A Hierarchical Low-Rank Approximation Based Network Solver for EMT Simulation

Abstract

In electromagnetic transient (EMT) simulation, 80–97% of the computational time is devoted to solving the network equations. A key observation is that the sub-matrix representing the interaction between two far-away groups of buses is usually sparse and can be approximated by a low-rank matrix. Based on this observation, we propose a novel low-rank approximation method which permits ${O(N \log N)}$ -time matrix-vector multiplication for each network solution time step. Comprehensive numerical studies are conducted on a 39-bus system and a 179-bus system from the literature, and large cases created from the two systems. The results demonstrate that the proposed approach is up to $2.8\times$ faster than the state-of-the-art sparse LU factorization based network solution, without compromising simulation accuracy. Since our low-rank approximation is highly parallelizable, further speedup may be possible.