Control Rod Pattern Research Articles

Reactor core design with enriched gadolinia burnable absorbers for soluble Boron-Free operation in the innovative SMR

Effective strategies for maintaining reactor reactivity at a consistent level are indispensable to enable soluble boron-free (SBF) operation in innovative small modular reactor (i-SMR) operation. This paper presents a reactor core design tailored for SBF operation in i-SMR, utilizing concentrated gadolinia burnable absorber rods. This investigation evaluates the concentration range of 155,157Gd and its reactivity characteristics, which are crucial for sustaining excess reactivity. The viability of employing enriched 155,157Gd for the i-SMR SBF operation is established through comprehensive analysis and simulations. Moreover, integrating 155,157Gd with integral gadolinia burnable absorber rods enhances the reactivity control and operational adaptability. Leveraging the spatial self-shielding effect of gadolinia extends the reactivity management capabilities and ensures the operational performance of the i-SMR as optimizing the cycle length. Core design considerations encompassing FA configurations and control rod patterns are investigated to ensure safety and performance across the initial and reload cycles. The feasibility of the SBF operation is verified by assessing compliance with the top-tier requirements of the i-SMR, thus underlining its potential for practical implementation.

Reactor core design with practical gadolinia burnable absorbers for soluble boron-free operation in the innovative SMR

The development of soluble boron-free (SBF) operation in the innovative Small Modular Reactor (i-SMR) requires effective strategies for managing excess reactivity over extended operational cycles. This paper introduces a practical approach to reactor core design for SBF operation in i-SMR, emphasizing the use of gadolinia burnable absorbers (BA). The study investigates the feasibility of Highly Intensive and Discrete Gadolinia/Alumina Burnable Absorber (HIGA) rods for controlling excess reactivity sustainably. Through comprehensive analysis and simulations, the reactivity behavior with varying quantities of HIGA rods is examined, leading to the development of optimized fuel assembly designs. Furthermore, the integration of HIGA rods with integral gadolinia BA rods is discussed to enhance reactivity control and operational flexibility further. This approach utilizes the spatial self-shielding effect of gadolinia for extended reactivity management, crucial for stable and efficient reactor performance. The paper thoroughly addresses core design considerations, including fuel assembly configurations and control rod patterns, to ensure safety and performance in initial and reload cycles. This research advances the development of SBF operation in i-SMR by offering practical reactivity management solutions.

Integrating core physics and machine learning for improved parameter prediction in boiling water reactor operations

This study introduces a novel method for enhancing Boiling Water Reactor (BWR) operation simulations by integrating machine learning (ML) models with conventional simulation techniques. The ML model is trained to identify and correct errors in low-fidelity simulation outputs, traditionally derived from core physics computations. These corrections aim to align the low-fidelity results closely with high-fidelity data. Precise predictions of nuclear reactor parameters like core eigenvalue and power distribution are crucial for efficient fuel management and adherence to technical specifications. Current high-fidelity transport calculations, while accurate, are impractical for real-time predictions due to extensive computational demands. Our approach, therefore, utilizes the standard two-step simulation process-assembly-level lattice physics calculations followed by whole-core nodal diffusion computations-to generate initial results, which are then refined using the ML-based error correction model. The methodology focuses on improving simulation accuracy in regular BWR operations rather than developing a universal ML predictor for reactor physics. By training an advanced neural network model on the difference in high-fidelity and low-fidelity simulations, the model can reduce the nodal power error from low-fidelity simulations to around 1% on average and the core eigenvalue down to under 100 pcm. This result is under the condition of the normal variations of control rod pattern and core flow rate changes in standard BWR operations used in the training and evaluation of the machine learning model. This work suggests a promising approach for achieving more accurate, computationally feasible simulation solutions in nuclear reactor operation and management.

A methodology for the analysis of In-Core fuel management configurations in BWR’s

A configuration for the integral problem of in-core fuel management consists of a fuel lattice and a fuel assembly designs, as well as a fuel reload and a control rod pattern design, so that the different criteria for the proper operation of a BWR reactor are met. Such a configuration or solution is not unique. There is an universe of potential candidate solutions that solve the problem in different ways. Departing from a database of candidate configurations, we describe and show the application of a multicriteria analysis methodology based on intervals and possibility function. The nuclear engineer must define his/her preferences in terms of the relevance assigned to the configurations’ features and next, using the methodology, those configurations are ranked. Besides this, the methodology can help us to identify the role that play some fuel lattice variables into the in-core fuel problem performance.

Trip turbine transient and stability analysis of two different fuel assembly designs aimed for the recycling of minor actinides and plutonium in BWRs

Recycling in thermal reactors is an alternative that could help to reduce minor actinide inventories produced by depleted fuel assemblies of nuclear reactors; the current paper assesses two proposed BWR fuel assemblies to recycle MA. These fuel designs aim to no introduce any perturbation in the electricity production from the Boiling Water Reactor, and they must satisfy the reactor core safety constraints. Such constraints must be considered under steady and transient conditions without the need to make any modification to the nuclear reactor safety systems. Previously, these two fuel designs were assessed under steady state conditions. In this study, the two proposed fuel assembly designs are tested for stability analysis and trip turbine transitory conditions. These fuel assembly designs are based on a 10 × 10 standard fuel assembly, and they have four MA-bearing rods that are replacing four fuel rod assemblies in three of the six axial fuel cells that compose the fuel assembly. The first design is a UO2 fuel assembly; the second one is a MOX fuel assembly where also, 8 fuel pin rods have been replaced by water rods in three of the six axial fuel cells that compose the fuel assembly. These two proposed fuel assemblies have been designed to be equivalent by producing the same amount of energy of the BWR reactor. The stability analysis is performed considering a global reactor oscillation; results show that in the MOX fuel assembly, the control rod pattern must be modified to provide an acceptable shutdown margin and to have adequate stability conditions. Both fuel designs provide acceptable conditions under the trip turbine transient condition and provide two fuel assembly designs that could be used for MA recycling in a BWR without any perturbation in energy production.

Truly-optimized PWR lattice for innovative soluble-boron-free small modular reactor

A novel re-optimization of fuel assembly and new innovative burnable absorber (BA) concepts are investigated in this paper to pursue a high-performance soluble-boron-free (SBF) small modular reactor (SMR), named autonomous transportable on-demand reactor module (ATOM). A truly optimized PWR (TOP) lattice concept has been introduced to maximize the neutron economy while enhancing the inherent safety of an SBF pressurized water reactor. For an SBF SMR design, the 3-D centrally-shielded BA (CSBA) design is utilized and another innovative 3-D BA called disk-type BA (DiBA) is proposed in this study. Both CSBA and DiBA designs are investigated in terms of material, spatial self-shielding effects, and thermo-mechanical properties. A low-leakage two-batch fuel management is optimized for both conventional and TOP-based SBF ATOM cores. A combination of CSBA and DiBA is introduced to achieve a very small reactivity swing (< 1000 pcm) as well as a long cycle length and high fuel burnup. For the SBF ATOM core, safety parameters are evaluated and the moderator temperature coefficient is shown to remain sufficiently and similarly negative throughout the whole cycle. It is demonstrated that the small excess reactivity can be well managed by mechanical shim rods with a marginal increase in the local power peaking, and a cold-zero shutdown is possible with a pseudo checker-board control rod pattern. In addition, a thermal–hydraulic-coupled neutronic analysis of the ATOM core is discussed.

A new methodology to optimize operation cycles in a BWR using heuristic techniques

A new system to optimize fuel assembly design, fuel reload design and control rod patterns design is shown. Fuel assembly optimization is made in two steps.In the first one, a recurrent neural network for the fuel lattice design of the bottom of the fuel assembly is used. In the second one, the top of the fuel assembly is built adding gadolinia to bottom fuel lattice. Fuel reload is optimized by another recurrent neural network whereas the control rod patterns are optimized by an ant colony method. This new system starts building a fresh fuel batch. Later, a seed fuel reload is optimized according to a Haling calculation. Afterwards an iterative process is started: firstly, control rod patterns through the cycle are optimized, once that a new fuel reload with previously optimized control rod patterns is found. If thermal limits cannot be satisfied in this iterative process after several iterations, a new seed fuel reload is designed. If cold shutdown margin cannot be fulfilled, then gadolonia concentration is increased into the fuel assembly. Finally, if energy requirements cannot be fulfilled, then the uranium enrichment of the fuel lattice of the bottom fuel assembly is increased. Results of this new system are successful: thermal limits and cold shutdown margin are fulfilled, and energy requirements are reached.

PLAYGO: Program for BWR LP-CRP Automatic Yielding by using GA Optimization

PLAYGO, the Program for Boiling Water Reactor Loading-pattern and control-rod-pattern Automatic Yielding by using Genetic algorithm Optimization, has been developed by the Institute of Nuclear Energy Research. This program utilizes a loading pattern scoping code, AUTOLPD, to search for an optimal loading pattern, and then uses a control rod pattern design code, AUTOROD, to generate a set of control rod patterns from the beginning of cycle to the end of cycle for the optimized loading pattern. PLAYGO offers two feedback mechanisms to adjust loading pattern in case the cycle length or the shutdown margin of the optimized loading pattern does not meet the specified criteria. Both AUTOLPD and AUTOROD use genetic algorithm as the optimization method. The automatic system has been tested through several actual cycles of Kuosheng Nuclear Power Plant. Results show that PLAYGO can be used to successfully find the optimal loading patterns and control rod patterns under different core conditions.

An innovative core design for a soluble-boron-free small pressurized water reactor

This research investigates the neutronic feasibility of a high-performance soluble-boron-free (SBF) small modular reactor (SMR) core based on a new burnable absorber concept called the “Burnable Absorber-Integrated Guide Thimble” (BigT). Three unique BigT designs were loaded into the core; each BigT design was judiciously ascertained from the core radial power profile to tailor the required reactivity depletion patterns for an SBF operation. The approach is demonstrated to work well as the SBF SMR design exceeds the targeted cycle length while successfully controlling its burnup reactivity swing between 634 and 800 pcm throughout most of its operation. This paper also describes the use of hafnium-doped stainless steel as mechanical shim (MS) rods to attain the core criticality. Because the worth of the MS rods is relatively small, insertion and withdrawal of the rods during operation hardly alter the core radial power distributions. The resulting axial power profile, meanwhile, displays a more refined bottom-skewed pattern during the early portion of the irradiation cycle due to partial top-half insertion of the MS rods. This investigation further deliberates on a modified checker board control rod pattern to assure safe cold shutdown of the core. All calculations in this multiphysics assessment of the 3D SBF SMR core were completed by using a 2-step Monte Carlo deterministic hybrid procedure based on the Monte Carlo Serpent and COREDAX diffusion codes with the ENDF/B-7.1 nuclear data library.

Using particle swarm optimization algorithm to search for a power ascension path of boiling water reactors

During the power ascension, the operating point is based on core power, core flow, control rod pattern, and concentrations of fission product, such as xenon. The thermal limits and fuel conditioning at the operating point should meet the constraints. ASCENTB is an automatic power ascension path searching program for boiling water reactors. The control rod movement is searched for by the particle swarm optimization (PSO) algorithm. The operating points of one control rod withdrawal sequence are based on the PSO1 or PSO2 strategy. The results of ASCENTB for two selected cycles are comparable with the power plant records.

SMR Fuel Cycle Optimization Using LWROpt

This article describes the light water reactor optimizer (LWROpt), a fuel cycle optimization code originally developed for BWRs, which has been adapted to perform core fuel reload and/or operational control rod management for pressurized water reactors (PWRs) and small modular reactors (SMRs), as well. Additionally, the eighth-core symmetric shuffle option is introduced to help expedite large-scale optimizations. These new features of the optimizer are tested by performing optimizations starting from a base case of an SMR core model that was developed manually and unrodded. The new fuel inventory (NFI) and loading pattern (LP) search in LWROpt was able to eliminate all of the constraint violations present in the initial base solution. However, independent control rod pattern (CRP) searches for the best several LPs found were not successful in generating CRPs without any constraint violations. This indicates that fully decoupling the fuel loading from the CRP optimization can increase the computational tractability of these calculations but at the expense of effectiveness. To improve on the individual search results, a coupled fuel loading (NFI and LP) and CRP search was performed, which produced a better overall result but still with some small constraint violations, emphasizing the fact that optimizing the fuel loading arrangement in a small high-leakage unborated core while concurrently determining its operational rod patterns for a 4-year operational cycle is no easy feat even to an experienced core designer; thus, this process can be greatly aided by employing automated combinatorial optimization tools.

Power–feedwater temperature operating domain for a BWR driven by natural convection

The aim of this work is to analyze feedwater temperature effects on reactor power in a BWR driven by natural convection (NCBWR) applying a methodology based on Monte Carlo's simulation. The analysis was performed with the reactor operating with different control rod patterns. The Monte Carlo's methodology was applied systematically to establish the operating domain, due that NCBWRs are not yet in operation, the analysis of the nuclear and thermal–hydraulic processes must rely on numerical modeling with the purpose of developing or confirming the design basis. The relative standard deviation obtained with a size of 20,000, data showed that for 2% change in the feedwater temperature, the response in thermal power change is 6.5% for 100% of rated power and 100% of rod pattern. Additionally five more rod patterns are presented in this paper. The regression analysis with the feedwater temperature showed statistically valid linear, quadratic and cubic representations, which are described in this paper for six different arrangements of reactor control rods. The results obtained in this study can be applied to operation and design of NCBWR.

BWROPT: A multi-cycle BWR fuel cycle optimization code

A new computer code for performing BWR in-core and out-of-core fuel cycle optimization for multiple cycles simultaneously has been developed. Parallel simulated annealing (PSA) is used to optimize the new fuel inventory and placement of new and reload fuel for each cycle considered. Several algorithm improvements were implemented and evaluated. The most significant of these are variable sampling probabilities and sampling new fuel types from an ordered array. A heuristic control rod pattern (CRP) search algorithm was also implemented, which is useful for single CRP determinations, however, this feature requires significant computational resources and is currently not practical for use in a full multi-cycle optimization. The PSA algorithm was demonstrated to be capable of significant objective function reduction and finding candidate loading patterns without constraint violations. The use of variable sampling probabilities was shown to reduce runtime while producing better results compared to using constant sampling probabilities. Sampling new fuel types from an ordered array was shown to have a mixed effect compared to random new fuel type sampling, whereby using both random and ordered sampling produced better results but required longer runtimes.

Automatic boiling water reactor control rod pattern design using particle swarm optimization algorithm and local search

This study developed a method for the automatic design of a boiling water reactor (BWR) control rod pattern (CRP) using the particle swarm optimization (PSO) algorithm. The PSO algorithm is more random compared to the rank-based ant system (RAS) that was used to solve the same BWR CRP design problem in the previous work. In addition, the local search procedure was used to make improvements after PSO, by adding the single control rod (CR) effect. The design goal was to obtain the CRP so that the thermal limits and shutdown margin would satisfy the design requirement and the cycle length, which is implicitly controlled by the axial power distribution, would be acceptable. The results showed that the same acceptable CRP found in the previous work could be obtained.

Automatic Boiling Water Reactor Control Rod Pattern Design Using Ant Colony Optimization Algorithm

A method for the automatic design of a boiling water reactor (BWR) control rod (CR) pattern (CRP) was developed using the rank-based ant system, which is an effective optimization algorithm for a combinatorial optimization problem. The designed BWR CRP followed either the A2-B1-A1-B2 or the A1-B2-A2-B1 sequence in this study. After the CRP was determined, the SIMULATE-3 code was used to calculate the axial power distribution, the effective multiplication factor keff, the shutdown margin, and three thermal limits–which were then used to evaluate the CRP and update the pheromone concentration. The developed methodology was demonstrated using design CRPs for several fuel loading patterns, showing that the designed patterns can be obtained within a reasonable computation time and with an acceptable cycle length.

Huitzoctli: A system to design Control Rod Pattern for BWR’s using a hybrid method

Huitzoctli system was developed to design Control Rod Patterns for Boiling Water Reactors (BWR). The main idea is to obtain a Control Rod Pattern under the following considerations: (a) the critical reactor core state is satisfied, (b) the axial power distribution must be adjusted to a target axial power distribution proposal, and (c) the maximum Fraction of Critical Power Ratio (MFLCPR), the maximum Fraction of Linear Power Density (FLPD) and the maximum Fraction of Average Planar Power Density (MPGR) must be fulfilled. Those parameters were obtained using the 3D CM-PRESTO code. In order to decrease the problem complexity, Control Cell Core load strategy was implemented; in the same way, intermediate axial positions and core eighth symmetry were took into account. In this work, the cycle length was divided in 12 burnup steps. The Fuel Loading Pattern is an input data and it remains without changes during the iterative process. The Huitzoctli system was developed to use the combinatorial heuristics techniques Scatter Search and Tabu Search. The first one was used as a global search method and the second one as a local search method. The Control Rod Patterns obtained with the Huitzoctli system were compared to other Control Rod Patterns designs obtained with other optimization techniques, under the same operating conditions. The results show a good performance of the system. In all cases the thermal limits were satisfied, and the axial power distribution was adjusted to the target axial power distribution almost completely. It is very important to point out that, even though the cycle length improvement was not the main idea of this work, the effective multiplication factor ( k eff ) at the end of the cycle was improved in all cases tested. The Huitzoctli system was programmed using Fortran 77 language in an Alpha Workstation with UNIX operating system.

BWR fuel cycle optimization using neural networks

In nuclear fuel management activities for BWRs, four combinatorial optimization problems are solved: fuel lattice design, axial fuel bundle design, fuel reload design and control rod patterns design. Traditionally, these problems have been solved in separated ways due to their complexity and the required computational resources. In the specialized literature there are some attempts to solve fuel reloads and control rod patterns design or fuel lattice and axial fuel bundle design in a coupled way. In this paper, the system OCONN to solve all of these problems in a coupled way is shown. This system is based on an artificial recurrent neural network to find the best combination of partial solutions to each problem, in order to maximize a global objective function. The new system works with a fuel lattices’ stock, a fuel reloads’ stock and a control rod patterns’ stock, previously obtained with different heuristic techniques. The system was tested to design an equilibrium cycle with a cycle length of 18 months. Results show that the new system is able to find good combinations. Cycle length is reached and safety parameters are fulfilled.

Automatic Power Ascension Search for a Boiling Water Reactor Using Ant Colony Optimization Algorithm

The ant colony optimization algorithm was used to search for a feasible power ascension path for a boiling water reactor. The control action of start-up operation includes control rod movements and core flow rate variations. During the process, the core status should satisfy some constraints such as thermal limits, preconditioning interior operating management recommendation guideline, and power flow operation domain. In addition, the control objective is to reach full power as soon as possible and approach the target control rod pattern as close as possible. The results show that the developed method can obtain the satisfactory power ascension path, which is also comparable to the operation record.

Nuclear Fuel Lattice Optimization Using Neural Networks and a Fuzzy Logic System

RENO-CC, a system to optimize nuclear fuel lattices for boiling water reactors using a multistate recurrent neural network, is shown. This kind of neural network is formed by only one layer of neurons. Each neuron is associated with a pin of the fuel lattice array. RENO-CC was tested through the fuel lattice design of 10 × 10 arrays with two water channels. Thus, the neural network has a total of 51 neurons; four neurons are associated with the channels (they correspond to a half fuel lattice). The neuron’s outputs are known as the neural states. The RENO-CC’s neural network works by changing the neural states in order to decrease or increase the value of an objective function. Neural states are chosen from an inventory of pins with different 235U enrichment and gadolinia concentrations. The objective function includes both the local power peaking factor and the infinite multiplication factor. These parameters are calculated with the HELIOS code. A fuzzy logic system is applied in order to decide if the designed fuel lattice is suitable to be evaluated by a three-dimensional reactor core simulator. To carry out the assessment, the fuel lattices with the best fuzzy qualification are placed at the bottom zone of a predesigned fuel assembly and predesigned fuel loading and control rod patterns. Fuel lattice performance is verified with the Core Master PRESTO core simulator. According to the obtained results, RENO-CC could be considered as a powerful tool to design fuel lattices. The system was programmed with Fortran 77 using a UNIX interface in an Alpha workstation.

On the use of the multivariate autoregressive and relative power contribution models for determination of transient root cause

The multivariate autoregressive (MAR) model and the relative power contribution (RPC) ratio are used in this work to determine the root causes of a power oscillation event and an apparent positive reactivity insertion transient occurred at the at the BWR/5 Units of the Laguna Verde Nuclear Power Plant (LVNPP) of México. The application of the MAR and PRC models leads to identify dominant frequencies and the contribution from other different signals to the dominant frequencies. The methodology firstly uses a linear model to estimate the response characteristics of the system and the spectra of the noise sources. The estimate of the process linear predictor is obtained by the ordinary least squares method. Then, the model performs a MAR analysis, and the RPC ratio is computed to determine the inter-relationship between the different reactor noise signals. The RPC ratio is an indication of how the fluctuation of one variable depends on other variables, at each frequency. Reactor signals acquired during the two transient operational events are used in the analysis. In the first event, a problem on the position controller of the flow control valve's stem induced the appearance of a power peak of 12% amplitude on the average power range monitors. Actual insertion of positive reactivity did not occur. The signals used for the analysis come from an average power range monitor, the position of the stem in the valve, controller of stem position, and controller of the recirculation flow. For the second transient, power oscillations of about 12% amplitude occurred. Signals from an average power range monitor, total flow through the core and flow through the 10 jet pump of each loop are analyzed. In both cases, some other signals were also used, but since they did not show appreciable influence on the RPC results, they were not considered for final analysis. The RPC results obtained in here confirmed previously known facts about the origin of the transients analyzed. Specifically, for the first transient, a dominant frequency of 1.7 Hz appeared on the power spectral densities of different signals from sensors on the recirculation loop B. At this 1.7 Hz frequency, the RPC ratio showed influence of such loop B spectra to the average reactor power spectrum, but no influence at all of the average reactor power to any of such loop B signals. The root cause, although not a real power transient event, therefore was not of neutronic nature, but related to recirculation flow. In the second transient, the prominent power oscillation frequency (0.54 Hz) was tracked within the spectral data of other signals. The RPC results for this case showed a strong influence of the average reactor power on the flow signals, but only a modest contribution from the flow signals to the average reactor power. The root cause therefore was of neutronic nature, due mainly to a combination of a particular core configuration and control rod pattern change at the moment of the event.