Power grids are undergoing a dominant transformation due to the increasing number of power electronic devices installed in generation, transmission, distribution, and demand, etc. Compared with traditional power systems dominated by synchronous generators, the growth of power electronics induces new behaviour of power network dynamics, physical constraints, running costs, etc, which urgently calls for a new framework of modeling, control, and stability analysis.

This thesis first focuses on the impedance method for modeling ac-dc power converters in power systems, designing the controllers, and analyzing the stability. A tool called Impedance circuit model is proposed to intuitively derive the impedance model of a grid-connected power converter. Compared with the conventional all-in-one impedance model, the proposed tool maps the control parameters explicitly to discrete virtual impedances in an impedance circuit and meanwhile captures the multi-control-loop interaction and coupling of a converter. Another tool named frame-dynamics-embedding impedance model is also proposed to systematically embed the frame dynamics (grid synchronization) of a power converter into its impedance model. This tool also enables the impedance model of power networks by making the reference frames of different devices consistent. The frame-transformation impedance model is finally proposed to reveal the relationship of impedance models in synchronous dq and stationary alpha/beta frames. These proposed tools make up an impedance modeling framework, which are applied to the most fundamental and widely-used converters in power systems [i.e., the voltage-source inverters (VSIs)] as examples in this thesis. Both simulation and experiment tests are conducted to validate the corresponding theoretical analysis.

VSIs are the widely-used ac-dc converters which integrate sources or loads to the utility ac grids. But with the increasing use of dc in the ac-dominated power systems, an ac-dc converter is also required to perform as an interlinking converter, which links dc networks and the utility ac grids. It forms hybrid ac-dc grids and brings more integration and control problems. Hence, in addition to conventional VSIs, this thesis also explores novel topologies and control algorithms of ac-dc converters with advanced features to connect dc networks to ac grids. They are able to improve the grid integration and enhance the grid reliability (e.g., bidirectional voltage stiffness transfer, bipolar-dc-imbalance handling, dc-side fault blocking, high-frequency galvanic isolation, etc). Down-scaled prototypes for them are built and tested to validate the corresponding theoretical analysis and the proposed control algorithms.

It is expected that the work in this thesis can inspire not only the fundamental framework of modeling and control analysis, but also the advanced development of converter topologies and control methods of power converters in power system applications.