Stability Analysis of BWRs Using Bifurcation Theory.

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This paper presents a new approach using the bifurcation theory for the stability analysis of BWRs. In this approach, the dependencies of the equilibrium states on the parameters that have a large influence on the stability are investigated topologically over a wide range of phase space. The stability information can be derived from the analysis of the bifurcation phenomena on the equilibrium states. This investigation enabled us to obtain qualitative and global information on the stability of a nonlinear system. The new approach was applied to the analysis of the stability associated with in-phase power oscillation (core reactivity stability). The loss of linear stability took place at a lower reactor power as the coolant flow rate decreased, and this instability occurs at the Hopf bifurcation point. The sensitivity analysis of the stability boundary for the various parameters revealed that the channel hydrodynamics heavily play a significant role in the stability. The Hopf bifurcation analysis proved that the periodic state bifurcating at the Hopf bifurcation point was orbitally unstable and a limit cycle attractor did not exist in the vicinity of the bifurcation point. This fact led to the conclusion that a limit cycle in-phase power oscillation observed in BWR instability was not excited directly by the bifurcation of the orbitally unstable periodic state.