NDLI: Deterministic Random Walk: A New Preconditioner for Power Grid Analysis

Content Provider	IEEE Xplore Digital Library
Author	Jia Wang Xuanxing Xiong Xingwu Zheng
Copyright Year	1993
Abstract	Iterative linear equation solvers rely on high-quality preconditioners to achieve fast convergence. For sparse symmetric systems arising from large power grid analysis problems, however, preconditioners generated by traditional incomplete Cholesky factorization are usually of low quality, resulting in slow convergence. On the other hand, preconditioners generated by random walks are quite effective to reduce the number of iterations, though requiring considerable amount of time to compute in a stochastic manner. We propose in this paper a new preconditioning technique for power grid analysis, named deterministic random walk that combines the advantages of the above two approaches. Our proposed algorithm computes the preconditioners in a deterministic manner to reduce computation time, while achieving similar quality as stochastic random walk preconditioning by modifying fill-ins to compensate dropped entries. We have proved that for such compensation scheme, our algorithm will always succeed, which otherwise cannot be guaranteed by traditional incomplete factorizations. We demonstrate that by incorporating our proposed preconditioner, a conjugate gradient solver is able to outperform a state-of-the-art algebraic multigrid preconditioned solver for dc analysis, and is very efficient for transient simulation on public IBM power grid benchmarks.
Sponsorship	IEEE Computer Society Association for Computing Machinery (ACM)/SIGDA IEEE Computer Society Technical Committee on Design Automation
Starting Page	2606
Ending Page	2616
Page Count	11
File Size	2182434
File Format	PDF
ISSN	10638210
Volume Number	23
Issue Number	11
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Power grids Vectors Approximation algorithms Monte Carlo methods Mathematical model Algorithm design and analysis Transient analysis random walks. Power gird analysis preconditioned conjugate gradient preconditioner random walks
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Software Hardware and Architecture

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