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.
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Pereira Batista, Enrique, "Multigrid for the Nonlinear Power Flow Equations" (2020). Mathematics Theses and Dissertations. 10.