Sparse Matrix Factorization using Diagonal Pivoting for Power Distribution Network Applications

Power distribution network (PDN) applications are real-time applications with complex data represented by sparse matrices that, depending on the application, may be positive definite or indefinite and irregular. Modifying existing algorithms to solve all types of PDN matrices would ease PDN solver design and reduce code maintenance cost, but that is very challenging task. Algorithms that deal with PDN matrices should provide stability to the system, yet process data fast and efficiently, utilizing the existing hardware architecture to the maximum. The algorithms that deal with PDN data are based on factorization of sparse matrices, where pivoting strategy may destabilize the system. The algorithms used in commercial software ensure the system stability, but are complex and hard to implement. In this paper, we propose the usage of partial diagonal pivoting, with minimum degree ordering for matrix factorization in the domain of PDN applications. Results show that this pivoting technique ensures the stability over the tested set of matrices, and outperforms the commercial software in terms of time efficiency.