Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear Optimization”

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

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

MO-AB-BRA-04: Correct Identification of Low-Attenuation Intracranial Hemorrhage and Calcification Using Dual-Energy Computed Tomography in a Phantom System

Purpose: Intracranial hemorrhage and calcification with Single-Energy CT (SECT) attenuation below 100HU cannot be reliably identified using currently clinically available means. Calcification is typically benign but hemorrhage can carry a risk of intracranial bleeding and contraindicate use of anticoagulant therapies. A biologically-relevant phantom was used to investigate identification of unknown intracranial lesions using dual-energy CT (DECT) as a verification of prior lesion differentiation results. Methods: Prior phantom work investigating calcification and hemorrhage differentiation resulted in 3D-DECT raw data (water density, calcium density, 68keV) for a range of DECT protocol variations: image thicknesses (1.25, 2.5, 3.75, 5mm), CTDIvol (36.7 to 132.6mGy) and reconstruction algorithms (Soft, Standard, Detail). Acquisition-specific raw data were used to create a plane of optimal differentiation based on the geometric bisector of 3D-linear regression of the two lesion distributions. Verification hemorrhage and calcification lesions, ranging in size from 0.5 to 1.5cm, were created at varying attenuation from 50 to 100HU. Lesions were inserted into a biologically-relevant brain phantom and scanned using SECT (3.75mm images, Standard, 67mGy) and a range of DECT protocols (3.75mm images, Standard, [67, 105.6, 132.6mGy]). 3D-DECT data were collected and blinded for analysis. The 3D-DECT distribution of the lesion was then compared to the acquisition-matched geometric bisector plane and the mean lesion value’s position relative to the plane, indicating lesion identity, and the percentage of voxels on the identified side of the plane, indicating identification confidence, were derived. Results: 98% of the 120 lesions investigated were identified correctly as hemorrhage or calcification. 74% were identified with greater than 80% confidence. Increases in CTDIvol and lesion diameter were associated with increased identification confidence. Conclusion: Intracranial lesions of unknown etiology were identified with 80% confidence for 74% of lesions investigated. These phantom data suggest that the identification of intracranial lesions below 100HU is clinically feasible using DECT. This research was conducted at the MD Anderson Center for Advanced Biomedical Imaging in-part with equipment support from General Electric Healthcare.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

WE-DE-201-08: Multi-Source Rotating Shield Brachytherapy Apparatus for Prostate Cancer

Purpose: To introduce a novel multi-source rotating shield brachytherapy (RSBT) apparatus for the precise simultaneous angular and linear positioning of all partially-shielded 153Gd radiation sources in interstitial needles for treating prostate cancer. The mechanism is designed to lower the detrimental dose to healthy tissues, the urethra in particular, relative to conventional high-dose-rate brachytherapy (HDR-BT) techniques. Methods: Following needle implantation, the delivery system is docked to the patient template. Each needle is coupled to a multi-source afterloader catheter by a connector passing through a shaft. The shafts are rotated by translating a moving template between two stationary templates. Shaft walls as well as moving template holes are threaded such that the resistive friction produced between the two parts exerts enough force on the shafts to bring about the rotation. Rotation of the shaft is then transmitted to the shielded source via several keys. Thus, shaft angular position is fully correlated with the position of the moving template. The catheter angles are simultaneously incremented throughout treatment as needed, and only a single 360° rotation of all catheters is needed for a full treatment. For each rotation angle, source depth in each needle is controlled by a multi-source afterloader, which is proposed as an array of belt-driven linear actuators, each of which drives a source wire. Results: Optimized treatment plans based on Monte Carlo dose calculations demonstrated RSBT with the proposed apparatus reduced urethral D{sub 1cc} below that of conventional HDR-BT by 35% for urethral dose gradient volume within 3 mm of the urethra surface. Treatment time to deliver 20 Gy with multi-source RSBT apparatus using nineteen 62.4 GBq {sup 153}Gd sources is 117 min. Conclusions: The proposed RSBT delivery apparatus in conjunction with multiple nitinol catheter-mounted platinum-shielded {sup 153}Gd sources enables a mechanically feasible urethra-sparing treatment technique for prostate cancer in a clinically reasonable timeframe.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Review—Development of Highly Active and Durable Hybrid Compressive Platinum Lattice Catalysts for Polymer Electrolyte Membrane Fuel Cells: Mathematical Modeling and Experimental Work

This review provides a comprehensive overview on the development of highly active and durable platinum catalysts with ultra-low Pt loadings for polymer electrolyte membrane fuel cells (PEMFCs) through a combined mathematical modeling and experimental work. First, simulation techniques were applied to evaluate the validity of the Tafel approximation for the calculation of the mass activity (MA) and specific activity (SA). A one-dimensional agglomeration model was developed and solved to understand the effects of exchange current density, porosity, agglomerate size, Nafion ® film thickness, and Pt loading on the MA and SA. High porosity (> 60%) and agglomerations at high Pt loadings cause the loss of the Tafel approximation and consequently the decrease in MA and SA. A new structure parameter was introduced to estimate the real porous structure using the fractal theory. The volumetric catalyst density was corrected by the fractal dimension (measured by Hg porosimetry), which gave a good agreement with the experimental values. The loading-dependent Tafel equation was then derived, which contains both the utilization and the non-linear scaling factor. Second, activated carbon composite support (ACCS) with optimized surface area, porosity, pore size, and pore size distribution was developed. The hydrophilic/hydrophobic ratio, structural properties (amorphous/crystalline ratio), and the number of active sites were optimized through metal-catalyzed pyrolysis. Stability of ACCS and Pt/ACCS were evaluated using an accelerated stress test (AST). The results indicated that Pt/ACCS showed no significant loss of MA and power density after 5,000 cycles at 1.0–1.5 V, while the commercial Pt/C catalysts showed drastic losses of MA and power density. Finally, monolayers of compressed Pt (core–shell-type Pt 3 Co 1 ) catalysts were structured by diffusing Co atoms (previously embedded in ACCS) into Pt. Compressive Pt lattice (Pt * ) catalysts were synthesized through an annealing procedure developed at the University of South Carolina (USC). The Pt * /ACCS catalyst showed high initial power density (rated) of 0.174 g Pt kW −1 and high stability (24 mV loss) at 0.8 A cm −2 after 30,000 cycles (0.6–1.0 V). The outstanding performance of Pt * /ACCS is due to the synergistic effect of ACCS and compressive Pt * lattice.

25 ENERGY STORAGE↗
DOE OSTI2026

HydraGNN v5.0

HydraGNN v5.0 expands the code base into a more portable, scalable, and flexible framework for scientific graph learning, with particular strength in atomistic machine-learning interatomic potentials and large-scale distributed training. The release adds Fully Sharded Data Parallel (FSDP) support alongside existing DDP and DeepSpeed paths, including FSDP-aware checkpointing and optimizer integration, and introduces a configurable multi-precision training workflow supporting FP32, BF16, and FP64 across GPUs and Intel XPUs. For atomistic modeling, HydraGNN v5.0 strengthens its MLIP capabilities through dynamic graph construction at every forward pass, energy-conserving force prediction via automatic differentiation, and per-atom energy loss formulations, while extending EGNN models to properly handle periodic boundary conditions. The release also broadens model expressiveness through graph-level attribute conditioning, adds new multi-task and model-parallel extensions such as MACE support and encoder/decoder branch optimization, and expands application coverage with integrated examples for datasets including OC25, Nabla2-DFT, QCML, Open Polymers 2026, and OPF. In parallel, HydraGNN v5.0 improves production readiness through performance optimizations for large-scale runs, stratified sampling and linear-regression preprocessing utilities, and tested installation scripts for DOE supercomputers including Frontier, Aurora, Perlmutter, and Andes. Overall, the release advances HydraGNN as a robust software platform for scalable graph neural networks across materials science, chemistry, and scientific machine learning workflows

Lupo Pasini, Massimiliano [Oak Ridge National Labo↗
DOE OSTI2014

Holographic Imaging of Evolving Laser-Plasma Structures

In the 1870s, English photographer Eadweard Muybridge captured motion pictures within one cycle of a horse’s gallop, which settled a hotly debated question of his time by showing that the horse became temporarily airborne. In the 1940s, Manhattan project photographer Berlin Brixner captured a nuclear blast at a million frames per second, and resolved a dispute about the explosion’s shape and speed. In this project, we developed methods to capture detailed motion pictures of evolving, light-velocity objects created by a laser pulse propagating through matter. These objects include electron density waves used to accelerate charged particles, laser-induced refractive index changes used for micromachining, and ionization tracks used for atmospheric chemical analysis, guide star creation and ranging. Our “movies”, like Muybridge’s and Brixner’s, are obtained in one shot, since the laser-created objects of interest are insufficiently repeatable for accurate stroboscopic imaging. Our high-speed photographs have begun to resolve controversies about how laser-created objects form and evolve, questions that previously could be addressed only by intensive computer simulations based on estimated initial conditions. Resolving such questions helps develop better tabletop particle accelerators, atmospheric ranging devices and many other applications of laser-matter interactions. Our photographic methods all begin by splitting one or more “probe” pulses from the laser pulse that creates the light-speed object. A probe illuminates the object and obtains information about its structure without altering it. We developed three single-shot visualization methods that differ in how the probes interact with the object of interest or are recorded. (1) Frequency-Domain Holography (FDH). In FDH, there are 2 probes, like “object” and “reference” beams in conventional holography. Our “object” probe surrounds the light-speed object, like a fleas swarming around a sprinting animal. The object modifies the probe, imprinting information about its structure. Meanwhile, our “reference” probe co-propagates ahead of the object, free of its influence. After the interaction, object and reference combine to record a hologram. For technical reasons, our recording device is a spectrometer (a frequency-measuring device), hence the name “frequency-domain” holography. We read the hologram electronically to obtain a “snapshot” of the object’s average structure as it transits the medium. Our published work shows numerous snapshots of electron density waves (“laser wakes”) in ionized gas (“plasma”), analogous to a water wake behind a boat. Such waves are the basis of tabletop particle accelerators, in which charged particles surf on the light-speed wave, gaining energy. Comparing our snapshots to computer simulations deepens understanding of laser wakes. FDH takes snapshots of objects that are quasi-static --- i.e. like Muybridge’s horse standing still on a treadmill. If the object changes shape, FDH images blur, as when a subject moves while a camera shutter is open. Many laser-generated objects of interest do evolve as they propagate. To overcome this limit of FDH, we developed .... (2) Frequency-Domain Tomography (FDT). In FDT, 5 to 10 probe pulses are fired simultaneously across the object’s path at different angles, like a crossfire of bullets. The object imprints a “streaked” record of its evolution on each probe, which we record as in FDH, then recover a multi-frame “movie” of the object’s evolving structure using algorithms of computerized tomography. When propagation distance exceeds a few millimeters, reconstructed FDT images distort. This is because the lenses that image probes to detector have limited depth of field, like cameras that cannot focus simultaneously on both nearby and distant objects. But some laser-generated objects of interest propagate over meters. For these applications we developed … (3) Multi-Object-Plane Phase-Contrast Imaging (MOP-PCI). In MOP-PCI, we image FDT-like probes to the detector from multiple “object planes” --- like recording an event simultaneously with several cameras, some focused on nearby, others on distant, objects. To increase sensitivity, we exploit a phase-contrast imaging technique developed by Dutch Nobel laureate Fritz Zernike in the 1930s. Using MOP-PCI we recorded single-shot movies of laser pulse tracks through more than 10 cm of air. We plan to record images of meter-long tracks of electron bunches propagating through plasma in an experiment at the Stanford Linear Accelerator Center (SLAC). This will help SLAC scientists understand, optimize and scale small plasma-based particle accelerators that have applications in medicine, industry, materials science and high-energy physics.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

The Effects of Market Concentration on Residential Solar PV Prices: Competition, Installer Scale, and Soft Costs

Competition among residential solar photovoltaic (PV) installers may reduce PV price markups and yield lower prices. At the same time, competition may reduce installer experience and opportunities for cost reductions through learning-by-doing and economies of scale. These dynamics suggest that PV non-hardware or 'soft' costs and installed prices depend on the distribution of market shares among installers, also known as market concentration. This study leverages a rich data set of 226,769 residential PV systems to examine the relationship between market concentration, soft costs, and PV prices. The results show that PV prices are lower, on average, in more concentrated markets, i.e., markets with fewer installers or where few installers hold high market share. The study provides evidence that this relationship is non-linear, such that prices are minimized in markets with an optimal balance of the benefits of market concentration and the benefits of competition.

14 SOLAR ENERGY↗
DOE OSTI2022

Accessing glue through photoproduction measurements at GlueX

Photoproduction experiments are a key tool in the investigation of the spectrum of hadronic states and the way gluons contribute to this spectrum. The GlueX experiment, located at Jefferson Lab, features a linearly polarized tagged photon beam and its detector system is optimized to measure a wide range of neutral and charged final states. GlueX offers unique capabilities to study the spectrum of hadrons and is dedicated to the search for hybrid mesons, states with gluonic degrees of freedom. This talk presents first results from our initial campaign of data taking which finished in 2018.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Multiplexed Anodic Stripping Voltammetry Detection of Heavy Metals in Water Using Nanocomposites Modified Screen-Printed Electrodes Integrated With a 3D-Printed Flow Cell

In this study, we present multiplexed anodic stripping voltammetry (ASV) detection of heavy metal ions (HMIs)—As(III), Cd(II), and Pb(II)—using a homemade electrochemical cell consisting of dual working, reference and counter screen-printed electrodes (SPE) on polyimide substrate integrated with a 3D-printed flow cell. Working and counter electrodes were fabricated by the screen-printing of graphite paste while the Ag/AgCl paste was screen-printed as a reference electrode (Ag/AgCl quasi-reference electrode). The working electrodes were modified with (BiO) 2 CO 3 -reduced graphene oxide (rGO)-Nafion [(BiO) 2 CO 3 -rGO-Nafion] and Fe 3 O 4 magnetic nanoparticles (Fe 3 O 4 MNPs) decorated Au nanoparticles (AuNPs)-ionic liquid (IL) (Fe 3 O 4 -Au-IL) nanocomposites separately to enhance HMIs sensing. Electrochemical detection was achieved using square wave ASV technique. The desired structure of the flow electrochemical cell was optimized by the computational fluid dynamic (CFD). Different experimental parameters for stripping analysis of HMIs were optimized including deposition time, deposition potential and flow rate. The linear range of calibration curves with the sensing nanocomposites modified SPE for the three metal ions was from 0–50 μg/L. The limits of detection (S/N = 3) were estimated to be 2.4 μg/L for As(III), 1.2 μg/L for Pb(II) and 0.8 μg/L for Cd(II). Furthermore, the homemade flow anodic stripping sensor platform was used to detect HMIs in simulated river water with a 95–101% recovery, indicating high selectivity and accuracy and great potential for applicability even in complex matrices.

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

Powering the Woods Hole X-Spar Buoy with Ocean Wave Energy—A Control Co-Design Feasibility Study

Despite its success in measuring air–sea exchange, the Woods Hole Oceanographic Institution’s (WHOI) X-Spar Buoy faces operational limitations due to energy constraints, motivating the integration of an energy harvesting apparatus to improve its deployment duration and capabilities. This work explores the feasibility of an augmented, self-powered system in two parts. Part 1 presents the collaborative design between X-Spar developers and wave energy researchers translating user needs into specific functional requirements. Based on requirements like desired power levels, deployability, survivability, and minimal interference with environmental data collection, unsuitable concepts are pre-eliminated from further feasibility study consideration. In part 2, we focus on one of the promising concepts: an internal rigid body wave energy converter. We apply control co-design methods to consider commercial of the shelf hardware components in the dynamic models and investigate the concept’s power conversion capabilities using linear 2-port wave-to-wire models with concurrently optimized control algorithms that are distinct for every considered hardware configuration. During this feasibility study we utilize two different control algorithms, the numerically optimal (but acausal) benchmark and the optimized damping feedback. We assess the sensitivity of average power to variations in drive-train friction, a parameter with high uncertainty, and analyze stroke limitations to ensure operational constraints are met. Our results indicate that a well-designed power take-off (PTO) system could significantly extend the WEC-Spar’s mission by providing additional electrical power without compromising data quality.

autonomous systems↗
DOE OSTI2016

An optimized treatment for algorithmic differentiation of an important glaciological fixed-point problem

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixed-point iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson (1994) for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. Finally, the methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a hybrid shallow ice/shallow shelf approximation to the Stokes equations.

58 GEOSCIENCES↗
DOE OSTI2017

Linear Power-Flow Models in Multiphase Distribution Networks: Preprint

This paper considers multiphase unbalanced distribution systems and develops approximate power-flow models where bus-voltages, line-currents, and powers at the point of common coupling are linearly related to the nodal net power injections. The linearization approach is grounded on a fixed-point interpretation of the AC power-flow equations, and it is applicable to distribution systems featuring (i) wye connections; (ii) ungrounded delta connections; (iii) a combination of wye-connected and delta-connected sources/loads; and, (iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. The proposed linear models can facilitate the development of computationally-affordable optimization and control applications -- from advanced distribution management systems settings to online and distributed optimization routines. Performance of the proposed models is evaluated on different test feeders.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Data Sciences Summer Institute Topology Optimization

DSSI_TOPOPT is a 2D topology optimization code that designs stiff structures made of a single linear elastic material and void space. The code generates a finite element mesh of a rectangular design domain on which the user specifies displacement and load boundary conditions. The code iteratively designs a structure that minimizes the compliance (maximizes the stiffness) of the structure under the given loading, subject to an upper bound on the amount of material used. Depending on user options, the code can evaluate the performance of a user-designed structure, or create a design from scratch. Output includes the finite element mesh, design, and visualizations of the design.

Watts, Seth↗
DOE OSTI2018

The Effects of Market Concentration on Residential Solar PV Prices: Competition, Installer Scale, and Soft Costs

Competition among residential solar photovoltaic (PV) installers may reduce PV price markups and yield lower prices. At the same time, competition may reduce installer experience and opportunities for cost reductions through learning-by-doing and economies of scale. These dynamics suggest that PV non-hardware or 'soft' costs and installed prices depend on the distribution of market shares among installers, also known as market structure. This study leverages a rich data set of 226,769 residential PV systems to examine the relationship between market structure, soft costs, and PV prices. The results show that PV prices are lower, on average, in more concentrated markets, i.e., markets with fewer installers or where a subset of installers holds a large market share. The study provides evidence that this relationship is non-linear, such that prices are minimized in markets with an optimal balance of the benefits of market concentration and the benefits of competition.

14 SOLAR ENERGY↗
DOE OSTI2014

In situ magnetic compensation for potassium spin-exchange relaxation-free magnetometer considering probe beam pumping effect

A novel method to compensate the residual magnetic field for an atomic magnetometer consisting of two perpendicular beams of polarizations was demonstrated in this paper. The method can realize magnetic compensation in the case where the pumping rate of the probe beam cannot be ignored. In the experiment, the probe beam is always linearly polarized, whereas, the probe beam contains a residual circular component due to the imperfection of the polarizer, which leads to the pumping effect of the probe beam. A simulation of the probe beam's optical rotation and pumping rate was demonstrated. At the optimized points, the wavelength of the probe beam was optimized to achieve the largest optical rotation. Although, there is a small circular component in the linearly polarized probe beam, the pumping rate of the probe beam was non-negligible at the optimized wavelength which if ignored would lead to inaccuracies in the magnetic field compensation. Therefore, the dynamic equation of spin evolution was solved by considering the pumping effect of the probe beam. Based on the quasi-static solution, a novel magnetic compensation method was proposed, which contains two main steps: (1) the non-pumping compensation and (2) the sequence compensation with a very specific sequence. After these two main steps, a three-axis in situ magnetic compensation was achieved. The compensation method was suitable to design closed-loop spin-exchange relaxation-free magnetometer. By a combination of the magnetic compensation and the optimization, the magnetic field sensitivity was approximately 4 fT/Hz{sup 1/2}, which was mainly dominated by the noise of the magnetic shield.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2016

Bidding strategy for microgrid in day-ahead market based on hybrid stochastic/robust optimization

In this paper, we propose an optimal bidding strategy in the day-ahead market of a microgrid consisting of intermittent distributed generation (DG), storage, dispatchable DG and price responsive loads. The microgrid coordinates the energy consumption or production of its components and trades electricity in both the day-ahead and real-time markets to minimize its operating cost as a single entity. The bidding problem is challenging due to a variety of uncertainties, including power output of intermittent DG, load variation, day-ahead and real-time market prices. A hybrid stochastic/robust optimization model is proposed to minimize the expected net cost, i.e., expected total cost of operation minus total benefit of demand. This formulation can be solved by mixed integer linear programming. The uncertain output of intermittent DG and day-ahead market price are modeled via scenarios based on forecast results, while a robust optimization is proposed to limit the unbalanced power in real-time market taking account of the uncertainty of real-time market price. Numerical simulations on a microgrid consisting of a wind turbine, a PV panel, a fuel cell, a micro-turbine, a diesel generator, a battery and a responsive load show the advantage of stochastic optimization in addition to robust optimization.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2015

Application of Fireworks Algorithm in Gamma-Ray Spectrum Fitting for Radioisotope Identification

We present that identification of radioisotopic signature patterns in gamma-ray spectra is of paramount importance in various applications of gamma spectroscopy. Therefore, there are several active research efforts to develop accurate and precise methods to perform automated spectroscopic analysis and subsequently recognize gamma-ray signatures. In this work, the authors present a new method for radioisotope identification in gamma-ray spectra obtained with a low resolution radiation detector. The method fits the obtained spectrum with a linear combina-tion of known template signature patterns. Coefficients of the linear combination are evaluated by computing the solution of a single objective optimization problem, whose objective is the Theil-1 inequality coefficient. Optimization of the problem is performed by the Fireworks Algorithm, which identifies a set of coefficients that minimize the Theil-1 value. The computed coefficients are statistically tested for being significantly different than zero or not, and if at least one is found to be zero then the Fireworks Algorithm is used to reiterate fitting using the non-zero templates. Fitting iterations are continued up to the point that no linear coefficients are found to be zero. The output of the method is a list that contains the radioisotopes that have been identified in the measured spectrum. The method is tested on a set of both simulated and real experimental gamma-ray spectra comprised of a variety of isotopes, and compared to a multiple linear regression fitting, and genetic algorithm Theil-1 based fitting. Finally, results demonstrate the potentiality of the Fireworks Algorithm based method, expressed as higher accuracy and similar precision over the other two tested methodologies for radioisotope signature pattern identification in the framework of gamma-ray spectrum fitting.

Theil Coefficient↗
DOE OSTI2013

Discrete-Time Pricing and Optimal Exercise of American Perpetual Warrants in the Geometric Random Walk Model

An American option (or, warrant) is the right, but not the obligation, to purchase or sell an underlying equity at any time up to a predetermined expiration date for a predetermined amount. A perpetual American option differs from a plain American option in that it does not expire. In this study, we solve the optimal stopping problem of a perpetual American option (both call and put) in discrete time using linear programming duality. Under the assumption that the underlying stock price follows a discrete time and discrete state Markov process, namely a geometric random walk, we formulate the pricing problem as an infinite dimensional linear programming (LP) problem using the excessive-majorant property of the value function. This formulation allows us to solve complementary slackness conditions in closed-form, revealing an optimal stopping strategy which highlights the set of stock-prices where the option should be exercised. The analysis for the call option reveals that such a critical value exists only in some cases, depending on a combination of state-transition probabilities and the economic discount factor (i.e., the prevailing interest rate) whereas it ceases to be an issue for the put.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Robust trajectory-constrained frequency control for microgrids considering model linearization error

Grid supportive modes integrated within inverter-based resources can improve the frequency response of renewable-rich microgrids. The synthesis of grid supportive modes to guarantee frequency trajectory constraints under a predefined disturbance set is challenging but essential. To tackle this challenge, a numerical optimal control (NOC)-based control synthesis methodology is proposed. Without loss of generality, a wind-diesel fed microgrid is studied, where we aim to design grid supportive functions in the wind turbine. In the control design, linearized models are used, and the linearization-induced errors are quantitatively analyzed by reachability and interval arithmetics and represented in the form of interval uncertainties. Then, the NOC problem can be formulated into a robust mixed-integer linear program. The control structure is strategically configured into two levels to realize online deployment. The proposed control is verified on the modified 33-node microgrid with a full-order three-phase nonlinear model in Simulink. In conclusion, the simulation results show the effectiveness of the proposed control paradigm and the necessity of considering linearization-induced uncertainty.

24 POWER TRANSMISSION AND DISTRIBUTION↗