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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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260 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Simulation to a Newborn Supernova Remnant from a Low-mass Iron Core Star

Supernova remnant observations show a high degree of asymmetry, mixing, and inhomogeneity. These asymmetries are seeded during the early seconds of the explosion and are further enhanced and modified as the shock and ejecta move through the stellar progenitor and into the circumstellar medium. We present simulations of a 9.6 M⊙ zero-metallicity progenitor initialized after shock revival and evolved for several years when the ejecta is in the circumstellar medium. A suite of 1D and 2D simulations examines the effects of neutron-star wind and radioactive decay heating. In 1D, decay heating forms a low-density bubble that suppresses the reverse shock. While in 2D, the heating is localized to metal-rich pockets, inflating them and compressing the surrounding material into dense shells. In 3D, the neutron-star wind and decay heating modify the plume morphology, producing more large-scale structures. The extended plume morphology leads to an asymmetrical shock breakout. After breakout, the leading plumes cannot keep up with the shock front, resulting in deceleration and fragmentation by the reverse shock while retaining the large-scale asymmetry. The projected ejecta morphology and velocities are strongly viewing angle dependent. The relatively uniform metal-rich distribution does not resemble the strongly inhomogeneous ejecta structure of Cas A. The 160-isotope decay network shows that 24.4% of the radioactive heating comes from decay chains other than the canonical 56Ni chain. The low explosion energy, low 56Ni yield, and Ni/Fe ratio greater than unity suggest an observational signature similar to an electron capture supernova.

Neopane, Sudarshan [University of Tennessee (UT)]↗
DOE OSTI2026

A strong and ductile Super Kovar alloy via fully coherent nanoprecipitates

Emerging high-precision technologies demand materials with exceptional dimensional stability and mechanical robustness, as even microscopic thermomechanical deformation can cause functional failure. However, a fundamental trilemma exists: High strength, ductility, and low thermal expansion are mutually exclusive, as strengthening-induced lattice distortions compromise the spin-lattice coupling, which is essential for low thermal expansion. Here, we overcome this trilemma by designing “Super Kovar,” an Fe-Ni-Co-Al-Ta alloy, featuring fully coherent nanoprecipitates. It unifies a 1.0-gigapascal ultimate tensile strength and ∼39% elongation with a Kovar-grade thermal expansion of 3.81 × 10−6 K−1 (100 to 410 K). The key is a dense dispersion of L12 nanoprecipitates that form an almost strain-free coherent interface with the ferromagnetic matrix. Beyond providing precipitation strengthening, these coherent interfaces suppress intrinsic phonons of nanoprecipitates via elastic coupling while avoiding magnetic domain pinning to preserve the Invar effect of the matrix. This reduces the thermal expansion of the precipitates by 56% and achieves a fourfold enhancement in the strength-ductility product, establishing a paradigm for dimensionally stable, ultrastrong alloys.

Yu, Chengyi [University of Science and Technology ↗
DOE OSTI2026

A transport-based framework for solidification cracking in Ni-based superalloys processed by laser powder bed fusion

Solidification cracking remains a persistent barrier to laser powder bed fusion (LPBF) processing of solid-solution-strengthened (SSS) Ni-based superalloys and is commonly attributed to carbide formation, liquation-type failure, or elemental segregation. In this work, the cracking behavior of three SSS Ni-based superalloys—Inconel 625 (625), Inconel 617 (617), and Haynes 230 (230)—is examined under comparable LPBF conditions to evaluate the origins of their cracking susceptibility. Carbides were present in both 625 and 230, yet cracking behavior differed significantly. MC-type carbides in 625 remain discrete and preserve liquid connectivity, whereas Cr-rich M23C6 carbides in 230 form at cellular triple junctions that bottleneck the interdendritic liquid network, influencing cracking through liquid connectivity rather than as an independent cause. Alloy 617 exhibited anomalous segregation without resolvable secondary phases yet cracked mildly, indicating that extensive carbide formation is not a prerequisite for cracking. To rationalize these observations, a transport-limited framework is proposed in which cracking occurs when terminal-liquid feeding cannot accommodate solidification-induced strain; among the mechanisms evaluated, this framework is most consistent with the physical constraints imposed by LPBF solidification. Transport-based crack-susceptibility indexes incorporating permeability, viscosity, and solidification kinetics distinguish the alloy hierarchy; permeability ratios Krat increased from approximately 7 (625) to 11.5 (617) and 14.5 (230), with corresponding increases in the μ-weighted mushy zone risk index (CSIMZRM). These results are consistent with transport-limited liquid feeding as a rate-limiting contributor to solidification cracking in LPBF-processed SSS Ni-based superalloys, providing a physically grounded basis for alloy and process design.

Hyer, Holden [ORNL] (ORCID:0000000343915561)↗
DOE OSTI2025

A Reductively Stable Electrolyte Realizes Deep Cycling Behavior in Anode‐free Sodium Batteries

For anode‐free sodium batteries to achieve practical consideration, highly reversible chemistries require exceptional ≥99.95% coulombic efficiencies that maintain over prolonged cycling periods. To do so, consumption of this severely limited sodium inventory must be restricted while metal nucleation processes that comprise the in situ formed metal anode are improved. Herein, we describe a fluorine‐free carborane electrolyte that satisfies these criteria by emphasizing reductive stability and weakly coordinating anion behavior as design principles. We find this approach promotes the development of a thin, robust SEI chemistry rich in both organic speciation and boron. The electrolyte described herein exhibits ideal metal nucleation behavior on one‐micron thin carbonaceous current collector surfaces and achieves a metal deposition/stripping efficiency near parity for 400 cycles. This novel anode chemistry is introduced to anode‐free full cell configurations where 87% of the initial discharge capacity is retained after 1000 cycles at 2.0 C. In conclusion, post‐test characterization of deep‐cycled anode‐free cells reveals suppressed capacity fade in these systems is attributed to the chemical stability of the carborane anion.

anode-free↗
DOE OSTI2025

Cooperative and bifunctional Ga-Ca-Cr 2 O 3 @CaO structured monoliths as versatile platform for reactive capture of CO 2 and its subsequent conversion to ethylene

Cooperative and bifunctional materials (BFMs) that integrate adsorbents and catalysts offer a promising strategy for the reactive capture of CO 2 to produce valuable fuels and chemicals. In this study, we developed structured BFMs via 3D printing that combine CaO as an adsorbent with Ga–Ca–Cr 2 O 3 metal oxides as the catalyst for the reactive capture of CO 2 and its subsequent conversion to C 2 H 4 via the oxidative dehydrogenation of C 2 H 6 (CO 2 -ODHE). Three different Ga–Ca compositions were used to modify the catalyst surface characteristics and enhance C 2 H 4 selectivity. In these formulations, Ga ions stabilize the oxygen lattice of the BFM, while Ca ions interact strongly with Cr to form CaCrO 4 , thereby altering the oxygen species and enhancing the material’s basic properties. Under adsorption–reaction conditions at 600–650 °C, the optimal BFM achieved an excellent C 2 H 4 selectivity of 96.4 %, attributed to a balanced redox process and improved basicity that facilitate efficient C 2 H 6 conversion and rapid desorption of C 2 H 4 without excessive oxidation. Overall, this work provides new insights into the formulation of BFMs monoliths and highlights the critical role of catalytic surface modification in enhancing C 2 H 4 selectivity in the CO 2 -ODHE reactive capture process.

C2H4 production↗
DOE OSTI2025

The Role of Asparagine as a Gatekeeper Residue in the Selective Binding of Rare Earth Elements by Lanthanide‐Binding Peptides

Abstract Lanthanide‐binding tag (LBT) peptides selectively complex lanthanide cations (Ln 3+ ) in their binding pockets and are promising for lanthanide separation. However, designing LBTs that selectively target specific Ln 3+ cations remains a challenge due to limited molecular‐level understanding and control of interactions within the lanthanide‐binding pocket. In this study, we reveal that the N5 asparagine residue acts as a gatekeeper in the binding pocket, resulting in a 100‐fold selectivity for smaller Lu 3+ over larger La 3+ cations. Nuclear magnetic resonance spectroscopy and molecular dynamics simulations show that the N5 residue weakly binds to the larger La 3+ cation, permitting H 2 O molecules inside the pocket. For the smaller Lu 3+ cations, the N5 residue forms an inter‐arm hydrogen bond with the E14 glutamic acid residue, locking the Lu 3+ cation in the pocket and preventing H 2 O infiltration. Mutating the N5 asparagine to a D5 aspartic acid prevents such a hydrogen bond, eliminating the gatekeeping mechanism and precipitously reducing selectivity. The resulting binding affinity to Ln 3+ cations is non‐monotonic but generally increases with cation size. These results suggest a molecular design paradigm: the reduced affinity for larger lanthanides is due to open pocket conformations, while the selectivity of smaller Ln 3+ cations over larger ones is due to the gatekeeping hydrogen bond.

Chemistry↗
DOE OSTI2025

Evaluation of U10Mo Fuel Plate Performance Modeling Over Hot Isostatic Press and Hydraulic Bending for MURR DDE Plates

The United States High Performance Research Reactor Program’s objective is to reduce the amount of highly enriched uranium currently implemented in research reactors. The conversion of these research reactors requires designing a monolithic U10Mo plate fuel, with the fuel plate geometry being dependent on each research reactor. The process of forming the plates includes a hot isostatic pressing (HIP) to manufacture a prototypic plate. In the case of the Missouri University Research Reactor (MURR) design demonstration element (DDE) plate manufacture, plates that have been through HIP are then curved using dies and a hydraulic press to impart the desired curvature. Both fabrication processes impart residual stresses into each fuel plate region, with the curvature of the plates taking some regions of the fuel plate up to their material yield stresses, accompanied by plastic strain. The amount of plastic strain and stress imparted onto each MURR DDE plate is determined by the radius of curvature, thickness of each region, and overall width of the fuel plates. Furthermore, this work aims to predict the yield stresses and strain using ABAQUS to simulate the proposed fabrication process of the MURR DDE plates, accompanied by discussion over the stresses and strains as to their relation to nuclear fuel performance and the impact they will have during early irradiation.

ABAQUS↗
DOE OSTI2024

Surface science insight note: A linear algebraic approach to elucidate native films on Fe 3 O 4 surface

Standard materials are often used to obtain spectra that can be compared to those from unknown samples. Spectra measured from these known substances are also used as a means of computing sensitivity factors to allow quantification by X-ray photoelectron spectroscopy (XPS) of less well-defined materials. Spectra from known materials also provide line shapes suitable for inclusion in spectral models which, when fitted to spectra, permit the chemical state for a sample to be assessed. Both types of information depend on isolating photoemission signals from the inelastically scattered signal. In this Insight note, technical issues associated with the use of XPS of as received Fe 3 O 4 powder sample surface are discussed. The Insight note is designed to show how linear algebraic techniques applied to data collected from a sample marketed as pure Fe 3 O 4 powder are used to verify that XPS has been performed on chemistry representative of the sample. The methods described in this Insight note can further be utilized in elucidating complex XPS data obtained from thin films formed or evolved during cyclic/non-steady use of complex (electro)catalyst surfaces, especially in the presence of contaminants.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Circumventing data imbalance in magnetic ground state data for magnetic moment predictions

Abstract Magnetic materials play a crucial role in the transition to more sustainable forms of energy and electric vehicles. There is an anticipated shortage in magnetic materials in the future, and as a result there is an urgent need to discover and design new magnetic materials. Computational magnetic material design using density functional theory is daunting because of the challenge in identifying magnetic ground states from a combinatorially large set of possibilities. Machine learning offers a path forward by enabling efficient surrogate models that can more readily enumerate these states, but there is a dearth of training data available, and what is available tends to be imbalanced with too much non-magnetic data. In this work we show that the discrete and previously tackled data imbalance that exists at the level of the magnetic ordering leads to an imbalanced continuous distribution with many zeros when the data is unraveled at the atomic magnetic moment level, which subsequently leads to models with low accuracy for magnetic properties. We mitigate this by using a two-part model framework. Our scheme is able to classify atoms into magnetic and non-magnetic with an F1 score and Matthew’s correlation coefficient (MCC) of ~91% and then to provide an implicit embedding representation that maps directly onto the magnitude of the magnetic moment with a mean absolute error of 0.1 μ B . Beyond screening for new magnetic materials, we demonstrate an additional practical use case of our scheme: the provision of good initial guesses for magnetic moments in first-principles electronic relaxations. Such initialization is shown to lead to faster convergence to configurations that lie closer to the ground state.

Computer Science↗
DOE OSTI2026

In Situ UV–vis Quantification of Chlorobasicity in Binary Molten Chlorides

Optical basicity measurements provide a basis for determining the relative chlorobasicity of a given molten salt composition. This study uses Bi3+ as a spectroscopic probe to investigate optical basicity across three binary molten chloride systems (LiCl-KCl, MgCl2–KCl, and ZnCl2–KCl) through in situ UV–vis spectroscopy measurements of the 1S0→3P1 transition. LiCl-KCl systems exhibit the highest optical basicity with minimal compositional dependence, while both divalent systems show stronger, yet nonlinear, dependence that is reminiscent of acid–base titration curves. The influence of cation electronegativity and polarizing power (Li+ < Mg2+ < Zn2+) directly reflects the basicity curves, with ZnCl2–KCl displaying the steepest gradients and lowest basicity values. Nonlinear dependencies in divalent systems indicate formation of chloride-bridged network structures with coordination states dictated by the amount of KCl in a salt composition, which was further investigated and validated by molecular dynamics simulations of polymeric structures formed in ZnCl2 and MgCl2-based salts using machine learning force fields. The temperature dependence of chlorobasicity in terms of optical basicity was investigated, and a loose, positive correlation between the two was revealed. These findings establish Bi3+ as a sensitive probe for understanding electronic environments in molten chloride systems and provide insights for predicting the chemical behavior of molten salts for use in high-temperature environments.

Buttice, Kailee [Department of Nuclear Engineering↗
DOE OSTI2026

Identifying microstructures susceptible to pulverization in commercially irradiated high burnup UO2 under LOCA conditions

High burnup fuel fragmentation (HBFF) has been a concern in the nuclear industry for many years. When UO2 reaches and exceeds pellet average burnups around 55 GWd/tU, microstructural changes in the fuel pellet begin to occur that render the pellet susceptible to fine fragmentation under loss-of-coolant accident (LOCA) conditions. During a LOCA event, the cladding balloons and bursts, potentially releasing part of these fine fuel fragments into the reactor pressure vessel. This process is known as fuel fragmentation, relocation, and dispersal (FFRD). Presently, the US nuclear industry is developing a safety basis for FFRD with the goal of increasing burnups and pressurized water reactor cycle lengths. Increased cycle lengths would push the burnup limits of the fuel rods past the known threshold for HBFF susceptibility. In this work, the microstructural impact on HBFF was investigated by comparing the microstructures of as-irradiated rod segments to their post-LOCA tested counterparts. This investigation found that varied operational histories result in different microstructural evolutions across the pellet radius, which impacts the fragmentation behavior and radial location of the fragmentation. It is noted that regions with a high bubble density and a high density of grain boundaries fragment under LOCA-relevant conditions. In addition to the fragmentation that has been previously reported at the periphery of the fuel, fragmentation was also noted in the dark zone toward the fuel center. Analysis of the power histories of the fuel samples suggests that the dark zone forms in the central regions of the pellet between temperatures of approximately 740 and 960 °C.

McKinney, Casey [ORNL] (ORCID:0000000335383614)↗
DOE OSTI2025

Modeling phase transformations in Mn-rich disordered rocksalt cathodes with machine-learning interatomic potentials

Mn-rich disordered rocksalt (DRX) cathode materials exhibit a phase transformation from a disordered to a partially disordered spinel-like structure (δ-phase) during electrochemical cycling. Here, in this computational study, we use charge-informed molecular dynamics with a fine-tuned CHGNet foundation potential to investigate the phase transformation in LixMn 0.8 Ti 0.1 O 1.9 F 0.1 . Our results indicate that transition metal migration occurs and reorders to form the spinel-like ordering in an FCC anion framework. The transformed structure contains a higher concentration of nontransition metal (0-TM) face-sharing channels, which are known to improve Li transport kinetics. Analysis of the Mn valence distribution suggests that the appearance of tetrahedral Mn 2+ is a consequence of spinel-like ordering, rather than the trigger for cation migration as previously suggested. Calculated equilibrium intercalation voltage profiles demonstrate that the δ-phase, unlike the ordered spinel, exhibits solid-solution signatures at low voltage. A higher Li capacity is obtained than in the DRX phase. This study provides atomic insights into solid-state phase transformation and its relation to experimental electrochemistry, highlighting the potential of machine-learning interatomic potentials for understanding complex oxide materials.

Zhong, Peichen [University of California, Berkeley↗
DOE OSTI2026

The impact of metastability on the high-pressure behavior of cerium

The structures adopted by solids under pressure are often assumed to reflect thermodynamic equilibrium, yet in many materials phase selection is strongly influenced by kinetic pathways and microstructural inheritance. Elemental cerium (Ce) exemplifies this challenge, with decades of conflicting reports describing different high-pressure crystal structures emerging under nominally identical conditions. Here we use neutron diffraction from large ( ~ 60 mm 3 ) sample volumes to follow the structural evolution in ultra-high-purity Ce during controlled pressure-temperature cycling between 85 and 295 K and up to 8 GPa. We find that the crystal structure formed at high pressure depends on the compression pathway: slow compression ( ~ 0.25 GPa hr −1 ) at room temperature favors an orthorhombic phase (α'), whereas slow ( ~ 0.25 GPa hr −1 ) and also moderately faster ( ~ 0.5 GPa hr −1 ) compression at low temperature stabilizes a pure monoclinic phase (α"). The low-temperature phase persists metastably over a wide temperature range but transforms irreversibly upon heating above ~ 280 K, or modest pressure cycling. Remarkably, the lower-pressure γ phase remains trapped far beyond the expected stability field, persisting to the highest pressures studied. These observations show that phase selection in Ce is governed by kinetics and microstructural memory rather than equilibrium thermodynamics or sample morphology alone, establishing path dependence as a defining feature of its high-pressure behavior.

Ridley, Christopher J. [Oak Ridge National Laborat↗
DOE OSTI2026

15.3% AM1.5G Efficiency GaAs Solar Cells Fabricated via an Epitaxy-Free Process

Here, we report simple and potentially low-cost techniques for creating high-quality n-type gallium arsenide (GaAs) and GaAs p/n junctions and fabricate GaAs p/n junction solar cells. Detailed-balance modeling suggests that 20% AM1.5G efficiency p/n homojunction devices may be possible if the surface doping concentration can be limited to values less than ∼ 5 × 10 19 cm −3 . Our process exploits an open-tube, vapor-phase, deposition-free, zinc diffusion technique for forming p-type layers in melt-grown n-GaAs substrates that results in sheet resistances less than 1 kΩ/$\square$. In addition, we have improved the minority carrier diffusion lengths of melt-grown GaAs from less than one micron to over five microns using an open-tube, vacuum-free, annealing process which reduces the density of EL2 midgap defects. Finally, we have combined these advances to fabricate epitaxy-free, GaAs solar cells with a validated AM1.5G efficiency of 15.3%.

14 SOLAR ENERGY↗
DOE OSTI2026

Knowledge-guided learning with curated prior genetic biomarkers for robust model interpretation

Abstract Motivation Knowledge-guided learning offers effective and robust model training strategies in data-scarce settings by incorporating established domain knowledge, thereby enhancing generalization, robustness, and interpretability. By contrast, conventional deep learning approaches rely purely on data-driven learning, which can limit robust model interpretability, particularly in high-dimensional settings with limited size samples. In computational biology, knowledge-guided learning has primarily leveraged network- and structural-based knowledge, leading to biologically interpretable representations and enhanced predictive performance compared to conventional approaches. However, curated biomarkers, one of the most accessible forms of biological knowledge, remain largely unexplored within knowledge-guided paradigms. Results In this study, we propose a model-agnostic training paradigm, Biomarker-driven Explainable Prior-guided Learning (BioExPL), that can be applied to any neural networks that incorporates curated prior knowledge. BioExPL enforces neural networks to reflect curated biomarker priors in their latent representations through a novel knowledge-alignment loss. BioExPL consistently demonstrated significantly improved predictive performance and enhanced model interpretability with minimized computational overhead in simulation studies and intensive experiments on multiple cancer datasets. BioExPL not only integrates prior curated knowledge into the model but also accurately identifies unknown associated signals additionally. BioExPL is model-agnostic and domain-independent, enabling its integration into diverse neural network architectures. Availability and implementation The open-source is publicly available at: https://github.com/datax-lab/BioExPL.

Baek, Beomsu [Department of Computer Science, Univ↗
DOE OSTI2026

Pivotal role of organic adsorbates for the creation of catalytic sites during dry reforming of methane

Inadvertent factors can sometimes be crucial for synthesis of catalysts. The use of polyalcohols is common in the synthesis of heterogeneous catalysts. Interactions between alcohols and heterogeneous catalysts have been shown to induce surface reconstructions that greatly impact catalytic performance. Thus, traces of these alcohol functionalities on the as-synthesized catalysts, combined with heat treatment, could be critical in the generation of catalytic sites. Here, we show that during the synthesis of a Ni–Mo/MgO catalyst using a polyol process, residual ethylene glycol (EG) on the surface plays a significant role in the generation of catalytic sites for dry reforming of methane (DRM). The as-synthesized catalyst presents dispersed cationic Ni. Under DRM reaction conditions, the presence of EG, and H2 generated in situ, promote the generation of co-localized Ni–Mo nanoparticles (NPs). Greater amount of EG in the as-synthesized catalyst prevented sintering, leading to better catalyst stability and higher rates. If the residual EG remaining post-synthesis is removed through calcination, before conducting DRM, NiO NPs are formed and the material is completely inactive for catalyzing the reaction. When using a different support, denoted MgO*, EG also proved indispensable to generate active sites, although Ni–Mo co-localization was not evident, and a combination of DRM-related species was needed to activate the catalyst, not just H2. This work systematically uncovers how the interactions between organic adsorbates, the supported metals and the catalyst support dictate the creation of catalytic active sites.

Polo Garzon, Felipe [ORNL] (ORCID:0000000265076183↗
DOE OSTI2026

Advanced blade-shaped thermal energy storage device: Development and application

Thermal energy storage (TES) using phase change materials (PCMs) is a promising approach for capturing and reusing excess thermal energy, yet widespread adoption is limited by low thermal conductivity, bulky configurations, and inadequate scalability. Here, this study presents a modular, blade-shaped TES prototype designed to address these challenges. The device integrates a lightweight aluminum shell, an embedded serpentine coil for active or passive heat exchange, and a cost-effective corrugated metal mesh for enhanced PCM thermal conductivity. With thickness-to-length and thickness-to-width ratios of 0.03 and 0.08, respectively, the blade-shaped TES achieves a compact, modular form factor suitable for space-constrained applications. Experimental testing demonstrated the efficient charge and discharge behavior of blade-shaped TES, capturing PCM superheating, phase-change transitions, and subcooling dynamics, with charging and discharging efficiencies of 94.9% and 94.6%, respectively. Also, the system can potentially achieve higher energy density than that of conventional TES designs. When integrated into a household refrigerator during the study, three blade-shaped TES modules successfully shifted 100% of peak-time compressor operation to off-peak hours, reducing energy consumption while maintaining more stable compartment temperatures. The blade-shaped TES's thin geometry, modularity, and enhanced thermal performance support scalable deployment across residential, commercial, and industrial applications, providing a versatile, cost-effective solution for high-efficiency, demand-flexible thermal energy management.

Blade-shaped↗
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↗