A novel approach for bifurcation analysis of out of phase xenon oscillations using multipoint reactor kinetics

In this paper, an approach for carrying out bifurcation analysis of out of phase xenon oscillations has been demonstrated using a reduced order model. The reduced order model consists of multipoint kinetic equations coupled with xenon and iodine equations along with a lumped power coefficient feedback. A large Pressurised Heavy Water Reactor (PHWR) has been considered. The reactor core is divided into two regions for the analysis to present a “proof of principle” for this approach. However, extension of this approach for multiple regions, for better accuracy, though not trivial is quite straight forward. Bifurcation analysis has been carried out using nonlinear analysis tools like MATCONT and BIFOR considering the operating power level of operation, power coefficient of reactivity and reactor size as bifurcation parameters. The results show the existence of Generalized Hopf (GH) points which divides the parameter space into subcritical and supercritical Hopf bifurcation regions. The identification of subcritical Hopf bifurcation is important as it shows unstable limit cycles in the region identified as stable by linear stability analysis.