  In power system dynamic simulation, up to 90% of the computational time is
devoted to solve the network equations, i.e., a set of linear equations.
Traditional approaches are based on sparse LU factorization, which is
inherently sequential. In this paper, an inverse-based network solution is
proposed by a hierarchical method for computing and store the approximate
inverse of the conductance matrix in electromagnetic transient (EMT)
simulations. The proposed method can also efficiently update the inverse by
modifying only local sub-matrices to reflect changes in the network, e.g., loss
of a line. Experiments on a series of simplified 179-bus Western
Interconnection demonstrate the advantages of the proposed methods.
