Pressurized Water Reactor Core Research Articles

Non-integer Order Control Scheme for Pressurized Water Reactor Core Power

Tracking load changes in a pressurized water reactor (PWR) with the help of an efficient core power control scheme in a nuclear power station is very important. The reason is that it is challenging to maintain a stable core power according to the reference value within an acceptable tolerance for the safety of PWR. To overcome the uncertainties, a non-integer-based fractional order control method is demonstrated to control the core power of PWR. The available dynamic model of the reactor core is used in this analysis. Core power is controlled using a modified state feedback approach with a non-integer integral scheme through two different approximations, CRONE (Commande Robuste d'Ordre Non Entier, meaning Non-integer order Robust Control) and FOMCON (non-integer order modeling and control). Simulation results are produced using MATLAB® program. Both non-integer results are compared with an integer order PI (Proportional Integral) algorithm to justify the effectiveness of the proposed scheme. Sate-space model Core power control Non-integer control Pressurized water reactor PI controller CRONE FOMCON.

Gradient descent-particle swarm optimization based deep neural network predictive control of pressurized water reactor power

A pressurized water reactor (PWR) is an integrated system of various interdependent subsystems that show highly nonlinear behavior, and each component is prone to uncertainties and malfunctions that initiate potential accidents. In contrast, PWR needs to be continuously monitored for stable and safe operation over a service time. In this study, a gradient descent-particle swarm optimization hybrid algorithm-based deep neural network (GD-PSO-based DNN) approach is proposed to monitor the PWR core power and outlet temperature. The Gaussian noise is introduced to the input signal, and the PWR core stability conditions are examined by using Lyapunov analysis. The simulation results verified under different conditions, in which the proposed control approach tracks the reference inputs successfully and enhances the stability as compared with the sliding mode control, linear quadratic regulator, and proportional-integral-derivative methods. The controller is validated by using the data from RELAP5 system codes, and the performance is examined using the mean square error, integral square error, integral absolute error, integral time square error, and integral time absolute error criterion functions. This study gives the benefit to apply the GD-PSO-based DNN control method for other nuclear engineering fields for system identification, prediction, and control.

Online learning based neural network adaptive controller for efficient power tracking of PWR type reactor with unknown internal dynamics

An online learning neural network (NN) based adaptive scheme has been proposed for tracking the power level of higher order point kinetic pressurized water reactor (PWR) with unknown dynamics under local and global load following conditions and emergency conditions. The PWR type of nuclear reactors are linear parameter varying (LPV) systems whose parameters vary with power, ageing effects and changes in nuclear core reactivity with fuel burn up. The drastic changes in plant parameters should be accommodated in a reactor control system through on-line identification to ensures safe operation for the power plant which demands for adaptive control system. To track the demand changes which happens during the load following and emergency conditions considered, the PID controller parameters needs to be varied. However, the proposed NN controller is based on feedback linearisation of nonlinear discrete time system with unknown internal dynamics by using a multilayer neural network acting as function approximator. Online weight tuning algorithm based on a modified delta rule and projection algorithm are used for the update of the weights of the proposed neural network controller along with conventional PID controller. Simulation studies with the proposed controller on a non linear PWR core shows that the proposed algorithm exhibits improved performance in terms of lesser ISE/ IAE/ ITAE over using PID controller under load following conditions. This new proposed power level controller has self learning capability and it needs the measurement of all the state variables and the desired trajectory.

Load following control of a pressurized water reactor via finite-time super-twisting sliding mode and extended state observer techniques

The problem of load following of a pressurized water reactor (PWR) has been extensively investigated in the last decades. However, most of the pre-existing controllers proposed in the literature rely on full system state measurements. This paper proposes a finite-time super-twisting sliding mode controller based on an extended state observer (FTSTSMC-ESO) for the load following of the PWR in the presence of compound disturbances, without assuming full system state measurements. First, a description of the PWR system with two-points kinetics equations is given. Then, an ESO that provides exact estimates of the compound disturbances simultaneously with the unmeasured states (relative density of delayed neutron precursor, average fuel temperature, temperature of the coolant, xenon concentration, and iodine concentration) is designed by employing the measurements of the PWR system. With the use of information from the ESO, a FTSTSMC is proposed to improve the load following performance and deal with the estimation errors of the ESO, while at the same time limiting the axial power difference of the PWR core. Theoretical analysis indicates that the stability of the proposed whole load following control system can be guaranteed by means of Lyapunov stability theory. Finally, simulation results reveal that the proposed FTSTSMC-ESO scheme can achieve satisfactory estimation performance and better load following performance in comparison with a proportional-integral-derivative (PID) controller, an active disturbance rejection controller (ADRC), and an extended state observer-based sliding mode controller (ESO-SMC).

Optimization of the loading pattern of the PWR core using genetic algorithms and multi-purpose fitness function

Abstract The study demonstrates an application of genetic algorithms (GAs) in the optimization of the first core loading pattern. The Massachusetts Institute of Technology (MIT) BEAVRS pressurized water reactor (PWR) model was applied with PARCS nodal-diffusion core simulator coupled with GA numerical tool to perform pattern selection. In principle, GAs have been successfully used in many nuclear engineering problems such as core geometry optimization and fuel configuration. In many cases, however, these analyses focused on optimizing only a single parameter, such as the effective neutron multiplication factor (k eff), and often limited to the simplified core model. On the contrary, the GAs developed in this work are equipped with multiple-purpose fitness function (FF) and allow the optimization of more than one parameter at the same time, and these were applied to a realistic full-core problem. The main parameters of interest in this study were the total power peaking factor (PPF) and the length of the fuel cycle. The basic purpose of this study was to improve the economics by finding longer fuel cycle with more uniform power/flux distribution. Proper FFs were developed, tested, and implemented and their results were compared with the reference BEAVRS first fuel cycle. In the two analysed test scenarios, it was possible to extend the first fuel cycle while maintaining lower or similar PPF, in comparison with the BEAVRS core, but for the price of increased initial reactivity.

Evaluating the Diffusion Approximation Capability on the Integral Pressurized Water Reactor (IPWR) Core Calculation

Diffusion approximation is an important approximation used to model a nuclear reactor core with a quite good accuracy and less computational cost. This approximation has been used widely around the globe for various kinds of nuclear reactors. This diffusion approximation is applied in a two-step method, a method combining a high fidelity transport code and low fidelity diffusion code. Meanwhile, innovations in the nuclear core model continue to make the nuclear reactor core safer, more robust, and smaller. The trend of creating smaller and more modular reactor core is emerging in the last ten years. These innovations will affect the core modeling system. Consequently, for smaller reactors, it is important to evaluate the capability of diffusion approximation if one wants to use a computationally cheaper method to model the reactor core. In this paper, neutron diffusion calculation for 160 MWth integral pressurized water reactor (IPWR) core was conducted using the PARCS nodal diffusion code employing the few-group spatially homogenized cross-sections generated by the Serpent Monte Carlo code. Due to its capability to model any reactor geometry in the high-resolution calculation, the results from Serpent were also used as a reference. Two important parameters are compared between PARCS and Serpent: effective neutron multiplication factor and core power distribution. For the full IPWR core model, a discrepancy of 564 pcm between PARCS and Serpent k eff was observed, while the radial power distribution had a maximum error of 4.71 %. It can be said, to some extent, that the diffusion approximation can be applied to IPWR core analysis. However, further improvement is indeed required if one wants more accurate results with low computational costs.

PWR core loading pattern optimization with adaptive genetic algorithm

In this paper, a new adaptive genetic algorithm (AGA) is proposed for the loading pattern optimization (LPO) of the pressurized water reactor (PWR) core. The tournament selection, the two-point crossover and the mutation based on randomly swapping positions between two fuel assemblies (FAs) are applied. New calculation formulae are introduced to adjust effectively the crossover and mutation probabilities according to the fitness value of the individual. The proposed algorithm is implemented in the LPO for the first core of the 1000 MWe PWR. The objective function is to minimize the maximum radial power peaking factor (RPPF) at the equilibrium of Xe under the constraint condition for the cycle length. The maximum RPPF of the obtained LP is decreased than that of the loading pattern (LP) by the designer. The results show that the proposed AGA is effective to improve the convergence rate of genetic algorithms (GAs) in the LPO.

Design and analysis of RIF scheme to improve the CFD efficiency of rod-type PWR core

This research serves to advance the development of engineering computational fluid dynamics (CFD) computing efficiency for the analysis of pressurized water reactor (PWR) core using rod-type fuel assemblies with mixing vanes (one kind of typical PWR core). In this research, a CFD scheme based on the reconstruction of the initial fine flow field (RIF CFD scheme) is proposed and analyzed. The RIF scheme is based on the quantitative regulation of flow velocities in the rod-type PWR core and the principle that the CFD computing efficiency can be improved greatly by a perfect initialization. In this paper, it is discovered that the RIF scheme can significantly improve the computing efficiency of the CFD computation for the rod-type PWR core. Furthermore, the RIF scheme also can reduce the computing resources needed for effective data storage of the large fluid domain in a rod-type PWR core. Moreover, a flow-ranking RIF CFD scheme is also designed based on the ranking of the flow rate, which enhances the utilization of the flow field with a closed flow rate to reconstruct the fine flow field. The flow-ranking RIF CFD scheme also proved to be very effective in improving the CFD efficiency for the rod-type PWR core.

Investigation of a two-year cycle pressurized water reactor core design with increased enrichment and extended burnup limits

Increasing the burnup limit from 62 GWd/MTU to 75 GWd/MTU can help increase the cycle length of a typical pressurized water reactor from 18 months to two years or longer. To meet this goal, the fuel enrichment limit must also be increased from 5.0 w/o to 6.0 w/o, however, this causes the excess reactivity to be unacceptably high near the beginning of a cycle. Previous attempts at solving this problem have examined using a single neutron poison to reduce the excess reactivity within the current burnup limit. This paper examines combining two separate neutron poisons (integrated fuel burnable absorbers, B2Zr, and gadolinia doped fuel rods, Gd2O3) to reduce the initial excess reactivity associated with higher enriched fuel and prevent fuel cladding rupture during a loss-of-coolant accident. Through a limited optimization, four unique cores were found. While no core was able to fulfill all the operational constraints, they were able to produce a longer core life while reducing core loading, which could provide utilities flexibility in their operational schedules. Along with this, additional optimization could yield practical two-year cycle lengths with the aforementioned benefits.

A New Embedded Analysis with Pinwise Discontinuity Factors for Pin Power Reconstruction

Based on embedded analysis, an accurate pin power reconstruction (PPR) method is proposed for conventional nodal analysis. Unlike the common form function (FF) method, the new PPR method, named the embedded pin power reconstruction (EPPR) method, directly solves a two-group fixed-source problem that is defined with pinwise homogenized group constants (HGCs) and coarse-mesh incoming partial currents on the boundary. In the EPPR scheme, the pinwise HGCs including the pinwise discontinuity factor are predetermined from single-assembly lattice calculations, and the boundary partial currents are obtained from two-step nodal analyses. Two EPPR approaches are proposed: One is a 3×3 extended color-set configuration, and the other is a smaller one considering the half-thickness of the surrounding fuel assemblies. The performance of the EPPR methods is evaluated with various benchmark problems including partially mixed oxide–loaded pressurized water reactor cores, and the results are compared with the conventional FF method. Comprehensive results of this work demonstrate that the new EPPR method can provide much better accuracy than the conventional FF-based PPR method.

Dynamic modeling and two-degree-of-freedom controller design for pressurized water reactor core

The task of this investigation is to model pressurized water reactor core and design a reactor power controller that has a strong robustness in various operating conditions. The comparisons of different nodal models of the reactor core, which includes point kinetics, heat transfer between fuel and coolant, and reactivity feedbacks, indicate that the 2C/1F finite-difference nodal model with four fuel nodes has sufficient transient response accuracy. Based on the transfer function model that is obtained by linearizing the nonlinear model, a two-degree-of-freedom controller is proposed to reduce the effect of power level variation on the system dynamics. The simulations demonstrate that the proposed two-degree-of-freedom controller can give satisfying performance for both reactor power and coolant temperature over a wide range of reactor operation.

Pattern Recognition–Based Technique for Control Rod Position Identification in Pressurized Water Reactors

This paper proposes the application of a pattern recognition–based technique to enhance the process of control rod position identification in pressurized water reactors (PWRs). The proposed technique employs a multivariant analysis technique, namely, principal component analysis (PCA) and clustering analysis (CA) to identify the position of the PWR control rod using its impact on the core radial thermal neutron flux along the axial track of motion. The results of these investigations have shown that the proposed technique successfully removed the limitation on the data size and any limitations imposed by outlier samples, extracted the noise, and provided near-instantaneous analytical and visual ways for position identification process with excellent generalization fitting and prediction efficiencies. In the context of this paper, multiple in-depth simulations are conducted to ascertain the efficiency of the proposed technique in identifying the control rod positions. These simulations have been conducted using a Westinghouse 2772-MW(thermal) PWR benchmark at 100% thermal power generation, where a three-dimensional TRITON FORTRAN-code has been utilized to simulate the radial thermal neutron flux of the PWR core. The PCA model is developed, tested, and generalized using the SIMCA software package. In addition, CA is also performed via the Minitab statistics software package in order to confirm the efficiency of the proposed technique.

Analytical investigation on rod bundle CHF-regime criterion based on dimensionless groups

The accurate prediction of rod bundle critical heat flux (CHF) is an important task for thermal-hydraulic design of pressurized water reactor (PWR) core. Under normal and transient conditions of PWR, based on the two-phase flow pattern, there are different CHF regimes. In order to correctly distinguish the CHF regimes in rod bundle, it is necessary to analytical investigate rod bundle CHF-regime criterion. In this study, a general dimensionless rod bundle CHF correlation is presented based on dimensional analysis method. The real vapor quality, Katto number and boiling length are introduced to establish the basic form of the dimensionless CHF correlation. According to the deep analysis of the distribution trend of typical CHF experimental data and the CHF characteristics of different CHF regimes, the CHF in rod bundle are separated into DO, DNB and HP-DNB regimes. Concise dimensionless CHF correlations corresponding to each regime are developed, and the dimensionless equations between the boundaries of each regime are established. Also, a clearly defined map of characteristic regimes of CHF in rod bundle is determined. This study proposes a classification criterion for rod bundle for rod bundle CHF regimes, and it is very important for the upcoming development of rod bundle CHF mechanistic model.

Linearized Mathematical Model for PWR Dynamics Simulation

A linearized mathematical model for the pressurized water reactor (PWR) core dynamics is presented based on conservation of energy and mass balance. The core and coolant system are treated as a lumped parameter while considering the delayed neutron effect. The developed model is controlled by negative feedback reactivity from the coefficients of reactivity in the fuel and reactor coolant. The model state variables are linearized first order differential equations with a steady state initial value and put in state space using Matlab/Simulink. The reactor core dynamic response is investigated through transients introduced to the core model inlets represented in external reactivity insertion eg. (0.001 Δk/k), 10% step decrease in core flow rate and 10 oF step decrease in core inlet coolant temperature. The simulation results demonstrated the role of feedback reactivity form coolant temperature and Doppler Effect in stabilizing the core power and affecting the steady state values of core variables.

Design of NDI-SMC based robust hybrid nonlinear controller for load following operation in pressurized water reactor

The pressurized water reactor (PWR) is a natural choice for the load following operation due to its inherent self-regulating nature. The nonlinear mathematical model of PWR is derived considering the large parametric uncertainties due to power variation, Xenon oscillations and external disturbances in the reactor core. This paper proposes a robust and tracking hybrid nonlinear state feedback tracking controller which combines nonlinear dynamic inversion (NDI) and the sliding mode control (SMC) algorithm to achieve a smooth load following operation for such complex system. The proposed nonlinear controller is able to ensure satisfactory performances e.g. smooth tracking of reference power and nullify the xenon oscillations in PWR core. This designed controller is also capable to satisfy the limits of the variables like (a) zonal coolant temperature, (b) average fuel temperature and (c) external control rod reactivity for such system in PWR core during the operation. The performance of the proposed nonlinear controller is further compared with the single NDI based controller to show the effectiveness of the proposed methodology against the varying parametric uncertainties and external disturbances. This paper demonstrates the simulation results using Matlab/Simulink platform.

Coupled 3D neutron kinetics/thermal-hydraulics calculation of PWR core using nodal Green's function method on Neumann boundary condition

In this paper, we proposed a numerical method to perform the coupled three dimensional (3D) neutron kinetics/thermal-hydraulics calculations for the pressurized water reactor (PWR) core and verified its accuracy. In the spatial neutron kinetics, the nodal Green's function method (NGFM) on Neumann boundary condition is applied for the space discretization procedure, and the implicit difference scheme is used for the time differential. It is assumed that the fission source term in the delayed neutron precursor concentration equation is linearly changed within each time step. For the thermal-hydraulic analysis, the single channel model in which a fuel assembly corresponds to one average thermal-hydraulic channel is applied, and cross flow between channels is not taken into account. And we considered the coolant as a single phase incompressible fluid. The model proposed in here was tested by comparison with the two dimensional (2D) TWIGL problem and the NEACRP-L-335 transient benchmark for the 3D PWR core. The numerical results are in good agreement with reference solutions.

Distributed-parallel CFD computation for all fuel assemblies in PWR core

To further understand and monitor the thermal–hydraulic (TH) status of large domain of pressurized water reactor (PWR) core, an applicable engineering approach with high efficiency and high spatial resolution is critical. Traditional engineering computational fluid dynamics (CFD) computation needs too many computing resources to effectively analyze large domain engineering application for PWR core. In this study, a distributed-parallel (DP) CFD scheme is presented. This scheme separates the large domain into some sub-domains in order to optimize computing time and resources. The design completely retains the complex structures and fine-scale CFD mesh. In addition, it also significantly reduces the computing resources and time, and a fine-scale, full-height CFD analysis can be done in hours for all assemblies. Moreover, important design requirements such as energy consumption ratio, relative computing domain, relative assembly number, and the ranking method of important locations are also designed to optimize the applications of DP scheme to satisfy different engineering demands. The performance of the proposed scheme is evaluated using the CFD computation of a representative region from all 121 assemblies in a PWR core. This research serves to advance the development of engineering CFD computation for PWR core.

A functional variable universe fuzzy PID controller for load following operation of PWR with the multiple model

To achieve core power control of Pressurized Water Reactor (PWR) over full power range under arbitrary initial power conditions, a global controller under the multiple model for reactor core load following is designed. Based on the nonlinear model of PWR core, the transfer function models at five power levels are chosen as local models of reactor core. The multiple model of PWR core in the global range of power level is the weighted sum of five local models with the triangle membership functions. Based on the multiple model of PWR core, a global controller, is contrived by five local controllers at different core power level with the Functional Variable Universe Fuzzy PID (FVUF-PID) controller. The simulation results show that the global controller has good convergence and performance robustness characteristics over a wide range of operational parameters.

Low resolution modelling of mixing phenomena in PWR fuel assemblies

Simulation of single-phase turbulent flow in the entire reactor core is a challenging task due to a complex geometry and a huge computational domain, which requires large number of computational cells. In order to reduce the size of a computational mesh, simplifications in the geometry are practically inevitable. Among the most challenging parts with many small details that affect the flow through a fuel assembly are mixing grids. There are several different designs of the mixing grids. One of the most frequently used designs consists of a strap, springs and dimples, which are used as a structural support for the fuel rods, and mixing vanes, which deflect the fluid and increase the mixing. Neglecting the effects of the mixing grid would result in a less accurate reproduction of the flow and temperature field, which may lead to too small inter sub-channel mixing in the fuel assembly. Hence, application of a porosity model is proposed for the mixing grid, which largely reduces the computational mesh. Additional momentum sources mimic the effect of the mixing vanes. This approach aims to fill the gap between three-dimensional well-resolved Computational Fluid Dynamics (CFD) and one-dimensional sub-channel or system codes. As such, they are able to provide valuable insights to the flow behaviour in the reactor core.The present study examines the possibility to model the effect of the mixing grid by applying momentum sources in the governing equations. A split-type mixing grid is considered, which is one of the most frequently used designs in a Pressurized Water Reactor (PWR) fuel assembly. The applied split-type mixing grid generates a particular pattern of swirl motion within each sub-channel as well as it increases the cross flow between neighbour sub-channels of the fuel bundle. Non-homogeneous momentum sources have been applied, which mimic the deflection of the flow and blockage by the mixing vanes. The obtained pattern of the secondary flow closely resembles the secondary flow, which has been obtained with a reference CFD simulation that included all detailed geometrical aspects of the grid spacer with mixing vanes. The magnitudes of the momentum sources have been tuned to generate similar magnitudes of the secondary flow and stream-wise vorticity as observed in the results of the reference CFD simulation. In the next step, this approach has been applied on successively coarser meshes to investigate its effectivity on low resolution (very coarse) meshes. It turned out that the proposed model is able to mimic the mixing effect between the sub-channels. However, discrepancies are observed in the development of the secondary flow in the stream-wise direction. In the last step, the coolant flow in a flow domain consisting of 9 fuel assemblies is reproduced for normal conditions inside a PWR core as well as for two off-normal scenarios, which consider two different blockages at the entrance of the central fuel assembly. This approach has a promising potential to perform a CFD simulation of a realistic fluid mixing inside and between adjacent fuel assemblies in an entire PWR reactor core.

MCS/TH1D analysis of VERA whole-core multi-cycle depletion problems

This paper presents the verification and validation elements of the UNIST in-house Monte Carlo code, MCS, for the multi-cycle and multi-physics analyses of high-fidelity, large-scale commercial pressurized water reactors (PWRs). Analysis on the neutronic performance with thermal/hydraulic (T/H) feedback is the key to detecting the complex behavior of an operating nuclear power reactor. The MCS solutions with T/H feedback, TH1D, of the consortium for advanced simulation of light water reactors (CASL) virtual environment for reactor applications (VERA) core physics benchmark progression problems 6 and 7 showed excellent agreement in eigenvalues, temperature and power profiles with the MC21/COBRA-IE, MC21/CTF and VERA-CS solutions for the single assembly and whole core of Watts Bar Nuclear 1 (WBN1) Cycle 1 under beginning-of-cycle and hot-full-power condition. Furthermore, the core depletion analysis is one of the most compelling advances for reactor analysis. Therefore, this work is significantly focused on the nuclide depletion simulation coupled with TH1D of the first two cycles of WBN1 to address the VERA core physics benchmark problems 9 and 10. MCS is one of the few Monte Carlo codes that have the capability of depletion calculation for both WBN1 Cycles 1 and 2. The accuracy of MCS simulation of WBN1 Cycle 1 is within 40 ppm and 30 ppm in critical boron concentration (CBC) for all burnup points, compared with the measured data and VERA-CS solutions, respectively. To demonstrate the multi-cycle refueling capability of MCS, the WBN1 Cycle 2 is simulated and compared with the solutions of VERA-CS only, because of the lack of available measured data. MCS shows excellent agreement compared with VERA-CS within 30 ppm in CBC, and the average bias for the entire Cycle 2 is approximately 20 ppm. These results provide confidence in MCS’s capability in high-fidelity, multi-cycle calculations of the practical PWR core.