Exploration of multifrontal method with GPU in power flow computation

Solving sparse linear equations is the key part of power system analysis. The Newton-Raphson and its variations require repeated solution of sparse linear equations; therefore improvement in efficiency of solving sparse linear equations will accelerate the overall power system analysis. This work integrates multifrontal method and graphic processing unit (GPU) linear algebra library to solve sparse linear equations in power system analysis. Multifrontal method converts factorization of sparse matrix to a series of dense matrix operations, which are the most computational intensive part of multifrontal method. Our work develops these dense kernel computations in GPU. Example systems from MATPOWER and random matrices are tested. Results show that performance improvement is highly related to the quantity and size of dense kernels appeared in the factorization of multifrontal method. Overall performance, quantity and size of dense kernels from both cases are reported.