Estimation of axial xenon oscillations with online parameter adaptation in the P.W.R nuclear reactors using Lyapunov approach based on the multipoint kinetics reactor model

In nuclear power plants, imbalance of axial power distribution induces xenon oscillations. These oscillations must be maintained within acceptable limits; otherwise, the nuclear power plant could become unstable. Therefore, axial xenon oscillations must be considered during the load-following operation. Besides, xenon concentration and axial xenon oscillations are not measurable in practice; therefore, they should be estimated using suitable observer. In this paper, in order to estimate the axial xenon oscillations for the load-following operation, an adaptive estimator is presented based on the multipoint kinetics reactor model. Besides, regarding the limitations of the xenon concentration and delayed neutron precursors densities measurement to design the nuclear reactor control systems, the presented observer can estimate their values, carefully. The adaptation laws for updating the reactor parameters are generated using the Lyapunov approach. In the proposed adaptive estimator, both parameters and state variables of the nuclear reactor are estimated simultaneously. Also, the stability analysis is given by means of Lyapunov approach, thus the system is guaranteed to be stable within a large range. Simulation results are presented to demonstrate the effectiveness of the proposed observer in terms of performance, robustness and stability and show that the adaptive estimator follows the actual system variables and parameters accurately and are satisfactory in the presence of the parameters uncertainties and disturbances.