<p>The ongoing and rapidly accelerating integration of inverter-based resources (IBRs), such as solar panels, into power distribution systems has heightened the importance of computational tools that can be used to study the dynamics of such systems. IBRs use power electronics to interface the energy sources to the grid, thereby introducing faster dynamics than their electromechanical counterparts, which could lead to instabilities in distribution systems and microgrids. Hence, there is a need for conducting simulations of distribution systems containing large numbers of single- and three-phase inverters, which could be operating under either grid-following or grid-forming modes.</p> <p>A key objective of this thesis is to derive detailed, high-fidelity models of inverters and their controls in the context of unbalanced distribution networks. In addition, a diesel synchronous generator model is derived, for the sake of completeness. The main contribution of this work is that these models are developed for use in a novel simulation toolbox called Dynamic Simulation Tool using a Sparse Tableau Approach in Python, DynaSTPy (pronounced dynasty). This thesis outlines how the components can be modeled in the sparse tableau framework as electrical networks with topology described using a node-branch incidence matrix. In addition, the thesis explains how controller dynamics and constraints can be handled within this framework. These models are tailored to seamlessly integrate into the DynaSTPy toolbox. The proposed approach can be readily extended to model other such components in the future.</p>