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A Nonlinear Algebraic Multigrid Framework for the Power Flow Equations

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/16m1109965· OSTI ID:1671184
 [1];  [2];  [1]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Cornell Univ., Ithaca, NY (United States). Dept. of Computer Science
+ Show Author Affiliations
Multigrid is a highly scalable class of methods most often used for solving large linear systems. In this paper we develop a nonlinear algebraic multigrid framework for the power flow equations, a complex quadratic system of the form $${diag}({v})\overline{Y{v}}={s}$$, where $$Y$$ is approximately a complex scalar rotation of a real graph Laplacian. This is a standard problem that needs to be solved repeatedly during power grid simulations. A key difference between our multigrid framework and typical multigrid approaches is the use of a novel multiplicative coarse-grid correction to enable a dynamic multigrid hierarchy. We also develop a new type of smoother that allows one to coarsen together the different types of nodes that appear in power grid simulations. In developing a specific multigrid method, one must make a number of choices that can significantly affect the method's performance, such as how to construct the restriction and interpolation operators, what smoother to use, and how aggressively to coarsen. In this paper, we make simple but reasonable choices that result in a scalable and robust power flow solver. Experiments demonstrate this scalability and show that it is significantly more robust to poor initial guesses than current state-of-the-art solvers.
Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
US Air Force Office of Scientific Research (AFOSR); USDOE Advanced Research Projects Agency - Energy (ARPA-E)
Grant/Contract Number:
AC52-07NA27344; AR0000230
OSTI ID:
1671184
Report Number(s):
LLNL-JRNL--717563; 861365
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 3 Vol. 40; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

Figures / Tables (9)

Table 1(p. 12)table Table 1
Fig. 1(p. 13)figure Fig. 1
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Fig. 7(p. 18)figure Fig. 7
Fig. 8(p. 20)figure Fig. 8

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Related Subjects

97 MATHEMATICS AND COMPUTING
algebraic multigrid
multiplicative correction
nonlinear multigrid
power flow