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DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

Optimization of commercial scale photonuclear production of radioisotopes

Photonuclear production of radioisotopes driven by bremsstrahlung photons using a linear electron accelerator in the suitable energy range is a promising method for producing radioisotopes. The photonuclear production method is capable of making radioisotopes more conveniently, cheaply and with much less radioactive waste compared to existing methods. Historically, photo-nuclear reactions have not been exploited for isotope production because of the low specific activity that is generally associated with this production process, although the technique is well-known to be capable of producing large quantities of certain radioisotopes. We describe an optimization technique for a set of parameters to maximize specific activity of the final product. This set includes the electron beam energy and current, the end station design (an integrated converter and target as well as cooling system), the purity of materials used, and the activation time. These parameters are mutually dependent and thus their optimization is not trivial. {sup 67}Cu photonuclear production via {sup 68}Zn({gamma}p){sup 67}Cu reaction was used as an example of such an optimization process.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2021

Biochemical inhibition of acid phosphatase activity in two mountain spruce forest soils

The product inhibition of the 4-Methylumbelliferyl phosphate (MUB-P) decay rate, a measure of potential acid phosphatase activity, has not been considered in most of the published kinetic studies. The aim of this study was to determine the type and strength of the product inhibition in order to better define reaction conditions at which the acid phosphatase activity assay produces unbiased results. The MUB-P decay rate was measured in the forest floor and topsoil organic horizons of two spruce forest catchments at different initial MUB-P and P-PO4 3- concentrations. Furthermore, the type and strength of the inhibition was analyzed by non-linear regression. We found that MUB-P decay was competitively inhibited by the P-PO4 3- but also by dissolved organic P. By using estimated kinetic parameters, we calculated an underestimation of potential acid phosphatase activity by up to ~20% at concentrations of added MUB-P as high as 300 µmol g-1 dry weight and an incubation time one hour due to background inorganic and organic P concentrations in range of units of µmol per gram of dry soil. We discuss approaches that can be used to minimize the underestimation and show that the previously defined recommendations might not be always sufficient to avoid the bias. Therefore, we recommend to analyze progress curves at a wide range of initial MUB-P concentrations using non-linear methods when the enzyme assay is optimized for a given soil. When changes in inorganic and/or organic P concentrations are expected, we further recommend measuring background inorganic and organic P concentrations.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Krylov subspace recycling for evolving structures

Krylov subspace recycling is a powerful tool when solving a long series of large, sparse linear systems that change only slowly over time. In PDE constrained shape optimization, these series appear naturally, as typically hundreds or thousands of optimization steps are needed with only small changes in the geometry. In this setting, however, applying Krylov subspace recycling can be a difficult task. As the geometry evolves, in general, so does the finite element mesh defined on or representing this geometry, including the numbers of nodes and elements and element connectivity. This is especially the case if re-meshing techniques are used. As a result, the number of algebraic degrees of freedom in the system changes, and in general the linear system matrices resulting from the finite element discretization change size from one optimization step to the next. Changes in the mesh connectivity also lead to structural changes in the matrices. In the case of re-meshing, even if the geometry changes only a little, the corresponding mesh might differ substantially from the previous one. Obviously, this prevents any straightforward mapping of the approximate invariant subspace of the linear system matrix (the focus of recycling in this work) from one optimization step to the next; similar problems arise for other selected subspaces. In this paper, we present an algorithm to map an approximate invariant subspace of the linear system matrix for the previous optimization step to an approximate invariant subspace of the linear system matrix for the current optimization step, for general meshes. This is achieved by exploiting the map from coefficient vectors to finite element functions on the mesh, combined with interpolation or approximation of functions on the finite element mesh. We demonstrate the effectiveness of our approach numerically with several proof of concept studies for a specific meshing technique.

42 ENGINEERING↗

DOE OSTI2020

Scenario Grouping and Decomposition Algorithms for Chance-Constrained Programs

A lower bound for a finite-scenario-based chance-constrained program is the quantile value corresponding to the sorted optimal objective values of scenario subproblems. This quantile bound can be improved by grouping subsets of scenarios at the expense of solving larger subproblems. The quality of the bound depends on how the scenarios are grouped. In this paper, we formulate a mixed-integer bilevel program that optimally groups scenarios to tighten the quantile bounds. For general chance-constrained programs, we propose a branch-and-cut algorithm to optimize the bilevel program, and for chance-constrained linear programs, a mixed-integer linear-programming reformulation is derived. Here, we also propose several heuristics for grouping similar or dissimilar scenarios. Our computational results demonstrate that optimal grouping bounds are much tighter than heuristic bounds, resulting in smaller root-node gaps and better performance of scenario decomposition for solving chance-constrained 0-1 programs. Also, the optimal grouping bounds can be greatly strengthened using larger group size.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Optimization of a Close-Fitting Volume RF Coil for Brain Imaging at 6.5 mT Using Linear Programming

Not provided.

Engineering↗

DOE OSTI2016

Optical Performance Prediction of Hyperlight Energy Collector With a New Optimized Secondary Reflector

This paper assesses the optical performance of a new linear Fresnel collector by Hyperlight Energy. It uses water as construction material to carry mini-size reflectors to save the cost. The secondary reflector adopts an optimal profile derived through a new adaptive optimization method by NREL. The optical performance of the optimal secondary reflector profile is also calculated at varying incidence angles. The results show that the secondary reflector profile possesses a constantly high performance over a wide range of incidence angle and exhibits its robustness.

Zhu, Guangdong↗

DOE OSTI2023

Design Considerations of a Coordinative Demand Charge Mitigation Strategy

This paper presents a coordinative demand charge mitigation (DCM) strategy for reducing electricity consumption during system peak periods. Available DCM resources include batteries, diesel generators, controllable loads, and conservation voltage reduction. All resources are directly controlled by load serving entities. A mixed integer linear programming based energy management algorithm is developed to optimally coordinate of DCM resources considering the load payback effect. To better capture system peak periods, two different kinds of load forecast are used: the day-ahead load forecast and the peak-hour probability forecast. Five DCM strategies are compared for reconciling the discrepancy between the two forecasting results. The DCM strategies are tested using actual utility data. Simulation results show that the proposed algorithm can effectively mitigate the demand charge while preventing the system peak from being shifted to the payback hours. We also identify the diminishing return effect, which can help load serving entities optimize the size of their DCM resources.

Hu, Rongxing↗

DOE OSTI2015

Compressible degree of freedom (CDOF): A potential strategy for improving wave energy capture

The addition of a compressible degree of freedom (CDOF) has been shown to significantly increase the power absorption compared to a traditional rigid WEC of the same shape and mass for a variety of architectures. The present study demonstrates that a compressible point absorber, with a passive power-take-off (PTO) and optimized damping, can also achieve at the same performance levels or better than an optimally controlled rigid point absorber using reactive power from the PTO. Eliminating the need for a reactive PTO would substantially reduce costs by reducing PTO design complexity. In addition, it would negate the documented problems of reactive PTO efficiencies on absorbed power. Improvements to performance were quantified in the present study by comparing a compressible point absorber to a conventional rigid one with the same shape and mass. Wave energy is converted to mechanical energy in both cases using a linear damper PTO, with the PTO coefficient optimized for each resonance frequency and compressible volume. The large compressible volumes required to tune the compressible point absorber to the desired frequency are a practical limitation that needs to be addressed with further research; especially for low frequencies. If fact, all compressible volumes exceed the submerged volume of the point absorber by significant amounts; requiring auxiliary compressible volume storage units that are connected to the air chamber in the submerged portion of the point absorber. While realistic, these auxiliary units would increase the Cap Ex and Op Ex costs, potentially reducing the aforementioned benefits gained by CDOF. However, alternative approaches can be developed to implement CDOF without the large compressible volume requirements, including the development of flexible surface panels tuned with mechanical springs.

42 ENGINEERING↗

DOE OSTI2014

SU-E-T-110: Development of An Independent, Monte Carlo, Dose Calculation, Quality Assurance Tool for Clinical Trials

Purpose: To develop a comprehensive end-to-end test for Varian's TrueBeam linear accelerator for head and neck IMRT using a custom phantom designed to utilize multiple dosimetry devices. Purpose: To commission a multiple-source Monte Carlo model of Elekta linear accelerator beams of nominal energies 6MV and 10MV. Methods: A three source, Monte Carlo model of Elekta 6 and 10MV therapeutic x-ray beams was developed. Energy spectra of two photon sources corresponding to primary photons created in the target and scattered photons originating in the linear accelerator head were determined by an optimization process that fit the relative fluence of 0.25 MeV energy bins to the product of Fatigue-Life and Fermi functions to match calculated percent depth dose (PDD) data with that measured in a water tank for a 10x10cm2 field. Off-axis effects were modeled by a 3rd degree polynomial used to describe the off-axis half-value layer as a function of off-axis angle and fitting the off-axis fluence to a piecewise linear function to match calculated dose profiles with measured dose profiles for a 40×40cm2 field. The model was validated by comparing calculated PDDs and dose profiles for field sizes ranging from 3×3cm2 to 30×30cm2 to those obtained from measurements. A benchmarking study compared calculated data to measurements for IMRT plans delivered to anthropomorphic phantoms. Results: Along the central axis of the beam 99.6% and 99.7% of all data passed the 2%/2mm gamma criterion for 6 and 10MV models, respectively. Dose profiles at depths of dmax, through 25cm agreed with measured data for 99.4% and 99.6% of data tested for 6 and 10MV models, respectively. A comparison of calculated dose to film measurement in a head and neck phantom showed an average of 85.3% and 90.5% of pixels passing a 3%/2mm gamma criterion for 6 and 10MV models respectively. Conclusion: A Monte Carlo multiple-source model for Elekta 6 and 10MV therapeutic x-ray beams has been developed as a quality assurance tool for clinical trials.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Parallel time integration software

This package implements an optimal-scaling multigrid solver for the (non) linear systems that arise from the discretization of problems with evolutionary behavior. Typically, solution algorithms for evolution equations are based on a time-marching approach, solving sequentially for one time step after the other. Parallelism in these traditional time-integrarion techniques is limited to spatial parallelism. However, current trends in computer architectures are leading twards system with more, but not faster. processors. Therefore, faster compute speeds must come from greater parallelism. One approach to achieve parallelism in time is with multigrid, but extending classical multigrid methods for elliptic poerators to this setting is a significant achievement. In this software, we implement a non-intrusive, optimal-scaling time-parallel method based on multigrid reduction techniques. The examples in the package demonstrate optimality of our multigrid-reduction-in-time algorithm (MGRIT) for solving a variety of parabolic equations in two and three sparial dimensions. These examples can also be used to show that MGRIT can achieve significant speedup in comparison to sequential time marching on modern architectures.

Source record↗

DOE OSTI2014

Parallel time integration software

Source record↗

DOE OSTI2024

Flexible dynamic boundary microgrid operation considering network and load unbalances

Flexible microgrids with dynamic boundaries have recently been introduced in the literature. With the ability to reconfigure the topology of the microgrids dynamically through remotely controlled switches, flexible microgrids with dynamic boundaries can further improve the resiliency and energy efficiency of microgrids with distributed energy resources (DERs). This paper focuses on the optimal operation considering one of the predominant characteristics of microgrids and distribution systems – unbalanced networks and loads. In existing literature, balanced modeling of microgrids is more common due to its attractive simplicity. The three-phase power unbalance has not been considered as a constraint on the generation units in a microgrid. Further, negative sequence constraints have also been neglected. In this article, we propose a set of constraints that is specifically related to the capabilities of inverter interfaced resources to supply unbalanced current/power when the microgrid is islanded from the main distribution grid. We incorporate the new set of constraints into two optimization formulations leveraging two convex relaxations of the three-phase power flow equations: mixed-integer linear programming (MILP) and mixed-integer semidefinite programming (MISDP) that optimize the dispatch of controllable switches and DERs in the microgrid. The algorithms are then extended to networked microgrids with grid-forming sources. We test the algorithms on a realistic community microgrid model in Puerto Rico as well as standardized IEEE distribution test feeders. The testing results demonstrate the performance of the proposed algorithms. The MILP is fast and scalable, and the MISDP enforces the negative sequence voltage constraints.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

Interaction Region Design and Detector Integration at JLab's MEIC

The Electron Ion Collider (EIC) will be a next-generation facility for the study of the strong interaction (QCD). JLab's MEIC is designed for high luminosities of up to 10^34 cm^-2 s^-1. This is achieved in part due to an aggressively small beta-star, which imposes stringent requirements on the collider rings' dynamical properties. Additionally, one of the unique features of MEIC is a full-acceptance detector with a dedicated, small-angle, high-resolution detection system, capable of covering a wide range of momenta (and charge-to-mass ratios) with respect to the original ion beam to enable access to new physics. The detector design relies on a number of features, such as a 50 mrad beam crossing angle, large-aperture ion and electron final focusing quads and spectrometer dipoles as well as a large machine-element-free detection space downstream of the final focusing quads. We present an interaction region design developed with close integration of the detector and beam dynamical aspects. The dynamical aspect of the design rests on a symmetry-based concept for compensation of non-linear effects. The optics and geometry have been optimized to accommodate the detection requirements and to ensure the interaction region's modularity for easiness of integration into the collider ring lattices. As a result, the design offers an excellent detector performance combined with the necessary non-linear dynamical properties.

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

Scalable Optimization Methods for Distribution Networks With High PV Integration

Here this paper proposes a suite of algorithms to determine the active- and reactive-power setpoints for photovoltaic (PV) inverters in distribution networks. The objective is to optimize the operation of the distribution feeder according to a variety of performance objectives and ensure voltage regulation. In general, these algorithms take a form of the widely studied ac optimal power flow (OPF) problem. For the envisioned application domain, nonlinear power-flow constraints render pertinent OPF problems nonconvex and computationally intensive for large systems. To address these concerns, we formulate a quadratic constrained quadratic program (QCQP) by leveraging a linear approximation of the algebraic power-flow equations. Furthermore, simplification from QCQP to a linearly constrained quadratic program is provided under certain conditions. The merits of the proposed approach are demonstrated with simulation results that utilize realistic PV-generation and load-profile data for illustrative distribution-system test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2018

Three-dimensional alignment of asymmetric-top molecules induced by polarization-shaped optimal laser pulses

Optimal control simulation is applied to numerically design nonresonant laser pulses that maximize the degrees of three-dimensional (3D) alignment of SO 2 using the lowest-order induced-dipole interaction. In our trials, combinations of more than two mutually orthogonal, linearly polarized subpulses are always obtained as the optimal solutions. Each subpulse in the optimal pulses impulsively excites the rotational wave packet. The optimal pulses effectively cooperate with the rotational dynamics up to only a few partial revival timings owing to the rotational dephasing that determines the effective control periods. The control mechanisms are interpreted in terms of the time derivatives of the expectation values of the squares of the direction cosines, that of the rotational energy, and the interplay between them. We find a special and important role of the last subpulses as they align the molecular axes using the interaction through the two smallest polarizability components, while the other subpulses excite the rotational wave packet mainly through the largest polarizability component. Lastly, the control pulses composed of the specified number of subpulses are also numerically optimized by actively utilizing the instantaneous penalty to systematically show the superiority of the use of more than two subpulses over that of two subpulses, the latter of which leads to the saturation of the degree of 3D alignment as a function of total fluence.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Solar Field Layout and Aimpoint Strategy Optimization

The existing methods that determine heliostat aiming strategies for concentrating solar power (CSP) central receiver plants typically use heuristics and/or are computationally expensive, and they lack flexibility for different desired flux profiles and receiver geometries. Because of the interaction between layout and aimpoint strategy, considering the former without accounting for the latter may yield solutions with superfluous heliostats that cannot be used efficiently without compromising receiver flux constraints. To that end, we develop a software decision tool that uses innovative optimization methods to both optimize aimpoint strategies and improve candidate layouts for the solar collection field of a CSP central receiver plant. A CSP plant’s effectiveness relies on the optical efficiency of the solar field, which may be limited by losses due to (i) the cosine effect, (ii) atmospheric attenuation, (iii) interference (i.e., shading and blocking) between heliostats, (iv) spillage as a result of heliostat positioning and geometry, and (iv) some heliostats’ inability to direct irradiance to the receiver without damage due to excessive thermal flux. The goal of this work is to obtain optimized aiming strategies and improved solar field layouts that reduce capital cost and increase field optical efficiency and utilization, while meeting the power requirements of a given CSP receiver design. We formulate the aimpoint optimization problem as a mixed-integer linear programming model, which we then decompose into submodels that we solve in parallel. The decomposition subdivides the solar field into sections, and aimpoint strategies for each section are obtained independently of the others. To improve existing layouts, we develop a utilization-weighted efficiency metric that we use to relocate heliostats to sections of the solar field with similar efficiency and higher utilization. Finally, to connect our software to high-fidelity flux models, we develop a Python application programming interface for SolarPILOT, a mature software package that characterizes solar field performance and generates the heliostat layouts and flux maps that serve as input to our models.

14 SOLAR ENERGY↗

DOE OSTI2016

SU-F-J-38: Dose Rates and Preliminary Evaluation of Contouring Similarity Metrics Using 4D Cone Beam CT

Purpose: 4D imaging modalities require detailed characterization for clinical optimization. The On-Board Imager mounted on the linear accelerator was used to investigate dose rates in a tissue mimicking phantom using 4D-CBCT and assess variability of contouring similarity metrics between 4D-CT and 4D-CBCT retrospective reconstructions. Methods: A 125 kVp thoracic protocol was used. A phantom placed on a motion platform simulated a patient’s breathing cycle. An ion chamber was affixed inside the phantom’s tissue mimicking cavities (i.e. bone, lung, and soft tissue). A sinusoidal motion waveform was executed with a five second period and superior-inferior motion. Dose rates were measured at six ion chamber positions. A preliminary workflow for contouring similarity between 4D-CT and 4D-CBCT was established using a single lung SBRT patient’s historical data. Average intensity projection (Ave-IP) and maximum intensity projection (MIP) reconstructions generated offline were compared between the 4D modalities. Similarity metrics included Dice similarity coefficient (DSC), Hausdorff distance, and center of mass (COM) deviation. Two isolated lesions were evaluated in the patient’s scans: one located in the right lower lobe (ITVRLL) and one located in the left lower lobe (ITVLLL). Results: Dose rates ranged from 2.30 (lung) to 5.18 (bone) E-3 cGy/mAs. For fixed acquisition parameters, cumulative dose is inversely proportional to gantry speed. For ITVRLL, DSC were 0.70 and 0.68, Hausdorff distances were 6.11 and 5.69 mm, and COM deviations were 1.24 and 4.77 mm, for Ave-IP and MIP respectively. For ITVLLL, DSC were 0.64 and 0.75, Hausdorff distances were 10.74 and 8.00 mm, and COM deviations were 7.55 and 4.3 mm, for Ave-IP and MIP respectively. Conclusion: While the dosimetric output of 4D-CBCT is low, characterization is necessary to assure clinical optimization. A basic workflow for comparison of simulation and treatment 4D image-based contours was established. This work was partially supported by a Research Scholar Grant (RSG-15-137-01-CCE) from the American Cancer Society.

60 APPLIED LIFE SCIENCES↗