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NREL Price Series Developed for the ARPA-E FLECCS Program

The price data for four regions (CAISO, ERCOT, MISO-W, and PJM-W) are developed using the ReEDS to PLEXOS conversion as described in (Gagnon et al. 2020). The reference ReEDS case chosen is based on the 2020 Standard Scenario Mid-case, which uses the 2020 ReEDS model version (Cole et al. 2020; Ho et al. 2021). All ReEDS model inputs use 2020 Standard Scenarios Mid-case assumptions except for CO2 prices, which are implemented as linearly increasing CO2 price trajectories beginning at $0/tCO2 in 2020 and ending at either $100/tCO2 or $150/tCO2 in 2035 to dive capacity expansion towards a low-carbon system that could support CCS deployment. However, these scenarios also prohibit CCS deployment in this time frame so that resulting price data are not influenced by the deployment and operation of CCS itself. Implementing the ReEDS to PLEXOS conversion tool, PLEXOS is then simulated using the 2035 ReEDS infrastructure for both CO2 price scenarios, with the following model version and setup: PLEXOS Version: 8.2 Solver: Xpress-MP 35.01.01 Mixed integer optimization relative gap 1% System configuration: • Total number of nodes: 134 (consistent with ReEDS balancing areas) • Line losses enforced using piecewise linear approximation • Energy dump was enabled Price data is aggregated to the ISO/RTO level using load-weighted averages. References: Cole, Wesley, Sean Corcoran, Nathaniel Gates, Daniel Mai, Trieu, and Paritosh Das. 2020. “2020 Standard Scenarios Report: A U.S. Electricity Sector Outlook.” NREL/TP-6A20-77442. Golden, CO: National Renewable Energy Laboratory. https://www.nrel.gov/docs/fy21osti/77442.pdf. Gagnon, Pieter, Will Frazier, Elaine Hale, and Wesley Cole. 2020. “Cambium Documentation: Version 2020.” NREL/TP-6A20-78239. National Renewable Energy Lab. (NREL), Golden, CO (United States). https://doi.org/10.2172/1734551. Ho, Jonathan, Jonathon Becker, Maxwell Brown, Patrick Brown, Ilya (ORCID:0000000284917814) Chernyakhovskiy, Stuart Cohen, Wesley (ORCID:000000029194065X) Cole, et al. 2021. “Regional Energy Deployment System (ReEDS) Model Documentation: Version 2020.” NREL/TP-6A20-78195. Golden, CO: National Renewable Energy Laboratory. https://doi.org/10.2172/1788425.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Restoration Strategy for Active Distribution Systems Considering Endogenous Uncertainty in Cold Load Pickup

Cold load pickup (CLPU) phenomenon is identified as the persistent power inrush upon a sudden load pickup after an outage. Under the active distribution system (ADS) paradigm, where distributed energy resources (DERs) are extensively installed, the decreased outage duration can induce a strong interdependence between CLPU pattern and load pickup decisions. In this paper, we propose a novel modelling technique to tractably capture the decision-dependent uncertainty (DDU) inherent in the CLPU process. Subsequently, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed, where first stage searches for the optimal switching sequences to decide step-wise network topology, and the second stage optimizes the detailed generation schedule of DERs as well as the energization of switchable loads. Further, to tackle the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test on modified IEEE 123-node test feeders has verified the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of DDU quantification.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Optimal Compression of Floating-Point Astronomical Images Without Significant Loss of Information

We describe a compression method for floating-point astronomical images that gives compression ratios of 6 - 10 while still preserving the scientifically important information in the image. The pixel values are first preprocessed by quantizing them into scaled integer intensity levels, which removes some of the uncompressible noise in the image. The integers are then losslessly compressed using the fast and efficient Rice algorithm and stored in a portable FITS format file. Quantizing an image more coarsely gives greater image compression, but it also increases the noise and degrades the precision of the photometric and astrometric measurements in the quantized image. Dithering the pixel values during the quantization process greatly improves the precision of measurements in the more coarsely quantized images. We perform a series of experiments on both synthetic and real astronomical CCD images to quantitatively demonstrate that the magnitudes and positions of stars in the quantized images can be measured with the predicted amount of precision. In order to encourage wider use of these image compression methods, we have made available a pair of general-purpose image compression programs, called fpack and funpack, which can be used to compress any FITS format image.

Pence, William D.↗

Automatic fitting of multiple-field solid-state NMR spectra

The NMR lineshapes produced by half-integer quadrupolar nuclei are sensitive to 11 distinct fit parameters per inequivalent site. To date, automatic fitting routines have failed to replace manual parameter insertion and evaluation due to the importance of local minima and the need for fitting multiple-field magic-angle spinning (MAS) and static spectra simultaneously. Herein we introduce a new tool, AMES-Fit (Automatic Multiple Experiment Simulation and Fitting), to automatically find the global best-fit simulation parameters for a series of multiple-field NMR lineshapes. AMES-Fit uses an adaptive step size random search algorithm to dynamically probe parameter space and requires minimal human input. Importantly, the best fits are obtained in a few minutes of computation time that would otherwise have required several person-hours of work. The program is freely available and open-source.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SIERRA/Aero User Manual - Version 5.8

SIERRA/Aero is a compressible fluid dynamics program intended to solve a wide variety compressible fluid flows including transonic and hypersonic problems. This document describes the commands for assembling a fluid model for analysis with this module, henceforth referred to simply as Aero for brevity. Aero is an application developed using the SIERRA Toolkit (STK). The intent of STK is to provide a set of tools for handling common tasks that programmers encounter when developing a code for numerical simulation. For example, components of STK provide field allocation and management, and parallel input/output of field and mesh data. These services also allow the development of coupled mechanics analysis software for a massively parallel computing environment. In the definitions of the commands that follow, the term Real_Max denotes the largest floating point value that can be represented on a given computer. Int_Max is the largest such integer value.

42 ENGINEERING↗

Constitutive modeling for isotropic materials (HOST)

This report presents the results of the second year of work on a problem which is part of the NASA HOST Program. Its goals are: (1) to develop and validate unified constitutive models for isotropic materials, and (2) to demonstrate their usefulness for structural analyses of hot section components of gas turbine engines. The unified models selected for development and evaluation are that of Bodner-Partom and Walker. For model evaluation purposes, a large constitutive data base is generated for a B1900 + Hf alloy by performing uniaxial tensile, creep, cyclic, stress relation, and thermomechanical fatigue (TMF) tests as well as biaxial (tension/torsion) tests under proportional and nonproportional loading over a wide range of strain rates and temperatures. Systematic approaches for evaluating material constants from a small subset of the data base are developed. Correlations of the uniaxial and biaxial tests data with the theories of Bodner-Partom and Walker are performed to establish the accuracy, range of applicability, and integability of the models. Both models are implemented in the MARC finite element computer code and used for TMF analyses. Benchmark notch round experiments are conducted and the results compared with finite-element analyses using the MARC code and the Walker model.

Lindholm, U. S.↗

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Supersonic Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. Assessing the blade structural integrity is a complex task requiring an initial characterization of whether resonance is possible and then performing a forced response analysis if that condition is met. The standard technique for forced response analysis in rocket engine turbines is to decompose a computational fluid dynamics (CFD).generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies using cyclically symmetric structural dynamic models. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non ]harmonic excitation sources that become present in complex flows. This complex content can only be captured by a CFD flow field encompassing at least an entire revolution. A substantial development effort to create a series of software programs to enable application of the 360 degree forcing function in a frequency response analysis on cyclic symmetric models has been completed (to be described in a future paper), but the question still remains whether the frequency response analysis itself is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, of bladed-disks undergoing this complex flow environment have been performed. The first is of a bladed disk with each blade modeled by simple beam elements and the disk modeled with plates (using the finite element code MSC/NASTRAN). The focus of this model is to be representative of response of realistic bladed disks, and so the dimensions are roughly equivalent to the new J2X rocket engine 1st stage fuel pump turbine. The simplicity of the model allows the CFD load to be able to be readily applied, along with analytical and experimental variations in both the temporal and spatial fourier components of the excitation. In addition, this model is a first step in identifying response differences between transient and frequency forced response analysis techniques. The second phase assesses this difference for a much more realistic solid model of a bladed-disk in order to evaluate the effect of the spatial variation in loading on blade dominated modes. Neither research on the accuracy of the frequency response method when used in this context or a comprehensive study of the effect of test-observed variation on blade forced response have been found in the literature, so this research is a new contribution to practical structural dynamic analysis of gas turbines. The primary excitation of the upstream nozzles interacts with the blades on fuel pump of the J2X causes the 5th Nodal diameter modes to be excited, as explained by Tyler and Sofrin1, so a modal analysis was first performed on the beam/plate model and the 5ND bladed-disk mode at 40167 hz was identified and chosen to be the one excited at resonance (see figure 1). The first forced response analysis with this model focuses on identifying differences between frequency and transient response analyses. A hypothesis going into the analysis was that perhaps the frequency response was enforcing a temporal periodicity that did not really exist, and so therefore it would overestimate the response. As high dynamic response was a considerable source of stress in the J2X, examining this concept could potentially be beneficial for the program.

Brown, Andrew M.↗

Noisy intermediate-scale quantum algorithms

A universal fault-tolerant quantum computer that can efficiently solve problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement toward realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e., qubits that are not error corrected, and therefore perform imperfect operations within a limited coherence time. In the search for achieving quantum advantage with these devices, algorithms have been proposed for applications in various disciplines spanning physics, machine learning, quantum chemistry, and combinatorial optimization. The overarching goal of such algorithms is to leverage the limited available resources to perform classically challenging tasks. In this review, a thorough summary of NISQ computational paradigms and algorithms is provided. The key structure of these algorithms and their limitations and advantages are discussed. Finally, a comprehensive overview of various benchmarking and software tools useful for programming and testing NISQ devices is additionally provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Optimization of rotor blades for combined structural, dynamic, and aerodynamic properties

Optimal helicopter blade design with computer-based mathematical programming has received more and more attention in recent years. Most of the research has focused on optimum dynamic characteristics of rotor blades to reduce vehicle vibration. There is also work on optimization of aerodynamic performance and on composite structural design. This research has greatly increased our understanding of helicopter optimum design in each of these aspects. Helicopter design is an inherently multidisciplinary process involving strong interactions among various disciplines which can appropriately include aerodynamics; dynamics, both flight dynamics and structural dynamics; aeroelasticity: vibrations and stability; and even acoustics. Therefore, the helicopter design process must satisfy manifold requirements related to the aforementioned diverse disciplines. In our present work, we attempt to combine several of these important effects in a unified manner. First, we design a blade with optimum aerodynamic performance by proper layout of blade planform and spanwise twist. Second, the blade is designed to have natural frequencies that are placed away from integer multiples of the rotor speed for a good dynamic characteristics. Third, the structure is made as light as possible with sufficient rotational inertia to allow for autorotational landing, with safe stress margins and flight fatigue life at each cross-section, and with aeroelastical stability and low vibrations. Finally, a unified optimization refines the solution.

He, Cheng-Jian↗

MOOSE Framework Meshing Enhancements to Support Reactor Analysis

MOOSE-based physics codes require an input finite element mesh on which the physics solution is calculated, reported, and transferred to other physics codes. The use of difficult-touse, external licensed software is often required to generate high quality meshes for reactor geometries. High-fidelity geometry modeling also requires elaborate tracking of groups of elements for material property assignment and output reporting which can be considerably complex for the user to identify and maintain. Under the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation (NEAMS) program, several meshingrelated enhancements have been developed for the MOOSE framework to address user challenges in creating finite element meshes for advanced reactor geometries. MOOSE mesh generators have been developed to mesh hexagonal geometries (pins, ducted assemblies, and cores) commonly found in liquid-metal cooled fast reactor concepts. The mesh generator used for hexagonal pin cells is generic for regular polygons and therefore may also be used for Cartesian pin cells. Hexagonal pin cells can be stitched into ducted assemblies, and assemblies can be stitched together into a core. The user may specify region ids, region names, and other preferences on the mesh. This control is useful for later material mapping in the MOOSE-based physics codes input. A capability was also developed for meshing rotating control drums including determination of material volume fractions in each mesh element as a function of time. Control drum meshes may be stitched to other hexagonal assemblies to create a core configuration. Additional mesh generators were developed that wrap around the hexagonal meshing capabilities and utilize “extra element integer” ID values on each element. In regular Cartesian or hexagonal assemblies or cores, the bookkeeping of element groups for both material assignment and output reporting can now be automated through assignment of pin, assembly, core, axial and depletion id values stored as extra element integers. The extra element tags on the mesh greatly speed the reactor analyst’s efforts to map materials to meshes, track depletion zones, and parse output such as axial pin power distributions. At the highest level, pin, assembly, and core mesh generators (with this reactor terminology) have also been developed to easily generate regular Cartesian and hexagonal cores, including axial extrusion. These reactor geometry builders call upon the previously mentioned capabilities to produce analysis-ready 3D meshes including material assignments. Open source mesh triangulation capabilities were also investigated for integration into the MOOSE framework to address the need for meshing the core periphery region which extends from the irregular outer assembly border to a cylindrical boundary. Options are limited due to licensing constraints, and the recommendation is pursue building a native MOOSE Delaunay triangulator routine with full functionality. Finally, a series of verification problems were performed with NEAMS physics tools. All developed capabilities will be available in the new open-source “Reactor” module of the MOOSE framework, which is accessible to any MOOSE-based NEAMS physics tool.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Characterization of Deficiencies in the Frequency Domain Forced Response Analysis Technique for Turbine Bladed Disks

Turbine blades in rocket and jet engine turbomachinery experience enormous harmonic loading conditions. These loads result from the integer number of upstream and downstream stator vanes as well as the other turbine stages. The standard technique for forced response analysis to assess structural integrity is to decompose a CFD generated flow field into its harmonic components, and to then perform a frequency response analysis at the problematic natural frequencies. Recent CFD analysis and water-flow testing at NASA/MSFC, though, indicates that this technique may miss substantial harmonic and non-harmonic excitation sources that become present in complex flows. These complications suggest the question of whether frequency domain analysis is capable of capturing the excitation content sufficiently. Two studies comparing frequency response analysis with transient response analysis, therefore, have been performed. The first is of a bladed disk with each blade modeled by simple beam elements. It was hypothesized that the randomness and other variation from the standard harmonic excitation would reduce the blade structural response, but the results showed little reduction. The second study was of a realistic model of a bladed-disk excited by the same CFD used in the J2X engine program. The results showed that the transient analysis results were up to 10% higher for "clean" nodal diameter excitations and six times larger for "messy" excitations, where substantial Fourier content around the main harmonic exists.

Brown, Andrew M.↗

BRAINSTACK – A Platform for Artificial Intelligence & Machine Learning Collaborative Experiments on a Nano-Satellite

As space missions continue to become more ambitious, complex, and distant to Earth, the need for advanced on-board intelligent decision making to guide everything from mission operations to fault detection and recovery has become a major front of space research. While the prevalence of research on such Artificial Intelligence / Machine Learning (AI/ML) modules has exploded, the capacity to experimentally validate such modules in space in a rapid and inexpensive format has not. To this end, the Nano Orbital Workshop (NOW) group at NASA Ames Research Center has been at the forefront of performing initial flight evaluation tests of ‘commercially’ available AI/ML computational platforms via the TechEdSat (TES-n) flight series as part of what is programmatically referred to as the BRAINSTACK. BRAINSTACK will provide an orbital AI/ML evaluation laboratory where computational experiments are pre-loaded into memory prior to launch, and then executed as desired during the mission, with results reported back and program tweaks or new data sets uploaded as needed. Processors selected as part of the BRAINSTACK are of ideal size, packaging, and power consumption for easy integration into a cube satellite structure. These experiments have included the evaluation of small, high-performance GPUs and more recently, neuromorphic processors in LEO operations. Neuromorphic processors are of particular interest due to their superior computational power efficiency over GPUs. The first TES-n flight test of an Intel first-generation Loihi neuromorphic processor launched on January 13, 2022 and continues to operate in orbit despite almost no space environment modifications. The Intel Loihi Gen-1 is characterized by a 14nm 128-core Spiking Neural Network (SNN) able to support on-chip training. This experiment utilized a Loihi packaged in the ‘Kapoho Bay’ USB module, providing a relatively straight-forward interface to the bus avionics system. The Kapoho Bay was in turn managed by a host Intel Pentium single-board computer to handle scheduling of the AI/ML application payloads, and communications with the satellite vehicle manager. The recently released Intel Loihi Gen-2, able to support integer-valued spike payloads and produced using 7nm process, will form part of the basis of the evolving BRAINSTACK in the upcoming three TES-n/NOW flights. Additionally, it is planned to measure the radiation environment these processors experience to understand any degradation or computational artifacts caused by long term space radiation exposure on these novel architectures. This evolving flexible and collaborative environment involving various research teams across NASA and other organizations is intended to be a convenient orbital test platform from which many anticipated future space AI/ML applications may be initially tested.

Artificial Intelligence↗

BRAINSTACK – A Platform for Artificial Intelligence & Machine Learning Collaborative Experiments on a Nano-Satellite

As space missions continue to become more ambitious, complex, and distant to Earth, the need for advanced on-board intelligent decision making to guide everything from mission operations to fault detection and recovery has become a major front of space research. While the prevalence of research on such Artificial Intelligence / Machine Learning (AI/ML) modules has exploded, the capacity to experimentally validate such modules in space in a rapid and inexpensive format has not. To this end, the Nano Orbital Workshop (NOW) group at NASA Ames Research Center has been at the forefront of performing initial flight evaluation tests of ‘commercially’ available AI/ML computational platforms via the TechEdSat (TES-n) flight series as part of what is programmatically referred to as the BRAINSTACK. BRAINSTACK will provide an orbital AI/ML evaluation laboratory where computational experiments are pre-loaded into memory prior to launch, and then executed as desired during the mission, with results reported back and program tweaks or new data sets uploaded as needed. Processors selected as part of the BRAINSTACK are of ideal size, packaging, and power consumption for easy integration into a cube satellite structure. These experiments have included the evaluation of small, high-performance GPUs and more recently, neuromorphic processors in LEO operations. Neuromorphic processors are of particular interest due to their superior computational power efficiency over GPUs. The first TES-n flight test of an Intel first-generation Loihi neuromorphic processor launched on January 13, 2022 and continues to operate in orbit despite almost no space environment modifications. The Intel Loihi Gen-1 is characterized by a 14nm 128-core Spiking Neural Network (SNN) able to support on-chip training. This experiment utilized a Loihi packaged in the ‘Kapoho Bay’ USB module, providing a relatively straight-forward interface to the bus avionics system. The Kapoho Bay was in turn managed by a host Intel Pentium single-board computer to handle scheduling of the AI/ML application payloads, and communications with the satellite vehicle manager. The recently released Intel Loihi Gen-2, able to support integer-valued spike payloads and produced using 7nm process, will form part of the basis of the evolving BRAINSTACK in the upcoming three TES-n/NOW flights. Additionally, it is planned to measure the radiation environment these processors experience to understand any degradation or computational artifacts caused by long term space radiation exposure on these novel architectures. This evolving flexible and collaborative environment involving various research teams across NASA and other organizations is intended to be a convenient orbital test platform from which many anticipated future space AI/ML applications may be initially tested.

Artificial Intelligence↗

BRAINSTACK – A Platform for Artificial Intelligence & Machine Learning Collaborative Experiments on a Nano-Satellite

As the space economy continues to expand through increasingly easy access to advanced and inexpensive technology, space missions themselves have become more ambitious with exploration targets growing ever distant while simultaneously requiring larger guidance and communication budgets. These conflicting desires of distance and control drive the need for advanced on-board intelligent decision making to reduce communication and control limitations by automating as many mission functions as possible in-situ. While the amount of research on such Artificial Intelligence and Machine Learning (AI/ML) software modules has grown exponentially, the capacity to experimentally validate such software modules in space in a rapid and inexpensive format has not. To this end, the Nano Orbital Workshop (NOW) group at NASA Ames Research Center has been at the forefront of performing initial flight evaluation tests of ‘commercially’ available bleeding-edge computational platforms via what is programmatically referred to as the BrainStack on the TechEdSat (TES-n) flight series. This on-orbit computational platform provides an evaluation laboratory where advanced software experiments are pre-loaded into memory prior to launch, then executed as payloads during mission operations with results reported back and program tweaks or new training sets uploaded as needed. Processors selected as part of the BrainStack are of ideal size, packaging, and power consumption for easy integration into a cube satellite structure. These experiments have included the evaluation of small, high-performance GPUs and, more recently, neuromorphic processors, in LEO operations. Neuromorphic processors are of particular interest due to their superior power efficiency over GPUs in intelligent automation applications. The first TES-n flight test of an Intel first-generation Loihi neuromorphic processor launched on TES-13, January 13, 2022, and continues to operate in orbit despite no significant modifications to harden the processor against the space environment. The Intel Loihi Gen-1 on TES-13 is characterized by a 14nm 128-core Spiking Neural Network (SNN) able to support on-chip training. The processor is packaged in the Kapoho Bay USB module, providing a relatively straight-forward interface to the bus avionics system. The Kapoho Bay was in turn managed by an Intel Pentium single-board computer to handle scheduling of the software application payloads and communications with the satellite’s primary computer. The recently released Intel Loihi Gen-2, able to support integer-valued spike payloads and produced using 7nm process, will form part of the continually evolving BrainStack in the upcoming three TES-n/NOW flights. The Kapoho Point unit will incorporate eight Loihi-2 processors, enabling neural networks of up to one million neurons and one billion synapsis. Additionally, it is planned to measure the radiation environment these processors experience to understand any degradation or computational artifacts caused by long term space radiation exposure on these novel architectures. This evolving flexible and collaborative environment involving various research teams across NASA and other organizations is intended to be a convenient orbital test platform from which many anticipated future space automation applications may be initially tested.

Artificial Intelligence↗

Dependence of the Element Patterns of HYDROSTAR on Mutual Coupling

HYDROSTAR is a hybrid synthesis radiometer, intended for spaceborne applications, which employs a real aperture (waveguide stick antenna) for resolution along track and employs aperture synthesis to obtain resolution across track. This L-band system is an extension of the successful aircraft prototype, the Electronically Steered Thinned Array Radiometer (ESTAR). A proof-of-concept, full size system was constructed (45 wavelength in the synthesis direction) and subjected to extensive antenna pattern and associated microwave component measurements in an outdoor antenna test facility. HYDROSTAR employs a thinned array of 16 elements each 5.8 inches long in the along track dimension and spanning 9.5 inches across track. Each element is a narrow-wall shunt slot array with 36 slots. The polarization is linear (along-track). In the across track dimension, the antennas are deployed in a minimum redundancy array which has 90 independent baselines spaced in integer multiples of half a wavelength. The closest spacings used are for the first three elements at each end, which are spaced by only one-half wavelength. This study was intended to assess how closely each of 16 stick element patterns compare with their nominal values (as an individual, isolated radiator), when installed in their intended composite thinned array configuration. Extensive pattern measurements of the 16 elements that constitute the HYDROSTAR antenna subsystem were conducted to observe their relative features along the synthesis plane. Data was also collected for the mutual coupling between pairs of selected antennas. All antenna patterns had features different from that of an isolated element indicating some level of interaction among neighboring radiators. Those elements which had nearest neighbors at least five wavelengths away were located near the middle of the array. Their radiation patterns displayed sonic small, symmetric ripple across their full azimuth range. The patterns of elements that lie within 2.5 wavelengths of their neighbors showed stronger and asymmetric features. These are believed to be caused by mutual coupling among these structures. Evidence for this was seen when an antenna position was displaced by 0.05 wavelengths, Its pattern and those of its near neighbors were seen to change. Displacement within the plane of the array were observed to have different effects than displacements out-of-plane. A program of data analysis and theoretical development is in progress to provide a physical interpretation of the properties of these antenna patterns and to develop methods which can optimize the performance of this synthetic aperture imaging system. This includes compensation for pattern asymmetries and element position perturbation.

Weissman, David E.↗

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Furthermore, our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

25 ENERGY STORAGE↗

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗

SEQ-GEN: A comprehensive multimission sequencing system

SEQ-GEN is a user-interactive computer program used to plan and generate a sequence of commands for spacecraft. Desired activities are specified by the user of SEQ-GEN; SEQ-GEN in turn expands these activities, deriving the spacecraft commands necessary to accomplish the desired activities. SEQ-GEN models the effects on the spacecraft of the commands, predicting the state as a function of time, flagging any conflicts and rule violations. These states, conflicts, and violations are viewable both graphically and textually at the user's request. SEQ-GEN also displays the entire sequence graphically, showing each requested activity as a bar on its graphical timeline. SEQ-GEN immediately revalidates the sequence, updating its models and calculations along with its displays based on these changes. Because it has the ability to recalculate spacecraft states immediately, the user is able to perform 'what-if' sessions easily. SEQ-GEN, a multimission tool, is adaptable to any flight project. A flight project writes its adaptation files containing project unique information including in its simplest form, only spacecraft commands. For more involved projects the adaptation files may also contain flight and mission rules, description of the spacecraft and ground models, and the definition of activities. SEQ-GEN operates at whatever level of detail the adaptation files imply. Simple adaptations are straight forward to do. There is, however, no limit to the complexity of activity definitions or of spacecraft models: both may involve unlimited logical decision points. Commands and activities may involve any number of parameters of a wide variety of data types, including integer, float, time, boolean, and character strings. SEQ-GEN will be used by the Mars Pathfinder, Cassini, and VIM (Voyager Interstellar Mission) project in an effort to speed up adaptation time and to keep sequence generation costs down. SEQ-GEN is hosted on UNIX workstations. It uses MOTIF and X for windowing, and was designed and coded in an object-oriented style in the language C++.

Salcedo, Jose↗