Bifurcation Analysis of Xenon Oscillations in Large Pressurized Heavy Water Reactors with Spatial Control

Large nuclear reactors operating in the thermal spectrum are prone to both global and regional oscillations in power due to variation of ¹³⁵Xe concentration. These power oscillations are self-stabilizing up to a certain operating power level, beyond which spatial power control becomes necessary for suppressing these oscillations. Especially for large pressurized heavy water reactors (PHWRs), which are natural uranium–fueled reactors using heavy water as coolant and moderator, the modes of xenon instabilities decide the extent and scheme for spatial power control. In this paper, the effect of spatial control on the bifurcation characteristics is demonstrated using a two-region model. The error signal for movement of the reactivity device has a global component for bulk power control and a local component for regional power control. The amount of regional power control determines the power level at which the spatial xenon oscillations stabilize. Using bifurcation analysis, it is found that in case of limited regional control, both supercritical and subcritical Hopf bifurcations exist, whereas in the case of increased regional control only supercritical Hopf bifurcations exist. However, these supercritical Hopf oscillations are due to time lag in control and have short timescales and lower amplitudes as compared to xenon oscillations. Hence, a proper choice of spatial control enables a PHWR to operate at rated full power capacity without any spatial Xenon instability.