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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2020

OPTIMAL CONTROL AND ENERGY-SAVING ANALYSIS OF COMMON PRESSURE RAIL ARCHITECTURES: HHEA & STEAM

In recent years several novel hydraulic architectures have been proposed with the intention of significantly increasing system efficiency. Two of these architectures, Steigerung der Energieeffizienz in der Arbeitshydraulik mobiler Arbeitsmaschinen (STEAM), and the Hybrid Hydraulic-Electric Architecture (HHEA), use a system of multiple common pressure rails (CPRs) to serve the multiple degrees-of-freedom of the machine. The key difference is that STEAM throttles hydraulic power from these rails while HHEA combines electric and hydraulic power to meet actuator demands. As a throttle-less architecture, HHEA is expected to save more energy than STEAM at the expense of added complexity. Therefore, it is useful to quantify this additional energy saving. Both systems have discrete operational choices corresponding to how the CPRs are utilized for each actuator. It is necessary to determine optimal operation for each of these architectures for analysis and fair comparison. Techniques for optimal operation of the HHEA have been developed previously from the Langrange multiplier method. Applying the same optimal control method to STEAM encountered some technical challenge leading to the optimal control algorithm not being able to satisfy certain constraints. The issue is analyzed and solved by adding noise to the optimization. Using this proposed algorithm, case studies are performed to compare the energy-saving potentials of STEAM and HHEA for two sizes of excavators and a wheel-loader performing representative duty cycles. The baseline is a standard load-sensing architecture. Results show that STEAM and HHEA can reduce energy consumption between 35-65% and 50-80% respectively

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Optimal investment strategies for distributed generation in distribution networks with real option analysis

Efficient and well‐timed investment in distributed generation (DG) in distribution networks in the electricity market environment presents a big challenge for distribution companies. In this study, a real option valuation framework is proposed to determine the optimal investment strategies for DG including the investment location, size, and timing. Within the proposed framework, the profit from investing in DG is modelled, where the benefits include the operation cost savings and capacity update deferral benefit compared with a no‐DG‐investment scenario over the study period. Future power demands and electricity prices are modelled as stochastic variables. The candidate DG investment plans are considered as multiple mutually exclusive options, and the corresponding managerial flexibility for seizing opportunities and mitigating risk of loss upon an unfavourable unfolding of future uncertainties is assessed with real option analysis using the extended least square Monte Carlo method. The distribution of future investment strategies and optimal initial investment threshold levels under various scenarios are analysed in a case study to demonstrate the characteristics of the proposed framework and methodology.

Zou, Bo↗
DOE OSTI2021

Optimization models for integrated biorefinery operations

Variations of physical and chemical characteristics of biomass lead to an uneven flow of biomass in a biorefinery, which reduces equipment utilization and increases operational costs. Uncertainty of biomass supply and high processing costs increase the risk of investing in the US’s cellulosic biofuel industry. We propose a stochastic programming model to streamline processes within a biorefinery. A chance constraint models system’s reliability requirement that the reactor is operating at a high utilization rate given uncertain biomass moisture content, particle size distribution, and equipment failure. The model identifies operating conditions of equipment and inventory level to maintain a continuous flow of biomass to the reactor. Furthermore, the sample average approximation method approximates the chance constraint and a bisection search-based heuristic solves this approximation. A case study is developed using real-life data collected at Idaho National Laboratory’s biomass processing facility. An extensive computational analysis indicates that sequencing of biomass bales based on moisture level, increasing storage capacity, and managing particle size distribution, increases utilization of the reactor and reduces operational costs.

09 BIOMASS FUELS↗
DOE OSTI2026

Data Summarization and Inference at Scale

This is the final report for the DOE ASCR grant SC-0022260, Data Summarization and Inference at Scale, PI: Alex Pothen, Purdue University. The goal of the project was to solve data-intensive and compute-intensive problems in the physical sciences, engineering, information science, data science, etc. by designing and implementing new algorithms that could work with a subset of the data. The four subgoals were: (a) The solution of problems where the data is too large to be stored in the memory of a computer. In this streaming model of computation, the data arrives as a stream of elements to the computer, each element is processed as it arrives, and a decision is made to discard the data or to store it; only a small subset of the data proportional to the size of the output solution is stored, and when all the data has been streamed, a solution to the problem is computed from the stored subset. (b) The use of machine learning methods to compute solutions to data-intensive problems. The use of GPUs is critical to obtain high performance on machine learning tasks, but their memory sizes are smaller relative to that of CPUs. For large-scale problems, the data is sampled many times, and small samples are used with repetition, for robustness, to compute solutions to inference tasks. This sampling reduces the memory required to solve the problem, but attention is needed to avoid slow convergence to the solutions, and reduced accuracy of inference. We propose submodular optimization, Large Language Models, and physics-informed neural networks to enable GPU computations here. (c) Modeling and visualization of high-dimensional data using interpretable features. Clinical proteomic data sets from immunology for the detection of cancer and other diseases are temporal and high-dimensional, and algorithms for visualizing these data sets using clinically interpretable features are lacking. We propose methods that compute distances based on the optimal transportation problem and graph edit distances to address this problem. We also propose the use of optimal transport-based distances, spatial statistics, and network structure to classify image data sets, We apply these algorithms to electron micrographs of the peripheral nervous system in the digestive tract. (d) The design of data-intensive algorithms on emerging architectures, specifically, noisy, intermediate-scale quantum (NISQ) devices. Quantum computers offer the possibility of exploring large solution spaces due to the principle of superposition, but current quantum computers are limited by few qubits, short coherence times due to noise, poor interconections among the qubits, etc. We propose the use of the divide and conquer paradigm to solve large-scale problems, wherein collections of small subproblems are solved on the quantum devices, and the solutions to the subproblems are integrated into a solution for the original problem on a classical computer.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

An in-depth field validation of “DUSST”: A novel low-maintenance soiling measurement device

This study presents indoor and field validation results for two versions of the “DUSST” optical soiling sensor, intended to be a low-cost and low-maintenance device for measuring photovoltaic soiling losses. Indoor testing covers irradiance calibration and temperature dependencies, which are necessary to achieve high accuracy, low uncertainty field measurements. Field testing includes an array of different environments including Saudi Arabia, California, Utah, and Colorado. DUSST versions include a configuration with a 530-nm light emitting diode (LED) (discussed in previous work) and a unit with seven white LEDs and a polycarbonate collimating optic. The new design increases light intensity fivefold and demonstrates a single linear calibration coefficient is effective to measure soiling losses as high as 75%. Field data from Utah and California demonstrate that daily soiling loss measurements and soiling rate calculations closely match both reference cell and full-size module measurements of soiling losses and soiling rates. Corrective methods employed on the Utah DUSST sensor suggest that it is possible to achieve measurement errors as low as ±0.1% at two standard deviations. Field data from both Colorado and Saudi Arabia demonstrate that LED lens soiling can occur and that further design optimizations are needed. The lesson learned from all the field deployment locations suggests directions for future design improvements.

14 SOLAR ENERGY↗
DOE OSTI2020

Achieving high volumetric EDLC carbons via hydrothermal carbonization and cyclic activation

A novel activation method involving hydrothermal carbonization (HTC) and a pressure-induced low temperature oxidation has been demonstrated for cellulose derived HTC char by using hydrogen peroxide as an active di-oxygen source. The optimized porosity versus gravimetric capacitance results from cellulose derived HTC char synthesized at 220 °C. Almost homogeneous and small particle size micro-ellipse/sphere, relatively high surface area and narrow pore size distributions lead to a high bulk density, i.e. 0.73 g cm -3 , of coating type electrodes, which is much denser than those manufactured from steam activated carbons for supercapacitor industry, i.e., 0.52 g cm -3 . The resulting carbon prepared herein achieves a relatively high volumetric capacitance in an organic electrolyte-based supercapacitor reaching a competitive value of industrial system with the features of environment friendly, cost-effective as well as high yield, and less energy consumption.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2017

Mouthpart conduit sizes of fluid-feeding insects determine the ability to feed from pores

Fluid-feeding insects, such as butterflies, moths, and flies (20% of all animal species), are faced with the common selection pressure of having to remove and feed on trace amounts of fluids from porous surfaces. Insects able to acquire fluids that are confined to pores during drought conditions would have an adaptive advantage and increased fitness over other individuals. Here we performed feeding trials using solutions with magnetic nanoparticles to show that butterflies and flies have mouthparts adapted to pull liquids from porous surfaces using capillary action as the governing principle. In addition, the ability to feed on the liquids collected from pores depends on a relationship between the diameter of the mouthpart conduits and substrate pore size diameter; insects with mouthpart conduit diameters larger than the pores cannot successfully feed, thus there is a limiting substrate pore size from which each species can acquire liquids for fluid uptake. In conclusion, given that natural selection independently favored mouthpart architectures that support these methods of fluid uptake (Diptera and Lepidoptera share a common ancestor 280 mya that had chewing mouthparts), we suggest that the convergence of this mechanism advocates this as an optimal strategy for pulling trace amounts of fluids from porous surfaces.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

On the Calculation of the Debye Temperature and Crystal–Liquid Phase Transition Temperature of a Binary Substitution Alloy

A method of estimating the interatomic pair interaction potential parameters for a binary substitution alloy with consideration for the deviation of its lattice parameter from the Vegard law is proposed. This method is used as a basis to calculate the Debye temperature and Grüneisen parameters of a SiGe alloy. It is shown that all these function nonlinearly variate with a change in the germanium concentration. Based on this technique and Lindemann's melting criterion, a method for calculating the liquidus and solidus temperatures of a disordered substitution alloy is proposed. The method is tested on the SiGe alloy and demonstrates good agreement with experimental data. It is shown that when the size of a nanocrystal of a solid substitution solution decreases, the difference between the liquidus and solidus temperatures decreases the more, the more noticeably the nanocrystal shape is deflected from the most energetically optimal shape.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Optimal dimensionality selection for independent component analysis of transcriptomic data

Independent component analysis is an unsupervised machine learning algorithm that separates a set of mixed signals into a set of statistically independent source signals. Applied to high-quality gene expression datasets, independent component analysis effectively reveals both the source signals of the transcriptome as co-regulated gene sets, and the activity levels of the underlying regulators across diverse experimental conditions. Two major variables that affect the final gene sets are the diversity of the expression profiles contained in the underlying data, and the user-defined number of independent components, or dimensionality, to compute. Availability of high-quality transcriptomic datasets has grown exponentially as high-throughput technologies have advanced; however, optimal dimensionality selection remains an open question. We computed independent components across a range of dimensionalities for four gene expression datasets with varying dimensions (both in terms of number of genes and number of samples). We computed the correlation between independent components across different dimensionalities to understand how the overall structure evolves as the number of user-defined components increases. We then measured how well the resulting gene clusters reflected known regulatory mechanisms, and developed a set of metrics to assess the accuracy of the decomposition at a given dimension. We found that over-decomposition results in many independent components dominated by a single gene, whereas under-decomposition results in independent components that poorly capture the known regulatory structure. From these results, we developed a new method, called OptICA, for finding the optimal dimensionality that controls for both over- and under-decomposition. Specifically, OptICA selects the highest dimension that produces a low number of components that are dominated by a single gene. We show that OptICA outperforms two previously proposed methods for selecting the number of independent components across four transcriptomic databases of varying sizes. OptICA avoids both over-decomposition and under-decomposition of transcriptomic datasets resulting in the best representation of the organism’s underlying transcriptional regulatory network.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Autonomous organic synthesis for redox flow batteries via flexible batch Bayesian optimization

Traditional trial-and-error methods for materials discovery are inefficient to meet the urgent demands posed by the rapid progression of climate change. This urgency has driven the increasing interest in integrating robotics and machine learning into materials research to accelerate experimental learning. However, idealized decision-making frameworks to achieve maximum sampling efficiency are not always compatible with high-throughput experimental workflows inside a laboratory. For multi-step chemical processes, differences in hardware capacities can complicate the digital framework by introducing constraints on the maximum number of samples in each step of the experiment, hence causing varying batch sizes in variable selection within the same batch. Therefore, designing flexible sampling algorithms is necessary to accommodate the multi-step synthesis with practical constraints unique to each high-throughput workflow. In this work, we designed and employed three strategies on a high-throughput robotic platform to optimize the sulfonation reaction of redox-active molecules used in flow batteries. Our strategies adapt to the multi-step experimental workflow, where their formulation and heating steps are separate, causing varying batch size requirements. By strategically sampling using clustering and mixed-variable batch Bayesian optimization, we were able to iteratively identify optimal conditions that maximize the yields. Our work presents a flexible approach that allows tailoring the machine learning decision-making to suit the practical constraints in individual high-throughput experimental platforms, followed by performing resource-efficient yield optimization using available open-source Python libraries.

Tamura, Clara [Univ. of Washington, Seattle, WA (U↗
DOE OSTI2022

Optimal operation and sizing of pumped thermal energy storage for net benefits maximization

Abstract Current trends in the modern grid are leading to the development and deployment of energy storage to help integrate increasing variable renewable energy sources into the grid. This paper studies a pumped thermal energy storage (PTES) system for multiple grid services including energy arbitrage, frequency regulation, spinning and non‐spinning reserve, and resource adequacy. Optimal dispatch methods are proposed for individual services as well as value stacking from multiple services to maximize the economic benefits. Assessment results demonstrate the superiority of value stacking. Specifically, the study shows the maximum revenue from an individual grid service with a 30‐MWh PTES system was $522,520, while the value stacking could increase the benefits to $678,477. In addition, sensitivity analyses were conducted to explore the cost‐effectiveness of a PTES system with different combinations of power transfer limits and energy capacity. It was found that the power transfer limit had a greater impact than the energy capacity on the benefits. The proposed method could help determine the optimal duration of a future PTES system.

25 ENERGY STORAGE↗
DOE OSTI2019

Digital memcomputing: From logic to dynamics to topology

Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear, point-dissipative dynamical systems engineered so that periodic orbits and chaos can be avoided. A given logic problem is first mapped into this type of dynamical system whose point attractors represent the solutions of the original problem. A DMM then finds the solution via a succession of elementary instantons whose role is to eliminate solitonic configurations of logical inconsistency (“logical defects”) from the circuit. By employing a supersymmetric theory of dynamics, a DMM can be described by a cohomological field theory that allows for computation of certain topological matrix elements on instantons that have the mathematical meaning of intersection numbers on instantons. We discuss the “dynamical” meaning of these matrix elements, and argue that the number of elementary instantons needed to reach the solution cannot exceed the number of state variables of DMMs, which in turn can only grow at most polynomially with the size of the problem. These results shed further light on the relation between logic, dynamics and topology in digital memcomputing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Optimized attenuated interaction: Enabling stochastic Bethe–Salpeter spectra for large systems

We develop an improved stochastic formalism for the Bethe–Salpeter equation (BSE), based on an exact separation of the effective-interaction W into two parts, W = (W – vW) + vW, where the latter is formally any translationally invariant interaction, vW(r – r'). When optimizing the fit of the exchange kernel vW to W, using a stochastic sampling W, the difference W – vW becomes quite small. Then, in the main BSE routine, this small difference is stochastically sampled. Furthermore, the number of stochastic samples needed for an accurate spectrum is then largely independent of system size. While the method is formally cubic in scaling, the scaling prefactor is small due to the constant number of stochastic orbitals needed for sampling W.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Variations of the physical parameters of the blazar Mrk 421 based on analysis of the spectral energy distributions

Abstract We report on the variations of the physical parameters of the jet observed in the blazar Mrk 421, and discuss the origin of X-ray flares in the jet, based on analysis of several spectral energy distributions (SEDs). The SEDs are modeled using the one-zone synchrotron self-Compton model, its parameters determined using a Markov chain Monte Carlo method. The lack of data at TeV energies means many of the parameters cannot be uniquely determined and are correlated. These are studied in detail. We find that the optimal solution can be uniquely determined only when we apply a constraint to one of four parameters: the magnetic field (B), the Doppler factor, the size of the emitting region, and the normalization factor of the electron energy distribution. We used 31 sets of SEDs from 2009 to 2014 with optical–UV data observed with UVOT/Swift and the Kanata telescope, X-ray data with XRT/Swift, and γ-ray data with the Fermi Large Area Telescope. The result of our SED analysis suggests that, in the X-ray faint state, the emission occurs in a relatively small area (∼1016 cm) with a relatively strong magnetic field (B ∼ 10−1 G). The X-ray bright state shows a tendency opposite to that of the faint state, that is, a large emitting area (∼1018 cm), probably downstream of the jet, and a weak magnetic field (B ∼ 10−3 G). The high X-ray flux was due to an increase in the maximum energy of electrons. On the other hand, the presence of two kinds of emitting areas implies that the one-zone model is unsuitable for reproducing at least part of the observed SEDs.

Yamada, Yurika↗
DOE OSTI2020

Learning to Solve Large-Scale Security-Constrained Unit Commitment Problems

Security-constrained unit commitment (SCUC) is a fundamental problem in power systems and electricity markets. In practical settings, SCUC is repeatedly solved via mixed-integer linear programming (MIP), sometimes multiple times per day, with only minor changes in input data. In this work, we propose a number of machine learning techniques to effectively extract information from previously solved instances in order to significantly improve the computational performance of MIP solvers when solving similar instances in the future. Based on statistical data, we predict redundant constraints in the formulation, good initial feasible solutions, and affine subspaces where the optimal solution is likely to lie, leading to a significant reduction in problem size. Computational results on a diverse set of realistic and large-scale instances show that using the proposed techniques, SCUC can be solved on average 4.3 times faster with optimality guarantees and 10.2 times faster without optimality guarantees, with no observed reduction in solution quality. Out-of-distribution experiments provide evidence that the method is somewhat robust against data-set shift. Summary of Contribution. The paper describes a novel computational method, based on a combination of mixed-integer linear programming (MILP) and machine learning (ML), to solve a challenging and fundamental optimization problem in the energy sector. The method advances the state-of-the-art, not only for this particular problem, but also, more generally, in solving discrete optimization problems via ML. We expect that the techniques presented can be readily used by practitioners in the energy sector and adapted, by researchers in other fields, to other challenging operations research problems that are solved routinely.

Machine Learning↗
DOE OSTI2022

Predicting Switchgrass Biomass Yields Using a Spectral Vegetation Index Derived from Multispectral Satellite Imagery

Successful scaling of perennial bioenergy crop production requires a landscape design that optimizes the benefits of finite lands for people, communities, and environments. Utilizing marginal areas is the key to sustainable bioenergy crop production (Ssegane et al., 2015, 2016). Marginal areas are often small-sized lands and unevenly distributed across the agricultural landscape (Ssegane et al., 2016); thus, a systematic, semi-automated remote sensing method is needed as an effective means of estimating bioenergy crop yields across landscapes. Argonne National Laboratory (Argonne) is currently developing a tool, Scaling Up Perennial Bioenergy Economics and Ecosystem Services Tool (SUPERBEEST), to identify marginal agricultural lands and quantify environmental and economic effects of perennial bioenergy crop production systems. The tool aims to provide users a path to foster the sustainable and productive integration of bioenergy crops in the Midwestern agricultural landscape. Reliable, cost-effective, and timely estimation of bioenergy crop yields using remote sensing would help calculate and track the success of integrated bioenergy crops in the landscape for those communities. Argonne previously conducted feasibility studies for estimating biomass yields for bioenergy feedstock, corn and perennial grass using spectral vegetation indices (SVIs)1 derived from optical imagery (Hamada et al., 2015, 2021). In both studies, SVIs, more specifically those sensitive to plant chlorophyll or nitrogen contents, showed potential for estimating or predicting biomass yields with a correlation of determination (R2) ranging from 0.54 to 0.96, indicating a value for further investigation as a viable means of quantifying bioenergy feedstock production across large landscapes. Thus, the goal of this study is to evaluate the feasibility of use of SVIs as a means of estimating or predicting switchgrass biomass yields at harvest using publicly available multispectral satellite imagery. The feasibility analysis was performed using four study areas of mature switchgrass located in Virginia. Objectives are to (1) examine the SVIs and establish their relationships with switchgrass biomass yields at harvest, (2) develop a parsimonious image processing model for predicting at-harvest yields by applying the relationships with the most promising spectral index and (3) map switchgrass yields predicted by the image processing model across the study sites. The calibration to field data will rely on switchgrass biomass yields determined by the baling method, representing a potential challenge to the analysis but an important practical aspect for future applications. With this research design, the study aimed to gain insights into enabling remote sensing-based estimation of bioenergy crop yields in a reliable, cost- effective, and timely manner across large, heterogeneous landscapes.

09 BIOMASS FUELS↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗