Cloud Computing and Artificial Intelligence, power electronics ensure that the computers and servers in data centers have a steady and reliable power supply for operation. However, using these advanced power electronics on a large scale, like in wind farms or data centers, can lead to challenges, including many reported system instability issues. These issues highlight the importance of a thorough analysis and understanding of the behavior and interaction of power electronics systems. In addressing these challenges, power electronics converters, conceptualized as a blend of circuits and control systems, demand comprehensive modeling from the ground up. Such modeling is essential to understanding their behavior, ranging from individual components to the entire system. This is key to establishing a clear connection between intricate design details and overall system performance. With power electronics systems becoming more complex and the continual emergence of new technologies, there remains a significant array of unanswered questions, especially in the domain of stability analysis for AC power electronics systems. This dissertation delves into two prominent modeling methods for stability analysis: impedance modeling and loop gain modeling. By exploring and addressing specific gaps identified in prior research, this work aims to contribute to a more profound understanding and enhanced application of these critical methods. The research presented in this dissertation is methodically divided into two main sections. The first section, including Chapter 2 to Chapter 4 is dedicated to exploring single-phase converter power supply units (PSUs) systems. This section introduces innovative models for analyzing their stability, applicable to single-phase PSUs in various system configurations, including both single-phase and three-phase setups. This modeling approach is a significant step forward in understanding and enhancing the stability of single-phase PSU loads. The second section, including Chapter 5 and Chapter 6, delves into the analysis of three-phase converters used in integrating renewable energy sources into microgrids. A notable feature of these converters is their grid-forming control mechanism, which includes a new frequency and power droop control loop. This part also explores modeling the impact of these converters on microgrid stability. Moreover, the issue of right-half-plane (RHP) poles in impedance analysis- a complex problem that can affect stability analysis is addressed. It proposes innovative methods for measuring stability in such conditions. In conclusion, this research made advancements in the modeling for stability analysis of power converter systems. For single-phase converters, the developed impedance model and loop gain model, based on dq-frame analysis, have been proven to be accurate. These models are versatile for stability analysis in various AC systems with single-phase PSU loads. In the study of three-phase converters, the grid-forming converter was successfully designed to support the grid as a distributed energy resource interface. This design contributes positively to microgrid stability. Furthermore, to address the presence of RHP poles in stability analysis, a new stability margin index was defined to better understand and manage these challenges. These findings represent important steps forward in the field of power electronics and contribute valuable insights for future research and development.

This work utilizes the small-signal impedance-based stability analysis method to develop stability assessment criteria for a single-aisle turboelectric aircraft with aft boundary-layer propulsion (STARC-ABL) system. The impedance-based stability analysis method outperforms other stability analysis methods because it does not require detailed information of individual components for system integration, therefore, a system integrator can just require the vendors to make the individual components meet the impedance specifications to ensure whole system stability. This thesis presents models of a generator, motor, housekeeping loads, and battery all with power electronics interface which form an onboard electrical system and analyzes the relationship between the impedance shape of each component and their physical design and control loop design. Based on the developed small-signal model of the turbine-generator-rectifier subsystem and load subsystem, this thesis analyzes the impact of electromechanical dynamics of the turbofan passed through the generator on the dc distribution system, concluding that the rectifier can mitigate the impact. Finally, to ensure the studied system stable operation during the whole flying profile, the thesis provides impedance specifications of the dc distribution system and verifies the specifications with several cases in time-domain simulations. / M.S. / Electric aircraft propulsion (EAP) technologies have been a trend in the aviation industry for their potential to reduce environmental emissions, increase fuel efficiency and reduce noise for commercial airplanes. Achieving these benefits would be a vital step towards environmental sustainability. However, the development of all-electric aircraft is still limited by the current battery technologies and maintenance systems. The single-aisle turboelectric aircraft with aft boundary-layer (STARC-ABL) propulsion concept is therefore developed by NASA aiming to bridge the gap between the current jet fuel-powered aircraft and future all-electric vehicles. The plane uses electric motors powered by onboard gas turbines and transfers the generated power to other locations of the airplane like the tail fan motor to provide distributed propulsion. Power electronics-based converter converts electricity in one form of electricity to another form, for example, from ac voltage to dc voltage. This conversion of power is very important in the whole society, from small onboard chips to Mega Watts level electrical power system. In the aircraft electrical power system context, power electronics converter plays an important role in the power transfer process especially with the recent trend of using high voltage dc (HVDC) distribution instead of conventional ac distribution for the advantage of increased efficiency and better voltage regulation. The power generated by the electric motors is in ac form. Power electronics converter is used to convert the ac power into dc power and transfer it to the dc bus. Because the power to drive the electric motor to provide distributed propulsion is also in ac form, the dc power needs to be converted back into ac power still through a power electronics converter. With a high penetration of power electronics into the onboard electrical power system and the increase of electrical power level, potential stability issues resulted from the interactions of each subsystem need to be paid attention to. There are mainly two stability-related studies conducted in this work. One is the potential cross-domain dynamic interaction between the mechanical system and the electrical system. The other is a design-oriented study to provide sufficient stability margin in the design process to ensure the electrical system’s stable operation during the whole flying profile. The methodology used in this thesis is the impedance-based stability analysis. The main analyzing process is to find an interface of interest first, then grouped each subsystem into a source subsystem and load subsystem, then extract the source impedance and load impedance respectively, and eventually using the Nyquist Criterion (or in bode plot form) to assess the stability with the impedance modeling results. The two stability-related issues mentioned above are then studied by performing impedance analysis of the system. For the electromechanical dynamics interaction study, this thesis mainly studies the rotor dynamics’ impact on the output impedance of the turbine-generator-rectifier system to assess the mechanical dynamics’ impact on the stability condition of the electrical system. It is found that the rotor dynamics of the turbine is masked by the rectifier; therefore, it does not cause stability problem to the pre-tuned system. For the design-oriented study, this thesis mainly explores and provides the impedance shaping guidelines of each subsystem to ensure the whole system's stable operation. It is found that the stability boundary case is at rated power level, the generator voltage loop bandwidth is expected to be higher than 300Hz, 60˚ to achieve a 6dB, 45˚ stability margin, and load impedance mainly depends on the motor-converter impedance.

Ces dernières années, un intérêt croissant pour les systèmes électroniques de puissance a été motivé par l'émergence de sources d'énergie distribuées et renouvelables raccordées aux réseaux électriques. Dans ce contexte, la nécessité de topologies de faibles puissances alimentées par quelques modules photovoltaïques, en évitant l'utilisation de transformateurs, a ouvert l'étude de convertisseurs spéciaux et l’étude des stratégies de commande associées afin d’assurer la stabilité, la fiabilité et un rendement élevé du dispositif. Une possible solution est d’utiliser un dispositif générique connu dans la littérature scientifique et commerciale comme « micro-onduleur » ou «convertisseur intégré au module » qui avec le module photovoltaïque définit un produit « plug and play » appelé "module AC".Ce travail est consacré à l'étude d'un micro-onduleur monophasé avec deux étapes sans transformateur raccordée au réseau. La topologie proposée est composé d’un convertisseur DC-DC non isolé élévateur avec un gain quadratique et un onduleur réducteur lié au réseau connectés en cascade. Le convertisseur DC-DC extrait en permanence la puissance maximale du module photovoltaïque malgré les changements dans les conditions environnementales. L'étape DC-AC injecte la puissance extraite par l'étape DC-DC dans le réseau et assure un niveau élevé de qualité de l’énergie. Les efforts de recherche de ce travail sont concentrés sur la mise au point de commandes utilisant comment base, la théorie de contrôle par mode de glissement, qui conduit à une mise en œuvre simple avec une description théorique complète validée á partir de simulations et expérimentations.Après avoir décrit l'état de l’art dans le premier chapitre, le manuscrit est divisé en quatre chapitres, qui sont dédiés respectivement à l’algorithme de recherche du point de puissance maximale (MPPT), á l’étape de conversion DC-DC, á l'étape de conversion DC-AC et finalement au micro-onduleur complet. Un nouvel algorithme de recherche extrémal du point de puissance maximale est développé (SM-ESC). Pour la étape DC-DC, le convertisseur élévateur quadratique avec seulement un interrupteur contrôlé est étudié utilisant le concept de résistance sans perte par mode de glissement (de l’acronyme anglais : Sliding-Mode Loss-Free-Resistor – SM-LFR) afin d’obtenir un gain de tension élevé avec un fonctionnement sûr et compatible avec l’algorithme MPPT. Pour la étape DC-AC, le convertisseur de pont complet est contrôlé comme un onduleur de source de puissance (de l’acronyme anglais : Power Source Inverter - PSI) en utilisant une commande par mode de glissement qui poursuit une référence sinusoïdale de courant de sortie. Cette commande est complétée par une boucle de régulation de la tension du bus DC qui assure une haute qualité d’énergie injectée dans le réseau. Enfin, les trois étapes constitutives sont fusionnées pour obtenir un micro-onduleur complètement contrôlé par la technique de mode de glissement, ce qui constitue le principal résultat et contribution de cette thèse. / These last years, a growing interest in power electronic systems has been motivated by the emergence of distributed renewable energy resources and their interconnection with the grid. In this context, the need of low power topologies fed by a few photovoltaic modules avoiding the use of transformers opens the study of special converters and the associated control strategies ensuring stability, reliability and high efficiency. A resulted generic device known in the commercial and scientific literature as “microinverter” or “module integrated converter” performs a plug and play product together with the PV module called an “AC module”.This work is devoted to the study of a transformer-less single-phase double-stage grid-connected microinverter. The proposed topology has a non-isolated high-gain boost type DC-DC converter and a non-isolated buck type DC-AC converter connected in cascade through a DC bus. The DC-DC converter permanently extracts the maximum power of the PV module ensuring at the same time a good performance coping with power changes introduced by the change in the environmental conditions. The DC-AC stage injects the power extracted by the DC-DC stage into the grid ensuring a high level of power quality. The research efforts focus on the involved control functions based on the sliding mode control theory, which leads to a simple implementation with a comprehensive theoretical description validated through simulation and experimental results.After giving the state-of-the-art in the first chapter, the manuscript is divided into four chapters, which are dedicated to the Maximum Power Point Tracking (MPPT), the DC-DC stage and its control, the DC-AC stage and its control and the complete microinverter. A new Extremum Seeking Control (ESC) MPPT algorithm is proposed. The single-switch quadratic boost converter is studied operating as a Loss-Free-Resistor (LFR) obtaining a high DC output voltage level with a safe operation. The full-bridge converter is controlled as a Power Source Inverter (PSI) using a simple sliding-mode based tracking law, regulating the voltage of the DC bus and then ensuring a high power quality level in the grid connection. Finally, the three building blocks are merged to obtain a sliding mode controlled microinverter constituting the main result and contribution of the work