Novel Power Grid Reduction Method based on L1 Regularization

Model order reduction exploiting the spectral properties of the admittance matrix, known as the graph Laplacian, to control the approximation accuracy is a promising new class of approaches to power grid analysis. In this paper we introduce a method that allows a dramatic increase in the resulting graph sparsity and can handle large dense input graphs. The method is based on the observation that the information about the realistic ranges of port currents can be used to significantly improve the resulting graph sparsity. In practice, port currents cannot vary unboundedly and the estimates of peak currents are often available early in the design cycle. However, the existing methods including the sampling-based spectral sparsification approach [11] cannot utilize this information. We propose a novel framework of graph Sparsification by L1 regularization on Laplacians (SparseLL) to exploit the available range information to achieve a higher degree of sparsity and better approximation quality. By formulating the power grid reduction as a sparsity-inducing optimization problem, we leverage the recent progress in stochastic approximation and develop a stochastic gradient descent algorithm as an efficient solution. Using established benchmarks for experiments, we demonstrate that SparseLL can achieve an up to 10X edge sparsity improvement compared to the spectral sparsification approach assuming the full range of currents, with an up to 10X accuracy improvement. The running time of our algorithm also scales quite favorably due to the low complexity and fast convergence, which leads us to believe that our algorithm is highly suitable for large-scale dense problems.