Electrical power is the bedrock of modern civilization, and the large-scale hierarchical structure of bulk generation, transmission, and distribution has served us well for more than one hundred years. Currently however, the landscape of energy production is shifting, as economic, environmental, and technological factors are pushing power generation towards a future dominated by distributed generation from renewable energy sources. While grid-wide control strategies and architectures in bulk power systems were designed for slow time-scales and large synchronous generators, renewable energy interfaced through power electronic inverters allows for rapid response and greater flexibility in both local controller design and grid-wide control architectures. This thesis focuses on exploring the limitations of both local controller design and control architectures for inverter-based power grids. Our contributions can be broadly divided into two categories.

First, we study the classic primary droop controllers proposed for inverter-based power grids, and provide the first nonlinear analysis of the closed-loop frequency and voltage dynamics resulting from the controllers. We present tight analytic conditions for the existence and uniqueness of stable equilibrium points, thereby quantifying the fundamental limits of these controllers. In the second portion of the thesis, we propose and analyze a distributed control architecture which takes the place of the classical centralized secondary control layer. The distributed controllers combine classic droop ideas from power systems with agreement algorithms studied in cooperative control and multi-agent systems, leading to a scalable control architecture which achieves centralized performance. The algorithms require only sparse communication between nearby inverters in the power grid, and require no a priori knowledge of the grid topology or load demands.

We present extensive analysis results, along with experimental results validating our designs, and outline directions for future research.