Contribution to BWR stability analysis Part I: Analytical approach using a reduced order model

• We construct a new reduced order model of boiling water reactors.
• Both thermal-hydraulic and automatic control system feedbacks are included.
• In-phase and out-of-phase oscillations are studied as bifurcations from steady state.
• Prompt-jump and effective life time approximation are applied to the dynamics.
• Analytical formulae for limit cycle oscillations are obtained.

In this first part, we justify the use of a simple nonlinear set of ordinary integral differential equation to study the onset of global and regional power oscillations due to neutron-thermo-hydraulic coupling and possible malfunctions of the automatic control system of a boiling water reactor. This approach is framed in the construction of a new nodal-modal reduced order model of the core. Symmetry considerations are applied in the derivation of analytical formulae for direct and cross reactivities, including thermo-hydraulic and automatic control terms. Local bifurcations from the steady state of the reactor are studied from an analytical point of view, using both prompt-jump and effective life time approximation. Both thermal–hydraulic and automatic control system feedbacks are included. Asymptotic methods are used in the derivation of closed form analytical formulae of the stability boundaries in the space of reactor parameters as well as for amplitudes and frequencies of global and regional power oscillations. Besides analytical formulae for limit cycle oscillations are obtained.