Modeling and control of xenon oscillations in thermal neutron reactors

We study axial core oscillations due to xenon poisoning in thermal neutron nuclear reactors with simple 1D models: a linear one-group model, a linear two-group model, and a non-linear model taking the Doppler effect into account. Even though nuclear reactor operators have some 3D computer codes to simulate such phenomena, we think that simple models are useful to identify the sensitive parameters, and study the efficiency of basic control laws. Our results are that, for the one-group model, if we denote the migration area by M-2 and by H the height of the core, the sensitive parameter is H/M. H being fixed, for the 2 groups model, there are still 2 sensitive parameters, the first one being replaced by M-1(2)+M-2(2) where M-1(2) denotes the migration area for fast neutrons and M-2(2) the migration area for thermal neutrons. We show that the Doppler effect reduces the instability of xenon oscillations in a significant way. Finally, we show that some proportional/integral/derivative (PID) feedback control law can damp out xenon oscillations in a similar way to the well-known Shimazu control law [Y. Shimazu, Continuous guidance procedure for xenon oscillation control, J. Nucl. Sci. Technol. 32, 1159 (1995)]. The numerical models described in our paper have been applied to PWR.