GPU-based two-step preconditioning for conjugate gradient method in power flow

With the development of the modern power system and the computational hardware, the industrial and research communities are more interested in simulating larger and more complicated power grids. Various iterative solvers for linear systems have been investigated with power system applications for its parallel potential in large scale linear computations. They usually require preconditioning to improve their convergence rate. This work will discuss three preconditioners: Jacobi preconditioner, Chebyshev preconditioner, and a two-step preconditioner with Jacobi first and then Chebyshev. The results show that the two-step preconditioner provides better preconditioning effects than using any of them alone. Besides, the GPU implementation of the iterative solver and preconditioners shows performance improvement over Matlab implementation. The improvement can reach up to 8.9× with the two-step preconditioner for the largest test system. These results demonstrate great potential for both preconditioned iterative solver and GPU application in power system simulations.