A Chain Method for Preconditioned Iterative Linear Solvers for Power System Matrices

Many power systems applications such as power flow and short-circuit analysis require very large sparse matrix computations. With the increase in reliance on our electric infrastructure, power systems are continually growing in size, creating greater computational complexity in solving these large linear systems within reasonable time. For sparse matrix applications, it is desirable to have an algorithm with low runtime complexity in terms of the number of nonzeros in the matrix. There have been several recent advances in computational methods in other fields that, if applied to power system, could make real-time dynamic simulation a reality. Much work has been done for specific types of these problems where the system is symmetric and diagonally dominant, similar to the form of power system matrices. This paper details an expansion on the current work in fast linear solvers to develop power system specific methods that show potential for accurate solutions in O(m log
²
n) run times, where n represents the number of nodes and m represents the number of nonzeros in the power system matrix. This paper presents the simulation validation of a recently developed recursively solved iterative chain method for sparse matrices using a low stretch spanning tree preconditioner.