Waveform relaxation methods for the simulation of systems of differential algebraic equations with applications to electric power systems
This thesis reports the continuing effort towards establishing a parallel numerical algorithm known as Waveform Relaxation (WR) for simulating large power system dynamics. Past work has shown the feasibility of this method for frequency studies involving the classical model generator and loads modeled as constant impedances. This work has been expanded to include voltage studies where the loads are modeled as constant power loads and the load terminals are kept intact, yielding a set of differential/algebraic equations (DAEs). In addition to power systems, systems of differential/algebraic equations arise in connection with singular perturbation, control theory, robot systems, and many other applications in the fields of mechanical and chemical engineering, economics, and physics. The main contribution of this thesis is to define and prove conditions under which the waveform relaxation algorithm for a general system of DAEs will converge. The algorithm is then tailored for the simulation of large-scale power systems. Power systems are shown to exhibit several dynamic characteristics which make them suitable for simulation by the waveform relaxation algorithm. One of the main contributions in this area includes a method for determining a fault-dependent partitioning of the power system for parallel implementation. Simulation results for small, medium, and large test systems are included.
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign