Axial Xenon Oscillations Research Articles

Load-following control of a nuclear reactor using optimized FOPID controller based on the two-point fractional neutron kinetics model considering reactivity feedback effects

Load-following control of a nuclear reactor core is very crucial. The main challenge in examining power distribution control of the reactor core is to perform axial power distribution control rather than handling radial power distribution.In this work, a new model consisting of fractional order derivatives and two nodes of the reactor core with reactivity feedbacks is presented named as the two-point fractional neutron point kinetics (TPFNPK) model. According to neutron diffusion phenomena, this modeling method has a better physical interpretation for a quick change of neutron flux in load-following operation mode.For load-following control, a fractional order PID controller is implemented. Optimization of the parameters of this controller (KP, KI, λ, KD, and μ) is carried out utilizing a genetic algorithm (GA) which is an evolutionary algorithm.The objective is the minimization of the weighted sum of the integral of time-weighted absolute error (ITAE), and the overshoot or the undershoot (MP).The new reactor core model is simulated in a MATLAB/SIMULINK environment coupled with a genetic algorithm.Different load patterns (the assumed tracking signal) considering different values of the model parameter (α) are introduced to address the effectiveness of the implemented control method.The simulation result demonstrates that the optimized control methods (GA-PID and GA-FOPID) have satisfactory and suitable functionality during load pattern tracking for all selected values of the model parameter. However, the GA-FOPID controller has a relatively better performance compared to the GA-PID controller. In all cases, it has lower costs and faster convergence. In addition, core normalized axial offset (AO) is always maintained within a certain limit during load-following operation for all the cases. Furthermore, in all the cases, the normalized axial xenon oscillation index (AXOI) remains bounded during the power transient.

EFFECTS OF FUEL TEMPERATURE-SHAPING FUNCTIONS ON XENON OSCILLATIONS

In coupled multiphysics simulations, single pin-averaged values are typically used to describe the temperature, power, and burnup within a given fuel pin. However, since xenon oscillations are largely driven by fuel temperatures, radially dependent quantities have been implemented in the Virtual Environment for Reactor Applications. These radial-shaping functions are based on Zernike polynomial expansions and allow information to pass effectively between codes with differing spatial meshes. This work examines the effects of radial fuel temperature-shaping functions on the behavior of axial xenon oscillations. A test problem was developed from full-core, multi-cycle depletions using as-built fuel data. The center 25 assemblies of the full-core case were used to test the radial-shaping function by inducing an axial xenon oscillation using an instantaneous control rod movement. The test case was run with and without the radial shapes, and each component was also run individually. Including the shaping functions significantly impacted the xenon oscillations for this problem; the magnitude and period of the oscillations were altered, and large pin power and soluble boron differences were observed. Testing each component individually showed that the radial fuel temperature-shaping function had the largest effect.

Assessment of the VVER-1200 reactivity coefficients on the basis of the data measured at the energy power levels

Abstract Reactivity coefficients in respect to the fuel temperature and coolant density are the important integral parameters, which determine behavior of nuclear reactors in case of accidents. Experimental justification of these coefficients in the operating reactor is a quite complicated task. Changes of the coolant density and fuel temperature are the interdependent processes, which are difficult to separate. Experiments with excitation of axial and diametrical xenon oscillations, which were initiated by moving of the CPS CR (control rods of the control and protection system) group or an individual CPS CR, were carried in the framework the commissioning tests in the VVER-1200 reactor. Using the methods of mathematical statistics, we carried out multiple modelling of experiments with excitation of axial and diametrical xenon oscillations. Actual values of the reactivity coefficients, as well as some other parameters ensuring the best agreement of the calculated and experimental data were evaluated with the help of Bayes theorem.

Control of a PWR nuclear reactor core power using scheduled PID controller with GA, based on two-point kinetics model and adaptive disturbance rejection system

Nuclear reactor dynamics has a non-linear nature, and some parameters depend on the output power level. Accordingly, a load-following issue is important. To this end, it is important to use the proper controller with a simple implementation such as a proportional-integral-derivative (PID). In this work, the load-following of a typical pressurized water reactor (PWR) is considered based on the two-point kinetic model and constant axial offset (AO) power-distribution strategy. Subsequently, the power level is controlled by the PIDs, which are tuned by a real-coded genetic algorithm (GA) with decision variables include the integral of time-weighted absolute error (ITAE) and a stability condition. The oscillations of the power distribution occur due to axial xenon oscillations in long-time operation conditions. Therefore, AO, normalized axial offset (ΔI), and axial xenon oscillation index (AXOI) must be considered. As well as, the Lyapunov approach is used to guarantee controlling system stability, and design an adaptive system to reject unwanted disturbance to the input of the plant. The simulation results show the high performance of the closed-loop real-coded GA-PID (RGA-PID) controller with the least errors. Also, the system outputs, ΔI, and AXOI are in the acceptable range based on constant AO power-distribution strategy, and these indexes are robust to parametric uncertainties of the dynamics model.

New monitoring procedure of axial xenon oscillation in large pressurized water reactors

Xenon oscillation is caused by imbalance of xenon distribution in nuclear reactors. Procedures have been developed in the past to dampen these oscillations. One of the procedures is known as quite simple and effective, which uses several constants obtained from reactor modeling codes in the analysis of xenon oscillations (not from actual data of the plant). This causes uncertainties in the solutions obtained and the need for an improved approach becomes apparent. This paper discusses a new methodology that allows the utilization of actual reactor data in the procedure’s analysis to dampen xenon oscillations. Moreover, it has been shown that only two constants are needed to fully express the xenon oscillation behavior.

Validation of New Procedure of Axial Xenon Oscillation Dampening in Pressurized Water Reactors (PWRs) – Case Study

Xenon oscillation is a serious issue in nuclear power plants that affects the efficiency of such power plants. Xenon oscillations result from the imbalance between three key parameters, flux distribution in the core, Xenon distribution, and lastly iodine distribution. An improved procedure to simulate and dampen Xenon oscillations by determining only two parameters is previously proposed by the authors (Shimazu, 2009; Al Nuaimi et al., 2019). These two parameters can be calculated from actual nuclear reactor data obtained from nuclear power plants during their operation. The previously mentioned improved procedure assists the nuclear operators in determining when to insert and withdraw the control rods and the number of control rods’ steps involved in order to eliminate Xenon oscillations. In this paper, the approach described earlier (Al Nuaimi et al., 2019) will be validated by solving for the two reactor parameters, namely, σaϕ and the proportional constant for Xenon concentration difference on axial offset K, through determination of the stability index, γ and angular velocity, ω. This can be done by using fitting algorithm on PWRs’ real data in order to characterize the expected Xenon oscillations behavior. The Axial Offset is plotted utilizing plant data obtained from a Generic PWR simulator. Using linear fitting, the values of γ and ω are then obtained to determine σaϕ and K which can be inserted in a twopoint model to plot the resultant Axial Offset. Both Axial Offset plots from the Generic PWR Simulator and the two-point model are quantitatively compared and evaluated in this present study.

Robust observer based control for axial offset in pressurized-water nuclear reactors based on the multipoint reactor model using Lyapunov approach

Abstract In nuclear reactor imbalance of axial power distribution induces xenon oscillations. These fluctuations must be maintained bounded within allowable limits. Otherwise, the nuclear power plant could become unstable. Therefore, bounded these oscillations is considered to be a restriction for the load following operation. Also, in order to design the nuclear reactor control systems, poisons concentrations, especially xenon must be accessible. But, physical measurement of these parameters is impossible. In this paper, for the first time, in order to estimate the axial xenon oscillations and ensures these oscillations are kept bounded within allowable limits during load-following operation, a robust observer based nonlinear control based on multipoint kinetics reactor model for pressurized-water nuclear reactors is presented. The reactor core is simulated based on the multi-point nuclear reactor model (neutronic and thermal-hydraulic). Simulation results are presented to demonstrate the effectiveness of the proposed observer based controller for the load-following operation.

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.

Feasibility Study of 1/3 Thorium-Plutonium Mixed Oxide Core

Thorium-plutonium mixed oxide (Th-MOX) fuel has become one of the most promising solutions to reduce a large and increasing plutonium stockpile. Compared with traditional uranium-plutonium mixed oxide (U-MOX) fuels, Th-MOX fuel has higher consumption rate of plutonium in LWRs. Besides, thorium based fuels have improved thermomechanical material properties compared with traditional U-MOX fuels. Previous studies on a full Th-MOX core have shown reduced efficiency in reactivity control mechanisms, stronger reactivity feedback, and a significantly lower fraction of delayed neutrons compared with a traditional uranium oxide (UOX) core. These problems complicate the implementation of a full Th-MOX core in a similar way as for a traditional U-MOX core. In order to reduce and avoid some of these issues, the introduction of a lower fraction of Th-MOX fuel in the core is proposed. In this study, one-third of the assemblies are Th-MOX fuel, and the rest are traditional UOX fuel. The feasibility study is based on the Swedish Ringhals-3 PWR. The results show that the core characteristics are more similar to a traditional UOX core, and the fraction of delayed neutrons is within acceptable limits. Moreover, the damping of axial xenon oscillations induced by control rod insertions is almost 5 times more effective for the 1/3 Th-MOX core compared with the standard core.

Integral and axial xenon oscillations superposition and vver-1000 core energy-release stability

The effects arising from the interaction between the xenon oscillations of the power and the axial distribution of the energy release in the core as well as the role of these effects in the stability of energy release in VVER≠1000 are examined. It is shown that the reactor poses self-regulation properties. The superposition of the integral and axial xenon oscillations combined with the operation of the automatic power regulator prevents the appearance of diverging xenon oscillations and suppresses low-amplitude oscillations without operator intervention.

Optimal Control Timing Search of Xenon Oscillations in Large PWRs Using a Characteristic Ellipse Trajectory Based on Three Axial Offsets

We have proposed a simplified control procedure for axial xenon oscillations in large PWRs based on a characteristic ellipse trajectory method. However, this procedure cannot guarantee that the desired control rod position can be achieved when the xenon oscillation is terminated. In a previous paper, we proposed an innovative and very simple procedure to generate the trajectory for the predicted oscillation behavior, which can be expressed by trigonometric functions multiplied by an exponential function. By using this prediction capability, it is shown that the optimal control timing can be easily determined to terminate the xenon oscillation at the desired control rod position. The optimal timing is obtained at the intersection or, cross point, of two predicted trajectories, the forward trajectory beginning from the current position and the backward trajectory that is generated based on the desired control rod position. Since the trajectories are calculated by simple trigonometric functions and an exponential function, the prediction takes only a few seconds using a PC.

Optimal Control Timing Search of Xenon Oscillations in Large PWRs Using a Characteristic Ellipse Trajectory Based on Three Axial Offsets

We have proposed a simplified control procedure for axial xenon oscillations in large PWRs based on a characteristic ellipse trajectory method. However, this procedure cannot guarantee that the desired control rod position can be achieved when the xenon oscillation is terminated. In a previous paper, we proposed an innovative and very simple procedure to generate the trajectory for the predicted oscillation behavior, which can be expressed by trigonometric functions multiplied by an exponential function. By using this prediction capability, it is shown that the optimal control timing can be easily determined to terminate the xenon oscillation at the desired control rod position. The optimal timing is obtained at the intersection or, cross point, of two predicted trajectories, the forward trajectory beginning from the current position and the backward trajectory that is generated based on the desired control rod position. Since the trajectories are calculated by simple trigonometric functions and an exponential function, the prediction takes only a few seconds using a PC.

Xenon-induced axial power oscillations in the 400 MW PBMR

The redistribution of the spatial xenon concentration in the 400 MW Pebble Bed Modular Reactor (PBMR) core has a non-linear, time-dependent feedback effect on the spatial power density during several types of operational transient events. Due to the inherent weak coupling that exists between the iodine and xenon formation and destruction rates, as well as the complicating effect of spatial variance in the thermal flux field, reactor cores have been analyzed for a number of decades for the occurrence and severity of xenon-induced axial power oscillations. Of specific importance is the degree of oscillation damping exhibited by the core during transients, which involves axial variations in the local power density. In this paper the TINTE reactor dynamics code is used to assess the stability of the current 400 MW PBMR core design with regard to axial xenon oscillations. The focus is mainly on the determination of the inherent xenon and power oscillation damping properties by utilizing a set of hypothetical control rod insertion transients at various power levels. The oscillation damping properties of two 100%–50%–100% load-follow transients, one of which includes the de-stabilizing axial effects of moving control rods, are also discussed in some detail. The study shows that, although first axial mode oscillations do occur in the 400 MW PBMR core, the inherent damping of these oscillations is high, and that none of the investigated load-follow transients resulted in diverging oscillations. It is also shown that the PBMR core exhibits no radial oscillation components for these xenon-induced axial power oscillations.

Xenon Oscillation Control in Large PWRs Using a Characteristic Ellipse Trajectory Drawn by Three Axial Offsets

We have proposed a very simple xenon oscillation control procedure for axial xenon oscillation control based on a characteristic trajectory. The trajectory is drawn by three offsets of power distributions, namely, AOp, AOi, and AOx, which are defined as the axial offset (AO) of power distribution, AO of power distribution under which the current iodine distribution is obtained as the equilibrium, and that for xenon distribution, respectively. When these offsets are plotted on the X-Y plane for (AOp − AOx, AOi − AOx) the trajectory shows a quite characteristic ellipse (or an elliptic spiral). When the plot is at the origin of the X-Y plane, no xenon oscillation exists. Using the characteristics of the ellipse, the xenon oscillation can be eliminated by guiding the plot to the origin with control rod operation. In this paper, we will present an innovative and very simple procedure to generate the trajectory for the prediction of the oscillation behavior. Using the prediction capability of the xenon oscillation, the optimal control search calculation can be done. Since it is calculated by simple trigonometric functions and an exponential function, the prediction takes less than 1 s with a PC. It is especially effective for radial xenon oscillation control when the control rod motion is not flexible as for axial xenon oscillation control.

Xenon Oscillation Control in Large PWRs Using a Characteristic Ellipse Trajectory Drawn by Three Axial Offsets

We have proposed a very simple xenon oscillation control procedure for axial xenon oscillation control based on a characteristic trajectory. The trajectory is drawn by three offsets of power distributions, namely, AOp, AOi, and AOx, which are defined as the axial offset (AO) of power distribution, AO of power distribution under which the current iodine distribution is obtained as the equilibrium, and that for xenon distribution, respectively. When these offsets are plotted on the X-Y plane for (AOp − AOx, AOi − AOx) the trajectory shows a quite characteristic ellipse (or an elliptic spiral). When the plot is at the origin of the X-Y plane, no xenon oscillation exists. Using the characteristics of the ellipse, the xenon oscillation can be eliminated by guiding the plot to the origin with control rod operation. In this paper, we will present an innovative and very simple procedure to generate the trajectory for the prediction of the oscillation behavior. Using the prediction capability of the xenon oscillation, the optimal control search calculation can be done. Since it is calculated by simple trigonometric functions and an exponential function, the prediction takes less than 1 s with a PC. It is especially effective for radial xenon oscillation control when the control rod motion is not flexible as for axial xenon oscillation control.

Monitoring and Control of Radial Xenon Oscillation in PWRs by a Three-Radial-Offset Concept

A new concept is presented for monitoring and control of radial xenon oscillation in PWRs. This concept is based on a similar concept which has been developed and verified in domestic PWR plants for axial xenon oscillation control. It utilizes not only axial offset or core tilt of power distributions but also uses information of power distributions inversely calculated from the current iodine and xenon concentrations in respective core regions. Based on this concept, the operators are provided with the information of the timing, the amount of steps and the direction of control rod operation from a trajectory on the monitor display. Xenon oscillation can be eliminated by guiding the plot to the origin of the trajectory on the monitor display.

Soft computing systems applied to PWR's xenon

The present work intends to introduce a soft computing technique as an effective and robust tool available to deal with nuclear engineering problems. This goal is reached by the presentation of an application: a genetic programming system (GP) able to automatically design a controller for the axial xenon oscillations in a pressurized water reactors (PWRs). The axial xenon oscillations control methodology is based on three axial offsets: the xenon axial offset ( AOx), the iodine axial offset ( AOi) and the neutron flux axial offset ( AOf), effectively used in former work. Simulations were made using a two-point xenon oscillation model which employs the non-linear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation, with non-linear power reactivity feedback, also proposed in the literature. Obtained results showed the ability of the GP in finding a strategy which can effectively control the axial xenon oscillations.

PWR's xenon oscillation control through a fuzzy expert system automatically designed by means of genetic programming

This work proposes the use of genetic programming (GP) for automatic design of a fuzzy expert system aimed to provide the control of axial xenon oscillations in pressurized water reactors (PWRs). The control methodology is based on three axial offsets of xenon (AOx), iodine (AOi) and neutron flux (AOf), effectively used in former work. Simulations were made using a two-point xenon oscillation model, which employs the non-linear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation, with non-linear power reactivity feedback, also proposed in the literature. Results have demonstrated the ability of the GP in finding a good fuzzy strategy, which can effectively control the axial xenon oscillations.

Xenon Oscillations in a VVÉR-1000 Core

Xenon oscillations – periodic redistribution of the power over the core volume – can occur in a VVER-1000 core because of the large size of this core. The xenon oscillations can be conventionally divided into axial, radial, diametral, and azimuthal. In the present paper, methods are described for initiating the oscillations and the results of experimental investigations of the characteristics of free axial, diametral, and azimuthal xenon oscillations in the reactor core in the No. 1 unit of the Rostov nuclear power plant are presented; the experiments were performed at the start of burnup of the first (head) fuel load, completely consisting, for the first time, of improved fuel assemblies. Among other things, it is established that the periods of all oscillations investigated are the same. The azimuthal xenon oscillations are most rapidly damped.

Two-Group, Flux-Coupled Xenon Oscillation Model with an Equation System of Axial Difference Parameters

An axial xenon oscillation model is developed for pressurized water reactor analysis. The model employs an equation system for axial difference parameters that is derived from xenon and iodine balance equations coupled with two-group, one-dimensional neutron diffusion equations. To treat nonlinear xenon-flux-coupled terms, the spatial distributions of xenon, iodine, and flux are expanded by the Fourier sine series. The equation with respect to the axial difference parameters can be analytically solved with the initial condition related to axial power difference, which can be measured in the reactor. The axial power difference variation during xenon oscillation is directly obtained, and it provides a prediction of xenon oscillation behavior. The accuracy of the model is verified by benchmark calculations with a three-dimensional reference core calculation code and measured data from a core startup test at Yonggwang Unit 3.