Optimal Control of a Large Core Reactor in Presence of Xenon

Changes in power level of large-core reactors are always accompanied by subsequent (transient as well as steady-state) changes in the concentration of Xenon. This, in turn, necessitates long-term control-rod operations to control the so-called "Xenon Oscillations". A method, based on optimal control theory, is presented in this paper to minimize the undesirable Xenon oscillations. It involves the programming of the reactivity changes necessary to accomplish the power level change, while minimizing the deviations of the power level as well as the Xenon and Iodine concentrations, from their final values. In accordance with optimal control theory and for an adequate problem formulation, a performance index is defined. The "penalty" associated with the deviations of the neutron flux, Xenon and Iodine concentrations, from their final values is to be minimized. A novel approach to bypass the difficulties encountered in the numerical solution of the resulting nonlinear Two Point Boundary Value Problem (TPBVP) is presented. The method uses an hierarchical structure to replace the actual nonlinear system by a set of sub-systems. The TPBVP for each subsystem is solved using the solution of the preceding one. This iterative method is discussed and is shown to achieve rapid convergence. Furthermore, the method reduces the amount of computational work needed, thus making it suitable for a minicomputer control application. The procedure described above yields a long-term optimal control law u*(t), i.e.