3D PWR power distribution on-line monitoring based on harmonics expansion

Harmonics expansion method is employed to obtain the spatially continuous 3D on-line power distribution based on the dispersed and limited detector measurements. Power distribution is expanded by harmonics which are high-order eigenfunctions of neutron diffusion equation. The expansion coefficients are determined by using in-core detector measurements. Krylov sub-space method is employed to obtain those harmonics, while least square principle is chosen for expansion coefficients calculation. Moreover, instead of the original quarter core finite differencing method, a whole core nonlinear iteration semi-analytic nodal method is used for harmonics calculation. It has been found that the nodal harmonics calculation runs about 100 times faster than the finite differencing one without any loss in accuracy. Based on these models, an on-line monitoring system named NECP-ONION has been developed. Real detector measurements from Unit 1 reactor of DayaBay NPP, a typical PWR reactor in China, are used for code verification and validation. Numerical results show that the root-mean-square errors of assembly averaged powers are less than 1.8% for different burnup steps during the entire cycle. In addition, it has been observed that the assembly power monitoring error can still be driven down to less than 2% even if only 60% of measurements are available.