On the nodal representation of multivariate reactor systems in steady state

Abstract

A method for deriving the nodal representation of multivariate linear systems in steady state is presented. The basic idea is to decompose the system into subsystems in each of which a representative variable is defined by the weighted sum of system variables. This is performed on the theory of orthogonal projection on a real vector subspace. A set of nodal equations for representative variables is derived rigorously and the critical condition is proved identical with that for the original system. The method is demonstrated with the applications to those such as the determination of equations for spatial nodes and for two coupled cores, and the derivation of a zero-power point reactor model for neutron and representative precursor from that for neutron and six-group precursors.