Dynamic simulation of a large-scale electric power system involves solving a large number of differential algebraic equations (DAEs) every simulation time-step. With the ever-growing size and complexity of power grid, dynamic simulation becomes more and more time-consuming and computationally difficult using conventional sequential simulation techniques. This thesis presents a fully distributed approach intended for implementation on High Performance Computer (HPC) clusters. A novel, relaxation-based domain decomposition algorithm known as Parallel-General-Norton with Multiple-port Equivalent (PGNME) is proposed as the core technique of a two-stage decomposition approach to divide the overall dynamic simulation problem into a set of sub problems that can be solved concurrently. While the convergence property has traditionally been a concern for relaxation-based decomposition, an estimation mechanism based on multiple-port network equivalent is adopted as the preconditioner to enhance the convergence of the proposed algorithm. The algorithm is presented in detail and validated both in terms of accuracy and capabilit