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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

PWR loading pattern optimization with reinforcement learning

The core loading pattern optimization problem belongs to the class of combinatorial optimization problem and has been studied since the dawn of commercial nuclear energy industry. It is characterized by multiple objectives and constraints, with a very high number of candidate patterns, which makes it impossible to solve explicitly. Stochastic optimization methodologies including Genetic Algorithms and Simulated Annealing are used by different nuclear utilities and vendors to perform fuel cycle reload design. Nevertheless, hand-designed solutions continue to be the prevalent method in the industry. To improve the state-of-the-art core reload patterns, we aim to create a method as scalable as possible, that agrees with the designer's goal of performance and safety. To help in this task Deep Reinforcement Learning (DRL), in particular Proximal Policy Optimization is leveraged. DRL has recently experienced a strong impetus from its successes applied to games, sometimes even reaching 'super-human' performances. This paper lays out the foundation of this method and proposes to study the behavior of several hyper-parameters that influence the DRL algorithm. The algorithm is highly dependent on multiple factors such as an exploration/exploitation trade-off that manifests through different parameters such as the number of loading patterns seen and the number of samples collected before a policy update, but also the shape of the objective function derived for the core design. Experimental results also demonstrate the effectiveness of the method in finding high-quality solutions from scratch within a reasonable amount of time. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

A deterministic method for PWR loading pattern optimization

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. Here 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.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2022

A Novel Method for Controlling Crud Deposition in Nuclear Reactors Using Optimization Algorithms and Deep Neural Network Based Surrogate Models

This work presents the use of a high-fidelity neural network surrogate model within a Modular Optimization Framework for treatment of crud deposition as a constraint within light-water reactor core loading pattern optimization. The neural network was utilized for the treatment of crud constraints within the context of an advanced genetic algorithm applied to the core design problem. This proof-of-concept study shows that loading pattern optimization aided by a neural network surrogate model can optimize the manner in which crud distributes within a nuclear reactor without impacting operational parameters such as enrichment or cycle length. Several analysis methods were investigated. Analysis found that the surrogate model and genetic algorithm successfully minimized the deviation from a uniform crud distribution against a population of solutions from a reference optimization in which the crud distribution was not optimized. Strong evidence is presented that shows boron deposition in crud can be optimized through the loading pattern. This proof-of-concept study shows that the methods employed provide a powerful tool for mitigating the effects of crud deposition in nuclear reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2019

Full-core analysis for FeCrAl enhanced accident tolerant fuel in boiling water reactors

The impact of replacing Zircaloy with FeCrAl, a candidate enhanced accident-tolerant fuel cladding material, was evaluated for 10 × 10 boiling water reactor fuel bundles. Results from a series of full-core parametric studies estimated that replacing UO 2 /Zircaloy with UO 2 /FeCrAl would require an average enrichment increase of 0.6% 235 U throughout the fuel lattice with the cladding and channel box thicknesses halved and fuel pellet diameter increased. Full-core results indicated that UO 2 /FeCrAl models with these geometric/enrichment specifications matched the base UO 2 /Zircaloy cycle length of 527 effective full power days. Optimization studies of the full-core design established loading and control blade patterns for both Zircaloy and FeCrAl models. A side study was conducted modeling a hybrid fuel bundle consisting of FeCrAl cladding and a SiC/Ni/Cr channel box. By halving the cladding thickness, the enrichment level required was less than that of the Zircaloy base case design after performing loading pattern optimization of the hybrid bundle core. Lastly, the thermomechanical performance of a Zircaloy-cladded fuel rod was compared to that of a FeCrAl system. Results from this analysis show that, if starting from the same fuel-cladding gap thickness, a FeCrAl-clad fuel rod operates with a greater average fuel centerline temperature, comparable axial elongation and radial displacement, and longer time to gap closure compared to a Zircaloy-clad fuel rod. Furthermore, this fuel performance analysis was primarily based on the commercial Kanthal APMT FeCrAl alloy but also used available data for the C35M FeCrAl alloy developed at Oak Ridge National Laboratory.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Optimization of Canister Loading Patterns in Dual Purpose Canisters for Criticality Suppression

This report documents work performed in support of the US Department of Energy Office of Nuclear Energy (NE) Spent Fuel and Waste Disposition, Spent Fuel and Waste Science and Technology, under work breakdown structure element 1.08.01.03.05, “Direct Disposal of Dual Purpose Canisters.” In particular, this report fulfills milestone M3SF-22PN010305094, “Application of AI/ML techniques to optimize DPC loading,” within work package SF-22PN01030509, “Direct Disposal of Dual Purpose Canisters - PNNL.” This report continues the process of examining the potential for using loading optimization as a disposal criticality suppression technique. This latest update to the report added: 1. A validation of the artificial neural network (ANN) reactivity prediction tool against as-loaded dual-purpose canisters from the UNF-ST&DARDS database 2. Refinement of the algorithm to incorporate an additional DPC design to improve the predictions 3. Investigation of a storage and transportation focused loading optimization algorithm. A key result from this year’s work is that the ANN performance was significantly improved by including the additional model for the NUHOMS canisters and it is apparent that fuel type specific modeling considerations should be incorporated into the ANN in future work. The GRASP-enabled adaptive multi-objective memetic algorithm with partial clustering (GAMMA-PC) algorithm was evaluated as a tool for storage and transportation oriented optimization. The GAMMA-PC optimization routine considers decay heat at loading, the time between loading and when the canister is eligible for transportation and minimizes the number of casks loaded. Future work will develop a dose minimization optimization routine.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

White Paper: Research & Development for the Time at Temperature Approach

Recent advancements in nuclear power research are greatly improving reactor safety and performance through the development of Accident Tolerant Fuel (ATF) and Low-Enriched Uranium Plus (LEU+). These innovations can address Departure from Nucleate Boiling (DNB) margins, which are vital for reactor safety. DNB happens when the coolant switches to film boiling, significantly decreasing heat transfer and posing a risk of fuel cladding failure. The U.S. Nuclear Regulatory Commission (NRC) employs conservative DNB criteria, which can potentially restrict the operational flexibility and efficiency of reactors. The Time at Temperature (TaT) approach could provide a more detailed and adaptable operational guideline by establishing acceptable time-temperature limits, accounting for the duration a material can withstand elevated temperatures without losing its integrity. This method allows reactors to operate more efficiently and safely, offering additional operational margins, faster power adjustments, and improved fuel cycle economics. TaT criteria allow for higher power levels and more flexible responses to operational transients, particularly applicable for anticipated operational occurrences (AOOs) that result in short durations of post-DNB conditions. It enhances plant operational flexibility, allows faster startup times, and enables quicker power level adjustments, optimizing fuel loading patterns and improving fuel cycle economics. Implementing TaT limits reduces core design constraints, lowers fuel usage, and reduces costs, essential for the long-term sustainability of Light Water Reactors (LWRs). TaT maximizes the use of advanced fuel technologies like ATF and LEU+, further enhancing their economic and environmental benefits. To apply the TaT approach in existing LWRs, collaborative research activities among various DOE-sponsored programs are essential. These efforts should incorporate fuel experiments, physics-based high-fidelity modeling, ML-based surrogate modeling, and optimization techniques. This whitepaper proposes four research and development areas: 1) Investigation of the feasibility of new operations of LWR with updated safety limits; 2) Assessment of reactor operation limits through uncertainty reduction; 3) Evaluation of power uprate in virtual environment; and 4) Lattice and reactor core design for power uprate. Each area includes why this research is in need and a suggested scope of work. These comprehensive research areas ensure practical and beneficial advancements for existing reactors, translating innovations in nuclear fuel and cladding technology into improved reactor performance and safety.

42 - ENGINEERING↗
DOE OSTI2025

Plant Reload Optimization (prlo)

The PRLO framework is built on a modular and extensible architecture that tightly couples advanced evolutionary optimization algorithms with nuclear fuel depletion solvers (i.e., nuclear physics neutronics code). It supports exploring complex, high-dimensional design spaces constrained by user-specified operational, safety, and economic constraints. Objectives such as minimizing fresh fuel enrichment, flattening radial and axial power distributions, and maximizing discharge burnup are evaluated. PRLO’s equilibrium cycle optimization capability enables the identification of core configurations that maintain fuel cycle sustainability over extended planning horizons. Its integration with the RAVEN platform facilitates optimization of loading patterns or fuel shuffling schemes across multiple cycles. The interface with SIMULATE, a licensed industry-standard nodal code developed by Studsvik, ensures accurate neutronic and thermal-hydraulic feedback for reactor core design. PRLO’s automated workflow engine supports iterative design refinement, enabling utilities to streamline core design processes and meet evolving performance and regulatory targets.

Kim, Junyung [Idaho National Laboratory] (00090005↗
DOE OSTI2026

Optimizing pressurized-water reactor equilibrium cycle using a novel loading pattern encoding and rule-based genetic crossover operators

This work presents an extended multi-batch approach applied in shuffling scheme optimization for equilibrium cycle for pressurized water reactors using Genetic Algorithms (GAs). A new ruled based GA crossover operator called Inherited Location and Batch (ILB) was introduced to enhance offsprings reproduction efficiency specialized for equilibrium cycle optimization problem. This approach was implemented within the Plant ReLoad Optimization (PRLO) framework and validated using a generic reactor model based on the AP1000 design, with core parameters calculated via the CASMO/SIMULATE software package. The ILB approach is then applied for both single and multi-objective problems in maximizing cycle length and core average exposure while minimizing the average enrichment of the 57 fresh fuel assemblies (FAs) per cycle. The optimal solutions are selected based on their dominance to the objectives from all feasible solutions. This research identified three optimal solutions satisfied safety constraints: The first solution minimizes feed enrichment costs with a cycle length of 338.8 days and core exposure of 25.39 MWd/MT; the second solution extends cycle length to 361.2 days, with the highest core exposure of 26.84 MWd/MT, using 3.75 wt% average fuel enrichment; the third solution balances both objectives with a cycle length of 349.6 days, core exposure of 25.82 MWd/MT with a slight enrichment increase compared to the first solution. Collectively, these findings underscore the efficiency and effectiveness of the proposed approach in achieving practical multi-objective optimal equilibrium cycle designs using GAs optimizer.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Gains in operational flexibility, safety margins, and cost efficiencies via integrated Plant Reload Optimization platform

The U.S. Department of Energy Light Water Reactor Sustainability Program Risk-Informed Systems Analysis Pathway Plant Reload Optimization Project aims to develop an integrated, comprehensive framework offering an all-in-one solution for reload evaluations with a special focus on optimizing core design. Optimizing the fuel loading pattern is one of the most important considerations in reducing the amount of new fuel used in the core. Due to thousands of possible core configuration options, finding optimal solutions is an unachievable task for a human. The Plant ReLoad Optimization platform, which supports artificial-intelligence-based reactor core designing, is now fully capable of handling realistic problems. The Plant ReLoad Optimization platform development project aims to build a reactor core design tool that includes reactor safety and fuel performance analyses and uses artificial intelligence to support the optimization of core design solutions. The NSGA-II (Non-dominated Sorting Genetic Algorithm II) optimizer was developed and tested within RAVEN (Risk Analysis and Virtual ENvironment) to handle many constraints by using an augmented objectives methodology. The demonstration was performed with constrained multiobjective optimization of a 17 × 17 pressurized-water reactor core loading patterns to minimize fuel cost and maximize fuel cycle length.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Multi-objective optimization of PWR core design using NSGA-II in RAVEN’s optimization framework

Designing an PWR loading pattern is a combinatorial problem challenging to solve by brute force or traditional methods due to the sheer amount of possible combination, and constraints. Nature-inspired algorithms, such as the genetic algorithm, have demonstrated the potential to tackle this problem. The goal of this work was to improve and demonstrate the capabilities for constrained, multi-objective optimization (MOO) of loading patterns using NSGA-II in RAVEN’s optimization framework.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Pressurized-Water Reactor Core Design using Multi-Objective Plant Fuel Reload Optimization Platform

The United States (U.S.) Department of Energy (DOE) Light Water Reactor Sustainability (LWRS) Program Risk-Informed Systems Analysis (RISA) Pathway Plant Reload Optimization Project aims to develop an integrated, comprehensive framework offering an all-in-one solution for reload evaluations with a special focus on optimization of core design. The optimization of the fuel loading pattern is one of the most important considerations in reducing the amount of new fuel used in the core. Due to thousands of possible options of core configuration, finding optimal solutions is an unachievable task for a human. The Plant ReLoad Optimization (PRLO) platform which supports artificial-intelligence-based reactor core designing is now fully capable of handling realistic problems. The PRLO Platform development project aims to build a reactor core design tool that includes reactor safety and fuel performance analyses and uses artificial intelligence to support the optimization of core design solutions. The NSGA-II (Non-dominated Sorting Genetic Algorithm-II) optimizer was developed and tested within RAVEN (Risk Analysis and Virtual Environment) to handle many constraints by using an augmented objectives methodology. The demonstration was performed with constrained multi-objective optimization of a 17 × 17 pressurized-water reactor core loading patterns to minimize fuel cost and maximize fuel cycle length.

42 ENGINEERING↗
DOE OSTI2019

Fuel Loading Optimization and Planning for the Versatile Test Reactor

The Versatile Test Reactor (VTR) mission is to enable accelerated testing of advanced reactor fuels and materials required for advanced reactor technologies. In service of this duty, the goal of the design is to maximize the peak fast flux and the experimental volume exposed to a fast flux above 4.0 × 1015n/cms s. Delivering the desired neutron fluence for each experiment requires the capability to optimize the fuel loading to achieve a specified cycle length and flux, while also satisfying other criteria such as thermal hydraulic design constraints. To achieve the desired conditions and cycle length, several measures may be taken, including optimization of the fuel loading pattern, moving partially-burned assemblies back and forth between the core and the in-vessel storage, and potentially shuffling fuel within the core. Optimizing in a "brute-force" manner by solving a wholecore transport equation for hundreds of configurations would be inefficient. A sufficiently refined DIF3D-VARIANT solution for the whole core requires on the order of 1 hour. Instead, we seek an approximate evaluation of the parameters for many variations on a base core configuration without directly solving a diffusion or transport equation for each.

fuel loading optimization↗
DOE OSTI2019

Intelligent load pattern modeling and denoising using improved variational mode decomposition for various calendar periods

This paper proposes a novel approach to identify the load patterns considering calendar impact and denoising process, which advances the state of art of load identification and load forecasting to a more flexible and adaptive extent by revealing the correlation between load profile and the substantial influence factors. With the rapid development and the promising application of energy intemet and grid modernization, the accurate load modeling and forecasting especially by load pattern modeling (LPM) have become more and more critical to observe and estimate load profile so as to optimize the operation efficiency of the power grid. Traditional methods mostly focus on the static LPM itself which are unable to account the non-linear and highly dynamic load fluctuations in order to balance the demand of the power grid during various calendar period (VCP) scheduling. In this paper, a load pattern modeling method for power grid considering the impact of typical calendar effects is proposed using a combination of improved variational mode decomposition (IVMD) and deep belief network (DBN) algorithm. Firstly, an index of load curve curvature (LCC) is proposed to improve the selection of value K in the conventional VMD algorithm. The value K of the intrinsic modality is determined by adopting LCC to better quantify the average instantaneous frequency of the modal decomposition of the VMD and to reduce the elevated stochasticity of k. Secondly, an optimization formulation is developed based on adaptive segmented loop decomposition of the typical correlation coefficient to suppress the edge effect in VMD decomposition, which would enable the reconstructed curve to incorporate the variabilities from the initial data. Finally, the IVMD and DBN algorithms are jointly implemented to optimize the accuracy of VCP load pattern modeling curve regression. Numerical examples have been performed with the results proving that the proposed method significantly outperforms the state-of-art in reducing the modeling error of VCP load curve, improving the overall forecasting accuracy, and reducing load dispatching cost.

deep belief network↗
DOE OSTI2023

Differences In High Burnup Fuel Management Strategies to Minimize FFRD and Increase Economic Viability

The nuclear industry is pursuing approval of an increase in the length of the pressurized water reactor (PWR) cycle from 18 months to 24 months to reduce reactor downtime and enhance the economic competitiveness of nuclear energy. Such an increase in reactor cycle length will require that the maximum rod average burnup exceeds the current regulatory limit of 62 GWd/MTU, and it could peak at approximately 75 GWd/MTU, posing potential reactor safety and performance concerns. One such concern is that fuel fragmentation, relocation, and dispersal (FFRD) could occur during a severe loss-of coolant accident (LOCA) in which a fuel rod balloons and bursts, and pulverized fuel fragments are dispersed throughout the reactor’s primary coolant system. Previous analyses have identified which reactor operating conditions leave the core more susceptible to FFRD and have shown that FFRD susceptibility is strongly linked to fuel rod burnup and linear heat rate (LHR) history. The work described in this report uses an optimization strategy known as parallel simulated annealing (PSA) and a coarse mesh Purdue Advanced Reactor Core Simulator (PARCS) reactor physics model to develop two core fuel loading patterns, each with a different optimization objective. One core optimization maximized the core’s cycle length while still respecting regulatory limits on the radial peaking factor and soluble boron concentration with a peak rod average burnup of 75 GWd/MTU. The second optimization was aimed at minimizing FFRD susceptibility while still targeting a 24-month cycle length and respecting regulatory limits. PARCS model predictions were verified using the high-fidelity Virtual Environment for Reactor Applications (VERA). The two core designs were compared to highlight core design strategies to minimize FFRD susceptibility and to maximize economic viability.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2019

Preliminary Evaluation of Fuel Management Strategies for the Versatile Test Reactor (VTR)

Different fuel management approaches have been investigated for the Versatile Test Reactor (VTR). The main design variables were the number of batches, the number of (orifice) zones, and the loading pattern within the core. The optimization criteria are maximizing the fast flux at the centermost position, minimizing the peak assembly power, and reducing fuel consumption. Design constraints were mainly driven by material limits such as peak clad temperature, and maximum fuel burnup. The exploratory study determined that active fuel shuffling only brought very limited benefits. A three-orifice region was found to provide enough flexibility to ensure thermal criteria were met. Lastly, a flexible batch loading termed ‘5-6-8’ was identified as a promising management strategy from a resource utilization standpoint.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation of fuel management multi-cycle optimization capabilities in RAVEN optimization framework

Optimization in nuclear fuel-management assists the core reload engineer with finding optimal out-of-core and in-core strategies. RAVEN is INL’s open source software that is equipped with fuel-management optimization capabilities including single-cycle, single- and multi-objective optimization of pressurized water reactors (PWRs) loading patterns (LP) of a fresh core using genetic algorithm (GA) and non-dominated sorting genetic algorithm (NSGA-II). In practice, however, medium and long term planning of fuel-management needs a multi-cycle approach, where the history and availability of fuel assemblies is considered in the optimization process. In this paper, we present a description of an initial expansion of RAVEN fuel-management optimization capabilities for a multi-cycle optimization framework. N-th cycle optimization capabilities that account for the unique history of recycled fuel assembly in the core were added. The multi-cycle optimization approach taken is formulated as a cycle-wise optimization problem where out-of-core decisions are used to onset each cycle optimization. Out-of-core decisions are managed externally to the in-core optimization by a fuel inventory management module. A proof-of-concept optimization problem is also presented.

42 - ENGINEERING↗