A simple analytical method for evaluation of limit-cycle oscillation amplitude in boiling water reactors

An analytical method to obtain the amplitude of limit-cycle in-phase oscillation in boiling water reactors is proposed, which is applicable to small-amplitude limit cycles actually observed in various stability tests. The expression of a zero-power transfer function including the limit-cycle amplitude can be derived by considering higher-order nonlinear interaction between neutron density and feedback reactivity. In a limit-cycle oscillation, the gain- and phase-margin of the open-loop transfer function, which is defined by the product of the zero-power and a feedback transfer function, must be zero. From this requirement the oscillation amplitude and resonance frequency can be determined. A numerical example indicates that the fifth-order nonlinear approximation is adequate for the evaluation of the amplitude and that the resonance frequency is only slightly dependent on the amplitude. Assuming the independence of the resonance frequency from the amplitude, a simple formula can also be derived. When a resonance frequency is obtained by linear stability analysis, the oscillation amplitude can be readily determined from the formula expressed as a function of the amplitude by a polynomial