The unconventional improvements in the power electronics field have been the primary reason for massive deployment of renewable energy sources in the electrical power grid over the past several decades. This needed trend, together with the increasing penetration of micro-, and nano- grids, is bringing significant improvements in system controllability, performance, and energy availability, but is fundamentally changing the nature of electronically-interfaced sources and loads, altering their conventionally mild aggregate dynamics, and inflicting low- and high- frequency dynamic interactions that never before existed at this magnitude. This problem is not restricted only to the grid; modern electronic power distribution systems built for airplanes, ships, electric vehicles, data-centers, and homes, comprise dozens, even hundreds of power electronics converters, produced by different manufacturers, who provide very limited details on converters' dynamic behavior - distinctiveness that has the highest impact on how two converters, or converter and a system interact. Consequently, substantial dispersion of power electronics into the future grid will significantly depend on engineers' capability to understand how to model and dynamically control power flow and subsystem interactions. It is therefore essential to continue developing innovative methods that allow easier system-level modeling, continuous monitoring of dynamic interactions, and advanced control concepts of power electronics converters and systems. The dissertation will start with a "black box" approach to modeling of three-phase power electronics converters, introducing a method to remove source and load dynamics from in-situ measured terminated frequency responses. It will be then shown how converter, itself, can perform an online stability assessment knowing its own unterminated dynamics, and being able to measure all terminal immittances. The dissertation will further advance into an approach to control power electronics converters based on the electro-mechanical duality with synchronous machines, and end with selected examples of system-level operation, where small-signal instability in multi-source power systems can be mitigated using this concept. / Ph. D. / The modern technological advancements and ever-increasing needs for a sustainable future silently demand a serious revision of the conventional practice in electricity production, distribution, and utilization. These technologies are already challenging the limits of the biggest and most complex system ever built by humankind - the electrical grid. One practical solution to this problem is much higher dispersion of electronic power conversion systems capable of decoupling dynamics between system sources, distribution, and loads, while improving system controllability, reliability, and efficiency. Such a trend is already happening, and there has been an increased immersion of power electronics converters in electric cars, ships, airplanes, and the grid, in an effort to replace their traditional thermal, mechanical, hydraulic, and pneumatic systems. The goals have been to reduce the size, weight, and operational costs while increasing efficiency and reliability. In all these applications, a majority of energy sources and loads are interfaced to the power system through power electronics converters ranging in power from few watts to hundreds of megawatts. However, massive dispersion of power electronics into the future grid will significantly depend on engineers’ capability to understand how to model and dynamically control power flow and subsystem interactions. It is important to continue researching innovative methods that allow easier system-level modeling, continuous monitoring of interactions, and advanced control concepts of power electronics converters and systems. This dissertation hence addresses modeling of power electronics converters using their behavioral models, and shows how these models can assist the stability assessment of the system converters operate in. Additionally, dissertation presents an alternative way to control power electronics converters to behave as synchronous machines, and how this concept can be used to mitigate some stability problems.