Effects of modeling assumptions on the stability domain of BWRs

Boiling Water Reactor (BWR) stability analyses are generally conducted using reduced order models employing various methods such as frequency domain stability analyses, bifurcation analyses and time domain numerical integration. One of the models used for these analyses is the March-Leuba et al. (1986) model, which couples temperature and void reactivity to point reactor kinetics. This model was later modified to include the effects of rate of temperature change on the excess void reactivity (March-Leuba, 1986b). Here, we show the effect of this higher order modeling on the overall stability of the BWR, which can be used in validating large-scale codes. The change in the stability boundaries from the earlier reduced order model to the modified model is determined by evaluating the eigenvalues of the Jacobian matrices. The size of the stable region increases with positive coefficient for rate of temperature change term, whereas it decreases for negative coefficient. The nonlinear model is also integrated numerically, and shows that for parameter values studied here, the system evolves to stable amplitude oscillations when operating in the unstable region close to the stability boundary. The effects of uncertainty in parameters on the system behavior are modeled by formulating and solving stochastic differential equations of the reduced order model. The results show significant impact of uncertainties in modeling parameters.