Comparison of Direct and Iterative Sparse Linear Solvers for Power System Applications on Parallel Computing Platforms

This paper presents a performance comparison of sparse linear solvers based on iterative and direct methods for power system applications implemented on parallel computing platform. The iterative sparse linear solver evaluated in this paper is based on the conjugate gradient algorithm with a Jacobi pre-conditioner executed on a general purpose graphic processing unit (GPGPU). The direct solvers are based on the SuiteSparseQR library implementing a QR factorization, and PARDISO, implementing a LU factorization, with both providing parallel implementations through Intel Threading Building Blocks and OpenMP respectively. The type of matrices tested during the evaluation are Jacobian and Gain matrices from state estimation applications, and DC power flow Jacobian matrices from power flow analysis and security constrained optimal power flow applications. The evaluation of the different solvers on each matrices showed that iterative methods are good candidates for power flow analysis application when the DC power flow Jacobian matrices are large and well conditioned. Direct methods based solvers outperform iterative solvers for matrices found in state estimation and security constrained power flow analysis application mainly due to the poor performances of iterative methods on ill-conditioned matrices.