Bifurcation analysis of out-of-phase oscillations in boiling water reactors using multipoint neutron kinetics

Abstract

Stability analysis is important for identifying the safe operating regimes in Boiling Water Reactors (BWRs). The power instabilities, due to the fuel and coolant void feedbacks, can be either in-phase or out-of-phase. The models used in earlier studies were quite complicated, hence, not suitable for bifurcation analysis. In this paper, a simpler model based on neutron multipoint kinetics coupled with coolant temperature feedbacks, with reasonable accuracy is presented for bifurcation analysis of spatial oscillations in BWRs. The stability maps in different parametric planes are constructed using MATCONT. Both supercritical and subcritical Hopf bifurcations are observed and the Generalized Hopf points are also identified. Identification of subcritical Hopf is important as the linearly stable region may have unstable limit cycles near the stability boundary. The region in the stability map where in-phase oscillations are stable whereas the out of phase oscillations are unstable is identified and verified by numerical simulations.