Maximizing the Average Fuel Burnup Over Entire Core: A Poison Management Optimization Problem for Multizone Light-Water Reactor Cores

The problem of optimal control rod withdrawal sequence is formulated for a multizone core model of a nuclear reactor. In particular, the maximum average burnup problem for light-water reactors is investigated to find the governing principles in optimal control rod programming. The optimal solution depends only on end-of-life (EOL) states, and in the optimal state, the control poisons are all withdrawn from the entire core and the power distribution will be as uneven as possible within the constraints on the power peaking factor. We define the core composition, including the control poison, which represents the nuclear performance of each zone and it is taken as an independent control vector. The admissible control is defined such that the control vector satisfies the criticality condition and the constraints of power peaking factor. Some complexities of the other constraints to be considered are resolved by determining the reachable region of the burnup of each zone which is chosen as a state vector. The method described in this study is based on a topological mapping theory, and for illustrative purposes, the results in the case of a two-zone model are shown by using the method.