Multidimensional Variability Analysis of Complex Power Distribution Networks via Scalable Stochastic Collocation Approach

This paper presents a novel SPICE-compatible stochastic collocation approach for the variability analysis of complex and irregular-shaped power distribution networks (PDNs). The proposed methodology relies on the Stroud cubature rules for locating the sparse set of collocation nodes within the multidimensional random space where the deterministic SPICE simulation of the PDN needs to be performed. The key advantage of the proposed Stroud cubature approach is that the number of collocation nodes required scales linearly with the number of random dimensions as opposed to the exponential or polynomial scaling exhibited by the conventional nonintrusive polynomial chaos approaches, thereby resulting in significantly faster simulations. The validity of the proposed approach for both single-layered and multilayered PDNs characterized by holes/apertures, narrow slots, and irregular geometries is established through multiple numerical examples.