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A deterministic method for PWR loading pattern optimization

ANNALS OF NUCLEAR ENERGY 2018年第Jul.期117卷 131-144页

作者： Rahman, Fariz B. Abdul Lee, John C. Franceschini, Fausto GE Hitachi Nucl Energy 3901 Castle Hayne Rd Wilmington NC 28402 USA Univ Michigan Ann Arbor MI 48109 USA Westinghouse Elect Co LLC Cranberry Township PA USA

A new deterministic approach to core loading optimization is presented. Selection of fuel enrichment and burnable poison (BP) arrangement in a pressurized water reactor (PWR) core are optimally determined subject to power peaking factor (PF) constraints. The deterministic approach is based on the method of Lagrange multipliers and the direct adjoining approach for the inequality power PF constraint. The optimality conditions are derived using calculus of variations resulting in the presence of jump conditions and a linear control Hamiltonian. The optimal control problems are addressed by simultaneously minimizing the Hamiltonian using the gradient method and performing Newton's method in different regions of the core to produce viable solutions for the controls. Without active control of the power profile in PWRs during depletion, our methodology is able to satisfy the power PF constraint at all times by proper loading selection at the beginning of cycle (BOC). This is achieved by promoting the proper burnup path forward in time during the calculation of the forward optimality conditions. This information is utilized in the adjoint burnup calculation, which acts to propagate the optimal control path back to the BOC during the calculation of the adjoint optimality conditions. The methodology has been developed into a new code DMCO (Deterministic Multi-Control optimization) which can produce two-dimensional two-group depletion results in approximately seven minutes per optimization iteration on a personal computer. No application of heuristics is required and the code is capable of finding solutions from initial control distributions. A preliminary case study is presented for the Westinghouse AP600 first cycle fuel loading design which achieved an extended fuel cycle while satisfying power PF constraints. (C) 2018 Elsevier Ltd. All rights reserved.

关键词： Deterministic method Multi-control loading pattern optimization

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Application of metaheuristics to loading pattern optimization problems based on the IAEA-3D and BIBLIS-2D data

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ANNALS OF NUCLEAR ENERGY 2018年第Jan.期111卷 329-339页

作者： de Moura Meneses, Anderson Alvarenga Araujo, Lenilson Moreira Nast, Fernando Nogueira da Silva, Patrick Vasconcelos Schirru, Roberto Fed Univ Western Para Inst Geosci & Engn Lab Computat Intelligence R Vera Paz S-N BR-68035110 Santarem PA Brazil Univ Fed Rio de Janeiro Nucl Engn Program COPPE Rio De Janeiro Brazil

The loading pattern optimization (LPO) of a Nuclear Power Plant (NPP), or in-core-fuel management optimization, is a real-world and prominent problem in Nuclear Engineering with the goal of finding an optimal (or near-optimal) loading pattern (LP), in terms of energy production, within adequate safety margins. Most of the reactor models used in the LPO problem are particular cases, such as research or power reactors with technical data that cannot be made available for several reasons, which makes the reproducibility of tests unattainable. In the present article we report the results of LPO of problems based upon reactor physics benchmarks. Since such data are well-known and widely available in the literature, it is possible to reproduce tests for comparison of techniques. We performed the LPO with the data of the benchmarks IAEA-3D and BIBLIS-2D. The Reactor Physics code RECNOD, which was used in previous works for the optimization of Angra 1 NPP in Brazil, was also used for further comparison. Four optimization Metaheuristics (OMHs) were applied to those problems: Particle Swarm optimization (PSO), Cross-Entropy algorithm (CE), Artificial Bee Colony (ABC) and Population-Based Incremental Learning (PBIL). For IAEA-3D, the best algorithm was the ABC. For BIBLIS-2D, PBIL was the best OMH. For Angra 1 / RECNOD optimization problem, PBIL, ABC and CE were the best OMHs. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： loading pattern optimization Nuclear Power Plant optimization Metaheuristics Pressurized water reactor Nuclear fuel

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A novel multi objective loading pattern optimization by Gravitational Search Algorithm (GSA) for WWER1.000 core

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PROGRESS IN NUCLEAR ENERGY 2016年 93卷 1-11页

作者： Aghaie, M. Mahmoudi, S. M. Shahid Beheshti Univ GC Dept Engn POB *** Tehran Iran Grad Univ Adv Technol Fac Elect & Comp Engn Kerman Iran

In this paper, a novel multi objective optimization algorithm, Gravitational Search Algorithm (GSA), is developed in order to implement in the loading pattern optimization (LPO) of a nuclear reactor core. In recent decades several metaheuristic algorithms or computational intelligence methods have been expanded to optimize reactor core loading pattern. Regarding the coupled behavior of Neutronic and Thermal-Hydraulic (NTH) dynamics in a nuclear reactor core, proper loading pattern of fuel assemblies (FAs) depends on NTH aspects, simultaneously. Thus, obtaining optimal arrangement of FAs, in a core to meet special objective functions is a complex problem. Gravitational Search Algorithm (GSA) is constructed based on the law of Gravity and the notion of mass interactions, using the theory of Newtonian physics and searcher agents are the collection of masses. In this work, for multi objective optimization, the NTH aspects are included in fitness function. Neutronic goals include increasing multiplication factor (Kell), decreasing of power picking factor (PPF) and flattening of the power density, also thermal-hydraulic (TH) goals include increasing critical heat flux (CHF) and decreasing average of fuel centers temperature. Therefore, at the first step, GSA method is compared with other metaheuristic algorithms on Shekel's Foxholes problem. In the second step for finding the best core pattern and implementation of the objectives listed, GSA algorithm has been performed for case of WWER1000 reactor. For the NTH calculations, PARCS (Purdue advanced reactor core simulator) and COBRA-EN codes are implemented, respectively. The results demonstrate that GSA algorithm have promising performance and can propose for other optimization problems of nuclear engineering field. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： loading pattern optimization Gravitational Search Algorithm Neutronic Thermal-hydraulic WWER1000 PARCS COBRA-EN

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Physics-informed Reinforcement Learning optimization of PWR core loading pattern

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ANNALS OF NUCLEAR ENERGY 2024年 208卷

作者： Seurin, Paul Shirvan, Koroush MIT 77 Massachusetts Ave Cambridge MA 02139 USA

The nuclear sector represents the largest single source of carbon-free energy in the United States. Nevertheless, keeping existing nuclear assets competitive on the grid is key to their ability to continue to provide dispatchable clean energy along side renewable generation. Optimizing the fuel cycle cost through the optimization of core loading patterns is one approach to addressing this lack of competitiveness. However, this optimization task involves multiple objectives and constraints, resulting in a vast number of candidate solutions that cannot be explicitly solved. While stochastic optimization (SO) methodologies are utilized by various nuclear utilities and vendors for fuel cycle reload design, manual design remains the preferred approach. To advance the state-of-the-art in core reload patterns, we have developed methods based on Deep Reinforcement Learning for single and multi-objective optimization. Previous research has laid the groundwork for these approaches and demonstrated its ability to discover high-quality patterns within a reasonable timeframe. Moreover, RL methods have shown superiority against SO in the multi-objective settings. In this paper, we introduce an innovative paradigm by incorporating multi-objective RL, interpretable AI, and physics knowledge to further improve the performance of the algorithms. When the problem increases in complexity, the classical single objective sometimes failed to even found feasible solutions. Leveraging physic-information becomes pivotal to find high-quality and more diverse solutions faster. These findings motivate incorporation of more physics to further aid in the quest of surpassing human intelligence. Future work will focus on scaling this method and addressing fuel performance and control rod limits to demonstrate that these new designs can be considered for a real reactor.

关键词： Reinforcement learning PEARL loading pattern optimization Interpretable AI

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Core loading pattern optimization of a typical two-loop 300 MWe PWR using Simulated Annealing (SA), novel crossover Genetic Algorithms (GA) and hybrid GA(SA) schemes

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ANNALS OF NUCLEAR ENERGY 2014年 65卷 122-131页

作者： Zameer, Aneela Mirza, Sikander M. Mirza, Nasir M. Pakistan Inst Engn & Appl Sci Dept Comp & Informat Sci Islamabad 45650 Pakistan Pakistan Inst Engn & Appl Sci Dept Phys & Appl Math Islamabad 45650 Pakistan

A comparative study of the Simulated Annealing and Genetic Algorithms based optimization of loading pattern with power profile flattening as the goal, has been carried out using the LEOPARD and MCRAC neutronic codes, for a typical 300 MWe PWR. At high annealing rates, Simulated Annealing exhibited tendency towards premature convergence while at low annealing rates, it failed to converge to global minimum. The new 'batch composition preserving' Genetic Algorithms with novel crossover and mutation operators are proposed in this work which, consistent with the earlier findings (Yamamoto, 1997), for small population size, require comparable computational effort to Simulated Annealing with medium annealing rates. However, Genetic Algorithms exhibit stagnation for small population size. A hybrid Genetic Algorithms (Simulated Annealing) scheme is proposed that utilizes inner Simulated Annealing layer for further evolution of population at stagnation point. The hybrid scheme has been found to escape stagnation in bcp Genetic Algorithms and converge to the global minima with about 51% more computational effort for small population sizes. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Simulated Annealing Genetic Algorithms loading pattern optimization Pressurized Water Reactors

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Development of CNN-Based surrogate models to predict power distributions in i-SMR

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ANNALS OF NUCLEAR ENERGY 2025年 213卷

作者： Kwon, Jungseok Park, Tongkyu Zee, Sung-kyun FNC Technol Heungdeok IT Valley Bldg 32F13 Heungdeok 1-ro Yongin 16954 Gyeonggi Do South Korea

This paper presents convolutional neural network (CNN)-based surrogate models for predicting the 2-D pin-wise power distribution and 3-D assembly-wise power distribution of i-SMR. The performance for the 2-D pin power prediction was evaluated by comparing each surrogate model's performance by employing the fuel and gadolinium enrichment maps, form functions, and/or control rod position data as input data. The results demonstrated that, considering the training time, utilizing form functions resulted in higher prediction accuracy. In both 2-D and 3-D predictions, integrating control rod position information improved the prediction performance. The 2-D pin power prediction achieved a global relative mean error of 0.821 %, while the error for the 3-D assembly-wise power distribution prediction was 2.080 %. The model took 5 s to predict 3,754 loading pattern (LP) cases, or 1.3 ms per case, for the time-consuming 2-D pin power prediction task, which has 5,720 value points (22 assemblies x 260 pins per assembly) for each LP. Leveraging the inherent rapid computational speed of these AI models is expected to expedite the reactor design process and provide guidelines for load- following operation and loading pattern optimization.

关键词： CNN Surrogate model loading pattern optimization Load following Operation i-SMR

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Impact of including fuel performance as part of core reload optimization: Application to power uprates

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NUCLEAR ENGINEERING AND DESIGN 2025年 433卷

作者： Seurin, Paul Halimi, Assil Shirvan, Koroush MIT 77 Massachusetts Ave Cambridge MA 02139 USA

Increasing the power output of existing nuclear power plants, known as performing a power uprate, could result in improved economic performance, especially with the recent introduction of production tax credits. However, beyond the neutronics and thermal-hydraulics analysis, a fuel performance analysis must be conducted due to the uprate's impact on core reload fuel licensing limits. Key fuel performance limits include pellet-cladding interaction, plenum pressure, and fuel temperature. Traditionally, these QoI are evaluated after core reload analyses using dedicated codes, which require significant computation time. Integrating QoI analyses within an optimization framework is advantageous, but necessitates tools capable of performing tens of thousands of these evaluations efficiently. This paper explores the use of fast-running surrogates to replace resource- intensive codes within a Reinforcement Learning-based core reload optimizer. A standard Westinghouse-type 4-loop Pressurized Water Reactor core rated at 111.7 kW/L and two uprates-118 kW/L on an 18-month cycle and 126.3 kW/L on a 12-month cycle-are examined. Deep learning ensemble models for each scenario were evaluated and integrated into the optimization process. Subsequently, the fuel performances of the best solutions were evaluated using the dedicated codes. Although the improvements in fuel performance were marginal, significant enhancements were observed in neutronics and thermal hydraulics licensing limits. The superiority of combining QoI together rather than decoupling them as it is classically done during optimization was observed consistently across different optimization simulation sets. This highlights an important mechanism of these novel algorithms: RL agents can leverage intrinsic physical correlations between objectives and constraints to navigate the search space optimally. Asa result, we suggest to perform the core reload design process coupling all core reload analysis limits.

关键词： Reinforcement Learning Power uprate Fuel performance analysis Deep learning ensemble Surrogate modeling loading pattern optimization

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AI-Based Prediction Module of Key Neutronic Characteristics to Optimize loading pattern for i-SMR with Flexible Operation

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KOREAN JOURNAL OF CHEMICAL ENGINEERING 2024年第10期41卷 2741-2759页

作者： Kwon, Jungseok Park, Tongkyu Zee, Sung Kyun FNC Technol Heungdeok IT Valley Bldg 32F13Heungdeok 1 Ro Yongin 16954 Gyeonggi Do South Korea

This paper proposes an AI-based module for a loading pattern (L/P) optimization algorithm applied to the i-SMR, designed for flexible operation. The AI module can be used as a surrogate model in the simulated annealing (SA) screening process, which allows for more efficient optimization. The convolution neural network (CNN) model was trained using reactor core L/Ps and corresponding core parameter values derived from a realistic core simulation code. For load-following operations, we selected core parameters such as control rod insertion depth, radial peaking factor, axial shape index, and effective multiplication factor. To calculate the objective function of an L/P during the SA process using core design codes, it takes approximately 3 s, while the AI-based module can predict the objective function within about 0.1 ms. During the prediction of selected parameters, we discovered two factors affecting prediction accuracy. First, the model exhibited a significant increase in error when trained on dataset containing negative values. Second, utilizing batch normalization (BN) layer and squeeze and excitation (SE) module, intended to improve accuracy, resulted in a decrease in performance of the model. Our study demonstrated that the CNN-based model achieves excellent prediction accuracy and has an ability to accelerate optimization algorithms by taking advantage of artificial intelligence's inherent computational speed.

关键词： Convolution neural network loading pattern optimization i-SMR (innovative small modular reactor) Flexible operation Screening technique Simulated annealing

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PWR loading pattern optimization using Harmony Search algorithm

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ANNALS OF NUCLEAR ENERGY 2013年 53卷 288-298页

作者： Poursalehi, N. Zolfaghari, A. Minuchehr, A. Shahid Beheshti Univ Dept Engn GC Tehran Iran

In this paper a core reloading technique using Harmony Search, HS, is presented in the context of finding an optimal configuration of fuel assemblies, FA, in pressurized water reactors. To implement and evaluate the proposed technique a Harmony Search along Nodal Expansion Code for 2-D geometry, HSNEC2D, is developed to obtain nearly optimal arrangement of fuel assemblies in PWR cores. This code consists of two sections including Harmony Search algorithm and Nodal Expansion modules using fourth degree flux expansion which solves two dimensional-multi group diffusion equations with one node per fuel assembly. Two optimization test problems are investigated to demonstrate the HS algorithm capability in converging to near optimal loading pattern in the fuel management field and other subjects. Results, convergence rate and reliability of the method are quite promising and show the HS algorithm performs very well and is comparable to other competitive algorithms such as Genetic Algorithm and Particle Swarm Intelligence. Furthermore, implementation of nodal expansion technique along HS causes considerable reduction of computational time to process and analysis optimization in the core fuel management problems. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Harmony Search algorithm Nodal expansion method Fitness function loading pattern optimization

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A novel multi-objective optimization method, imperialist competitive heck for algorithm, for fuel loading pattern of nuclear reactors

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PROGRESS IN NUCLEAR ENERGY 2018年 108卷 391-397页

作者： Akbari, R. Abbasi, M. Faghihi, F. Mirvakili, S. M. Mokhtari, J. Islamic Azad Univ Isfahan Khorasgan Branch Dept Math Esfahan Iran Shiraz Univ Sch Mech Engn Dept Nucl Engn Shiraz *** Iran Shiraz Univ Radiat Res Ctr Shiraz *** Iran NSTRI Reactor Res Sch Tehran *** Iran

Imperialist Competitive Algorithm (ICA) has been successfully applied to the various optimization problems and has demonstrated great results in both the global optimal achievement and the convergence rate. In this work, the ICA has been applied to achieve the best fuel arrangement of the VVER-1000 reactor core during the cycle. Bushehr Nuclear Power Plant (BNPP) core optimal arrangement has been searched by considering the minimization of the power peaking factor, flattening of the radial neutron flux distribution and maximizing the effective multiplication factor (K-eff) of the core. Cross section and power distribution calculations have been performed by DRAGON-4 and CITATION codes, respectively. The algorithm implementation has been carried out in MATLAB framework for optimization of one-sixth (1/6) and one-twelfth (1/12) symmetry of the core. The results show that this method can be used as an efficient computational method for finding an optimized multi objective loading pattern in a reactor core.

关键词： Imperialist competitive algorithm (ICA) Fuel management VVER-1000 loading pattern optimization

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