Abstract
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 the original model. Motivated by this technique,
a new multigrid method for the AC power flow equations is developed using this
coarsening procedure. The AMG coarsening procedure is used to build a multilevel
hierarchy of admittance matrices, which automatically leads to a hierarchy of
nonlinear power flow equations. The hierarchy of power flow equations is then used
in a full approximation scheme (FAS) and a multiplicative correction multigrid
framework to produce multilevel solvers for the power flow equations.
Degree Date
Fall 12-19-2020
Document Type
Dissertation
Degree Name
Ph.D.
Department
Mathematics
Advisor
Barry Lee
Subject Area
Computer Science
Number of Pages
97
Format
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License
Recommended Citation
Pereira Batista, Enrique, "Multigrid for the Nonlinear Power Flow Equations" (2020). Mathematics Theses and Dissertations. 10.
https://scholar.smu.edu/hum_sci_mathematics_etds/10
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Power and Energy Commons
