A systematic core design method for reduction of critical boron concentration in APR 1400 with gadolinia-bearing assembly

• A systematic core design method reduces CBC of APR 1400.
• The core design method solves a non-linear programming problem.
• The solution is a set of new Gd-bearing fuel assembly design.
• LP loading new Gd-bearing fuel assembly designs achieves target CBCs.
• Lower L/H ratio shows longer hold-down effect than higher L/H ratio.

A systematic core design method is developed to design Gd-bearing fuel assembly having two types of Gd rods, low-wt%-Gd rod and high-wt%-Gd rod. The purpose of the method is to lower the critical boron concentration (CBC) of a preliminary core loading pattern, and consequently to achieve more negative or less positive moderator temperature coefficient (MTC). The proposed core design method is a process of solving a non-linear programming problem stated with a system of equations. In this method, both the ratio of the number of low-wt%-Gd rod to the number of high-wt%-Gd rod (r) and the assembly average Gd wt% (w) are the solution variables of the system of equations. The target function is the amount of soluble boron concentration reduction, ΔCBC, which is correlated with the reactivity change, ΔkFA, per Gd-bearing fuel assembly by a quadratic reactivity equation. The coefficients of the quadratic equations are calculated prior to the determination of Gd-bearing fuel assembly pattern, using the least square method. The constraints required to determine (r, w) are physically realizable Gd rods pattern, Δki close to ΔkFA derived from ΔCBC  , etc. An objective function, minf∑i(ΔkFA-Δki), enables a final loading pattern to reach a target CBC. This design methodology is applied to APR 1400. Total six cases with various target CBCs are investigated to validate the proposed method. CASMO-3/MASTER calculations with new design assemblies produce lower CBCs at BOC than target CBCs keeping maximum pin power below the safety limit, and thus show more negative MTC.