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DOE OSTI2021

Optimal Power Flow in DC Networks with Robust Feasibility and Stability Guarantees

With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in DC networks such that stability and operational constraint satisfaction are of concern. Most existing DC network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. Here, in contrast, this paper studies a DN-OPF formulation which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this paper's robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the stability set using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator set-points are obtained by optimizing over the proposed convex stability set. The validity and effectiveness of the propose algorithm is demonstrated through various DC networks adapted from IEEE test cases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Communication-Constrained Robust Control and Learning of Grid-Connected

The electric grid of things (EGoT) promises great potential for innovative grid services by tapping into vast load flexibility. However, the unique characteristics of EGoT, being a part of the cyber-physical electric power system, present both opportunities and challenges, especially concerning supply-demand balancing, stability, and communication constraints. Traditionally, centralized control was employed to ensure balance and stability in power systems. However, with the massive influx of EGoT devices, new strategies are needed to efficiently coordinate and control these distributed devices for optimal grid operations. While some studies have explored efficiency and economic models, there remains a gap in ensuring reliability under everyday operations and resilience during extreme conditions. Addressing this gap, this project develops the technology for an Energy Service Interface (ESI) that includes novel pricing, control, learning, and distributed optimization algorithms, which will enable utilities to recruit EGoT assets for crucial grid services such as load flexibility, voltage regulation, and situation-awareness. The key novelty of the proposed technology is the careful distribution of learning and control functions across utility and EGoT asset owners such that provably efficient and resilient grid operations are attained while respecting communication and information-exchange constraints. Specifically, the project team develops machine-learning enhanced load modeling methods to allow EGoT asset owners to learn their load capability and flexibility, and develops pricing-based and decentralized learning-based control so that asset owners can coordinate to meet system-wide demand-supply balance and reliability goals. For extreme situations involving high-impact, low-probability catastrophic events (termed the “black-sky” events), the team also develops (1) a “Feeder-Operating Center-on-a-Laptop” (FOCAL) software that can assist utility personnel in leveraging EGoT assets to accelerate the service recovery of damaged feeders, and (2) distributed optimization algorithms that can coordinate the operation points of EGoT devices under severe communication constraints. The proposed technology has been extensively tested and evaluated through simulations and on a testbed. In summary, as we transition into a more interconnected and digital power grid era, our project’s findings and developments offer a pivotal step toward guaranteeing both efficiency and resilience in the face of both everyday operations and rare “black-sky” events.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2017

LMI-Based Fuzzy Optimal Variance Control of Airfoil Model Subject to Input Constraints

This paper presents a study of fuzzy optimal variance control problem for dynamical systems subject to actuator amplitude and rate constraints. Using Takagi-Sugeno fuzzy modeling and dynamic Parallel Distributed Compensation technique, the stability and the constraints can be cast as a multi-objective optimization problem in the form of Linear Matrix Inequalities. By utilizing the formulations and solutions for the input and output variance constraint problems, we develop a fuzzy full-state feedback controller. The stability and performance of the proposed controller is demonstrated through its application to the airfoil flutter suppression.

optimal variance control↗

DOE OSTI2015

Dark energy and equivalence principle constraints from astrophysical tests of the stability of the fine-structure constant

Astrophysical tests of the stability of fundamental couplings, such as the fine-structure constant α, are becoming an increasingly powerful probe of new physics. Here we discuss how these measurements, combined with local atomic clock tests and Type Ia supernova and Hubble parameter data, constrain the simplest class of dynamical dark energy models where the same degree of freedom is assumed to provide both the dark energy and (through a dimensionless coupling, ζ, to the electromagnetic sector) the α variation. Specifically, current data tightly constrains a combination of ζ and the present dark energy equation of state w{sub 0}. Moreover, in these models the new degree of freedom inevitably couples to nucleons (through the α dependence of their masses) and leads to violations of the Weak Equivalence Principle. We obtain indirect bounds on the Eötvös parameter η that are typically stronger than the current direct ones. We discuss the model-dependence of our results and briefly comment on how the forthcoming generation of high-resolution ultra-stable spectrographs will enable significantly tighter constraints.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

S-type and P-type habitability in stellar binary systems: A comprehensive approach. I. Method and applications

A comprehensive approach is provided for the study of both S-type and P-type habitability in stellar binary systems, which in principle can also be expanded to systems of higher order. P-type orbits occur when the planet orbits both binary components, whereas in the case of S-type orbits, the planet orbits only one of the binary components with the second component considered a perturbator. The selected approach encapsulates a variety of different aspects, which include: (1) the consideration of a joint constraint, including orbital stability and a habitable region for a putative system planet through the stellar radiative energy fluxes ({sup r}adiative habitable zone{sup ;} RHZ), needs to be met; (2) the treatment of conservative, general, and extended zones of habitability for the various systems as defined for the solar system and beyond; (3) the provision of a combined formalism for the assessment of both S-type and P-type habitability; in particular, mathematical criteria are presented for the kind of system in which S-type and P-type habitability is realized; (4) applications of the attained theoretical approach to standard (theoretical) main-sequence stars. In principle, five different cases of habitability are identified, which are S-type and P-type habitability provided by the full extent of the RHZs; habitability, where the RHZs are truncated by the additional constraint of planetary orbital stability (referred to as ST- and PT-type, respectively); and cases of no habitability at all. Regarding the treatment of planetary orbital stability, we utilize the formulae of Holman and Wiegert as also used in previous studies. In this work, we focus on binary systems in circular orbits. Future applications will also consider binary systems in elliptical orbits and provide thorough comparisons to other methods and results given in the literature.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

MASCOT - MATLAB Stability and Control Toolbox

MASCOT software was created to provide the conceptual aircraft designer accurate predictions of air vehicle stability and control characteristics. The code takes as input mass property data in the form of an inertia tensor, aerodynamic loading data, and propulsion (i.e. thrust) loading data. Using fundamental non-linear equations of motion, MASCOT then calculates vehicle trim and static stability data for any desired flight condition. Common predefined flight conditions are included. The predefined flight conditions include six horizontal and six landing rotation conditions with varying options for engine out, crosswind and sideslip, plus three takeoff rotation conditions. Results are displayed through a unique graphical interface developed to provide stability and control information to the conceptual design engineers using a qualitative scale indicating whether the vehicle has acceptable, marginal, or unacceptable static stability characteristics. This software allows the user to prescribe the vehicle s CG location, mass, and inertia tensor so that any loading configuration between empty weight and maximum take-off weight can be analyzed. The required geometric and aerodynamic data as well as mass and inertia properties may be entered directly, passed through data files, or come from external programs such as Vehicle Sketch Pad (VSP). The current version of MASCOT has been tested with VSP used to compute the required data, which is then passed directly into the program. In VSP, the vehicle geometry is created and manipulated. The aerodynamic coefficients, stability and control derivatives, are calculated using VorLax, which is now available directly within VSP. MASCOT has been written exclusively using the technical computing language MATLAB . This innovation is able to bridge the gap between low-fidelity conceptual design and higher-fidelity stability and control analysis. This new tool enables the conceptual design engineer to include detailed static stability and trim constraints in the conceptual design loop. The unique graphical interface developed for this tool presents the stability data in a format that is understandable by the conceptual designer, yet also provides the detailed quantitative results if desired.

Kenny, Sean↗

NASA NTRS1980

Impact of longitudinal flying qualities upon the design of a transport with active controls

Direct constrained parameter optimization was used to optimally size a medium range transport for minimum direct operating cost. Several stability and control constraints were varied to study the sensitivity of the configuration to specifying the unaugmented flying qualities of transports designed with relaxed static stability. Additionally, a number of handling quality related design constants were studied with respect to their impact to the design.

Sliwa, S. M.↗

NASA NTRS1982

A note on the limits of Rossby wave amplitudes

Quasi-geostrophic dynamics, as usually formulated, centers on the conservation of pseudopotential vorticity (PV) on isobaric surfaces. The present study has the objective to investigate some simple constraints which conservation of PV imposes on internal Rossby waves. Attention is given to some of the limitations that conservation of potential vorticity imposes on the dynamics of the stratosphere. Another possible constraint imposed by hydrodynamic stability is also discussed. The quantitative limitations these constraints put on the amplitudes of internal Rossby waves are assessed and compared with observations of the lower stratosphere.

Lindzen, R. S.↗

NASA NTRS1980

Economic evaluation of flying-qualities design criteria for a transport configured with relaxed static stability

Direct constrained parameter optimization was used to optimally size a medium range transport for minimum direct operating cost. Several stability and control constraints were varied to study the sensitivity of the configuration to specifying the unaugmented flying qualities of transports designed to take maximum advantage of relaxed static stability augmentation systems. Additionally, a number of handling qualities related design constants were studied with respect to their impact on the design.

Sliwa, S. M.↗

DOE OSTI2014

Stabilization of linear higher derivative gravity with constraints

We show that the instabilities of higher derivative gravity models with quadratic curvature invariant αR{sup 2}+βR{sub μν}R{sup μν} can be removed by judicious addition of constraints at the quadratic level of metric fluctuations around Minkowski/de Sitter background. With a suitable parameter choice, we find that the instabilities of helicity-0, 1, 2 modes can be removed while reducing the dimensionality of the original phase space. To retain the renormalization properties of higher derivative gravity, Lorentz symmetry in the constrained theory is explicitly broken.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

On Practical Aspects of Variational Consistency in Contact Dynamics

Usage of contact mechanics methodologies is a pervasive modeling requirement in dynamic simulations. While for some trivial problems, solutions taken from analytical geometry are available, use of a finite element framework is common to achieve formulation generality. This work explores two dynamic contact formulations: one based on the traditional node-to-segment (NTS) approach, and a variationally consistent segment-to-segment (STS) mortar formulation. The NTS formulation employed here enforces the constraints kinematically (i.e., the interpenetration is enforced to the solver tolerance), whereas the mortar approach uses Lagrange multipliers to enforce the contact constraints. Both approaches are implemented in the open-source finite element framework Multiphysics Object-Oriented Simulation Environment (MOOSE). The results highlight two relevant contact-interface-related dynamic phenomena in finite element simulations. First, stabilization of contact constraints is discussed, taking into account the evolution of the total energy in a benchmark problem. Second, the influence of finite element discretization on both of the aforementioned contact formulations is analyzed by exercising a large-deformation example with continuous relative sliding. Variationally consistent contact approaches such as the mortar formulation lead to improved energy preservation and avoid spurious excitation of the system's frequencies. This is especially relevant in settings where inertia and vibrations are of importance.

42 ENGINEERING↗

DOE OSTI2024

New Constraints on the Melting Temperature and Phase Stability of Shocked Iron up to 270 GPa Probed by Ultrafast X-Ray Absorption Spectroscopy

Studying the properties and phase diagram of iron at high-pressure and high-temperature conditions has relevant implications for Earth’s inner structure and dynamics and the temperature of the inner core boundary (ICB) at 330 GPa. Also, a hexagonal-closed packed to body-centered cubic (bcc) phase transition has been predicted by many theoretical works but observed only in a few experiments. The recent coupling of high-power laser with advanced x-ray sources from synchrotrons allows for novel approaches to address these issues. Here, we present a study on shock compressed iron up to 270 GPa and 5800 K probed by single-pulse (100 ps FWHM) x-ray absorption spectroscopy (XAS). Based on the analysis of the XAS spectra, we provide structural identification and bulk temperature measurements along the Hugoniot up to the melting. These results rule out the predicted transition to a high-temperature bcc phase and allow one to discriminate among existing equations of state models and melting curves. In particular, we report the first bulk temperature measurement in shock compressed iron on the melting plateau at 240(20) GPa and 5345(600) K. The melting curve resulting from our work extrapolates to a temperature of 6202(514) K at 330 GPa and represents a refined upper bound for the ICB temperature. Published by the American Physical Society 2024

Balugani, S.↗

DOE OSTI2021

Dark Energy Survey Year 3 Results: Constraints on cosmological parameters and galaxy bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

We constrain cosmological parameters and galaxy-bias parameters using the combination of galaxy clustering and galaxy-galaxy lensing measurements from the Dark Energy Survey Year-3 data. We describe our modeling framework and choice of scales analyzed, validating their robustness to theoretical uncertainties in small-scale clustering by analyzing simulated data. Using a linear galaxy bias model and redMaGiC galaxy sample, we obtain constraints on the matter content of the universe to be $\Omega_{\rm m} = 0.325^{+0.033}_{-0.034}$. We also implement a non-linear galaxy bias model to probe smaller scales that includes parameterizations based on hybrid perturbation theory, and find that it leads to a 17% gain in cosmological constraining power. Using the redMaGiC galaxy sample as foreground lens galaxies, we find the galaxy clustering and galaxy-galaxy lensing measurements to exhibit significant signals akin to decorrelation between galaxies and mass on large scales, which is not expected in any current models. This likely systematic measurement error biases our constraints on galaxy bias and the $S_8$ parameter. We find that a scale-, redshift- and sky-area-independent phenomenological decorrelation parameter can effectively capture this inconsistency between the galaxy clustering and galaxy-galaxy lensing. We perform robustness tests of our methodology pipeline and demonstrate stability of the constraints to changes in the theory model. After accounting for this decorrelation, we infer the constraints on the mean host halo mass of the redMaGiC galaxies from the large-scale bias constraints, finding the galaxies occupy halos of mass approximately $1.5 \times 10^{13} M_{\odot}/h$.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

An embedded mesh method using piecewise constant multipliers with stabilization: mathematical and numerical aspects

An embedded mesh method using piecewise constant multipliers originally proposed by Puso et al. (CMAME, 2012) is analyzed here to determine effects of the pressure stabilization term and small cut cells. The approach is implemented for transient dynamics using the central difference scheme for the time discretization. It is shown that the resulting equations of motion are a stable linear system with a condition number independent of mesh size. Furthermore, we show that the constraints and the stabilization terms can be recast as non-proportional damping such that the time integration of the scheme is provably stable with a critical time step computed from the undamped equations of motion. Effects of small cuts are discussed throughout the presentation. A mesh study is conducted to evaluate the effects of the stabilization on the discretization error and conditioning and is used to recommend an optimal value for stabilization scaling parameter. Several nonlinear problems are also analyzed and compared with comparable conforming mesh results. Finally, we show several demanding problems highlighting the robustness of the proposed approach.

42 ENGINEERING↗

DOE OSTI2022

Dark Energy Survey year 3 results: Constraints on cosmological parameters and galaxy-bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

We constrain cosmological parameters and galaxy-bias parameters using the combination of galaxy clustering and galaxy-galaxy lensing measurements from the Dark Energy Survey (DES) year-3 data. We describe our modeling framework and choice of scales analyzed, validating their robustness to theoretical uncertainties in small-scale clustering by analyzing simulated data. Using a linear galaxy-bias model and redMaGiC galaxy sample, we obtain 10% constraints on the matter density of the Universe. Here, we also implement a nonlinear galaxy-bias model to probe smaller scales that includes parametrization based on hybrid perturbation theory and find that it leads to a 17% gain in cosmological constraining power. We perform robustness tests of our methodology pipeline and demonstrate stability of the constraints to changes in the theory model. Using the redMaGiC galaxy sample as foreground lens galaxies and adopting the best-fitting cosmological parameters from DES year-1 data, we find the galaxy clustering and galaxy-galaxy lensing measurements to exhibit significant signals akin to decorrelation between galaxies and mass on large scales, which is not expected in any current models. This likely systematic measurement error biases our constraints on galaxy bias and the S 8 parameter. We find that a scale-, redshift- and sky-area-independent phenomenological decorrelation parameter can effectively capture this inconsistency between the galaxy clustering and galaxy-galaxy lensing. We trace the source of this correlation to a color-dependent photometric issue and minimize its impact on our result by changing the selection criteria of redMaGiC galaxies. Using this new sample, our constraints on the S 8 parameter are consistent with previous studies and we find a small shift in the Ω m constraints compared to the fiducial redMaGiC sample. We infer the constraints on the mean host-halo mass of the redMaGiC galaxies in this new sample from the large-scale bias constraints, finding the galaxies occupy halos of mass approximately 1.6 × 10 13 M ⊙ /h.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

Navigation on the Line: Traversability Analysis and Path Planning for Extreme-Terrain Rappelling Rovers

Many areas of scientific interest in planetaryexploration, such as lunar pits, icy-moon crevasses, and Martiancraters, are inaccessible to current wheeled rovers. Rappellingrovers can safely traverse these steep surfaces, but requiretechniques to navigate their complex terrain. This dynamicnavigation is inherently time-critical and communication constraints(e.g. delays and small communication windows) willrequire planetary systems to have some autonomy.Autonomous navigation for Martian rovers is well studiedon moderately sloped and locally planar surfaces, but thesemethods do not readily transfer to tethered systems in nonplanar3D environments. Rappelling rovers in these situationshave additional challenges, including terrain-tether interactionand its effects on rover stability, path planning and control.This paper presents novel traversability analysis and pathplanning algorithms for rappelling rovers operating on steepterrains that account for terrain-tether interaction and theunique stability and reachability constraints of a rapellingsystem. The system is evaluated with a series of simulations andan analogue mission. In simulation, the planner was shown toreliably find safe paths down a 55 degree slope when a stabletether-terrain configuration exists and never recommended anunsafe path when one did not. In a planetary analogue mission,elements of the system were used to autonomously navigateAxel, a JPL rappelling rover, down a 30 degree slope with95% autonomy by distance travelled over 46 meters.

Nesnas, Issa↗

DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗

NASA NTRS1978

On the optimization of discrete structures with aeroelastic constraints

The paper deals with the problem of dynamic structural optimization where constraints relating to flutter of a wing (or other dynamic aeroelastic performance) are imposed along with conditions of a more conventional nature such as those relating to stress under load, deflection, minimum dimensions of structural elements, etc. The discussion is limited to a flutter problem for a linear system with a finite number of degrees of freedom and a single constraint involving aeroelastic stability, and the structure motion is assumed to be a simple harmonic time function. Three search schemes are applied to the minimum-weight redesign of a particular wing: the first scheme relies on the method of feasible directions, while the other two are derived from necessary conditions for a local optimum so that they can be referred to as optimality-criteria schemes. The results suggest that a heuristic redesign algorithm involving an optimality criterion may be best suited for treating multiple constraints with large numbers of design variables.

Mcintosh, S. C., Jr.↗