Variational analysis of large power grids by exploring statistical sampling sharing and spatial locality

We propose a parametric random walk algorithm to facilitate a feasible evaluation of a few critical network nodes under the influence of a large number of variation sources in a power grid. By combining statistical sampling sharing with random walks, we devise an efficient localized sensitivity analysis for large power distribution networks such that the analysis can be conducted without solving the complete network. We further show that this sampling-based parametric analysis can be extended from the first order sensitivity analysis to a more accurate second order analysis. By exploiting the natural spatial locality inherent in our algorithm formulation, the second order parametric analysis can be conducted very efficiently even for a large number of global and local variation sources. The proposed approach is demonstrated by analyzing large power grids under the influence of process and current loading variations to which the application of the standard brutal-force circuit simulation becomes completely infeasible. Our results have demonstrated the superior performance of the proposed algorithm both in terms of accuracy and runtime.