Development of Spectral History and Pin Power Correction Methods for Pin-by-Pin Core Analysis Method Using Three-Dimensional Direct Response Matrix

Spectral history and pin power correction methods have been developed for the pin-by-pin core analysis method using the three-dimensional direct response matrix (3D-DRM). The direct response matrix is formalized using four subresponse matrices in order to respond to a core eigenvalue k and thus it can be recomposed at each outer iteration in the core analysis. For core analysis, it is necessary to take into account the historical effect, which is related to spectral heterogeneity. The spectral history method is used to evaluate the nodal burn-up spectrum obtained by using the outgoing neutron current instead of the nodal flux because the 3D-DRM method does not use the nodal flux. The pin power correction method corrects the fuel rod neutron production rates obtained in the pin-by-pin calculation. These two methods were tested in a heterogeneous system. The test results show that the neutron multiplication factor error and nodal neutron production rate errors can be reduced by half during burn-up. The root-mean-square differences between the relative fuel rod neutron production rate distributions and the maximum error of relative fuel rod production rate can also be reduced by half. This means that the developed methods can reflect the effects of intra- and interassembly heterogeneities during burn-up and can be used for core analysis.