A Control Algorithm For Reactor Spatial Control During Nuclear Station Load Cycling

A multivariable reactivity control algorithm is developed to maintain acceptable reactor spatial kinetics response during reactor power cycling. A modal model for describing the space-time kinetics response of a CANDU (Canadian Deuterium Uranium) reactor is devised and ultilized in the control study. A one neutron energy group approximation and other assumptions appropriate to the CANDU reactor studied are used to derive a diffusion equation from the linearized Boltzman equation. The effects of Xe¹³⁵ and I¹³⁵ are incorporated in the model. The kinetics variables are expanded in terms of an infinite series of eigenfunctions which are solutions of the scalar Helmholtz equation solved on the volume of the reactor. The control reactivities are modelled as an evenly distributed reactivity for gross reactor load cycling and point reactivity devices for spatial control. The system dynamics equations are written in a bilinear state space form. An algorithm is devised to determine the control vector required to achieve a desired kinetics behaviour about the nominal response. The algorithm is illustrated for a typical load cycle by means of a digital computer program.