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.

The power converter is one of the key components in power system applications such as high voltage direct current (HVDC) systems and the grid connection of intermittent sources such as wind and solar power. However, the increased penetration of converter-based generation introduces challenges, such as sub-synchronous interaction between the converter control system and the grid. These control interactions are characterized by fast-growing, subsynchronous oscillations (SSO). This thesis deals with the analysis of sub-synchronous control interactions (SSCI) between doubly-fed induction generator (DFIG)-based wind farms and series compensated transmission lines. Moreover, the thesis aims to identify a method for mitigating the sub-synchronous oscillations using a static synchronous compensator (STATCOM), with a supplementary damping controller. The study is based on work in PSCAD/EMTDC and uses a system based on the IEEE first benchmark model, acting as a grid, and the scaled power output of a DFIG turbine model, modeling a wind farm. Initial impedance-based analysis in the frequency domain shows that the DFIG wind farm has a negative resistance throughout the sub-synchronous frequency range. A negative resistance may result in negative damping of the system and further introduce the risk of instability. The wind farm resistance and, in turn, system stability is affected by the current control loop of the DFIG-converter. The transmission line compensation factor largely impacts the system stability, while the power output has a minor effect. A time-domain analysis is performed to verify the result of the frequency domain analysis. Further on, a grid-forming STATCOM is added to the system for VAr compensation. Additional stability analysis shows that even though improvingthe stability, the STATCOM alone is not adequate to mitigate the SSCI. The proposed damping strategy is based on modifying the STATCOM voltage reference andcan be divided into three steps: detecting the SSO, estimating the sub-synchronous component, and modifying the extracted signal. The detection algorithm is based on a half-cycle comparator, while the modification is done through a proportional gain. When estimating the sub-synchronous components, two methods are proposed and compared. The first estimation method is based on a conventional power system stabilizer (PSS) method, and the second is afilter-less method.