Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic m...Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.展开更多
Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor...Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.展开更多
文摘Fractional stochastic kinetics equations have proven to be valuable tools for the point reactor kinetics model, where the nuclear reactions are not fully described by deterministic relations. A fractional stochastic model for the point kinetics system with multi-group of precursors,including the effect of temperature feedback, has been developed and analyzed. A major mathematical and inflexible scheme to the point kinetics model is obtained by merging the fractional and stochastic technique. A novel split-step method including mathematical tools of the Laplace transforms, Mittage–Leffler function, eigenvalues of the coefficient matrix, and its corresponding eigenvectors have been used for the fractional stochastic matrix differential equation. The validity of the proposed technique has been demonstrated via calculations of the mean and standard deviation of neutrons and precursor populations for various reactivities: step, ramp, sinusoidal, and temperature reactivity feedback. The results of the proposed method agree well with the conventional one of the deterministic point kinetics equations.
文摘Nuclear power plants exhibit non-linear and time-variable dynamics.Therefore,designing a control system that sets the reactor power and forces it to follow the desired load is complicated.A supercritical water reactor(SCWR)is a fourth-generation conceptual reactor.In an SCWR,the non-linear dynamics of the reactor require a controller capable of control-ling the nonlinearities.In this study,a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding mode,and the reactor outgoing steam temperature and pressure were controlled simultaneously.In an SCWR,the temperature,pressure,and power must be maintained at a setpoint(desired value)during power maneuvering.Reactor point kinetics equations with three groups of delayed neutrons were used in the simulation.Higher-order and classic sliding mode controllers were separately manufactured to control the plant and were compared with the PI controllers speci-fied in previous studies.The controlled parameters were reactor power,steam temperature,and pressure.Notably,for these parameters,the PI controller had certain instabilities in the presence of disturbances.The classic sliding mode controller had a higher accuracy and stability;however its main drawback was the chattering phenomenon.HOSMC was highly accurate and stable and had a small computational cost.In reality,it followed the desired values without oscillations and chattering.
