The paralleling of power converters connected to the grid for power-sharing is a widely used technique. In this context, the design framework for a low-cost, lightweight, compact, and high-performance optimum configuration is an open research problem. This thesis proposes an innovative Multi-Objective Hierarchical Optimization Design Framework (MO-HO-DF) for an Alternating Current (AC) grid interface with N interleaved H-bridges, each with M parallel ``to-be-determined'' switches, connected through coupling inductances (Lf). A total of eight Figures of Merit (FOMs) were identified for the design framework optimization. A rigorous model of the power electronic system is presented. Next, a highly computationally efficient algorithm for the estimation of the required frequency modulation ratio (mf) to meet current harmonic performance requirements for any given configuration is proposed. Then, the concept and implementation of the algorithm are presented for the MO-HO-DF. The effectiveness of the design optimization framework is demonstrated by comparing it to a base case solution. Finally, the design calculations are validated via Piecewise Linear Electrical Circuit Simulation (PLECS) software with manufacturer-provided Three-Dimensional (3D) power semiconductor models that include thermal modelling.

In particular, when an H-bridge is interfaced with a single-phase grid, it requires controllers to regulate the voltages and currents in the system. In this context, the static optimization of controllers responsible for Direct Current (DC) bus voltage regulation and AC regulation, considering time-domain and frequency-domain behaviours, is an open research problem. Firstly, this thesis proposes a method to obtain FOMs with the use of inbuilt functions in MATLAB software. Then for the Type-II Proportional+Integral (PI) controller, a single-variable two-objective convex optimization is proposed. Next, for the Proportional+Multi-Resonant (PMR) controller, three-variable five-objective convex optimization is proposed. The design of the PMR controller is a multi-variable problem that can inherit the principles of a hierarchical framework and leverage the effect of a design variable on the final optimization result. Thus, the work on PMR controller design optimization is extended to a three-level hierarchical design framework and evaluates all six possible paths for optimization. Finally, enhanced macro-model-based MATLAB simulation results are provided to verify the performance of controller designs and generate statistical insights.