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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.

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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

HARD: A performance portable radiation hydrodynamics code based on FleCSI framework

Hydrodynamics And Radiation Diffusion (HARD) is an open-source application for high-performance simulations of compressible hydrodynamics with radiation-diffusion coupling. Built on the FleCSI (Bergen et al., 2021 [1]) (Flexible Computational Science Infrastructure) framework, HARD expresses its computational units as tasks whose execution can be orchestrated by multiple back-end runtimes, including Legion (Bauer et al., 2012 [2]), MPI (Forum, 1994 [3]), and HPX (Kaiser et al., 2020 [4]). Node-level parallelism is handled through Kokkos (Edwards et al., 2014 [5]), providing a single-source, portable code base that runs efficiently on laptops, small homogeneous clusters, and the largest heterogeneous supercomputers currently available. To ensure scientific reliability, HARD includes a regression test suite that automatically reproduces canonical verification problems such as the Sod and LeBlanc shock tubes, and the Sedov blast wave, comparing numerical solutions against known analytical results. The project is distributed under an OSI-approved license, hosted on GitHub, and accompanied by reproducible build scripts and continuous integration workflows. This combination of performance portability, verification infrastructure, and community-focused development makes HARD a sustainable platform for advancing radiation hydrodynamics research across multiple domains.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2010

Metrics for Offline Evaluation of Prognostic Performance

Prognostic performance evaluation has gained significant attention in the past few years. Currently, prognostics concepts lack standard definitions and suffer from ambiguous and inconsistent interpretations. This lack of standards is in part due to the varied end-user requirements for different applications, time scales, available information, domain dynamics, etc. to name a few. The research community has used a variety of metrics largely based on convenience and their respective requirements. Very little attention has been focused on establishing a standardized approach to compare different efforts. This paper presents several new evaluation metrics tailored for prognostics that were recently introduced and were shown to effectively evaluate various algorithms as compared to other conventional metrics. Specifically, this paper presents a detailed discussion on how these metrics should be interpreted and used. These metrics have the capability of incorporating probabilistic uncertainty estimates from prognostic algorithms. In addition to quantitative assessment they also offer a comprehensive visual perspective that can be used in designing the prognostic system. Several methods are suggested to customize these metrics for different applications. Guidelines are provided to help choose one method over another based on distribution characteristics. Various issues faced by prognostics and its performance evaluation are discussed followed by a formal notational framework to help standardize subsequent developments.

Saxena, Abhinav↗
DOE OSTI2026

Poisson-response Tensor-on-Tensor Regression and Applications

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed of counts are common data in fields such as inter national relations, social networks, epidemiology, and medical imaging, where events occur across multiple dimensions like time, location, and dyads. PToTR accommodates such tensor responses alongside tensor covariates, providing a versatile tool for multi dimensional data analysis. We propose algorithms for maximum likelihood estimation under a canonical polyadic (CP) structure on the regression coefficient tensor that satisfy the positivity of Poisson parameters and then provide an initial theoretical error analysis for PToTR estimators. We also demonstrate the utility of PToTR through three concrete applications: longitudinal data analysis of the Integrated Crisis Early Warning System database, positron emission tomography (PET) image reconstruction, and change-point detection of communication patterns in longitudinal dyadic data. These applications highlight the versatility of PToTR in addressing complex, structured count data across various domains.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Real-Time Lifetime Prediction of Semiconductor Devices Using Hardware-in-the-Loop

This paper presents a unique approach to enable real-time lifespan prediction of semiconductor power modules using a Hardware-in-the-Loop (HIL) system. By integrating the module's overall loss characteristics-specifically switching and conduction losses-with a thermoelectric model of the thermal management system, this research demonstrates that the model can dynamically estimates the junction temperature profile of the semiconductor devices in response to a changing torque demand profile for the motor drive system. This capability enables continuous monitoring of the module's operational time and cumulative stress induced on the devices to compute accumulated remaining lifetime or time-to-failure (TTF). This study provides an architectural framework for the HIL system with high-fidelity component models of multiple physical domains, allowing simulation of dynamic behaviors of a closely-coupled motor drive system. The advanced real-time computation and measurement functionalities of the HIL system allow for both dynamic lifetime calculations based on simulated data and aggregate lifetime predictions utilizing historical data. Moreover, this paper details an algorithm that not only computes cumulative damage but also synthesizes these data into a comprehensive aggregated lifetime metric. This methodology can enhance the maintenance scheduling strategies and operational reliability of semiconductor devices in critical applications, ultimately extending their service life while optimizing performance.

hardware-in-the-loop (HIL)↗
NASA NTRS2011

Numerical Solution of the Radiative Transfer Equation: X-Ray Spectral Formation from Cylindrical Accretion onto a Magnetized Neutron Star

Predicting the emerging X-ray spectra in several astrophysical objects is of great importance, in particular when the observational data are compared with theoretical models. This requires developing numerical routines for the solution of the radiative transfer equation according to the expected physical conditions of the systems under study. Aims. We have developed an algorithm solving the radiative transfer equation in the Fokker-Planck approximation when both thermal and bulk Comptonization take place. The algorithm is essentially a relaxation method, where stable solutions are obtained when the system has reached its steady-state equilibrium. Methods. We obtained the solution of the radiative transfer equation in the two-dimensional domain defined by the photon energy E and optical depth of the system pi using finite-differences for the partial derivatives, and imposing specific boundary conditions for the solutions. We treated the case of cylindrical accretion onto a magnetized neutron star. Results. We considered a blackbody seed spectrum of photons with exponential distribution across the accretion column and for an accretion where the velocity reaches its maximum at the stellar surface and at the top of the accretion column, respectively. In both cases higher values of the electron temperature and of the optical depth pi produce flatter and harder spectra. Other parameters contributing to the spectral formation are the steepness of the vertical velocity profile, the albedo at the star surface, and the radius of the accretion column. The latter parameter modifies the emerging spectra in a specular way for the two assumed accretion profiles. Conclusions. The algorithm has been implemented in the XPEC package for X-ray fitting and is specifically dedicated to the physical framework of accretion at the polar cap of a neutron star with a high magnetic field (approx > 10(exp 12) G). This latter case is expected to be of typical accreting systems such as X-ray pulsars and supergiant fast X ray transients.

Fairnelli, R.↗
NASA NTRS1998

Instrument Remote Control via the Astronomical Instrument Markup Language

The Instrument Remote Control (IRC) project ongoing at NASA's Goddard Space Flight Center's (GSFC) Information Systems Center (ISC) supports NASA's mission by defining an adaptive intranet-based framework that provides robust interactive and distributed control and monitoring of remote instruments. An astronomical IRC architecture that combines the platform-independent processing capabilities of Java with the power of Extensible Markup Language (XML) to express hierarchical data in an equally platform-independent, as well as human readable manner, has been developed. This architecture is implemented using a variety of XML support tools and Application Programming Interfaces (API) written in Java. IRC will enable trusted astronomers from around the world to easily access infrared instruments (e.g., telescopes, cameras, and spectrometers) located in remote, inhospitable environments, such as the South Pole, a high Chilean mountaintop, or an airborne observatory aboard a Boeing 747. Using IRC's frameworks, an astronomer or other scientist can easily define the type of onboard instrument, control the instrument remotely, and return monitoring data all through the intranet. The Astronomical Instrument Markup Language (AIML) is the first implementation of the more general Instrument Markup Language (IML). The key aspects of our approach to instrument description and control applies to many domains, from medical instruments to machine assembly lines. The concepts behind AIML apply equally well to the description and control of instruments in general. IRC enables us to apply our techniques to several instruments, preferably from different observatories.

Sall, Ken↗
NASA NTRS2010

Sources of Uncertainty in Predicting Land Surface Fluxes Using Diverse Data and Models

In the domain of predicting land surface fluxes, models are used to bring data from large observation networks and satellite remote sensing together to make predictions about present and future states of the Earth. Characterizing the uncertainty about such predictions is a complex process and one that is not yet fully understood. Uncertainty exists about initialization, measurement and interpolation of input variables; model parameters; model structure; and mixed spatial and temporal supports. Multiple models or structures often exist to describe the same processes. Uncertainty about structure is currently addressed by running an ensemble of different models and examining the distribution of model outputs. To illustrate structural uncertainty, a multi-model ensemble experiment we have been conducting using the Terrestrial Observation and Prediction System (TOPS) will be discussed. TOPS uses public versions of process-based ecosystem models that use satellite-derived inputs along with surface climate data and land surface characterization to produce predictions of ecosystem fluxes including gross and net primary production and net ecosystem exchange. Using the TOPS framework, we have explored the uncertainty arising from the application of models with different assumptions, structures, parameters, and variable definitions. With a small number of models, this only begins to capture the range of possible spatial fields of ecosystem fluxes. Few attempts have been made to systematically address the components of uncertainty in such a framework. We discuss the characterization of uncertainty for this approach including both quantifiable and poorly known aspects.

Dungan, Jennifer L.↗
NASA NTRS2020

Evaluating Precipitation Features and Rainfall Characteristics in a Multi‐Scale Modeling Framework

Cloud and precipitation systems are simulated with a multi‐scale modeling framework (MMF) and compared over the Tropics and Subtropics against the Tropical Rainfall Measuring Mission (TRMM) Radar‐defined Precipitation Features (RPFs) product. A methodology, in close analogy to the TRMM RPFs, is developed to produce simulated precipitation features (PFs) from the output of the embedded two‐dimensional (2D) cloud‐resolving models (CRMs) within an MMF. Despite the limitations of 2D CRMs, the simulated population distribution, horizontal and vertical structure of PFs, and the geographical location and local rainfall contribution of mesoscale convective systems (MCSs) are in good agreement with the TRMM observations. However, some model discrepancies are found and can be identified and quantified within the PF distributions. Using model biases in relative population and rainfall contributions, PFs can be characterized into four size categories: small, medium to large, very large, and extremely large. Four different major mechanisms might account for the model biases in each different category: (1) the two‐dimensionality of the CRMs, (2) a positive convection‐wind‐evaporation feedback loop, (3) an artificial dynamic constraint in a bounded CRM domain with cyclic boundaries, and (4) the limited CRM domain size. The second and fourth mechanisms tend to contribute to the excessive tropical precipitation biases commonly found in most MMFs, whereas the other mechanisms reduce rainfall contributions from small and very large PFs. MMF sensitivity experiments with various CRM domain sizes and grid spacings showed that larger domains (higher resolutions) tend to shift PF populations toward larger (smaller) sizes.

Jiun-Dar Chern↗
DOE OSTI2025

Tailoring composition and deformation modes at the microstructural level for next generation low-cost high-strength austenitic stainless steels

The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.

08 HYDROGEN↗
NASA NTRS2013

Downscaling Satellite Precipitation with Emphasis on Extremes: A Variational 1-Norm Regularization in the Derivative Domain

The increasing availability of precipitation observations from space, e.g., from the Tropical Rainfall Measuring Mission (TRMM) and the forthcoming Global Precipitation Measuring (GPM) Mission, has fueled renewed interest in developing frameworks for downscaling and multi-sensor data fusion that can handle large data sets in computationally efficient ways while optimally reproducing desired properties of the underlying rainfall fields. Of special interest is the reproduction of extreme precipitation intensities and gradients, as these are directly relevant to hazard prediction. In this paper, we present a new formalism for downscaling satellite precipitation observations, which explicitly allows for the preservation of some key geometrical and statistical properties of spatial precipitation. These include sharp intensity gradients (due to high-intensity regions embedded within lower-intensity areas), coherent spatial structures (due to regions of slowly varying rainfall),and thicker-than-Gaussian tails of precipitation gradients and intensities. Specifically, we pose the downscaling problem as a discrete inverse problem and solve it via a regularized variational approach (variational downscaling) where the regularization term is selected to impose the desired smoothness in the solution while allowing for some steep gradients(called 1-norm or total variation regularization). We demonstrate the duality between this geometrically inspired solution and its Bayesian statistical interpretation, which is equivalent to assuming a Laplace prior distribution for the precipitation intensities in the derivative (wavelet) space. When the observation operator is not known, we discuss the effect of its misspecification and explore a previously proposed dictionary-based sparse inverse downscaling methodology to indirectly learn the observation operator from a database of coincidental high- and low-resolution observations. The proposed method and ideas are illustrated in case studies featuring the downscaling of a hurricane precipitation field.

Hurricanes↗
DOE OSTI2025

A segmented approach to modeling building height: Delineating high-rise and low-rise buildings for enhanced height estimation

Understanding building height is imperative to the overall study of energy efficiency, population distribution, urban morphologies, emergency response, among others. Currently, existing approaches for modeling building height at scale are hindered by two pervasive issues. First, there is no consistent approach to quantify what a high-rise building is at a macro scale, leaving researchers unable to accurately compare results across geographies and domains. Second, high-rise buildings represent a small fraction of the built environment, implying data imbalance challenges that negatively affect current approaches. This is a problem of practical relevance since information on high-rise buildings is important for studies on urban heat islands, population dynamics, and pollution dispersion. Here, we introduce a novel approach to map building height which first identifies two distinct distributions within the built environment, with one being composed of low-rise buildings and one composed of high-rise buildings. We then develop an ensemble scheme where discrete specialist models are trained for each subset of low-rise buildings and high-rise buildings to infer building height from morphology features. For experiments mapping heights of 4.85 million buildings in Japan, we show an increase of 34 % in accuracy within 3m error when compared to the current state-of-the-art when modeling high-rise buildings, which based on KNN experimentation we define as any building > 12m . Our findings show that such an ensemble framework outperforms the current state-of-the-art approaches, which is especially relevant in relation to inferring height for high-rise buildings, a prominent issue of existing approaches for mapping the built environment.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2006

Slat Cove Unsteadiness Effect of 3D Flow Structures

Previous studies have indicated that 2D, time accurate computations based on a pseudo-laminar zonal model of the slat cove region (within the framework of the Reynolds-Averaged Navier-Stokes equations) are inadequate for predicting the full unsteady dynamics of the slat cove flow field. Even though such computations could capture the large-scale, unsteady vorticity structures in the slat cove region without requiring any external forcing, the simulated vortices were excessively strong and the recirculation zone was unduly energetic in comparison with the PIV measurements for a generic high-lift configuration. To resolve this discrepancy and to help enable physics based predictions of slat aeroacoustics, the present paper is focused on 3D simulations of the slat cove flow over a computational domain of limited spanwise extent. Maintaining the pseudo-laminar approach, current results indicate that accounting for the three-dimensionality of flow fluctuations leads to considerable improvement in the accuracy of the unsteady, nearfield solution. Analysis of simulation data points to the likely significance of turbulent fluctuations near the reattachment region toward the generation of broadband slat noise. The computed acoustic characteristics (in terms of the frequency spectrum and spatial distribution) within short distances from the slat resemble the previously reported, subscale measurements of slat noise.

Choudhari, Meelan M.↗
DOE OSTI2025

Correspondence between Color Glass Condensate and High-Twist Formalism

The color glass condensate (CGC) effective theory and the collinear factorization at high twist (HT) are two well-known frameworks describing perturbative QCD multiple scatterings in nuclear media. It has long been recognized that these two formalisms have their own domain of validity in different kinematic regions. Taking direct photon production in proton-nucleus collisions as an example, we clarify for the first time the relation between CGC and HT at the level of a physical observable. We show that the CGC formalism beyond shock-wave approximation, and with the Landau-Pomeranchuk-Migdal interference effect is consistent with the HT formalism in the transition region where they overlap. Such a unified picture paves the way for mapping out the phase diagram of parton density in nuclear medium from dilute to dense region.

Parton distribution functions↗
DOE OSTI2026

Grid Architecture Mapping to Understand Transformation (GAMUT): Methods and Framework Architecture

Grid architecture (GA) is a concept that was developed to address the need for a comprehensive view of power grid challenges. GA can be viewed as a relatively consistent and fixed high-level approach; however, for any instantiation of grid structures, a combinatorial explosion results from each lower-layer expansion. This constitutes the main challenge with GA—it is a grid architect’s view of the system, which might not be very informative at the implementation level. Grid Architecture Mapping to Understand Transformation (GAMUT project) seeks to bridge that gap by integrating subject matter expertise across GA structures, providing users who lack expertise in GA approaches with valuable insights and informational materials. GAMUT seeks to answer feasibility questions for the approach. System-level expectations are that a GA baseline needs to be established in order for GA to be the common framework to which any lower layer approach is tied. This report explores a potential information ingestion and documentation framework to support GAMUT. The main concepts that enable the solution domain of GAMUT are discussed, and examples are provided. The solution domain leverages already-existing technology and concepts related to GA, knowledge management, and other relevant areas. To assess GAMUT building blocks and the overall approach, a feasibility assessment is proposed, rooted in systems engineering and GA architecture evaluation concepts.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Summary of GFL Inverter Capability and Performance: Malawi [Slides]

This presentation provides a comprehensive comparison of inverter-based resource (IBR) technical requirements across multiple international grid codes - including IEEE 2800, ESO, EirGrid, and Malawi's evolving regulatory framework - to support capacity building for electricity-sector institutions in Malawi. It highlights key performance expectations for grid-following (GFL) inverters across critical domains such as primary and fast frequency response, ramping behavior, frequency and voltage ride-through capabilities, reactive power and voltage control, ROCOF withstand, phase jump tolerance, system strength considerations, protection schemes, and dynamic modeling requirements. Emphasizing a "Do no harm, do something, do more" philosophy, the document synthesizes best practices and operational benchmarks to guide the integration and stability of inverter-based resources within Malawi's power system. The presentation forms part of the SABESS Center of Excellence initiative supported by the Global Energy Alliance for People and the Planet.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2022

Soil Moisture Estimation in South Asia via Assimilation of SMAP Retrievals

A soil moisture retrieval assimilation framework is implemented across South Asia in an attempt to improve regional soil moisture estimation as well as to provide a consistent regional soil moisture dataset. This study aims to improve the spatiotemporal variability of soil moisture estimates by assimilating Soil Moisture Active Passive (SMAP) near-surface soil moisture retrievals into a land surface model. The Noah-MP (v4.0.1) land surface model is run within the NASA Land Information System software framework to model regional land surface processes. NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA2) and Global Precipitation Measurement (GPM) Integrated Multi-satellitE Retrievals (IMERG) provide the meteorological boundary conditions to the land surface model. Assimilation is carried out using both cumulative distribution function (CDF)-corrected (DA-CDF) and uncorrected SMAP retrievals (DA-NoCDF). CDF matching is applied to correct the statistical moments of the SMAP soil moisture retrieval relative to the land surface model. Comparison of assimilated and model-only soil moisture estimates with publicly available in situ measurements highlights the relative improvement in soil moisture estimates by assimilating SMAP retrievals. Across the Tibetan Plateau, DA-NoCDF reduced the mean bias and RMSE by 8.4 % and 9.4 %, even though assimilation only occurred during less than 10 % of the study period due to frozen (or partially frozen) soil conditions. The best goodness-of-fit statistics were achieved for the IMERG DA-NoCDF soil moisture experiment. The general lack of publicly available in situ measurements across irrigated areas limited a domain-wide direct model validation. However, comparison with regional irrigation patterns suggested correction of biases associated with an unmodeled hydrologic phenomenon (i.e., anthropogenic influence via irrigation) as a result of SMAP soil moisture retrieval assimilation. The greatest sensitivity to assimilation was observed in cropland areas. Improvements in soil moisture potentially translate into improved spatiotemporal patterns of modeled evapotranspiration, although limited influence from soil moisture assimilation was observed on modeled processes within the carbon cycle such as gross primary production. Improvement in fine-scale modeled estimates by assimilating coarse-scale retrievals highlights the potential of this approach for soil moisture estimation over data-scarce regions.

Jawairia Ahmad↗
NASA NTRS2001

Linear and Order Statistics Combiners for Pattern Classification

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the 'added' error. If N unbiased classifiers are combined by simple averaging. the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the i-th order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.

Tumer, Kagan↗
DOE OSTI2026

Joint scheduling of energy, fast and primary frequency response reserves in integrated transmission–distribution networks

Inverter-based distributed energy resources (DERs) connected to distribution networks (DNs) can provide fast frequency support, but their reserve deliverability depends on feeder constraints and differs from synchronous primary frequency response (PFR). Existing transmission–distribution coordination studies usually treat reserve generically or neglect feeder-level feasibility, while frequency-security scheduling studies rarely represent distribution feeders explicitly. This paper develops a bi-level day-ahead scheduling framework for integrated transmission–distribution networks that jointly clears energy, transmission-side PFR, and distribution-side fast frequency response (FFR) under exogenous hourly inertia and largest-loss inputs from an external unit commitment (UC) schedule. The transmission problem is modeled with DC-optimal power flow (OPF) and closed-form second-order cone (SOC) frequency-security constraints, whereas each DN is represented by a reserve-aware branch-flow AC-OPF so that scheduled fast reserves remain deliverable during activation. The bi-level problem is reformulated through Karush–Kuhn–Tucker (KKT) conditions into a mixed-integer SOC program, and a penalty term is used to tighten the distribution-network relaxation. In the reduced test system, lower exogenous inertia increased the required primary response from 179.64 MW to 191.08 MW, distribution-side fast response reduced total frequency-response procurement by up to 4.9%, and neglecting distribution constraints overstated the combined distribution-side energy and reserve award by up to 18%. In the expanded study, the largest case was solved in 2.02 s with a 0.00% optimality gap. Time-domain simulations kept the frequency nadir above 59.0 Hz in all tested hours. These results demonstrate the value of fast-response modeling and distribution-feasible reserve delivery in coordinated market clearing.

Noh, Seung-Gil↗