BWR stability analysis with sub-diffusive and feedback effects

Highlights: •Feedback stability of the fractional reducer-order model (F-ROM). •F-ROM considers sub-diffusive effects and thermal-hydraulics feedback. •The results are compared with the classical ROM. •F-ROM can be utilized to design robust control systems for nuclear reactor. -- Abstract: The aim of this work is to investigate the Boiling Water Reactor (BWR) stability with sub-diffusive effects and thermal-hydraulics feedback, using frequency domain method. The fractional neutron point kinetics (FNPK) equation is used to approximate the sub-diffusive effects, and a reducer-order model (ROM) is employed for void fraction and fuel temperature feedback. As a consequence a novel linear fractional reducer-order model (F-ROM) is proposed. The F-ROM is a compact set of five differential equations for BWR dynamics. The analysis is carried out for three values of anomalous diffusion coefficient representing three levels of sub-diffusion in reactor core. It is shown with extensive simulations that all the F-ROM exhibit closed-loop stability. The results are compared with the classical ROM.