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One of the important operations in nuclear power plants is load-following in which the imbalance in axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits otherwise the nuclear power plant could become unstable. Therefore, bounded xenon oscillation is considered to be a constraint for the load-following operation. On the other hands, precursors produce delayed neutrons which are important with respect to reactor period and control, but xenon concentration and precursors densities cannot be measured directly. In this paper, the non-linear sliding mode observer which has the robust characteristics facing the parameters uncertainties and disturbances is proposed based on the two point nuclear reactor model equations with three groups of the delayed neutrons to estimate the xenon concentration and delayed neutrons precursor densities of the pressurized-water nuclear reactor (PWR) using reactor power measurements. The stability analysis is provided by means of the Lyapunov approach, thus the system is guaranteed to be stable over a wide range. The employed method is easy to implement. This estimation is done taking into account the effects of reactivity feedback due to temperature and xenon concentration. Simulation results clearly show that the sliding mode observer follows the actual system variables accurately and is satisfactory in the presence of the parameter uncertainties and disturbances. [ABSTRACT FROM AUTHOR]

• The system is stable over its entire power range. • The difference between the results of linearized and nonlinear models is negligible. • An increase in chimney height improves system inherent safety. • Higher operational limits can be achieved by applying a heater and a spray. The stability analysis of a natural circulation integrated self-pressurized water reactor is investigated by the Lyapunov approach. The analysis of the pressurized water reactors (PWRs), particularly the integrated self-pressurized water reactors, is essential in keeping the neutronic and thermal-hydraulic parameters of the system stable. An appropriate nonlinear dynamic model is introduced based on conservation of mass, momentum and energy which is then linearized, in a state-space model. The Lyapunov approach and Routh-Hurwitz criterion are applied to assess the stability of this linearized system over its entire power range. The analysis is done for the primary coolant circuit in the RPV by assuming the steam dome pressure as the fixed parameter. It is found that the system remains stable over its entire power range. The influence of different geometrical features is studied at nominal conditions. It has been found that by reducing the chimney height results in a decrease in the coolant flow rate and a downward motion of the onset of flashing while the average core coolant temperature rises. For lower values of friction losses coefficient, the coolant flow rate increases, and the onset of flashing moves upward and the average core coolant temperature decreases. A change in independent parameters, which are effective in generating the natural circulation of the coolant, can influence the inherent safety of the system: An increase in reactor power and chimney height and a decrease in friction losses coefficient improve the system inherent safety. Two input functions as extra reactivity for increasing and decreasing the power from the nominal state are implemented into the dynamic model and the model response is therefore assessed by considering the lack of two phase flow entry to the core restriction. The boundary of the system stability lies in the range 32–107 MWt and using the system outside this range the system pressure needs to be controlled through spray and heater systems. The obtained results are based on the initial information, data and primary design of these types of reactors. Determining a more accurate boundary requires more detailed design and assessment together with experimental test facilities with respect to other restricting parameters of the system. The results presented in this paper can be implemented in further research on this type of reactors, particularly for nonlinear stability analysis and finding nonlinear Lyapunov function. [ABSTRACT FROM AUTHOR]