Sparse Solutions Using Hash Storage

An efficient computer program which permits rapid calculations for solving a large sparse system of linear equations, which arise in most power system network problems, is described here. This procedure will have an application to any system having a similar admittance matrix to the power system, such as a weather prediction or transportation system. The basic powerful tool¿direct hash technique¿ is used to store the nonzero elements of the sparse matrix. The two main features, triangular factorization of the given sparse matrix and use of this factored form to find the direct solution to the system, are used to estimate a post-transient steady state of a power system. Updating the node admittance matrix after a change in the system structure is also performed in factored matrix form. In both factoring the Jacobian and in changing the the system structure, the introduction of additional non-zero terms in a sparse matrix is easily handled without prior knoledge of the new locations.