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DOE OSTI2019

Distributed biomass supply chain cost optimization to evaluate multiple feedstocks for a biorefinery

Conventional practices of siting all biomass preprocessing operations at the biorefinery is widely believed to be the most cost-effective solution for feedstock supply because of economies of scale. Yet, biomass preprocessing operations could be decentralized by moving the preprocessing operations to distributed biomass preprocessing centers, also known as “depots” located near biomass sources. We present a comparative case study with multiple biomass resources to analyze biorefinery feedstock supply logistics designs having distributed depots and a primary depot co-located with the biorefinery. A mixed-integer linear programming model was developed to simultaneously optimize feedstock sourcing decisions, and optimal preprocessing depot locations and size, utilizing biomass resources from agricultural residue, energy and municipal solid waste to meet carbohydrate specifications and feedstock demand for a biochemical conversion process. Findings from a case study in the US showed that a biorefinery could increase its feedstock supply draw area and supply volume by 57.3%, 177.4% respectively without increasing the feedstock delivered cost by adopting distributed depot-in the feedstock supply chain design. A distributed-depot-based supply chain can be more economical by selecting optimal mix of biomass resource, optimal siting and depot scales during feedstock supply chain design. The results from this study indicate that a biorefinery can utilize dynamic blending to meet the feedstock quality specifications as well as larger supply radius in the distributed depot-based supply chain design to access more available biomass to handle potential feedstock supply uncertainty.

09 BIOMASS FUELS↗

DOE OSTI2020

Models and Strategies for Optimal Demand Side Management in the Chemical Industries

Deregulation and the increase of renewable electricity generation from wind and solar photovoltaics have transformed the U.S. electricity market. Economic and environmental benefits notwithstanding, the presence of renewables has increased variability and uncertainty on the supply side of the grid. Managing demand, rather than generation – a strategy referred to as “demand response (DR)” – is an attractive approach for mitigating this imbalance. DR efforts aim to reduce electricity usage during peak demand times, lessening stress on the grid. Industrial users are particularly attractive entities for DR participation since they present large, localized loads that can provide significant relief on grid demand and –unlike other large loads, such as buildings – are minimally dependent on human needs and preferences. In this project, we accomplished three main objectives. (1) We developed data-driven low-order DR scheduling-relevant dynamic models of chemical processes. Concurrently, we studied the formulation and solution of the associated optimal DR production scheduling problems. (a) A prototype air separation unit (ASU) model was used to generate simulated operating data for initial modeling efforts, which enabled the later use of industrial data for data-driven modeling. (b) We utilized Hammerstein-Wiener (HW) and Finite Step Response (FSR) models to represent nonlinear plant dynamics. (c) The HW models were linearized using exact linearization so they could potentially be embedded in power system models, which are formulated as mixed integer linear programs (MILPs). (d) We solved DR optimization problems under uncertainty and found that even naïve predictions of electricity price and product demand led to significant cost savings benefits. (2) Our DR scheduling optimization problem formulations are amenable to real-time solution. (a) We utilized Lagrangian Relaxation (LR) to efficiently solve the optimization problem by decoupling subproblems linked by complicating constraints. (b) We have achieved computation times for the 3-day DR scheduling problem of an ASU as low as 1.88 minutes. (3) Our representations of the DR behavior of chemical process as grid-level batteries were embedded in power system models. (a) For a small-scale grid, we found that incorporating the dynamics of the chemical plant in the optimal power flow calculations resulted in better resource management leading to up to 15% and 46% cost reduction for the grid and chemical plant operations, respectively, during periods of power line congestion. We have published several works dedicated to modeling and solving DR optimization problems from the user side. These were published in top peer-reviewed journals and are summarized in this report. The most recent work (and papers in preparation) considers DR scheduling from the grid side. Future efforts will consider networked plants (e.g., air separation units operating on a common pipeline) for DR participation, which is expected to amplify the capabilities of industrial DR participants to perform load-shifting. Our consideration of uncertainty in DR has inspired future directions in this area as well: we plan to develop multistage methods to fully account for the effects of uncertainty in DR scheduling.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

PETSc/TAO Users Manual V.3.21

This manual describes the use of the Portable, Extensible Toolkit for Scientific Computation (PETSc) and the Toolkit for Advanced Optimization (TAO) for the numerical solution of partial differential equations (PDEs) and related problems on high-performance computers. PETSc/TAO is a suite of data structures and routines that provide the building blocks for implementing large-scale application codes on parallel (and serial) computers. PETSc uses the MPI standard for all distributed memory communication. PETSc/TAO includes a large suite of parallel linear solvers, nonlinear solvers, time integrators, and optimizers that may be used in application codes written in Fortran, C, C++, and Python (via petsc4py; see Getting Started ). The library is organized hierarchically, enabling users to employ the abstraction level most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Optimizing Kernel Machines Using Deep Learning

Building highly non-linear and non-parametric models is central to several state-of-the-art machine learning systems. Kernel methods form an important class of techniques that induce a reproducing kernel Hilbert space (RKHS) for inferring non-linear models through the construction of similarity functions from data. These methods are particularly preferred in cases where the training data sizes are limited and when prior knowledge of the data similarities is available. Despite their usefulness, they are limited by the computational complexity and their inability to support end-to-end learning with a task specific objective. On the other hand, deep neural networks have become the de facto solution for end-to-end inference in several learning paradigms. In this article, we explore the idea of using deep architectures to perform kernel machine optimization, for both computational efficiency and end-to-end inferencing. To this end, we develop the DKMO (Deep Kernel Machine Optimization) framework, that creates an ensemble of dense embeddings using Nystrõm kernel approximations and utilizes deep learning to generate task-specific representations through the fusion of the embeddings. Intuitively, the filters of the network are trained to fuse information from an ensemble of linear subspaces in the RKHS. Furthermore, we introduce the kernel dropout regularization to enable improved training convergence. Finally, we extend this framework to the multiple kernel case, by coupling a global fusion layer with pre-trained deep kernel machines for each of the constituent kernels. Using case studies with limited training data, and lack of explicit feature sources, we demonstrate the effectiveness of our framework over conventional model inferencing techniques.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Exploring Enhanced Dominant Resource Fairness Using Linear Programming Calculated Weights

Maintaining resource fairness while achieving optimization for various performance metrics such as resource utilization, turnaround time and job latency is a well-known resource scheduling challenge in cloud computing. Despite the significant progress made with the introduction of dominant resource fairness by Ghodsi et al., which ensures major allocation properties such as sharing incentive, strategy-proofness, envy-freeness and Pareto efficiency to be achieved

Yan, Bo [Binghamton University]↗

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↗