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DOE OSTI2015

Security-Constrained Unit Commitment with Linearized AC Optimal Power Flow.

We propose a mathematical programming-based approach to optimize the security-constrained unit commitment problem with a full AC transmission network representation. Our approach is based on our previously introduced successive linear programming (SLP) approach to solving the non-linear, nonconvex AC optimal power flow (ACOPF) problem. By linearizing the ACOPF, we are able to leverage powerful commercial mixed-integer solvers to iteratively optimize the combined unit commitment plus ACOPF model. We demonstrate our approach on six-bus, IEEE RTS-96, and IEEE 118-bus test systems. We perform a comparative analysis of the relative impacts of singlebus, DC, and AC transmission network models on the unit commitment and dispatch solutions and their associated costs.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2017

The Recommendations for Linear Measurement Techniques on the Measurements of Nonlinear System Parameters of a Joint.

In the study of the dynamics of nonlinear systems, experimental measurements often convolute the response of the nonlinearity of interest and the effects of the experimental setup. To reduce the influence of the experimental setup on the deduction of the parameters of the nonlinearity, the response of a mechanical joint is investigated under various experimental setups. These experiments first focus on quantifying how support structures and measurement techniques affect the natural frequency and damping of a linear system. The results indicate that support structures created from bungees have negligible influence on the system in terms of frequency and damping ratio variations. The study then focuses on the effects of the excitation technique on the response for a linear system. The findings suggest that thinner stingers should not be used, because under the high force requirements the stinger bending modes are excited adding unwanted torsional coupling. The optimal configuration for testing the linear system is then applied to a nonlinear system in order to assess the robustness of the test configuration. Finally, recommendations are made for conducting experiments on nonlinear systems using conventional/linear testing techniques.

36 MATERIALS SCIENCE↗

DOE OSTI2019

Performance Improvement of the Linear System Solver for CMFD Acceleration in PROTEUS-MOC

The PROTEUS code developed under the DOE NEAMS program is a high-fidelity capable whole core transports solver based on unstructured finite element meshes [1]. PROTEUS includes three distinct transport solvers: SN, MOC and NODAL. Among them, the PROTEUS-MOC is the 3D method of characteristics (MOC) solver for extruded geometries. In order to accelerate the convergence of 3D MOC calculation, the CMFD acceleration method was implemented in PROTEUS-MOC [2]. For solving the CMFD linear system, the unpreconditioned GMRES algorithm was used in the previous work [3, 4] for implementing the CMFD scheme because of low computation cost of coarse mesh calculations. In the performance tests, we found that the overhead of the CMFD acceleration became non-negligible as the condition number of the CMFD linear system and the size of problem increase. This indicated that the CMFD overhead should be reduced in the preconditioning technique in order to improve the computational performance. In this work, the performance of CMFD acceleration was notably improved by developing and implementing the new formulation of CMFD linear system and preconditioning technique.

Jung, Yeon Sang↗

DOE OSTI2019

GraphBLAST: A High-Performance Linear Algebra-based Graph Framework on the GPU

High-performance implementations of graph algorithms are challenging to implement on new parallel hardware such as GPUs, because of three challenges: (1) difficulty of coming up with graph building blocks, (2) load imbalance on parallel hardware, and (3) graph problems having low arithmetic intensity. To address these challenges, GraphBLAS is an innovative, on-going effort by the graph analytics community to propose building blocks based in sparse linear algebra, which will allow graph algorithms to be expressed in a performant, succinct, composable and portable manner. In this paper, we examine the performance challenges of a linear algebra-based approach to building graph frameworks and describe new design principles for overcoming these bottlenecks. Among the new design principles is exploiting input sparsity, which allows users to write graph algorithms without specifying push and pull direction. Exploiting output sparsity allows users to tell the backend which values of the output in a single vectorized computation they do not want computed. Load-balancing is an important feature for balancing work amongst parallel workers. We describe the important load-balancing features for handling graphs with different characteristics. The design principles described in this paper have been implemented in "GraphBLAST", the first open-source linear algebra-based graph framework on GPU targeting high-performance computing. The results show that on a single GPU, GraphBLAST has on average at least an order of magnitude speedup over previous GraphBLAS implementations SuiteSparse and GBTL, comparable performance to the fastest GPU hardwired primitives and shared-memory graph frameworks Ligra and Gunrock, and better performance than any other GPU graph framework, while offering a simpler and more concise programming model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

System and method for determining linear density of carbon fiber

A method for determining a linear density of a carbon fiber tow. The method includes providing a pulse of air directed toward the carbon fiber tow, determining, via a first sensor, an air pressure of the pulse of air, and measuring, via a second sensor, a displacement of the carbon fiber tow in response to the pulse of air directed toward the carbon fiber tow. The method further includes calculating, via a controller, a linear density of the carbon fiber tow based on the air pressure and the displacement, and outputting, via the controller, the linear density.

Koester, David Joseph↗

DOE OSTI2022

Catalytic synthesis of super linear alkenyl arenes using rhodium catalysts

Catalytic methods for synthesis of super linear alkenyl arenes and alkyl arenes are provided. The methods are capable of synthesizing super linear alkyl and alkenyl arenes from simple arene and olefin starting materials and with high selectivity for linear coupling. Methods are also provided for making a 2,6-dimethylnapthalene (DMN) or 2,6-methylethylnapthalene (MEN).

Schinski, William↗

DOE OSTI2015

Linear Vlasov Solver For Microbunching Gain Estimation With Inclusion of CSR, LSC And Geometric Impedances

As is known, microbunching instability (MBI) has been one of the most challenging issues in designs of magnetic chicanes for short-wavelength free-electron lasers or linear colliders, as well as those of transport lines for recirculating or energy recovery linac machines. To more accurately quantify MBI in a single-pass system and for more complete analyses, we further extend and continue to increase the capabilities of our previously developed linear Vlasov solver [1] to incorporate more relevant impedance models into the code, including transient and steady-state free-space and/or shielding coherent synchrotron radiation (CSR) impedances, the longitudinal space charge (LSC) impedances, and the linac geometric impedances with extension of the existing formulation to include beam acceleration [2]. Then, we directly solve the linearized Vlasov equation numerically for microbunching gain amplification factor. In this study we apply this code to a beamline lattice of transport arc [3] following an upstream linac section. The resultant gain functions and spectra are presented here, and some results are compared with particle tracking simulation by ELEGANT [4]. We also discuss some underlying physics with inclusion of these collective effects and the limitation of the existing formulation. It is anticipated that this more thorough analysis can further improve the understanding of MBI mechanisms and shed light on how to suppress or compensate MBI effects in lattice designs.

Tsai, C. -Y.↗

DOE OSTI2013

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear operator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approximation and the mean chord approximation are applied to estimate the leakage fraction of stochastic histories from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem to test the models for symmetric operators. In general, the derived approximations show good agreement with measured computational results. (authors)

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Pulsed source for driving non-linear current dependent loads

A pulsed current source comprises a power source, a discharge capacitor, and an inductive element. The discharge capacitor is selectively coupled to either of the power source or the inductive element. When coupled to the power source, the discharge capacitor is charged. The inductive element can be connected to a load. The load can have a current-dependent impedance. When the discharge capacitor is coupled to the inductive element, the discharge capacitor discharges through the inductive element and the load. The discharge capacitor and the inductive element are configured so that the current through the load exhibits a substantially linear rise in a linear operational region. The inductive element is configured to saturate during discharge of the capacitor through the load, so that the saturation of the inductive element causes the current through the load to continue to rise in a substantially linear fashion.

Curtis, III, William C.↗

DOE OSTI2022

Linear source method of characteristics in HELIOS2

The Studsvik Scandpower code HELIOS2 is a fast lattice transport code that has gained wide use for reactor fuel cycle analysis in commercial, regulatory, and research environments. It contains two transport solvers - Collision Probabilities (CP) and Method of Characteristics (MoC) - with a general geometry ability and generalized depletion for a variety of fuel types, experimental facilities, and isotope production applications. The HELIOS2 lattice code has been extended with the development of a linear source MoC option. The linear source equations are derived within the scope of the HELIOS2 general geometry and non-cyclic ray tracing. The implementation was tested for fine and coarse spatial mesh models of the 2D C5G7 MOX computational benchmark, which provides a pure and extreme test of a transport solver. The linear source yields at least comparable accuracy with reduced computational resource requirements relative to the flat-source approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

A Mixed Integer Linear Programming-basedDistributed Energy Management for Three-phaseUnbalanced Active Distribution Network

A mixed integer linear programming (MILP)–baseddistributed energy management for three-phase unbalancedactive distribution network is proposed. Modern distributionnetworks have becoming more and more active with increasingdeployment of microgrids, distributed energy resources (DERs)as well as controllable loads. Considering various ownership andcontrol models of microgrids, DERs and controllable loads, adistributed energy management was formulated using the alternatingdirection method of multipliers (ADMM) algorithm. ByADMM, the distribution management system (DMS) and theseactive components are coordinated through price signals, whichare adjusted according to the generation-load mismatch per nodeper phase. To enable resolution of the ADMM-based distributedoptimization using more accessible and popular MILP solver,different linearization techniques were proposed to linearize theaugmented Lagrangian terms and other nonlinear terms. Resultsof case studies on a three-phase active distribution network withthree microgrids and several DERs and controllable loads validatedthe effectiveness of proposed MILP-based distributed energymanagement. In addition, the capability of proposed method inmitigating phase power unbalance has been demonstrated.

Liu, Guodong↗

DOE OSTI2025

Compensating for Amplifier Non-Linearity in a SEL Controller

The Self-Excited Loop (SEL) architecture, used in some continuous-wave (CW) superconducting linacs, relies on a positive feedback mechanism that requires carefully defined operating limits to ensure stable operation. These limits are typically derived from amplifier calibration, which characterizes the relationship between forward power and DAC drive. However, amplifier non-linearity often prevents a simple linear fit of this characteristic, introducing errors that can compromise stability. To address this, we present a modified calibration procedure that incorporates amplifier non-linearity into the SEL framework. The approach is validated with test data from a 32 kW solid-state amplifier (SSA) and a cavity emulator developed for the Fermilab PIP-II linac.

Raman, S. [Fermilab] (ORCID:0009000735937206)↗

DOE OSTI2014

Contact nonlinearities and linear response in jammed particulate packings

Packings of frictionless athermal particles that interact only when they overlap experience a jamming transition as a function of packing density. Such packings provide the foundation for the theory of jamming. This theory rests on the observation that, despite the multitude of disordered configurations, the mechanical response to linear order depends only on the distance to the transition. We investigate the validity and utility of such measurements that invoke the harmonic approximation and show that, despite particles coming in and out of contact, there is a well-defined linear regime in the thermodynamic limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Iteration-based Linearized Distribution-level Locational Marginal Price for Three-phase Unbalanced Distribution Systems

Distributed energy resources (DERs) are rocking the utilities’ business landscape. It calls for competitive market environments that incentivize DERs to form maximum operating efficiency. Among proposed pricing schemes, distribution-level locational marginal price (DLMP) is effective in signaling the marginal generation cost differences driven by energy losses and network constraints. It can be derived from a distribution-level optimal power flow (OPF) framework, as it essentially presents the sensitivity of optimized generation cost towards incremental loads. However, due to the high resistance-to-inductance ratio and unbalanced characteristics of distribution networks, computational affordable DLMPs are highly challenged. This article provides a linear-approximated DLMP that can be solved efficiently and generalized to account for reactive power flow, three-phase unbalanced loads and meshed network structure. The successive linear programming technique is introduced to enhance the model accuracy. Case studies on an IEEE 123-Bus system validate its accuracy against a nonlinear benchmark and capability in offering proper incentives.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2014

MCTP system model based on linear programming optimization of apertures obtained from sequencing patient image data maps

Purpose: The authors present a hybrid direct multileaf collimator (MLC) aperture optimization model exclusively based on sequencing of patient imaging data to be implemented on a Monte Carlo treatment planning system (MC-TPS) to allow the explicit radiation transport simulation of advanced radiotherapy treatments with optimal results in efficient times for clinical practice. Methods: The planning system (called CARMEN) is a full MC-TPS, controlled through aMATLAB interface, which is based on the sequencing of a novel map, called “biophysical” map, which is generated from enhanced image data of patients to achieve a set of segments actually deliverable. In order to reduce the required computation time, the conventional fluence map has been replaced by the biophysical map which is sequenced to provide direct apertures that will later be weighted by means of an optimization algorithm based on linear programming. A ray-casting algorithm throughout the patient CT assembles information about the found structures, the mass thickness crossed, as well as PET values. Data are recorded to generate a biophysical map for each gantry angle. These maps are the input files for a home-made sequencer developed to take into account the interactions of photons and electrons with the MLC. For each linac (Axesse of Elekta and Primus of Siemens) and energy beam studied (6, 9, 12, 15 MeV and 6 MV), phase space files were simulated with the EGSnrc/BEAMnrc code. The dose calculation in patient was carried out with the BEAMDOSE code. This code is a modified version of EGSnrc/DOSXYZnrc able to calculate the beamlet dose in order to combine them with different weights during the optimization process. Results: Three complex radiotherapy treatments were selected to check the reliability of CARMEN in situations where the MC calculation can offer an added value: A head-and-neck case (Case I) with three targets delineated on PET/CT images and a demanding dose-escalation; a partial breast irradiation case (Case II) solved with photon and electron modulated beams (IMRT + MERT); and a prostatic bed case (Case III) with a pronounced concave-shaped PTV by using volumetric modulated arc therapy. In the three cases, the required target prescription doses and constraints on organs at risk were fulfilled in a short enough time to allow routine clinical implementation. The quality assurance protocol followed to check CARMEN system showed a high agreement with the experimental measurements. Conclusions: A Monte Carlo treatment planning model exclusively based on maps performed from patient imaging data has been presented. The sequencing of these maps allows obtaining deliverable apertures which are weighted for modulation under a linear programming formulation. The model is able to solve complex radiotherapy treatments with high accuracy in an efficient computation time.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Rational Design of Methylated Triazine‐Based Linear Conjugated Polymers for Efficient CO 2 Photoreduction with Water

The development of semiconducting conjugated polymers for photoredox catalysis holds great promise for sustainable utilization of solar energy. In this work, a new family of porous methylated triazine‐based linear conjugated polymers is reported that enable efficient photoreduction of carbon dioxide (CO 2 ) with water (H 2 O) vapor, in the absence of any additional photosensitizer, sacrificial agents or cocatalysts. It is demonstrated that the key lies in the generation of methylated triazine linkages through a facile condensation reaction between benzamidine and acetic anhydride, which impedes the formation of conventional triazine‐based frameworks. It is also shown that regulating conjugated linear backbones with different lengths of electron‐donated benzyl units provides a facile means to modulate their optical properties and the exciton dissociation, thereby affording more long‐lived photogenerated charge carriers and boosting charge separation and transfer. A high‐performance carbon monoxide (CO) production rate of 218.9 µmol g −1 h −1 is achieved with ≈ 100% CO selectivity, which is accompanied by exceptional H 2 O oxidation to oxygen (O 2 ). It anticipates this new study will advance synthetic approaches toward polymeric semiconductors and facilitate new possibilities for triazine‐based conjugated polymers with promising potential in artificial photocatalysis.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Non‐Linear Kinetics of The Lithium Metal Anode on Li 6 PS 5 Cl at High Current Density: Dendrite Growth and the Role of Lithium Microstructure on Creep

Abstract Interfacial instability, viz., pore formation in the lithium metal anode (LMA) during discharge leading to high impedance, current focusing induced solid–electrolyte (SE) fracture during charging, and formation/behaviour of the solid–electrolyte interphase (SEI), at the anode, is one of the major hurdles in the development of solid‐state batteries (SSBs). Also, understanding cell polarization behaviour at high current density is critical to achieving the goal of fast‐charging battery and electric vehicle. Herein, via in situ electrochemical scanning electron microscopy (SEM) measurements, performed with freshly deposited lithium microelectrodes on transgranularly fractured fresh Li6PS5Cl (LPSCl), the LiǀLPSCl interface kinetics are investigated beyond the linear regime. Even at relatively small overvoltages of a few mV, the LiǀLPSCl interface shows non‐linear kinetics. The interface kinetics possibly involve multiple rate‐limiting processes, i.e., ion transport across the SEI and SE|SEI interfaces, as well as charge transfer across the LiǀSEI interface. The total polarization resistance R P of the microelectrode interface is determined to be ≈ 0.8 Ω cm 2 . It is further shown that the nanocrystalline lithium microstructure can lead to a stable LiǀSE interface via Coble creep along with uniform stripping. Also, spatially resolved lithium deposition, i.e., at grain surface flaws, grain boundaries, and flaw‐free surfaces, indicates exceptionally high mechanical endurance of flaw‐free surfaces toward cathodic load (>150 mA cm −2 ). This highlights the prominent role of surface defects in dendrite growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2018

Convergence of the multigrid reduction in time algorithm for the linear elasticity equations

This paper presents some recent advances for parallel-in-time methods applied to linear elasticity. With recent computer architecture changes leading to stagnant clock speeds, but ever increasing numbers of cores, future speedups will be available through increased concurrency. Thus, sequential algorithms, such as time stepping, will suffer a bottleneck. This paper explores multigrid reduction in time (MGRIT) for an important application area, linear elasticity. Previously, efforts at parallel-in-time for elasticity have experienced difficulties, for example, the beating phenomenon. As a result, practical parallel-in-time algorithms for this application area currently do not exist. This paper proposes some solutions made possible by MGRIT (e.g., slow temporal coarsening and FCF-relaxation) and, more importantly, a different formulation of the problem that is more amenable to parallel-in-time methods. Using a recently developed convergence theory for MGRIT and Parareal, we show that the changed formulation of the problem avoids the instability issues and allows the reduction of the error using two temporal grids. We then extend our approach to the multilevel case, where we demonstrate how slow temporal coarsening improves convergence. Finally, the paper ends with supporting numerical results showing a practical algorithm enjoying speedup benefits over the sequential algorithm.

97 MATHEMATICS AND COMPUTING↗