The Least-Squares Method for Three-Dimensional Core Power Distribution Monitoring in Pressurized Water Reactors

A least-squares method is presented that is designed for an advanced core power distribution monitoring calculation of pressurized water reactors (PWRs) and its applicability to the Yonggwang Unit 3 (YGN-3) PWR in terms of computational speed and accuracy. The method here makes use of the solution to the normal equation that is derived from solving the overdetermined system of equations comprising the fixed in-core detector response equations and the nodal neutronics design equations in the least-squares principle. In order to ensure high computational accuracy and speed of power distribution monitoring calculations, the nonlinear analytical nodal method (ANM) is employed for accurate core neutronics calculations, and a preconditioned conjugate gradient normal residual iteration algorithm is adopted for speedy solution to the normal equation. The applicability of the least-squares method for the core power distribution monitoring of the YGN-3 PWR is examined by pure numerical experiments in which the reference three-dimensional (3-D) power distribution is calculated by the 36 node-per-fuel-assembly (N/A) nonlinear ANM. Simulated detector signals are derived from the reference power distribution to establish detector response equations. The 3-D monitored core power distribution is obtained from the 1 or 4 N/A solution to the normal equation and compared with the reference power distribution to determine the prediction accuracy. It is shown that the least-squares method can predict a very accurate 3-D power distribution within the acceptable computation time of a few seconds on a 733-MHz personal computer.