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DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗

NASA NTRS1974

Creep behavior of tantalum alloy T-222 at 1365 to 1700 K

High vacuum creep tests on the tantalum T-222 alloy at 0.42 to 0.52 T sub m show that the major portion of the creep curves, up to at least 1 percent strain, can be best described by an increasing creep rate, with strain varying linearly with time. Correlation and extrapolation of the creep curves on the basis of increasing creep rates results in more accurate engineering design data than would use of approximated linear rates. Based on increasing creep rates, the stress for 1 percent strain in 10,000 hours for T-222 is about four times greater than for the Ta-10W alloy. Increasing the grain size results in increased creep strength. Thermal aging prior to testing caused precipitation of the hexagonal close packed (Hf,Ta) sub 2 C, which initially increased creep strength. However, this dimetal carbide was converted during creep testing to face-centered cubic (Hf,Ta)C.

Titran, R. H.↗

NASA NTRS1979

ATS-5 and ATS-6 potentials during eclipse

The ATS 5 and ATS 6 data for spacecraft charging during eclipse conditions is analyzed. The ATS 5 and ATS 6 charged to voltages greater than 100 volts for about 55 percent of the eclipse periods examined. The mean spacecraft potential during eclipse was 2 keV for ATS 5, and the highest potential measured was 10 kilovolts. For ATS 6, the mean potential during eclipse was 4 keV, the highest potential measured 20 keV. The average measured spacecraft potentials for both ATS 5 and 6 depend approximately linearly upon Kp. This relationship is due mainly to the dependence of electron current density on Kp near midnight. Spacecraft potentials at geosynchronous orbit may, to a rough approximation, thus be inferred from ground-based measurements of Kp, the planetary 3-hour index.

Rubin, A. G.↗

NASA NTRS1975

Hydromagnetic waves and cosmic-ray diffusion theory

Pitch-angle (and energy) diffusion of cosmic rays in hydromagnetic wave fields is considered. The treatment remains strictly within the quasi-linear approximation. It is shown that the popular assumption of an isotropic power spectrum tensor of magnetic fluctuations requires in this case equal forms and magnitudes of Alfven and magnetosonic wave spectra - a situation which is generally unlikely. The relative contributions to the pitch-angle diffusion coefficient from the cyclotron resonances and Landau resonance due to the different types of waves are evaluated for a typical situation in the solar wind. Since the Landau resonance in this approximation also does not lead to particle reflections, a proper consideration of the nonlinear particle orbits is indeed necessary to overcome the well-known difficulties of quasi-linear scattering theory for cosmic rays near 90 deg pitch angle.

Lee, M. A.↗

NASA NTRS2003

Rapid Acceleration of a Coronal Mass Ejection in the Low Corona and Implications of Propagation

A high-velocity Coronal Mass Ejection (CME) associated with the 2002 April 21 X1.5 flare is studied using a unique set of observations from the Transition Region and Coronal Explorer (TRACE), the Ultraviolet Coronagraph Spectrometer (UVCS), and the Large-Angle Spectrometric Coronagraph (LASCO). The event is first observed as a rapid rise in GOES X-rays, followed by simultaneous conjugate footpoint brightenings connected by an ascending loop or flux-rope feature. While expanding, the appearance of the feature remains remarkably constant as it passes through the TRACE 195 A passband and LASCO fields-of-view, allowing its height-time behavior to be accurately determined. An analytic function, having exponential and linear components, is found to represent the height-time evolution of the CME in the range 1.05-26 R. The CME acceleration rises exponentially to approx. 900 km/sq s within approximately 20-min, peaking at approx.1400 m/sq s when the leading edge is at approx. 1.7 R. The acceleration subsequently falls off as a slowly varying exponential for approx.,90-min. At distances beyond approx. 3.4 R, the height-time profile is approximately linear with a constant velocity of approx. 2400 km/s. These results are briefly discussed in light of recent kinematic models of CMEs.

Gallagher, Peter T.↗

NASA NTRS2002

Controls on Martian Hydrothermal Systems: Application to Valley Network and Magnetic Anomaly Formation

Models of hydrothermal groundwater circulation can quantify limits to the role of hydrothermal activity in Martian crustal processes. We present here the results of numerical simulations of convection in a porous medium due to the presence of a hot intruded magma chamber. The parameter space includes magma chamber depth, volume, aspect ratio, and host rock permeability and porosity. A primary goal of the models is the computation of surface discharge. Discharge increases approximately linearly with chamber volume, decreases weakly with depth (at low geothermal gradients), and is maximized for equant-shaped chambers. Discharge increases linearly with permeability until limited by the energy available from the intrusion. Changes in the average porosity are balanced by changes in flow velocity and therefore have little effect. Water/rock ratios of approximately 0.1, obtained by other workers from models based on the mineralogy of the Shergotty meteorite, imply minimum permeabilities of 10(exp -16) sq m2 during hydrothermal alteration. If substantial vapor volumes are required for soil alteration, the permeability must exceed 10(exp -15) sq m. The principal application of our model is to test the viability of hydrothermal circulation as the primary process responsible for the broad spatial correlation of Martian valley networks with magnetic anomalies. For host rock permeabilities as low as 10(exp -17) sq m and intrusion volumes as low as 50 cu km, the total discharge due to intrusions building that part of the southern highlands crust associated with magnetic anomalies spans a comparable range as the inferred discharge from the overlying valley networks.

Harrison, Keith P.↗

NASA NTRS1986

Circuit transients due to negative bias arcs-II

Two new models of negative-bias arcing on a solar cell power system in Low Earth Orbit are presented. One is an extended, analytical model and the other is a non-linear, numerical model. The models are based on an earlier analytical model in which the interactions between solar cell interconnects and the space plasma as well as the parameters of the power circuit are approximated linearly. Transient voltages due to arcs struck at the negative thermal of the solar panel are calculated in the time domain. The new models treat, respectively, further linear effects within the solar panel load circuit and non-linear effects associated with the plasma interactions. Results of computer calculations with the models show common-mode voltage transients of the electrically floating solar panel struck by an arc comparable to the early model but load transients that differ substantially from the early model. In particular, load transients of the non-linear model can be more than twice as great as those of the early model and more than twenty times as great as the extended, linear model.

Metz, R. N.↗

NASA NTRS2017

On High-Order Upwind Methods for Advection

In the fourth installment of the celebrated series of five papers entitled "Towards the ultimate conservative difference scheme", Van Leer (1977) introduced five schemes for advection, the first three are piecewise linear, and the last two, piecewise parabolic. Among the five, scheme I, which is the least accurate, extends with relative ease to systems of equations in multiple dimensions. As a result, it became the most popular and is widely known as the MUSCL scheme (monotone upstream-centered schemes for conservation laws). Schemes III and V have the same accuracy, are the most accurate, and are closely related to current high-order methods. Scheme III uses a piecewise linear approximation that is discontinuous across cells, and can be considered as a precursor of the discontinuous Galerkin methods. Scheme V employs a piecewise quadratic approximation that is, as opposed to the case of scheme III, continuous across cells. This method is the basis for the on-going "active flux scheme" developed by Roe and collaborators. Here, schemes III and V are shown to be equivalent in the sense that they yield identical (reconstructed) solutions, provided the initial condition for scheme III is defined from that of scheme V in a manner dependent on the CFL number. This equivalence is counter intuitive since it is generally believed that piecewise linear and piecewise parabolic methods cannot produce the same solutions due to their different degrees of approximation. The finding also shows a key connection between the approaches of discontinuous and continuous polynomial approximations. In addition to the discussed equivalence, a framework using both projection and interpolation that extends schemes III and V into a single family of high-order schemes is introduced. For these high-order extensions, it is demonstrated via Fourier analysis that schemes with the same number of degrees of freedom 𝐾 per cell, in spite of the different piecewise polynomial degrees, share the same sets of eigenvalues and thus, have the same stability and accuracy. Moreover, these schemes are accurate to order 2𝐾−1, which is higher than the expected order of 𝐾.

high-order methods↗

NASA NTRS1996

Measurements of Ocean Features With AIRSAR

Here we discuss an indirect approach for measuring ocean features from synthetic aperture radar (SAR) imagery. The approach is based on the refraction of swell that can be seen in the SAR imagery. Locally, swell refraction is due only to changes in bathymetry and surface current shear and it is easy to separate these two effects. It has been shown that linear energetic shears can be detected and measured from high resolution images of the ocean. A simple approach to measuring surface velocity and shear is to divide the imagery into smaller segments where the shear in each segment is approximately linear. The known linear algorithm would then be applied to each segment and the velocity/shear distribution can then be determined by assembling the segments with linear shear into an estimate of the actual shear/velocity distribution.

Sheres, David↗

NASA NTRS1988

Error assessments of widely-used orbit error approximations in satellite altimetry

From simulations, the orbit error can be assumed to be a slowly varying sine wave with a predominant wavelength comparable to the Earth's circumference. Thus, one can derive analytically the error committed in representing the orbit error along a segment of the satellite ground track by a bias; by a bias and tilt (linear approximation); or by a bias, tilt, and curvature (quadratic approximation). The result clearly agrees with what is obvious intuitively, i.e., (1) the fit is better with more parameters, and (2) as the length of the segment increases, the approximation gets worse. But more importantly, it provides a quantitative basis to evaluate the accuracy of past results and, in the future, to select the best approximation according to the required precision and the efficiency of various approximations.

Tai, Chang-Kou↗

NASA NTRS1993

Asteroid orbit determination using Bayesian probabilities

Bayesian a priori and a posteriori probability densities are employed to determine asteroid orbital elements from optical astrometric observations. For near-earth asteroids and Jupiter Trojans, the two-body approximation can yield grossly erroneous uncertainty estimates because of the scattering effect of close planetary encounters or prolonged weak planetary perturbations. For main-belt asteroids, the two-body approximation works efficiently, from which it is inferred that, although the ephemeris must be computed from an integrated orbit, only approximate partial derivatives are needed to attain sufficient accuracy in predicting ephemeris uncertainties. The semimajor and semiminor axes of the 2D 1-sigma sky-plane uncertainty ellipse during the years 1993 to 2005 in the many-body and two-body linear approximations are shown.

Muinonen, Karri↗

NASA NTRS1994

Fractionated martian atmosphere in the nakhlites?

Considerable evidence points to a martian origin of the shergottite-nakhlite-chassignite (SNC) meteorites. Noble gas isotopic compositions have been measured in most SNC meteorites. The Xe-129/Xe-132 vs. Kr-84/Xe-132 ratios in Chassigny, most shergottites, and lithology C of EETA 79001 define a linear array. This array is thought to be a mixing line between martian mantle and martian atmosphere. One of the SNC meteorites, Nakhla, contains a leachable component that has an elevated Xe-129/Xe-132 ratio relative to its Kr-84/Xe-132 ratio when compared to this approximately linear array. The leachable component probably consists in part of iddingsite, an alteration product produced by interaction of olivine with aqueous fluid at temperatures lower than 150 C. The elevated Xe isotopic ratio may represent a distinct reservoir in the martian crust or mantle. More plausibly, it is elementally fractionated martian atmosphere. Formation of sediments fractionates the noble gases in the correct direction. The range of sediment/atmosphere fractionation factors is consistent with the elevated Xe-129/Xe-132 component in Nakhla being contained in iddingsite, a low temperature weathering product. The crystallization age of Nakhla is 1.3 Ga. Its low-shock state suggests that it was ejected from near the surface of Mars. As liquid water is required for the formation of iddingsite, these observations provide further evidence for the near surface existence of aqueous fluids on Mars more recently than 1.3 Ga.

Drake, Michael J.↗

NASA NTRS2017

Comparison of EKF and UKF for Robotic Missions to Mars

The batched Kalman lter works well for a wide variety of orbit determination scenarios but requires linearized approximations to the underlying dynamical system. Furthermore, implementation depends on the computation of partial derivatives for all measurements and parameters used in the lter, a non-trivial task even when analytical derivations are possible. To address these limitations, many extensions and modi - cations to the linear Kalman lter have been proposed over the years since Kalman's initial publication. Our investigation examines two popular variants of the Kalman lter, namely the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF), within the context of spacecraft missions to Mars. The EKF relies on the same mathematical basis as the classic version of the lter, however it sequentially updates the linearization as the ltering process is conducted. In contrast, the UKF is built upon the unscented transform which samples the nearby solution space and numerically propagates perturbed trajectories as part of the update / estimation process. We assess the performance of the ltering algorithms under a variety of mission scenarios with the goal of establishing decision criteria for which implementation to use under di ering circumstances.

Ely, Todd↗

NASA NTRS1993

Possible near-IR channels for remote sensing precipitable water vapor from geostationary satellite platforms

Remote sensing of troposheric water vapor profiles from current geostationary weather satellites is made using a few broadband infrared (IR) channels in the 6-13 micron region. Uncertainties greater than 20% exist in derived water vapor values just above the surface from the IR emission measurements. In this paper, we propose three near-IR channels, one within the 0.94-micron water vapor band absorption region, and the other two in nearby atmospheric windows, for remote sensing of precipitable water vapor over land areas, excluding lakes and rivers, during daytime from future geostationary satellite platforms. The physical principles are as follows. The reflectance of most surface targets varies approximately linearly with wavelength near 1 micron. The solar radiation on the sun-surface-sensor ray path is attenuated by atmospheric water vapor. The ratio of the radiance from the absorption channel with the radiances from the two window channels removes the surface reflectance effects and yields approximately the mean atmospheric water vapor transmittance of the absorption channel. The integrated water vapor amount from ground to space can be obtained with a precision of better than 5% from the mean transmittance. Because surface reflectances vary slowly with time, temporal variation of precipitable water vapor can be determined reliably. High spatial resolution, precipitable water vapor images are derived from spectral data collected by the Airborne Visable-Infrared Imaging Spectrometer, which measures solar radiation reflected by the surface in the 0.4-2.5 micron region in 10-nm channels and has a ground instantaneous field of view of 20 m from its platform on an ER-2 aircraft at 20 km. The proposed near-IR reflectance technique would complement the IR emission techniques for remote sensing of water vapor profiles from geostationary satellite platforms, especially in the boundary layer where most of the water vapor is located.

Gao, B.-C.↗

NASA NTRS1996

DCTune Perceptual Optimization of Compressed Dental X-Rays

In current dental practice, x-rays of completed dental work are often sent to the insurer for verification. It is faster and cheaper to transmit instead digital scans of the x-rays. Further economies result if the images are sent in compressed form. DCTune is a technology for optimizing DCT (digital communication technology) quantization matrices to yield maximum perceptual quality for a given bit-rate, or minimum bit-rate for a given perceptual quality. Perceptual optimization of DCT color quantization matrices. In addition, the technology provides a means of setting the perceptual quality of compressed imagery in a systematic way. The purpose of this research was, with respect to dental x-rays, 1) to verify the advantage of DCTune over standard JPEG (Joint Photographic Experts Group), 2) to verify the quality control feature of DCTune, and 3) to discover regularities in the optimized matrices of a set of images. We optimized matrices for a total of 20 images at two resolutions (150 and 300 dpi) and four bit-rates (0.25, 0.5, 0.75, 1.0 bits/pixel), and examined structural regularities in the resulting matrices. We also conducted psychophysical studies (1) to discover the DCTune quality level at which the images became 'visually lossless,' and (2) to rate the relative quality of DCTune and standard JPEG images at various bitrates. Results include: (1) At both resolutions, DCTune quality is a linear function of bit-rate. (2) DCTune quantization matrices for all images at all bitrates and resolutions are modeled well by an inverse Gaussian, with parameters of amplitude and width. (3) As bit-rate is varied, optimal values of both amplitude and width covary in an approximately linear fashion. (4) Both amplitude and width vary in systematic and orderly fashion with either bit-rate or DCTune quality; simple mathematical functions serve to describe these relationships. (5) In going from 150 to 300 dpi, amplitude parameters are substantially lower and widths larger at corresponding bit-rates or qualities. (6) Visually lossless compression occurs at a DCTune quality value of about 1. (7) At 0.25 bits/pixel, comparative ratings give DCTune a substantial advantage over standard JPEG. As visually lossless bit-rates are approached, this advantage of necessity diminishes. We have concluded that DCTune optimized quantization matrices provide better visual quality than standard JPEG. Meaningful quality levels may be specified by means of the DCTune metric. Optimized matrices are very similar across the class of dental x-rays, suggesting the possibility of a 'class-optimal' matrix. DCTune technology appears to provide some value in the context of compressed dental x-rays.

Watson, Andrew B.↗

NASA NTRS1977

Extreme ultraviolet spectrograph ATM experiment S082B

The extreme-ultraviolet double-dispersion photographic spectrograph for the Apollo Telescope Mount (ATM) experiment S082B on Skylab is described. Novel features were the use of a predisperser grating with a ruling whose spacing varied approximately linearly with distance for the purpose of increasing the instrument speed by reducing the astigmatism and a photoelectric servosystem to stabilize to 1 sec of arc the solar image at various near-limb positions. The 970-3940-A range was covered in two sections with effective resolving power of approximately 30,000 from 1100 A to 1970 A. The spatial resolution was 2 x 60 solar sec of arc. During the Skylab mission 6400 exposures were made with the instrument pointed by an astronaut at selected and recorded solar positions.

Bartoe, J.-D. F.↗

NASA NTRS1979

Comparison of inlet suppressor data with approximate theory based on cutoff ratio

Inlet suppressor far-field directivity suppression was quantitatively compared with that predicted using an approximate linear design and evaluation method based upon mode cutoff ratio. The experimental data was obtained using a series of cylindrical point-reacting inlet liners on a YF102 engine. The theoretical prediction program is based upon simplified sound propagation concepts derived from exact calculations. These indicate that all of the controlling phenomenon can be approximately correlated with mode cutoff ratio which itself is intimately related to the angles of propagation within the duct. The theory-data comparisons are intended to point out possible deficiencies in the approximate theory which may be corrected. After all theoretical refinements are made, then empirical corrections can be applied.

Rice, E. J.↗

NASA NTRS1994

Age as a diagnostic of stratospheric transport

Estimates of stratospheric age from observations of long-lived trace gases with increasing tropospheric concentrations invoke the implicit assumption that an air parcel has been transported intact from the tropopical tropopause. However, because of rapid and irreversible mixing in the stratosphere, a particular air parcel cannot be identified with one that left the troposphere at some prior time. The parcel contains a mix of air with a range of transit times, and the mean value over this range is the most appropriate definition of age. The measured tracer concentration is also a mean over the parcel, but its value depends both on the transit time distribution and the past history of the tracer in the troposphere. In principle, only if the tropospheric concentration is increasing linearly can the age be directly inferred. We illustrate these points by employing both a one-dimensional diffusive analog of stratospheric transport, and the general circulation model (GCM) of the Goddard Institute for Space Studies (GISS). Within the limits of the GCM, we estimate the time over which tropospheric tracer concentrations must be approximately linear in order to determine stratospheric age unambiguously; the concentration of an exponentially increasing tracer is a function only of age if the growth time constant is greater than about 7 years, which is true for all the chlorofluorocarbons. More rapid source variations (for example, the annual cycle in CO2) have no such direct relationship with age.

Hall, Timothy M.↗