Optimal burnable poison loading strategy.

Abstract

The optimal axial loading strategy of burnable poison in pressurized water reactors is investigated to obtain, for a given fuel loading, maximum cycle length or equivalently maximum reactivity at the end of cycle (EOC). Pontryagin's maximum principle is used, together with a direct adjoining approach in state-constrained optimal control theory, to derive the necessary conditions of optimality subject to a power peaking constraint. A new method utilizing Weilandt's shifted eigenvalue approach has been developed for backward solution of the inhomogeneous adjoint equations, with the standard power iteration method for forward solution of the system equations, in a conjugate gradients algorithm. The search length in the conjugate gradients algorithm is obtained through first-order perturbation theory. To satisfy the power peaking constraint, we have developed a new infeasible solution algorithm called the augmented Lagrange multiplier (ALM) method, which avoids the need to search explicitly for the constraint arc. The ALM method directly factors into an augmented Lagrange multiplier the information on the location and magnitude of the constraint violation in the forward solution so that the constraint violation can be reduced in the next conjugate gradients iteration and eventually eliminated. With the reactivity represented in terms of first-order perturbation theory, a one-group, one-dimensional neutron diffusion theory code was used to solve the EOC reactivity maximization problem through the ALM method. The optimal burnable poison loading strategy suggests less neutron absorber in the peripheral regions of the core and more in the central part. For an annual cycle with a power peaking limit of 1.40, the excess reactivity at the end of cycle is increased by 0.19% $\Delta$k/k and the cycle length extended by 4.2 days, compared with those for a uniform burnable poison distribution. Parametric studies show that the more the safety margin can be relaxed, the longer the cycle length can be extended. Our ALM results are similar to the optimal burnable poison distributions obtained with the penalty function method, suggesting that the burnable poison optimization problem has a broad range of near-optimal solutions.