DETERMINISTIC METHODS FOR PWR FUEL LOADING OPTIMIZATION

摘要

We have developed a multi-control fuel loading optimization code for pressurized water reactors (PWRs) based on deterministic methods. The objective is to flatten the fuel burnup profile, which maximizes overall energy production. The optimal control problem is formulated using the method of Lagrange multipliers and the direct adjoining approach for treatment of the inequality power peaking constraint. The optimality conditions are derived for a multi-dimensional multi-group optimal control problem via calculus of variations. Due to the Hamiltonian having a linear control, our optimal control problem is solved using the gradient method to minimize the Hamiltonian and a Newton step formulation to obtain the optimal control. We are able to satisfy the power peaking constraint during depletion with the control at beginning of cycle (BOC) by building the proper burnup path forward in time and utilizing the adjoint burnup to propagate the information back to the BOC. Our test result for the multi-control fuel loading design is able to achieve the same fuel cycle length as the AP600 first cycle loading with an average reduction of 0.02 wt% ~(235)U enrichment.