Numerical Analysis and Computation Commons^™

Multigrid For The Nonlinear Power Flow Equations, Enrique Pereira Batista

Mathematics Theses and Dissertations

The continuously changing structure of power systems and the inclusion of renewable
energy sources are leading to changes in the dynamics of modern power grid,
which have brought renewed attention to the solution of the AC power flow equations.
In particular, development of fast and robust solvers for the power flow problem
continues to be actively investigated. A novel multigrid technique for coarse-graining
dynamic power grid models has been developed recently. This technique uses an
algebraic multigrid (AMG) coarsening strategy applied to the weighted
graph Laplacian that arises from the power network's topology for the construction
of coarse-grain approximations to …

Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad

Electronic Thesis and Dissertation Repository

Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits.

The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic …

An Adaptive Approach To Gibbs’ Phenomenon, Jannatul Ferdous Chhoa

Master's Theses

Gibbs’ Phenomenon, an unusual behavior of functions with sharp jumps, is encountered while applying the Fourier Transform on them. The resulting reconstructions have high frequency oscillations near the jumps making the reconstructions far from being accurate. To get rid of the unwanted oscillations, we used the Lanczos sigma factor to adjust the Fourier series and we came across three cases. Out of the three, two of them failed to give us the right reconstructions because either it was removing the oscillations partially but not entirely or it was completely removing them but smoothing out the jumps a little too much. …