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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 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Engineering of Lead Selenide Quantum Dot Based Devices and Core/Shell Heterostructures

Near infrared (NIR) emitting colloidal quantum dots (QDs) such as PbSe are interesting materials for implementation in various optoelectronic devices such as solar cells, photodetectors, and radiation detectors. Material properties like size tunable emission wavelengths, facile solution processability, the possibility of carrier multiplication and Auger assisted up-conversion, and high Z number provide PbSe QDs with unique advantages over many currently available commercial materials used in these devices. In this dissertation, after an introduction to QDs in general, we first focus on synthesis of PbSe-based heterostructured QDs for study via optical spectroscopy. PbSe/CdSe QDs synthesized via cation exchange reaction were used as seeds to study the proper conditions for further CdSe or CdS shell growth. Optical spectroscopy studies show that growth of thicker CdSe shells leads to tunable visible emission, while growth of thick CdS shells can greatly increase the photoluminescence quantum yield (PLQY) observed from the intermediate CdSe shell. NIR PL lifetimes can be greatly enhanced by the growth of CdS shells, due to strong delocalization of the hole wavefunction within the PbSe core, while the electron is delocalized throughout the QD including in the CdS shell, resulting in radiative lifetimes in the tens of microseconds. Two pulse delay measurements show that Auger assisted up conversion is also taking place in these engineered QD dot heterostructures. In the sections that follow, we look at QD devices, first with a focus on novel devices fabricated from PbSe QDs, using an amine synthesis method that allows for facile in-solution ligand exchange. QD film mobilities are measured for PbSe QDs capped with various short ionic ligands. Carrier densities in PbSe QD films are calculated from C-V measurements, showing for the first time that carrier densities can be modulated by simply changing the capping ligand. vii Radiation detectors utilizing PbSe QDs capped with KI and NH4I ligands show tangible response to incident alpha radiation. Current output response to alpha radiation is dependent on strength of radiation source and amount of bias voltage applied. In the final section a critical review of hybrid layered 2D-QD photodetectors is presented. In a typical example, PbSe and PbS QDs act as the absorbing layer in phototransistor devices which utilize layered 2D materials such as graphene and transition metal dichalcogenides as transport layers. Resulting devices display high gains and improved directivities compared to QD only and 2D only devices.

36 MATERIALS SCIENCE↗
NASA NTRS1994

Optimization of Residual Stresses in MMC's Using Compensating/Compliant Interfacial Layers. Part 2: OPTCOMP User's Guide

A user's guide for the computer program OPTCOMP is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in uni-directional metal matrix composites subjected to combined thermo-mechanical axisymmetric loading using compensating or compliant layers at the fiber/matrix interface. The user specifies the architecture and the initial material parameters of the interfacial region, which can be either elastic or elastoplastic, and defines the design variables, together with the objective function, the associated constraints and the loading history through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the elastoplastic response of an arbitrarily layered multiple concentric cylinder model that is coupled to the commercial optimization package DOT. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.

Pindera, Marek-Jerzy↗
DOE OSTI2023

Analysis of picosecond coherent anti-Stokes Raman spectra for gas-phase diagnostics

We present a hybrid frequency- and time-domain solution, applicable to the case of picosecond coherent anti-Stokes Raman scattering (CARS), for gas-phase diagnostics. A solution has been derived based on both physical arguments and four-wave mixing equations for picosecond CARS, with pulse durations that are comparable to the dephasing time scale for gas-phase Raman coherence—a regime where commonly employed solutions for impulsive (femtosecond) or cw (nanosecond) pump/Stokes forcing are not strictly valid. We present the ps-CARS spectrum in the form of incoherent sums of CARS intensity spectra, calculated from the fundamental solution for impulsive pump/Stokes Raman preparation. The solution was examined for temperatures from 1000–3000 K, for four plausible experimental configurations, with laser pulse durations of 50–150 ps, and probe pulse delays from −20 to 240 ps. Approximations based on cw and impulsive pump/Stokes preparation to fit picosecond CARS spectra at atmospheric pressure were examined and the relative thermometric accuracy and computational cost of these approximations were quantified for the case of a zero nonresonant CARS contribution, and a nonresonant susceptibility equal to 10% of the Raman-resonant value at the N 2 bandhead. The nanosecond CARS approximation can result in large fitting errors when the probe pulse time delay is less than the probe pulse duration. Errors as large as 10–20% are observed in the fit temperatures for a zero picosecond probe pulse delay, when the nonresonant background is neglected, largely due to an inability of the time-independent cw model to capture transient frequency spread dephasing effects at the Q -branch bandhead. The inclusion of a nonresonant background results in 40–60% thermometry errors with a nanosecond model at a zero-probe delay. Time-dependent impulsive calculations used for femtosecond CARS better approximate the structure of the N 2 bandhead, reducing temperature fitting errors to 5–10% at a short probe pulse delay. The impulsive approximation results in errors up to 10% at intermediate probe pulse delays, where the coherence of the pump and probe pulses leads to multiple terms in the picosecond CARS solution. Both approximations improve as the probe pulse delay exceeds the probe duration. The nanosecond approximation results in a 2–3% error, while the impulsive model results in differences of less than 1% in some cases. Fits to experimental data obtained using short, ∼60ps pulses at a zero probe time delay and longer 100 ps pulses at a substantial 200 ps delay are presented with accuracies of 1–3% in the fit temperature.

Kearney, Sean P.↗
NASA NTRS1994

Conductance measurement circuit with wide dynamic range

A conductance measurement circuit to measure conductance of a solution under test with an output voltage proportional to conductance over a 5-decade range, i.e., 0.01 uS to 1000 uS or from 0.1 uS to 10,000 uS. An increase in conductance indicates growth, or multiplication, of the bacteria in the test solution. Two circuits are used each for an alternate half-cycle time periods of an alternate squarewave in order to cause alternate and opposite currents to be applied to the test solution. The output of one of the two circuits may be scaled for a different range optimum switching frequency dependent upon the solution conductance and to enable uninterrupted measurement over the complete 5-decade range. This circuitry provides two overlapping ranges of conductance which can be read simultaneously without discontinuity thereby eliminating range switching within the basic circuitry. A VCO is used to automatically change the operating frequency according to the particular value of the conductance being measured, and comparators indicate which range is valid and also facilitate computer-controlled data acquisition. A multiplexer may be used to monitor any number of solutions under test continuously.

Mount, Bruce E.↗
NASA NTRS2012

A Spacecraft Housekeeping System-on-Chip in a Radiation Hardened Structured ASIC

Housekeeping systems are essential to health monitoring of spacecraft and instruments. Typically, sensors are distributed across various sub-systems and data is collected using components such as analog-to-digital converters, analog multiplexers and amplifiers. In most cases programmable devices are used to implement the data acquisition control and storage, and the interface to higher level systems. Such discrete implementations require additional size, weight, power and interconnect complexity versus an integrated circuit solution, as well as the qualification of multiple parts. Although commercial devices are readily available, they are not suitable for space applications due the radiation tolerance and qualification requirements. The Housekeeping System-o n-A-Chip (HKSOC) is a low power, radiation hardened integrated solution suitable for spacecraft and instrument control and data collection. A prototype has been designed and includes a wide variety of functions including a 16-channel analog front-end for driving and reading sensors, analog-to-digital and digital-to-analog converters, on-chip temperature sensor, power supply current sense circuits, general purpose comparators and amplifiers, a 32-bit processor, digital I/O, pulse-width modulation (PWM) generators, timers and I2C master and slave serial interfaces. In addition, the device can operate in a bypass mode where the processor is disabled and external logic is used to control the analog and mixed signal functions. The device is suitable for stand-alone or distributed systems where multiple chips can be deployed across different sub-systems as intelligent nodes with computing and processing capabilities.

Suarez, George↗
DOE OSTI2022

Growth mechanisms of large, faceted crystals grown from solutions

Here, the paper describes optical techniques and methods used to study growth mechanisms and phenomena occurring on multiple faces of real bulk crystals grown from aqueous and organic solutions. Using examples of ionic KDP and molecular trans-stilbene crystals, it shows how in-situ and ex-situ surface observations can be applied to identify growth structures characteristic for the dislocation, two-dimensional (2D), and 3D cluster deposition mechanisms. Results are analyzed and applied to understanding of defects origins and methods for their elimination in practical growth of large, high optical quality crystals.

2D growth mechanism↗
NASA NTRSDate not supplied

Sensing Small Uncrewed Aerial Vehicles with Distributed Radars for Advanced Air Mobility Surveillance

In the context of Advanced and Urban Air Mobility major attention is being reserved to the development of sensing strategies for small Uncrewed Aerial Vehicles (sUAVs) to enable their safe operations in and around urban areas. Such strategies should rely on non-cooperative distributed sensors to strengthen the surveillance solution towards the unreliability of Global Navigation Satellite System (GNSS) positioning information, which is typical for low-altitude-flying platforms in urban regions, and increase the monitored airspace volume. To this aim, this paper proposes a fusion solution for a network of distributed ground-based radars, which can be exploited to not only increase the coverage over large airspace volumes but also improve the overall detectability and traceability of sUAVs by leveraging on multiple views over the same area. The solution exploits a centralized fusion scheme in which measurements collected by each radar are shared with a Fusion Center where Kalman Filtering is exploited to build a unique, fused track. Tests conducted on experimental data collected using two sUAVs as flying targets and three distributed radars showed that the proposed solution can produce an increase in coverage from about 20 % (single radar configuration) to about 80 % of the targets’ flight path, as well as a finer accuracy yielding meter and meter-per-second root mean square error values on position and velocity components.

Federica Vitiello↗
NASA NTRS1992

A study of equation solvers for linear and non-linear finite element analysis on parallel processing computers

Concurrent computing environments provide the means to achieve very high performance for finite element analysis of systems, provided the algorithms take advantage of multiple processors. The authors have examined several algorithms for both linear and nonlinear finite element analysis. The performance of these algorithms on an Alliant FX/80 parallel supercomputer has been studied. For single load case linear analysis, the optimal solution algorithm is strongly problem dependent. For multiple load cases or nonlinear analysis through a modified Newton-Raphson method, decomposition algorithms are shown to have a decided advantage over element-by-element preconditioned conjugate gradient algorithms.

Watson, Brian C.↗
DOE OSTI2020

Localized High Concentration Electrolytes for High Voltage Lithium-Metal Batteries: Correlation between the Electrolyte Composition and Its Reductive/Oxidative Stability

We demonstrate a first-principles screening methodology as an effective tool to explore electrolyte formulations for the new generation of high energy density rechargeable batteries. We study the liquid structure and electronic properties in dilute electrolytes, high concentration electrolytes (HCE), and localized high concentration electrolytes (LHCE), with focus on electrolyte formulations based on lithium bis(fluorosulfonyl)imide (LiFSI), dimethyl carbonate (DMC), and bis(2,2,2-trifluoroethyl) ether (BTFE) as a diluent. We describe the solvation complexes in the dilute electrolyte and explore structural changes triggered by the increase in lithium salt concentration for HCEs and the diluent effects in LHCEs. In HCE formulations, there is a 4-fold coordination environment of lithium-ions as in the dilute electrolyte, but the number of lithium-ion interactions with O atoms from FSI- anions dominates. In these solutions, the ability of the FSI- anions to interact with multiple lithium-ions allows complex 3D network formation and influences the reductive/oxidative behavior of the electrolyte. Interestingly, in LHCEs, the BTFE diluent molecules do not change the 3D solution structure when diluting the HCE formulation from 5.49 to 3.83 M. However, there is a composition threshold where the structural and electronic behavior may change. We show that diluting the HCE electrolyte with BTFE down to 1.77 M breaks the three-dimensional solution structure into an island-like solvation complex. We relate these structural changes to the electronic properties of the electrolytes finding a causal relationship between the reductive/oxidative behavior and the lithium-oxygen interaction mechanisms in the solvated complexes. The coordination with lithium-ions lowers the electrolyte LUMO and HOMO levels: the higher is the number of interactions with lithium-ions, the more likely the solvent molecule, FSI- anion, or diluent molecule is to be reduced and the less likely it is to become oxidized. The evolution of the solvated ion structure in HCE and LHCE suggests a close connection to a corresponding change in the lithium-ion transport mechanisms for these electrolytes.

anions, molecules, oxygen, solvents, electrolytes↗
DOE OSTI2020

Sparse Matrix-Based HPC Tomography

Tomographic imaging has benefited from advances in X-ray sources, detectors and optics to enable novel observations in science, engineering and medicine. These advances have come with a dramatic increase of input data in the form of faster frame rates, larger fields of view or higher resolution, so high performance solutions are currently widely used for analysis. Tomographic instruments can vary significantly from one to another, including the hardware employed for reconstruction: from single CPU workstations to large scale hybrid CPU/GPU supercomputers. Furthermore, flexibility on the software interfaces and reconstruction engines are also highly valued to allow for easy development and prototyping. This paper presents a novel software framework for tomographic analysis that tackles all aforementioned requirements. The proposed solution capitalizes on the increased performance of sparse matrix-vector multiplication and exploits multi-CPU and GPU reconstruction over MPI. Furthermore, the solution is implemented in Python and relies on CuPy for fast GPU operators and CUDA kernel integration, and on SciPy for CPU sparse matrix computation. As opposed to previous tomography solutions that are tailor-made for specific use cases or hardware, the proposed software is designed to provide flexible, portable and high-performance operators that can be used for continuous integration at different production environments, but also for prototyping new experimental settings or for algorithmic development. The experimental results demonstrate how our implementation can even outperform state-of-the-art software packages used at advanced X-ray sources worldwide.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Propagation of wide bandwidth signals through strongly turbulent ionized media

Analytic and numerical techniques are presented which directly address the problem of propagation of wide bandwidth signals through random ionized media. This work is applicable to the problems of satellite communication and space based radar observation through a disturbed ionospheric propagation channel that would result from a high altitude chemical release or nuclear detonation. An analytic solution is presented for the two-position, two-frequency mutual coherence function for spherical wave propagation in the strong scattering limit. This solution is used to derive simple expressions for the power impulse response function and to determine its relationship to the important parameters of decorrelation distance and coherence bandwidth which describe the disturbed propagation channel. Results for mean time delay and time delay jitter are presented and compared to direct simulation results and to other theoretical calculations. A numerical/analytical solution to the parabolic wave equation is presented in the form of a multiple phase-screen (MPS) propagation simulation. In this very general solution technique, the random medium is divided into a finite number of layers. The field fluctuation through each layer is obtained by replacing the layer by a centrally located thin phase-screen, whose statistical properties are determined from the statistics of the electron-density irregularities. The waveform then propagates from phase-screen to phase-screen via an exact solution to the Fresnel-Kirchnoff equation. For wide bandwidth waveforms, numerical solutions are obtained at a number of discrete frequencies centered about the carrier and then time-domain solutions are obtained by Fourier transform techniques. Detailed results are presented for a number of interesting cases including propagation of a 20 MHz bandwidth signal through a finite barium cloud at a carrier frequency of 100 MHz. One of the major uses of the MPS propagation simulation has been to provide realizations of the received signal after propagation through a disturbed channel. The MPS simulation obtains a general solution of the parabolic wave equation under both weak and strong scattering conditions. A second technique to directly obtain realizations of wide bandwidth waveforms is presented here. This technique is limited to the case of strong scattering but requires only a fraction of the computer resources needed for MPS signal generation. Detailed comparisons of the two signal generation techniques are presented.

Random Media↗
DOE OSTI2020

Theoretical examination of covalency in berkelium(IV) carbonate complexes

Experimental studies on the speciation of berkelium in carbonate media have shown that complexation of berkelium(III) by carbonate results in spontaneous oxidation to berkelium(IV) and that multiple species can be present in solution. We studied two proposed structures present in solution based on theoretical comparisons with spectroscopic data previously reported for Bk(IV) carbonate solutions. The multiconfigurational character of the ground and low-lying excited states in both complexes is demonstrated to result from the strong spin-orbit coupling. Although bonding in Bk(IV) carbonate and carbonate-hydroxide complexes is dominated by strong Coulombic forces, the presence of non-negligible covalent character is supported by ligand-field theory, natural localized orbitals, topological studies of the electron density, and energy transition state natural orbitals for chemical valence. Bond orders based on natural localized molecular orbitals show that Bk-OH bonds possess enhanced orbital overlap, which is reflected in the bond strength. This is also observed in the decomposition of the orbital interaction energy into individual deformation density pairs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

The gallium anomaly

In order to test the end-to-end operations of gallium solar neutrino experiments, intense electron-capture sources were fabricated to measure the responses of the radiochemical SAGE and GALLEX/GNO detectors to known fluxes of low-energy neutrinos. Such tests were viewed at the time as a cross-check, given the many tests of 71 Ge recovery and counting that had been routinely performed, with excellent results. However, the four 51 Cr and 37 Ar source experiments yielded rates below expectations, a result commonly known as the Ga anomaly. As the intensity of the electron-capture sources can be measured to high precision, the neutrino lines they produce are fixed by known atomic and nuclear rates, and the neutrino absorption cross section on 71 Ga is tightly constrained by the lifetime of 71 Ge, no simple explanation for the anomaly has been found. To check these calibration experiments, a dedicated experiment BEST was performed, utilizing a neutrino source of unprecedented intensity and a detector optimized to increase statistics while providing some information on counting rate as a function of distance from the source. The results BEST obtained are consistent with the earlier solar neutrino calibration experiments, and when combined with those measurements, yield a Ga anomaly with a significance of approximately 4𝜎, under conservative assumptions. But BEST found no evidence of distance dependence and thus no explicit indication of new physics. In this review we describe the extensive campaigns carried out by SAGE, GALLEX/GNO, and BEST to demonstrate the reliability and precision of their experimental procedures, including 71 Ge recovery, counting, and analysis. We also describe efforts to define uncertainties in the neutrino capture cross section, which now include estimates of effects at the ≲ 0.5% level such as radiative corrections and weak magnetism. With the results from BEST, an anomaly remains even if one retains only the transition to the 71 Ge ground state, whose strength is fixed by the known lifetime of 71 Ge. We then consider the new-physics solution most commonly suggested to resolve the Ga anomaly, oscillations into a sterile fourth neutrino, 𝜈 𝑒 → 𝜈 𝑠 . We find such a solution generates substantial tension with several null experiments, owing to the large mixing angle required. While this does not exclude such solutions – the sterile sector might include multiple neutrinos as well as new interactions – it shows the need for more experimental constraints, if we are to make progress in resolving the Ga and other low-energy neutrino anomalies. We conclude by consider the role future low-energy electron-capture sources could play in this effort.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Superior performance enabled by supramolecular interactions in metal-organic cathode: the power of weak bonds

Metal–organic-based electrode materials are increasingly appealing because both metal and organic linker are capable of undergoing redox processes, thus offering a high specific capacity. High porosity which can be achieved by the rational design of these materials is generally perceived as one of the major criteria for high rate performance. However, while Li-ion transport may be possible, oftentimes the counteranions (e.g., PF 6 - ) and solvent molecules are co-inserted into the porous host lattice, potentially hindering Li-ion diffusion pathways. Here, in this study, we propose the concept of close-packed metal–organic cathode stabilized by multiple supramolecular interactions as a viable solution for exceptional electrochemical performance. This is illustrated in a modularly designed redox-active [CuL(Py) 2 ] n (LH 4 = 1,4-dicyano-2,3,5,6-tetrahydroxybenzene, Py = pyridine). The mechanistic studies and DFT calculations confirm that the supramolecular interactions between its close-packed chains are the key to the flexible host lattice which only allows desolvated Li + to intercalate, while these weak bonds also stabilize the inserted Li in the preferred hopping sites, creating optimal diffusion paths. The performance observed in this work is found to be among the best ever reported for metal–organic cathodes with a capacity as high as 255 mA h g -1 at 65 mA g -1 (0.25C) and a reversible capacity of 59 mA h g -1 at ~26 A g -1 (100C) corresponding to 81% retention after 1000 cycles. These findings reveal a potential new strategy towards metal–organic-based electrodes with high performance and enhanced cycling stability.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Alkali triel chalcogenide nanocrystals: a molecular reactivity approach to ternary phase selectivity

Alkali-metal-based materials are promising building blocks for energy conversion and storage technologies. Here, we use a molecular reactivity-based solution-phase approach to selectively synthesize multiple phases and specific polymorphs of lithium- and sodium-containing triel chalcogenide nanocrystals, LiTrCh 2 , NaTrCh 2 , and NaTr 3 Ch 5 , where Tr = Ga and In and Ch = S, Se, and Te. Analogous to the case of binary II–VI and III–V tetrahedral semiconductors, where the two commonly isolated zinc blende and wurtzite polymorphs are separated by only 1–50 meV f.u. −1 , we find that LiTrCh 2 nanocrystals easily adopt tetragonal (chalcopyrite) and orthorhombic polymorphs separated by only 2.7–6.2 meV f.u. −1 Because of this small energy difference, soft colloidal synthesis succeeds in accessing either one of these polymorphs, depending on the specific dichalcogenide precursor used. Highly reactive diethyl diselenide favors the thermodynamically more stable tetragonal I$\bar{4}2$d phase, whereas mildly reactive diphenyl diselenide favors the kinetic, metastable orthorhombic Pna2 1 phase. Density functional theory calculations confirm the relative energies among multiple LiTrCh 2 polymorphs and also model the observed powder X-ray diffraction pattern of a new C2 NaIn 3 Te 5 phase. 7 Li, 69 Ga, and 77 Se solid-state NMR spectra are consistent with phase-pure ternary LiGaSe 2 nanocrystals. A majority of the nanocrystal compositions are visible-light emitters. This work opens the door to new Li/Na-based ternary triel chalcogenide nanostructures for energy storage and conversion applications.

Pavel, Md Riad Sarkar [Iowa State Univ., Ames, IA ↗
DOE OSTI2020

A semblance measure for model comparison

Algorithmic and computational advances have made it possible that geophysical survey and earth model design can be aided by many systematic trial inverse-modelling runs with synthetic data. Such may, for example, come up in machine-learning approaches. Automated image appraisal pertaining to such applications will involve common statistical tests for goodness-of-data fit as a primary evaluation method. However, solution non-uniqueness may render multiple images equivalent in terms of their data fit, requiring secondary categorizers. A logical choice for classifying synthetic-imaging results quantifies the goodness of model fit where a known reference model replaces the observational input. The task of model intercomparison in terms of measuring the resemblance to the reference model poses challenges to common distance-based metrics like root mean square error and mean absolute error. First, distance-based metrics can introduce spurious contributions when smooth models with fuzzy target contours are to be compared against a sharp reference. Second, large differences due to parameter-estimation overshoots can dominate distance metrics. Here, we propose a remedy that is referred to as semblance and is based on the idea of logistic functions, where a binary-dependent variable adds non-zero or zero accumulation terms for the, respectively, passing or failing of preset target thresholds. This classifying approach is amenable to an objective where model feature recognition is primary. Numerical comparisons to distance-based metrics provide evidence for the advantages of the semblance in view of this objective. Geophysical imaging in conjunction with machine-learning is seen as a benefitting upcoming application area.

58 GEOSCIENCES↗
DOE OSTI2025

Distribution System Blackstart and Restoration Using DERs and Dynamically Formed Microgrids

Extreme weather events have led to long-duration outages in the distribution system (DS), necessitating novel approaches to blackstart and restore the system. Existing blackstart solutions utilize blackstart units to establish multiple microgrids (MGs), sequentially energize non-blackstart units, and restore loads. However, these approaches often result in isolated MGs. In DERs-aided blackstart, the continuous operation of these MGs is limited by the finite energy capacity of commonly used blackstart units like battery energy storage (BES)-based gridforming inverters (GFMIs). To address this issue, this article proposes a holistic blackstart and restoration framework that incorporates synchronization between dynamic MGs and the entire DS with the transmission grid (TG). To support synchronization, we leveraged virtual synchronous generator-based control for GFMIs to estimate their frequency response to load pick-up events using only initial/final quasi-steady-state points. Subsequently, a synchronization switching condition is developed to model synchronizing switches, aligning them seamlessly with a linearized branch flow problem. Finally, we designed a bottomup blackstart and restoration framework that considers the switching structure of the DS, energizing/synchronizing switches, DERs with grid-following inverters, and BES-based GFMIs with frequency security constraints. In conclusion, the proposed framework is validated in IEEE-123-bus system, considering cases with two and four GFMIs under various TG recovery instants.

24 POWER TRANSMISSION AND DISTRIBUTION↗