Stability analysis of linear FNPK model considering reactivity feedback effects for a research nuclear reactor

Fractional neutron point kinetics (FNPK) model has been known for some researchers in the field of nuclear science and engineering for less than a decade. This modeling has a better approximation and physical interpretation for some phenomena, specially, when large variations of neutron cross sections occur and the dynamic behavior of neutron is different. This paper, for the first time, presents a fractional neutron point kinetics model which consists of three delayed neutron groups and the reactivity feedback effects (temperature feedbacks and poison feedbacks). Also, Stability Analysis of linear FNPK model considering reactivity feedback effects for a Research Nuclear Reactor is done. The model has been linearized around the equilibrium operating point. Then, the closed-loop linear fractional neutron point kinetics model considering reactivity feedback effects is transformed from S-domain to W-domain. For stability evaluation, two strategies have been implemented. The first strategy is the assessment of the region of closed-loop poles in the principal Riemann sheet (PRS) for the transformed system. The second one is the step response evaluation of the linear fractional-order closed-loop model for different values of the model parameters (including relaxation times and anomalous diffusion coefficients). Simulation results demonstrate that the stability of the system depends on the values of these model parameters and for one scenario, the closed-loop poles are located in the unstable region of PRS and the step response is unstable. However, for the others, it is stable and settles at an equilibrium value. In addition, a smaller anomalous diffusion coefficient (alpha), leads to a more unstable closed-loop model (have poles closer or inside the unstable region). Comparative analysis is shown that reactivity feedback effects are considerable on the stability of the research nuclear reactor. Specially, feedback by xenon has a negative effect on the stability and reduces the stability of system. Also, the stability highly depends on the values of alpha and tau.