Randomized Cholesky Factorization With Threshold-Based Multisampling for Power Grid Simulation

Zhiqiang Liu, Wenjian Yu

Abstract: Transient simulation of large power grids (PGs) can be extremely challenging because linear equation systems with millions of unknowns need to be solved at each time step. The iterative equation solvers can be more scalable and efficient than direct solvers, thanks to the preconditioning approaches. Recently, randomized Cholesky factorization (RChol) was proposed, showing promising performance in preconditioning symmetric diagonally dominant M-matrices (SDDMs). However, it does not allow to include more fill-ins, making it less flexible and less efficient in problems like PG transient simulation. In this work, a RChol with a threshold-based multisampling strategy (RCholT) is proposed. RCholT allows to control the sparsity of preconditioners by a user-defined threshold and can construct more effective preconditioners than RChol. As the result, the RCholT-based transient simulator is $1.7\times $ faster than the RChol-based one and $2.3\times $ faster than the graph sparsification-based one on SDDM and PG benchmarks.