Abstract
In this chapter, we present a novel scalable statistical simulation approach for large power grid network analysis considering process variations[92]. The new algorithm is very scalable for large networks with a large number of random variables. Our work is inspired by the recent work on variational model order reduction using fast balanced truncation method (called variational Poor man’s TBR method, or varPMTBR [134]). The new method, called varETBR, is based on the recently proposed ETBR method[9394]. To consider the variational parameters, we extend the concept of response Gramian, which was used in ETBR to compute the reduction projection subspace, to the variational response Gramian. Then MC-based numerical integration is employed to multiple-dimensional integrals. Different from traditional reduction approaches, varETBR calculates the variational response Gramians, considering both system and input source variations, to generate the projection subspace. In this way, much more efficient reduction can be performed for interconnects with massive terminals like power grid networks[177]. Furthermore, the new method is based on the globally more accurate balanced truncation reduction method instead of the less accurate Krylov subspace method as in EKS/IEKS[191,89].
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Notes
- 1.
Practically, the interesting frequency range is always bounded.
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Shen, R., Tan, S.XD., Yu, H. (2012). Statistical Power Grid Analysis by Variational Subspace Method. In: Statistical Performance Analysis and Modeling Techniques for Nanometer VLSI Designs. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0788-1_10
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