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NASA NTRS1976

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

South, J. C., Jr.↗

NASA NTRS1981

Use of MAGSAT anomaly data for crustal structure and mineral resources in the US Midcontinent

The analysis and preliminary interpretation of investigator-B MAGSAT data are addressed. The data processing included: (1) removal of spurious data points; (2) statistical smoothing along individual data tracks, to reduce the effect of geomagnetic transient disturbances; (3) comparison of data profiles spatially coincident in track location but acquired at different times; (4) reduction of data by weighted averaging to a grid with 1 deg xl deg latitude/longitude spacing, and with elevations interpolated and weighted to a common datum of 400 km; (5) wavelength filtering; and (6) reduction of the anomaly map to the magnetic pole. Agreement was found between a magnitude data anomaly map and a reduce-to-the-pole map supporting the general assumption that, on a large scale (long wavelength), it is induced crustal magnetization which is responsible for major anamalies. Anomalous features are identified and explanations are suggested with regard to crustal structure, petrologic characteristics, and Curie temperature isotherms.

Carmichael, R. S.↗

NASA NTRS1982

Cloud fluctuation statistics

A space-time statistical analysis of total outgoing infrared radiation is used to determine the gross features of day-to-day cloudiness fluctuations over the Pacific Ocean in summer and winter. IR fluctuations arise from the passage of cloudiness systems through a grid box as well as the creation and destruction of cloudiness in the box. Which process dominates depends upon the size of the box relative to the size, speed and persistence time of a typical cloudiness system. In most regions the statistical analysis yields advection speeds characteristic of 700 mb mean flow with spatial dependence resembling the 300 mb mean flow. Spatial scales less than 2000 km predominate, smaller scales having less persistence. Characteristic time scales are on the order of one or two days, even for a grid box spanning the entire North Pacific storm track. This result is remarkable in view of the much longer time scales commonly associated with atmospheric disturbances. Apparently many cloudiness systems are created and destroyed during the lifetime of a single disturbance.

Cahalan, R. F.↗

NASA NTRS1990

Two-dimensional Euler and Navier-Stokes Time accurate simulations of fan rotor flows

Two numerical methods are presented which describe the unsteady flow field in the blade-to-blade plane of an axial fan rotor. These methods solve the compressible, time-dependent, Euler and the compressible, turbulent, time-dependent, Navier-Stokes conservation equations for mass, momentum, and energy. The Navier-Stokes equations are written in Favre-averaged form and are closed with an approximate two-equation turbulence model with low Reynolds number and compressibility effects included. The unsteady aerodynamic component is obtained by superposing inflow or outflow unsteadiness to the steady conditions through time-dependent boundary conditions. The integration in space is performed by using a finite volume scheme, and the integration in time is performed by using k-stage Runge-Kutta schemes, k = 2,5. The numerical integration algorithm allows the reduction of the computational cost of an unsteady simulation involving high frequency disturbances in both CPU time and memory requirements. Less than 200 sec of CPU time are required to advance the Euler equations in a computational grid made up of about 2000 grid during 10,000 time steps on a CRAY Y-MP computer, with a required memory of less than 0.3 megawords.

Boretti, A. A.↗

DOE OSTI2026

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

This paper is the basis for a presentation help at the 2026 Georgia Tech Fault & Disturbance Analysis Conference, which can be found at OSTI # 3168287 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danovo Energy Solutions]↗

DOE OSTI2022

Security Enhancements for Distributed Energy Resource Systems Interconnected with Distribution Networks: Final Technical Report

The revised IEEE 1547 Standard defines new complex communication-adjustable voltage and frequency regulation and ride-through characteristics, while maintaining the general antiislanding requirement for unintentional islanding situations. Unintentional islanding is prohibited while intentional islanding is specifically allowed, thus effectively enabling microgrid operation mode. Further, IEEE 1547-2018 Standard introduces new requirements in terms of interoperability so that the DER plant/circuit segments may be seamlessly integrated with the utility networks but at the same time become vulnerable to a cyber-attack. Traditional cybersecurity measures including encryption, authentication and role-based access control may not be fully implementable to all communication protocols specified in the IEEE 1547 Standard. Therefore, in this project we have identified, researched, implemented and tested several cyberphysical approaches that rely mostly on the behavior of the DER circuit and may help with validating the incoming command and control action potentially coming through an insecure communications channel. Additionally, we have built semantic models and communications profiles for DER facilities and have implemented lightweight IEC 61850 based publisher-subscriber GOOSE messaging mechanism, with security extensions in terms of authentication and encryption. The project proposed information models for integration into UCA OpenFMB 2.0 profiles focusing on grid code compliance.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Background Information on the Protection Requirements in IEEE Std 1547-2018

As the DER penetration level has risen significantly in recent times, parameter settings and configuration of installed DERs are having direct impact on local electric distribution utilities as well as bulk power systems during normal and abnormal grid conditions. On the other hand, all grid-connected DERs in the United States of America must conform to the interconnection requirements prescribed in the IEEE Std 1547-2018. Because of these reasons, it is crucial to understand the expected DER performance during abnormal grid conditions considering the requirements of the IEEE Std 1547-2018. The aim of this document is twofold: (1) to summarize requirements in IEEE Std 1547-2018 having direct implications in distribution network protection, and (2) to provide the reader with knowledge and information that will be required for users to apply the requirements specified. Since the focus of this document is on distribution network protection in the presence of DERs, it is assumed that the readers have basic understanding of distribution network protection as well as working principles of DERs. This document starts with a brief introduction on protection systems for distribution network followed by a discussion on the impact of DER on the protection systems. Current practices to provide network protection in the presence of DER is briefly discussed. The document then explores the DER performance requirements in IEEE Std. 1547-2018; especially on those related to distribution network protection. Section 6.1 in IEEE Std. 1547-2018 provides an overview of capabilities and control requirements for DER under abnormal operating conditions. This section also introduces abnormal operating performance categories I, II, III. The DER response to various types of faults and grid conditions such as short-circuit faults and open phase conditions are discussed in section 6.2 in the standard while requirements for coordination with the Area EPS reclosing scheme are provided in section 6.3. Section 6.4 in the IEEE Std 1547-2018 specifies requirements for mandatory voltage tripping and ride-through requirements during low and high voltage disturbances and section 6.5 specifies similar requirements for low and high frequency disturbances. IEEE Std. 1547 requires that the conformance of the DERs to IEEE Std 1547-2018 requirements should be verified in accordance with IEEE Std. 1547. 1. There are several parameters and settings of DERs that need to be properly selected for reliable operation during abnormal grid condition while applying the requirements of IEEE Std 1547-2018. Key decisions for proper selections of parameter and settings are: 1. Determination of required DER abnormal operating performance category, 2. Determination of DER response (shall trip) to abnormal voltages and 3. Determination of DER response (shall trip) to abnormal frequency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Comparison of Power System Current Sensors via Playback of Electrical Disturbances

The need to accurately measure high-frequency content in power system voltage and current phenomena is increasingly becoming more of a priority. As the amount of distributed energy resources (DER) and nonlinear loads penetrating the grid increases, so do challenges associated with traditional measurement and metering applications. In this paper, three commercially-available medium-voltage-level current sensors are characterized in terms of their harmonic amplitude and phase performance against reference signals that are “played back” through the sensors through the use of an arbitrary waveform generator. It is shown that none of the three sensors studied are able to faithfully replicate all of the input signals completely, though there are advantages and disadvantages to each in terms of noise, resonance, and induced phase drift. Additionally, the Goodness-of-Fit metric, typically used for PMU model validation, is used to generate side-by-side comparisons of sensor accuracy over a small window around the events under study.

Wilson, Aaron↗

NASA NTRS2002

Development of Computational Aeroacoustics Code for Jet Noise and Flow Prediction

Accurate prediction of jet fan and exhaust plume flow and noise generation and propagation is very important in developing advanced aircraft engines that will pass current and future noise regulations. In jet fan flows as well as exhaust plumes, two major sources of noise are present: large-scale, coherent instabilities and small-scale turbulent eddies. In previous work for the NASA Glenn Research Center, three strategies have been explored in an effort to computationally predict the noise radiation from supersonic jet exhaust plumes. In order from the least expensive computationally to the most expensive computationally, these are: 1) Linearized Euler equations (LEE). 2) Very Large Eddy Simulations (VLES). 3) Large Eddy Simulations (LES). The first method solves the linearized Euler equations (LEE). These equations are obtained by linearizing about a given mean flow and the neglecting viscous effects. In this way, the noise from large-scale instabilities can be found for a given mean flow. The linearized Euler equations are computationally inexpensive, and have produced good noise results for supersonic jets where the large-scale instability noise dominates, as well as for the tone noise from a jet engine blade row. However, these linear equations do not predict the absolute magnitude of the noise; instead, only the relative magnitude is predicted. Also, the predicted disturbances do not modify the mean flow, removing a physical mechanism by which the amplitude of the disturbance may be controlled. Recent research for isolated airfoils' indicates that this may not affect the solution greatly at low frequencies. The second method addresses some of the concerns raised by the LEE method. In this approach, called Very Large Eddy Simulation (VLES), the unsteady Reynolds averaged Navier-Stokes equations are solved directly using a high-accuracy computational aeroacoustics numerical scheme. With the addition of a two-equation turbulence model and the use of a relatively coarse grid, the numerical solution is effectively filtered into a directly calculated mean flow with the small-scale turbulence being modeled, and an unsteady large-scale component that is also being directly calculated. In this way, the unsteady disturbances are calculated in a nonlinear way, with a direct effect on the mean flow. This method is not as fast as the LEE approach, but does have many advantages to recommend it; however, like the LEE approach, only the effect of the largest unsteady structures will be captured. An initial calculation was performed on a supersonic jet exhaust plume, with promising results, but the calculation was hampered by the explicit time marching scheme that was employed. This explicit scheme required a very small time step to resolve the nozzle boundary layer, which caused a long run time. Current work is focused on testing a lower-order implicit time marching method to combat this problem.

Keith, Theo G., Jr.↗

DOE OSTI2025

Virtual Self-Excited Induction Generator-Based Grid-Forming Inverter Control for Robust Voltage Regulation Under Nonideal Loading

This paper presents a generator-inspired control methodology for grid-forming (GFM) inverters that deliberately emulates a self-excited induction generator so that the inverter can hold its voltage and frequency under difficult loading and severe terminal disturbances across wide voltage and frequency ranges. The design integrates a Lyapunov energy function-based inner loop to provide high bandwidth and strong disturbance rejection, and it complements this with a passivity-based argument that furnishes a coherent large-signal stability guarantee beyond small-signal limits. Analytical insights are developed via the Krylov-Bogoliubov-Mitropolsky averaging method, which reveals an intrinsic resistive droop characteristic; these closed-form relations both explain the observed dynamics and yield simple, decentralized tuning rules. The methodology is validated on a controller-hardware-in-the-loop platform and exercised in real time across balanced, unbalanced, and nonlinear loads, as well as during parallel operation. Across these scenarios, the inverter maintains balanced three-phase voltages, limits harmonic content, settles quickly with well-damped transients, and remains resilient when multiple units operate in parallel. The contributions are a self-excited-machine-inspired GFM controller with enhanced dynamic performance and robustness, a single stability rationale grounded in passivity, closed-form expressions that guide tuning, and comprehensive hardware-in-the-loop validations demonstrating effectiveness and superiority under challenging operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

A high resolution, gridded product for vapor pressure deficit using Daymet

Vapor pressure deficit (VPD) is a critical variable in assessing drought conditions and evaluating plant water stress. Gridded products of global and regional VPD are not freely available from satellite remote sensing, model reanalysis, or ground observation datasets. We present two versions of the first gridded VPD product for the Continental US and parts of Northern Mexico and Southern Canada (CONUS+) at a 1 km spatial resolution and daily time step. We derived VPD from Daymet maximum daily temperature and average daily vapor pressure and scale the estimates based on (1) climate determined by the Köppen-Geiger classifications and (2) land cover determined by the International Geosphere-Biosphere Programme. Ground-based VPD data from 253 AmeriFlux sites representing different climate and land cover classifications were used to improve the Daymet-derived VPD estimates for every pixel in the CONUS+ grid to produce the final datasets. We evaluated the Daymet-derived VPD against independent observations and reanalysis data. The CONUS+ VPD datasets will aid in investigating disturbances including drought and wildfire, and informing land management strategies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Frequency Control and Dynamics (Part 1) [Slides]

This presentation provides an introductory overview of system dynamics and frequency control in electric power systems, with a focus on concepts relevant to small and interconnected grids such as those in Malawi. It explains foundational principles of AC system frequency, the relationship between generation-demand balance and frequency deviations, and the operational limits of generators and end-use equipment. The deck discusses frequency stability within broader system stability classifications and illustrates how inertia and turbine-governor dynamics shape system response to disturbances. It then outlines the tiered approach to frequency control - primary, secondary, and tertiary - detailing the roles, characteristics, timescales, and response mechanisms of each. Special emphasis is placed on hydro and thermal unit behavior, area control error (ACE), automatic generation control (AGC), and the operational implications of interconnecting small systems with larger grids. The material was developed to support Malawi's electricity sector and the establishment of the Southern Africa Battery Energy Storage Center of Excellence (SABESS CoE).

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Frequency Control and Dynamics (Part 2) [Slides]

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events

Danovo Energy Solution's presented its paper named: Feature-Based PMU Event Classification under Variable PMU Participation and Overlapping Events at the 2026 Georgia Tech Fault & Disturbance Analysis Conference. The full paper can be found at OSTI ID# 3169150 Paper Abstract—Phasor Measurement Units (PMUs) stream time synchronized, high-resolution measurements from the grid, enabling data-driven techniques for event detection and classification. Accurate event classification improves grid reliability and stability. Events can be detected by varying numbers of PMUs and exhibit different durations depending on the event type. This variability challenges standard classifiers that require uniform input sizes. Moreover, multiple events may coincide, which increases classification complexity. Standard classifiers assign each instance to the class with the highest predicted probability, whereas overlapping events may exhibit comparable probabilities across multiple classes. In this study, to handle data size variability, we extract a wide range of time–frequency domain features from all available PMUs for each event into a fixed-length vector, facilitating the application of standard machine learning classifiers, including Random Forest, XGBoost, LightGBM, Support Vector Machine, and Multilayer Perceptron. To account for overlapping events, a probabilistic post-processing step is applied. For a given data instance, if multiple predicted class probabilities exceed 30% and the differences between them are less than 10%, the event is assigned to multiple classes. Experiments using real-world PMU data demonstrate that the Random Forest and XGBoost models achieve the highest accuracy, while the proposed post-processing method yields perfect classification performance on external unseen test sets.

Nematirad, Reza [Danova Energy Solutions]↗

NASA NTRS2009

Conical-Domain Model for Estimating GPS Ionospheric Delays

The conical-domain model is a computational model, now undergoing development, for estimating ionospheric delays of Global Positioning System (GPS) signals. Relative to the standard ionospheric delay model described below, the conical-domain model offers improved accuracy. In the absence of selective availability, the ionosphere is the largest source of error for single-frequency users of GPS. Because ionospheric signal delays contribute to errors in GPS position and time measurements, satellite-based augmentation systems (SBASs) have been designed to estimate these delays and broadcast corrections. Several national and international SBASs are currently in various stages of development to enhance the integrity and accuracy of GPS measurements for airline navigation. In the Wide Area Augmentation System (WAAS) of the United States, slant ionospheric delay errors and confidence bounds are derived from estimates of vertical ionospheric delay modeled on a grid at regularly spaced intervals of latitude and longitude. The estimate of vertical delay at each ionospheric grid point (IGP) is calculated from a planar fit of neighboring slant delay measurements, projected to vertical using a standard, thin-shell model of the ionosphere. Interpolation on the WAAS grid enables estimation of the vertical delay at the ionospheric pierce point (IPP) corresponding to any arbitrary measurement of a user. (The IPP of a given user s measurement is the point where the GPS signal ray path intersects a reference ionospheric height.) The product of the interpolated value and the user s thin-shell obliquity factor provides an estimate of the user s ionospheric slant delay. Two types of error that restrict the accuracy of the thin-shell model are absent in the conical domain model: (1) error due to the implicit assumption that the electron density is independent of the azimuthal angle at the IPP and (2) error arising from the slant-to-vertical conversion. At low latitudes or at mid-latitudes under disturbed conditions, the accuracy of SBAS systems based upon the thin-shell model suffers due to the presence of complex ionospheric structure, high delay values, and large electron density gradients. Interpolation on the vertical delay grid serves as an additional source of delay error. The conical-domain model permits direct computation of the user s slant delay estimate without the intervening use of a vertical delay grid. The key is to restrict each fit of GPS measurements to a spatial domain encompassing signals from only one satellite. The conical domain model is so named because each fit involves a group of GPS receivers that all receive signals from the same GPS satellite (see figure); the receiver and satellite positions define a cone, the satellite position being the vertex. A user within a given cone evaluates the delay to the satellite directly, using (1) the IPP coordinates of the line of sight to the satellite and (2) broadcast fit parameters associated with the cone. The conical-domain model partly resembles the thin-shell model in that both models reduce an inherently four-dimensional problem to two dimensions. However, unlike the thin-shell model, the conical domain model does not involve any potentially erroneous simplifying assumptions about the structure of the ionosphere. In the conical domain model, the initially four-dimensional problem becomes truly two-dimensional in the sense that once a satellite location has been specified, any signal path emanating from a satellite can be identified by only two coordinates; for example, the IPP coordinates. As a consequence, a user s slant-delay estimate converges to the correct value in the limit that the receivers converge to the user s location (or, equivalently, in the limit that the measurement IPPs converge to the user s IPP).

Sparks, Lawrence↗

NASA NTRS2018

Vegetation Change Detection in Southern California Solar Energy Developments

Change detection from satellite sensor vegetation indices (VIs) presents an opportunity to monitor trends and disturbances at the regional scale for southern California's Mojave and Lower Colorado Deserts. Renewable energy sites are being constructed in this region on public lands under the Bureau of Land Management (BLM). We have developed a framework for VI change detection over the past two decades, with initial focus on three sites, Joshua Tree National Park, Mojave National Preserve, and a proximal group of Development Focus Areas (DFAs), for comparison between protected and development-targeted lands. Three Terra MODIS VIs (normalized difference [NDVI], enhanced [EVI], soil-adjusted [SAVI]) were evaluated in the Breaks for Additive Season and Trend (BFAST) setting for the regional MODIS 250-m resolution grid to estimate significant time series shifts (breakpoints) from February 2000 to May 2018. All three VIs tended to detect the maximum number of breakpoints at a grid location, but cross-correlations with precipitation and comparison with timing of wildfire burns near the study sites for breakpoint density (proportion of area with a breakpoint) showed that NDVI had the strongest response to these major disturbances, supporting its use for subsequent analysis. Time series of NDVI breakpoint change densities for individual solar energy sites did not have a consistent vegetation response following construction. Bootstrapping showed that the DFAs had significantly larger kurtosis and variance in the positive NDVI breakpoint distribution than did the protected sites, but there was no significant difference in the negative distribution for all three sites. The inconsistent post-construction NDVI signal and the large number of breakpoints overall suggested that the largest changes in vegetation cover density were tied to seasonal precipitation amounts. The distributional results indicated that existing site-specific conditions were the main control on VI responses, given the history of human disturbances in the DFAs. Although the results do not support persistent VI disturbances resulting from recent solar energy development, continued monitoring and examination of other ecological variables and surface temperatures will be vital to the long-term protection of this desert environment.

Potter, Christopher S.↗

DOE OSTI2022

Simulation and Postmortem Analysis of Angeles Forest Disturbance Event

Multiple unexpected solar photovoltaic (PV) plant responses in the California region following contingencies in recent years warrant postmortem analysis leveraging digital fault recorder (DFR) data for a better understanding of such events and preventing similar events in the future. Most utilities in US, in general, possess transient stability (TS) phasor-domain models of the power grid. Since traditional phasor-based transient stability planning models cannot perform such analysis, this paper presents an approach to extract a region of such models and convert it to Electromagnetic transient (EMT) models. The approach is based on the determination of the minimum impedance-weighted spanning tree between the fault location and affected PV plants in a Western Electricity Coordinating Council (WECC) planning model followed by conversion of this region into an EMT model. The accuracy of the proposed approach is validated against DFR records obtained from the 2018 Angeles Forest disturbance event.

Samanta, Sayan↗

DOE OSTI2024

Stability-Constrained Learning for Frequency Regulation in Power Grids With Variable Inertia

The increasing penetration of converter-based renewable generation has resulted in faster frequency dynamics, and low and variable inertia. As a result, there is a need for frequency control methods that are able to stabilize a disturbance in the power system at timescales comparable to the fast converter dynamics. This paper proposes a combined linear and neural network controller for inverter-based primary frequency control that is stable at time-varying levels of inertia. We model the time-variance in inertia via a switched affine hybrid system model. We derive stability certificates for the proposed controller via a quadratic candidate Lyapunov function. We test the proposed control on a 12-bus 3-area test network, and compare its performance with a base case linear controller, optimized linear controller, and finite-horizon Linear Quadratic Regulator (LQR). Our proposed controller achieves faster mean settling time and over 50% reduction in average control cost across 100 inertia scenarios compared to the optimized linear controller. Unlike LQR which requires complete knowledge of the inertia trajectories and system dynamics over the entire control time horizon, our proposed controller is real-time tractable, and achieves comparable performance to LQR.

data-driven control↗