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 o scillation 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 nonl inear 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 approximat ion is adequate for the evaluation of the amplitude and that the reson ance frequency is only slightly dependent on the amplitude. Assuming t he independence of the resonance frequency from the amplitude, a simpl e 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. (C) 1998 Elsevier Science Ltd. All rights reserved.