Stochastic variational analysis of large power grids considering intra-die correlations

Praveen Ghanta, Sarma Vrudhula, Sarvesh Bhardwaj, Rajendran Panda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

12 Scopus citations


For statistical timing and power analysis that are very importantproblems in the sub-100nm technologies, stochastic analysis of power grids that characterizes the voltage fluctuations due to process variations is inevitable. In this paper, we propose an efficient algorithm for the variational analysis of large power grids in the presence of a significant number of Gaussian intra-die process variables that are correlated. We consider variations in the power grid's electrical parameters as spatial stochastic processes and express them as linear expansions in an orthonormal series of random variables using the Karhunen-Loéve(KLE) method. The voltage response is then represented as an orthonormal polynomial series and the coefficients are obtained optimally using the Galerkin method. We propose a novel method to separate the stochastic analysis for the random variables that effect only the inputs (e.g, drain currents) and for those that effect the system parameters as well (e.g., conductance, capacitance). We show that this parallelism can result in significant speed-ups in addition to the speed-ups inherent to Galerkin-based methods. Our analysis has been applied to several industrial power grids and the results show speed-ups of up to two orders of magnitude over Monte Carlo simulations for comparable accuracy.

Original languageEnglish (US)
Title of host publication2006 43rd ACM/IEEE Design Automation Conference, DAC'06
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)1595933816, 1595933816, 9781595933812
StatePublished - 2006
Event43rd Annual Design Automation Conference, DAC 2006 - San Francisco, CA, United States
Duration: Jul 24 2006Jul 28 2006

Publication series

NameProceedings - Design Automation Conference
ISSN (Print)0738-100X


Conference43rd Annual Design Automation Conference, DAC 2006
Country/TerritoryUnited States
CitySan Francisco, CA


  • Correlations
  • Orthonormal polynomials
  • Polynomial chaos
  • Power grids
  • Process variations
  • Stochastic analysis

ASJC Scopus subject areas

  • Hardware and Architecture
  • Control and Systems Engineering


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