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At least 757 records · Page 42

Novel Geochemistry Determined from High Pressure, High Temperature Simulation Experiments of Hydraulic Fracture Test Site 2

A standard method in unconventional oil and gas production is the process of hydraulic fracturing followed by a shut-in period, during which the fracture fluid remains pressurized in the reservoir for up to three weeks before production begins. Despite this widely used process, very little is known about what occurs in the reservoir during this shut-in process. In order to properly delineate potential reservoir reactions that may occur during shut-in that would lead to corrosion and scaling events, experiments were conducted in high pressure, high temperature reactors to simulate conditions of the Wolfcamp Formation in the Delaware Basin. Experimental design allowed the assessment of the effect of proppant, microbiology, and time on the mineralogy and fluid chemistry in the reservoir. Results suggest the biggest impact on fluid chemistry and shale mineralogy during shut-in is time. Analyses demonstrate dissolution of the shale material, with maximum dissolved ions occurring after 7 days of the shut-in period. After 21 days, results suggest precipitation occurs. The Delaware Basin is demonstrated to be high in sulfate content, which further increases in the fluid due to dissolution reactions during shut-in. The pressure vessel experiments suggest there was no significant contribution to reactions from microbiology during the shut-in period. Furthermore, early production samples demonstrate a significant selection of the microorganism Caminicella, a genus of which has previously been correlated to corrosion and sulfide production. Results suggest shut-in conditions may provide high sulfate concentrations that could later be utilized by a shifted microbial community to drive potential well infrastructure failure. This is the first study to incorporate microbiology, mineralogy, and fluid chemistry to investigate the fundamental geochemical reactions that occur during shut-in and early phase production of the Delaware Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/21URTC/2-21URTC/D021S032R001/2477425/urtec-2021-5219-ms.pdf/1 by Carol Worster on 28 February 2022 Basin. Results from this study can complement observations from the Hydraulic Fracture Test Site 2 observations

58 GEOSCIENCES↗

ESR Dipole Power Supply Current Ripple and Noise Specifications

This note presents key findings for the ESR main magnet dipole power supplies (PS), where we find the current ripple specification to be close to or beyond the state-of-the-art. These specifications originate from beam-beam considerations, with the requirement to limit the ripple-induced hadron emittance growth to below 10%/hour. Beam dynamics that drive this PS ripple specification arise from the beam motions at the Interaction Point (IP). The frequency of the motions can be separated into "low", compared to the betatron frequency, and "high", i.e. around the betatron frequency and harmonics. In terms of the driving frequency, "low" implies ƒ<<ƒ 0 v x,y and "fast" means ƒ≈{ƒ 0 v x,y , ƒ 0 (1- v x,y , etc.}, where ƒ 0 =1/ T 0 =78.2 kHz is the revolution frequency, and v x,y are the fractional parts of the betatron tunes. Frequencies higher than ƒ 0 /2 will be folded back due to the particles sampling the field once per turn. To provide flexibility for future lattice adjustments and working point variations, we do not consider the tunes as fixed. Instead, we assume a certain margin and allow them to potentially fall within the range of 0.1< v x,y <0.5. In other words, the high-frequency region spans approximately from 8kHz to 40 kHz. Consequently,, we definte the dipole PS ripple in two distinct frequency ranges: the low-frequency range of [1-8000] Hz and the high-frequency range of [8-40] kHz. For the physics effects we analyzed in this note, there is no distinction between the ripple (which can be approximately reproduced in the frequency domain) and the random noise if both have some power within the frequency bandwidth of interest. Therefore, while we will use the term "ripple" for short, it should always be understood that we are referring to "ripple plus noise." Except for the lower end of the low-frequency range, the impact of the rippling PS current on the beam will be considerably reduced due to the eddy currents induced in the walls of the vacuum chamber. We will account for this effect in the PS ripple specifications to follow. The remaining sections of this note are structure as follows: Section II outlines the beam-beam physics requirements for the positional stability of the beam at the IP. Section III describes the anticipated shielding effect of the eddy currents induced in the vacuum chamber. Section IV derives the ripple requirement for the low-frequency range by propagating the closed orbit ripple resulting from the rippling dipoles to the IP (relevant lattice simulation results are summarized in the Appendix). In Section V, we present the analytical criterion for the ripple in the high-frequency range by considering resonant oscillations of the electron beam around a stable closed orbit near the betatron frequency. Finally, Section VI provides a summary of our findings and discusses related work.

43 PARTICLE ACCELERATORS↗

Current measurements in the intermittent-contact mode of atomic force microscopy using the Fourier method: a feasibility analysis

Atomic force microscopy (AFM) is an important tool for measuring a variety of nanoscale surface properties, such as topography, viscoelasticity, electrical potential and conductivity. Some of these properties are measured using contact methods (static contact or intermittent contact), while others are measured using noncontact methods. Some properties can be measured using different approaches. Conductivity, in particular, is mapped using the contact-mode method. However, this modality can be destructive to delicate samples, since it involves continuously dragging the cantilever tip on the surface during the raster scan, while a constant tip–sample force is applied. In this paper we discuss a possible approach to develop an intermittent-contact conductive AFM mode based on Fourier analysis, whereby the measured current response consists of higher harmonics of the cantilever oscillation frequency. Such an approach may enable the characterization of soft samples with less damage than contact-mode imaging. To explore its feasibility, we derive the analytical form of the tip–sample current that would be obtained for attractive (noncontact) and repulsive (intermittent-contact) dynamic AFM characterization, and compare it with results obtained from numerical simulations. Although significant instrumentation challenges are anticipated, the modelling results are promising and suggest that Fourier-based higher-harmonics current measurement may enable the development of a reliable intermittent-contact conductive AFM method.

14 SOLAR ENERGY↗

Cascade flutter analysis with transient response aerodynamics

Two methods for calculating linear frequency domain aerodynamic coefficients from a time-marching Full-Potential cascade solver are developed and verified. In the first method, the Influence Coefficient method, solutions to elemental problems are superposed to obtain the solutions for a cascade in which all blades are vibrating with a constant interblade phase angle. The elemental problem consists of a single blade in the cascade oscillating while the other blades remain stationary. In the second method, the Pulse Response method, the response to the transient motion of a blade is used to calculate influence coefficients. This is done by calculating the Fourier transforms of the blade motion and the response. Both methods are validated by comparison with the Harmonic Oscillation method and give accurate results. The aerodynamic coefficients obtained from these methods are used for frequency domain flutter calculations involving a typical section blade structural model. An eigenvalue problem is solved for each interblade phase angle mode and the eigenvalues are used to determine aeroelastic stability. Flutter calculations are performed for two examples over a range of subsonic Mach numbers using both flat plates and actual airfoils.

Bakhle, Milind A.↗

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction—the dissociation of molecular nitrogen on ruthenium—at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an “on-top” adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. Finally, these findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of Collective Dynamics and Anharmonicity on Entropy in Heterogenous Catalysis: Building the Case for Advanced Molecular Simulations

In this paper, we present a perspective on the computational determination of entropy and its effects and consequences on heterogeneous catalysis. Special attention is paid to the role of anharmonicity and the deviations from the standard harmonic oscillator approximations which can fail to provide a reliable assessment of entropy. To address these challenges, advanced methodologies are needed that can explicitly account for these thermodynamic drivers through the appropriate statistical sampling of reactive free energy surfaces. We discuss where anharmonicity should be expected, where it has been observed from a theoretical perspective, and the methods currently employed to address it. We concentrate on three types of systems where we have observed major, nonnegligible anharmonic effects: (1) supported nanoparticles, where the migration of metal atoms, complexes, and entire clusters exhibit anharmonic behavior in their dynamic motion; (2) porous solids where confinement effects distort potential energy surfaces and hinder molecular motions resulting in large entropic terms; and (3) solid/liquid interfaces, where interactions between solvent molecules and adsorbed species can result in large solvent organization free energy and unique reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Above-threshold multiphoton photoemission from noble metal surfaces

Exciting solids with intense femtosecond laser pulses prompts electrons of the interrogated material to respond in a highly nonlinear manner, as is evident in the emission of high-order harmonic radiation and photoelectrons with kinetic energies well above that of the driving photons. Such high-field interactions can be resolved, for example, in above-threshold multiphoton photoemission (ATP) spectroscopy. In this work, we interrogate the nonlinear photoelectric responses of the pristine copper, silver, and gold noble metal surfaces in (111) and (100) crystal orientations in the perturbative regime. Using multiphoton photoemission spectroscopy (mPP) excited by finely tuned optical fields, we characterize enhancement of the mPP and ATP yields from (111) surfaces in selected k||-momentum ranges when the occupied Shockley surface (SS) states are (near-)resonantly coupled by multiphoton transitions to image potential (IP) intermediate states in the excitation process. The ATP signal from the IP states of (111) surfaces is largely defined by their formation through polarization of SS electrons; this observation is contrasted with ATP experiments from the Ag(100) surface, for which the SS becomes an unoccupied resonance and the IP states can only be excited from bands with significantly more bulk character. In addition, based on the optical power and nonlinear order-dependent mPP spectra, we provide evidence for ATP being a one-step, rather than a sequential process, as previously postulated.

74 ATOMIC AND MOLECULAR PHYSICS↗

A Numerical Investigation of Turbine Noise Source Hierarchy and Its Acoustic Transmission Characteristics

Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. The investigation relies on highly detailed numerical simulations of the unsteady flowfield inside a modern high-pressure turbine (HPT). The simulations are developed using TURBO, which is an unsteady Reynolds-averaged Navier-Stokes (URANS) code capable of multi-stage simulations. The purpose of this study is twofold. First, to determine an estimate of the relative importance of the contributions to the coherent part of the acoustic signature of a turbine from the three potential sources of turbine noise generation, namely, blade-row viscous interaction, potential field interaction, and entropic source associated with the interaction of the blade rows with the temperature nonuniformities caused by the incomplete mixing of the hot fluid and the cooling flow. Second, to develop an understanding of the turbine acoustic transmission characteristics and to assess the applicability of existing empirical and analytical transmission loss models to realistic geometries and flow conditions for modern turbine designs. The investigation so far has concentrated on two simulations: (1) a single-stage HPT and (2) a two-stage HPT and the associated inter-turbine duct/strut segment. The simulations are designed to resolve up to the second harmonic of the blade passing frequency tone in accordance with accepted rules for second order solvers like TURBO. The calculations include blade and vane cooling flows and a radial profile of pressure and temperature at the turbine inlet. The calculation can be modified later to include the combustor pattern factor at the turbine inlet to include that contribution to turbine noise. We shall present preliminary analysis of the results obtained so far in order to assess the validity of such an approach and to seek feedback on improving the approach. This work addresses both Area 1 (Turbine Tone Noise) and Area 5 (Influence of the Turbine on Combustor Noise) topics.

VanZante, Dale↗

A Comparative Techno-Economic Analysis of Sustainable Methanol Synthesis Pathways from Biomass and CO2

The call to reduce global CO2 emissions is at the forefront of research and development in the transportation and petrochemical industries. A potential solution which intersects both sectors is the adoption and commercialization of more sustainable technologies for methanol production. Currently, methanol is gaining popularity as a possible fuel additive, and as a polymer precursor via established methanol-to-olefins routes which are increasing in capacity and utilization, putting methanol in the spotlight and global methanol production on the rise. At the same time, experimental and computational studies have surged, illuminating a wide array of novel process designs to introduce sustainable methanol into the market. However, with numerous competing pathways identified across a variety of fossil and non-fossil feedstocks, there is a need to harmonize the analyses of these pathways using a consistent techno-economic approach and compare them to current commercial pathways to better understand the benefits or limitations inherent to each technology. In this work we conduct a consistent comparative analysis of three sustainable methanol synthesis pathways versus a commercial baseline, with biomass, CO2, and natural gas as the carbon sources. The three sustainable pathways of interest are biomass gasification to syngas with subsequent catalytic conversion of syngas to methanol, indirect conversion of CO2 to syngas via electrolysis with subsequent catalytic conversion of syngas to methanol, and direct conversion of CO2 to methanol via electrolysis. To elucidate the challenges and opportunities in the path to commercialization of each sustainable pathway, we investigate five key process metrics: production cost, carbon efficiency, carbon intensity, energy efficiency, and technology readiness level (TRL).

biomass↗

Becoming a 10: A Closer Look at the U.S. Department of Energy Home Energy Score's Updates, Improvements, and Expansion

The U.S. Department of Energy (DOE)'s Home Energy Score provides homeowners, buyers, and renters directly comparable and credible information about a home's estimated energy use and costs. Certified Qualified Assessors conduct low-cost assessments to provide each home a 1-10 score alongside a set of cost-effective upgrades to improve the score. As of February 2022, hundreds of assessors have delivered over 175,000 scores to homes across the country. Originally released in 2012 using DOE2.1e as the modeling backend, after years of effort, a new version of Home Energy Score was released in 2021 utilizing DOE's flagship energy modeling software, EnergyPlus. The updated architecture leverages modeling advancements and enables new building technologies to be added to the Scoring Tool. The new release represents a leap forward in harmonizing modeling assumptions across DOE and industry programs. In this paper we discuss the rigorous approach to model comparison with DOE2 undertaken prior to the update, utilizing test homes and real homes from the Home Energy Score database to strike a balance between consistency and more accurate energy predictions. We also discuss additional new capabilities, including improvements made to the upgrade recommendations methodology, the inclusion of an energy cost estimate metric based on ResStock analysis for use in home appraisals, and improved data analysis for quality assurance. Finally, we look at the impact Home Energy Score has had over the last decade and its future potential as its uptake in state energy plans, local ordinances, utility programs, and real estate data continues to grow.

building energy modeling↗

Analog Quantum Simulation of the Dynamics of Open Quantum Systems with Quantum Dots and Microelectronic Circuits

We introduce a general setup for the analog quantum simulation of the dynamics of open quantum systems based on semiconductor quantum dots electrically connected to a chain of quantum RLC electronic circuits. The dots are chosen to be in the regime of spin-charge hybridization to enhance their sensitivity to the RLC circuits while mitigating the detrimental effects of unwanted noise. In this context, we establish an experimentally realizable map between the hybrid system and a qubit coupled to thermal harmonic environments of arbitrary complexity that enables the analog quantum simulation of open quantum systems. We assess the utility of the simulator by numerically exact emulations that indicate that the experimental setup can faithfully mimic the intended target even in the presence of its natural inherent noise. We further provide a detailed analysis of the physical requirements on the quantum dots and the RLC circuits needed to experimentally realize this proposal that indicates that the simulator can be created with existing technology. The approach can exactly capture the effects of highly structured non-Markovian quantum environments typical of photosynthesis and chemical dynamics, and offer clear potential advantages over conventional and even quantum computation. The proposal opens a general path for effective quantum dynamics simulations based on semiconductor quantum dots.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Coherent spin wave excitation with radio-frequency spin–orbit torque

Spin waves, collective perturbations of magnetic moments, are both fundamental probes for magnetic physics and promising candidates for energy-efficient signal processing and computation. Traditionally, coherent propagating spin waves have been generated by radio frequency (RF) inductive Oersted fields from current-carrying electrodes. An alternative mechanism, spin–orbit torque (SOT), offers more localized excitation through interfacial spin accumulation but has been mostly limited to DC to kHz frequencies. SOT driven by RF currents, with potentially enhanced pumping efficiency and unique spin dynamics, remains largely unexplored, especially in magnetic insulators. Here, we conduct a comprehensive theoretical and computational investigation into the generation of coherent spin waves via RF-SOT in the prototypical yttrium iron garnet. We characterize the excitation of forward volume, backward volume, and surface modes in both linear and nonlinear regimes, employing single and interdigitated electrode configurations. We reveal and explain several unique and surprising features of RF-SOT compared to inductive excitation, including higher efficiency, distinct mode selectivity, and directional symmetry, a ~ $3π/4$ phase offset, reduced anharmonic distortion in the nonlinear regime, and the absence of second harmonic generation. These insights position RF-SOT as a promising new mechanism for future magnonic and spintronic applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Mode transitions and spoke structures in E × B Penning discharge

Two-dimensional particle-in-cell simulations in the (radial-azimuthal) plane perpendicular to the axial direction of a cylindrical $E$ x $B$ Penning discharge are presented. The low-pressure discharge is self-consistently supported by plasma ionization from the electron beam injected axially, along the direction of the external magnetic field. It is shown that with the increasing strength of the external magnetic field, the discharge undergoes a sequence of transitions between several azimuthal modes. Azimuthal m > 1 spiral arm structures are excited at low magnetic field values as plasma confinement improves and the radial density profile becomes peaked. With a larger field, spiral arms with m > 1 are replaced by the m = 1 spoke mode, most clearly seen in plasma density. A transition from spiral arms to the spoke regime occurs when the plasma potential in the center changes from weakly positive (or zero) to negative. Further increase in the magnetic field results in a well-developed m = 1 spoke mode with additional small-scale higher-frequency m > 1 structures inside and around the spoke. It is shown that while ionization and collisions affect some characteristics of the observed fluctuations, the basic features of the spoke and m > 1 spiral structure remained similar without ionization. The role of energy conservation in small-scale high-frequency modes and spoke dynamics is discussed. It is demonstrated that in regimes with the m = 1 spoke mode, additional m = 4 harmonics of the ion and electron fluxes to the wall appear due to the square boundary. The frequency of the m = 1 mode is weakly affected by the geometry of the boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Multiphoton and Harmonic Imaging of Microarchitected Materials

Microadditive manufacturing has revolutionized the production of complex, nano- to microscale components across various fields. This work investigates two-photon (2P) and three-photon (3P) fluorescence imaging, as well as third-harmonic generation (THG) microscopy, to examine periodic microarchitected lattice structures fabricated using multiphoton lithography (MPL). By immersing the structures in refractive index matching fluids, we demonstrate high-fidelity 3D reconstructions of both fluorescent structures using 2P and 3P microscopy as well as low-fluorescence structures using THG microscopy. These results show that multiphoton fluorescence (MPF) imaging offers reduced signal decay with respect to depth compared to single-photon techniques in the examined structures. We further demonstrate the ability to nondestructively identify intentional internal modifications of the structure that are not immediately visible with scanning electron microscope (SEM) images and compression-induced fractures, highlighting the potential of these techniques for quality control and defect detection in microadditively manufactured components.

36 MATERIALS SCIENCE↗

Frequency-domain computing using nonlinear acoustic-wave device on lithium niobate

Abstract Multiply-accumulation are crucial computing operations in signal processing, numerical simulations, and machine learning. In recent years, optical analog approaches have demonstrated higher computing performance and better power efficiency than their digital counterparts. However, analog computing chips usually need large areas and complex structures for parallel computing, as a single device element only executes one computing operation at a single time. Here, we demonstrate frequency-domain computing using the nonlinear acoustic-wave devices on lithium niobate, featuring a normalized external second-harmonic generation conversion efficiency of ~ 5.7 × 10-4 W-1. The second-order sum-frequency nonlinear process of lithium niobate enables multiplication of inputs encoded in the frequency domain. Compared to the analog schemes, our device features a notably simpler design, and nanofabrication requires only one lift-off. Using a single acoustic-wave device within an area of 0.03 mm2, we can simultaneously conduct over 130,000 multiply-accumulation operations. Our acoustic-wave device shows applications in real and complex vector convolutions and image processing. This demonstration sets the stage for experimental realizations into frequency-domain integrated nonlinear acoustic computing systems, potentially shaping future developments in acoustic neural networks and quantum computing.&#xD;

chai, mingzhao (ORCID:0009000466226341)↗

Black Start of Unbalanced Microgrids Harmonizing Single- and Three-Phase Grid-Forming Inverters

As power systems are transforming with increasing penetrations of inverter-based resources (IBRs), system restoration using IBRs has drawn attention. Using distributed grid-forming (GFM) assets located near critical loads, either three-phase or single-phase, to establish microgrid voltages in the absence of a bulk grid, a distribution system could obtain high system survivability. For swift and secure recovery of a critical load in a single-phase lateral, local single-phase GFM inverters can form a microgrid, and then it can be combined with a neighbouring grid with the inverters remaining in GFM mode for voltage and frequency regulation until the bulk grid comes online. It leads to dynamic interoperation of single-phase GFM inverters with three-phase ones in the black start process. This paper studies the novel approach with electromagnetic transient (EMT) simulations. To evaluate the potential and the technical challenges of the heterogeneous IBR-driven black start, three-phase and single-phase GFM inverter models are developed, including negative-sequence control for voltage balance and a phase-by-phase current limiter (three-phase) and current magnitude limiter (single-phase). To examine dynamic aspects of the black-start process, the EMT simulation also models transformer and motor dynamics emulating their inrush and startup behavior as well as network dynamics. Involvement of grid-following assets to facilitate the black-start process is also modeled. By allowing multiple GFM inverters to collectively black start without leader-follower coordination, regardless of phases, a system can achieve extreme resilience. An inverter-driven black start of a heavily unbalanced 2-MVA distribution feeder using 1 three-phase and 3 single-phase GFM inverters is demonstrated. The simulation shows the heterogeneous system can maintain stability with the single-phase GFM dynamics coupled with the three-phase one.

grid-forming inverter↗

Applications of the Kustaanheimo-Stieffel transformation of the perturbed two-body problem

The Newtonian differential equations of motion for the two-body problem can be transformed into four linear harmonic-oscillator equations by simultaneously applying the regularization step dt/ds = r and the Kustaanheimo-Stieffel (KS) transformation. The regularization step changes the independent variable from time to a new variable s, and the KS transformation transforms the position and velocity vectors from Cartesian space into a four-dimensional space. A derivation of a uniform, regular solution for the perturbed two-body problem in the four-dimensional space is presented. The variation-of-parameters technique is used to develop expressions for the derivatives of ten elements (which are constants in the unperturbed motion) for the general case that includes both perturbations which can arise from a potential and perturbations which cannot be derived from a potential. This ten-element solution has mixed secular terms that degrade the long-term accuracy during numerical integration. Therefore, to eliminate these terms, the solution is modified by introducing two additional elements.

Bond, V. R.↗

Black Start of Unbalanced Microgrids Harmonizing Single- and Three-Phase Grid-Forming Inverters: Preprint

As power systems are transforming with increasing penetrations of inverter-based resources (IBRs), system restoration using IBRs has drawn attention. Using distributed grid-forming (GFM) assets located near critical loads, either three-phase or single-phase, to establish microgrid voltages in the absence of a bulk grid, a distribution system could obtain high system survivability. For swift and secure recovery of a critical load in a single-phase lateral, local single-phase GFM inverters can form a microgrid, and then it can be combined with a neighbouring grid with the inverters remaining in GFM mode for voltage and frequency regulation until the bulk grid comes online. It leads to dynamic interoperation of single-phase GFM inverters with three-phase ones in the black start process. This paper studies the novel approach with electromagnetic transient (EMT) simulations. To evaluate the potential and the technical challenges of the heterogeneous IBR-driven black start, three-phase and single-phase GFM inverter models are developed, including negative-sequence control for voltage balance and a phase-by-phase current limiter (three-phase) and current magnitude limiter (single-phase). To examine dynamic aspects of the black-start process, the EMT simulation also models transformer and motor dynamics emulating their inrush and startup behavior as well as network dynamics. Involvement of grid-following assets to facilitate the black-start process is also modeled. By allowing multiple GFM inverters to collectively black start without leader-follower coordination, regardless of phases, a system can achieve extreme resilience. An inverter-driven black start of a heavily unbalanced 2-MVA distribution feeder using 1 three-phase and 3 single-phase GFM inverters is demonstrated. The simulation shows the heterogeneous system can maintain stability with the single-phase GFM dynamics coupled with the three-phase one.

grid-forming inverter↗