Modeling and control of xenon oscillations in thermal neutron reactors

Abstract

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 M12+M22 where M12 denotes the migration area for fast neutrons and M22 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.

A simplified analysis of the Chernobyl accident

“…The ratio M/H is an indicator to measure the stability of a nuclear reactor. According to reference [3], M/H in PWR is approximately 0.025, while M/H in the RBMK reactor obtained here is approximately 0.020, this means that in terms of xenon oscillation, the RBMK core is more unstable than the PWR.…”

“…So these pressure tubes will eventually depressurize as follows. The initial distribution of the volumic mass is r z; 0 ð Þ ¼ 705 kg=m 3 ; 0 z 24m:…”

“…In Sections 3-6, we shall study the stability and the reactivity control of the RBMK reactor under xenon poisoning by using 1D 1group axial simulations (see [3]) to prove that, with a weak power counter-reaction coefficient, such as the one we have on a RBMK of the 2 nd generation, the reactor is rather unstable.…”

Designing an automated control system for changing NPU energy release compensating for arising internal disturbing factors based on their approximation model

“…Our review [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] reveals the need to find a method for displaying the results of solving systems of nonlinear differential equations of several arguments in the form of an approximation model. It can be used to modernize the computational and control subsystem, which is part of the intra-reactor control system.…”