  In this paper, we investigate the impact of interconnect and device process
variations on voltage fluctuations in power grids. We consider random
variations in the power grid's electrical parameters as spatial stochastic
processes and propose a new and efficient method to compute the stochastic
voltage response of the power grid. Our approach provides an explicit
analytical representation of the stochastic voltage response using orthogonal
polynomials in a Hilbert space. The approach has been implemented in a
prototype software called OPERA (Orthogonal Polynomial Expansions for Response
Analysis). Use of OPERA on industrial power grids demonstrated speed-ups of up
to two orders of magnitude. The results also show a significant variation of
about $\pm$ 35% in the nominal voltage drops at various nodes of the power
grids and demonstrate the need for variation-aware power grid analysis.
