GPU-based power flow analysis with Chebyshev preconditioner and conjugate gradient method

• In this paper, a GPU-based Chebyshev preconditioner is developed with the integration of an iterative conjugate gradient (CG) solver.
• This work targets at solving the power flow equations in power systems, as well as any sparse linear systems that are symmetric positive definite.
• Our work considers Chebyshev preconditioner and conjugate gradient method together to choose the proper degree for Chebyshev preconditioner.
• The max speedup can reach 46× for Chebyshev preconditioner and 4× for CG solver among all sample systems over the corresponding Matlab baseline.
• The results suggest that the iterative solver should be considered to further improve the overall performance of solving linear equations.

Traditionally, linear equations in power system applications are solved by direct methods based on LU decomposition. With the development of advanced power system controls, the industrial and research community is more interested in simulating larger, interconnected power grids. Iterative methods such as the conjugate gradient method have been applied to power system applications in the literature for its parallelism potential with larger systems. Preconditioner, used for preconditioning the linear system for a better convergence rate in iterative computations, is an indispensable part of iterative solving process. This work implemented a polynomial preconditioner Chebyshev preconditioner with graphic processing unit (GPU), and integrated a GPU-based conjugate gradient solver. Results show that GPU-based Chebyshev preconditioner can reach around 46× speedup for the largest test system, and conjugate gradient can gain more than 4× speedup. This demonstrates great potentials for GPU application in power system simulation.