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At least 343 records · Page 19

5f-Shell Covalency in Actinide Complexes

This talk will focus on the theoretical description & analysis of 5f-shell covalency in actinide complexes, as well as the manifestation of this covalency in spectroscopic parameters such as the pre-edge peak energies and intensities in X-ray absorption near-edge structure (XANES) and related types of spectra, or ligand NMR chemical shifts, according to quantum chemical calculations. We are now able to analyze 5f covalency in the context of the participating atomic orbitals, their energies and interactions in a given molecule, and their overlap. A related issue is the assignment of oxidation states. Examples that will be discussed in the talk are [AnCl6](2-) with An = U, Np, Pu, various organometallic complexes with U and Th, and a recently reported ‘berkelocene’ sandwich complex.

Autschbach, Jochen↗

A Deep Learning Pipeline for Optimizing Large-scale Phase Field Simulations

Phase field (PF) simulations are computationally expensive but remain a key analysis tool to understand the complex mechanisms of additive manufacturing (AM) processes. Each PF simulation-aided analysis requires thousands of node hours on leadership-class supercomputers. One of the main goals of these analyses is the study of microstructure evolution during the build process which begins with the onset of nucleation. Nucleation occurs under certain thermomechanical conditions which are not known a priori and many PF simulations are required to identify ranges of input thermo-mechanical parameters that can result in the onset of nucleation. Since many of the simulations do not result in nucleation, an analysis campaign often ends up wasting tremendous amounts of precious computing resources executing nucleation-absent simulations. The goal of this work is to design and train deep learning models to inform a PF simulation about the likelihood of the occurrence of nucleation in a future simulation time-step based on the state summary over a finite number of past time-steps of a running simulation. If the prediction determines that the running simulation is unlikely to reach nucleation in the allotted time, then its execution is stopped immediately ultimately resulting in vast reduction in wasted computations when accrued over all the PF simulations typically performed in a single or multiple analysis campaign(s). The paper presents the performance of a machine learning pipeline that uses a convolutional neural network (CNN) model to learn an embedding which is then used with a self-attention network to build a multi-task deep learning model to predict the likelihood of nucleation. The model also predicts the input parameters used in a simulation. Performance is compared with a baseline pipeline that uses an off-the-shelf LeNet-5 model to learn the initial embedding. Despite their smaller size, performance results indicate significant improvement in accuracy of the proposed models compared to the larger baseline models.

Kannan, Ramakrishnan {ramki}↗

Soil Carbon and Nitrogen Elemental Analysis and Middle Infrared Spectroscopy from the Kougarok Fire Complex, Seward Peninsula, Alaska, 2022

In September and October of 2022, soil samples were collected at the Kougarok Fire Complex near mile marker 86 of the Nome-Taylor Highway on the Seward Peninsula of Alaska. This study site was chosen due to its unique fire history, as the Kougarok Fire Complex has experienced multiple wildfires since 1971. As the Arctic warms, the risk of Arctic tundra fires continues to increase due to warmer summer temperatures and higher frequency of lightning. Burned soil carbon or pyrogenic carbon (PyC) is an important component of C cycling after wildfire, and one that is often overlooked in tundra systems where wildfires are historically rare. To better understand PyC signatures and quantify PyC presence in post-regeneration permafrost regions, soils were sampled from soil pits within the 1971, 2002, and 2019 burn sites, as well as two unburned control sites. At each site, three soil pits were dug to the permafrost table. Soil samples were collected with a trowel from the face of each pit at 10 cm increments down to the permafrost table. Thaw depth, maximum vegetation height, vegetation species composition, and O horizon depth were also collected at each soil pit. An HS2 Hydrosense II Handheld Soil Moisture Sensor was used to collect volumetric soil moisture content at each 10 cm sampling increment. This dataset includes one *.csv of middle infrared spectroscopy measurements of soil samples, one *.csv of field observations, one *.csv of carbon and nitrogen analysis of soil samples, and one *.kml of sampling locations.The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic) was a 15-year research effort (2012-2027) to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy’s Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy’s Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗

Analysis of Transient Pressure and Rate Data in a Complex of Enhanced Oil Recovery Fields in Northern Michigan

The Midwest Regional Carbon Sequestration Partnership (MRCSP) was founded in 2003 as part of the U.S. Department of Energy’s (DOE’s) Regional Carbon Sequestration Partnership initiative. Since its founding, MRCSP has made significant strides toward making CCUS a viable option for states in the region. The public/private consortium, funded through the DOE Regional Carbon Sequestration Initiative, brings together nearly 40 industry partners and 10 states. Battelle, as the project lead, oversees research, development and operations and coordinates activities among the partners. The incremental, phased approach has built a valuable knowledge base for the industry and paved the way for commercial-scale adoption of CCUS technologies. From 2008 to 2020, MRCSP Phase III focused on the development of large-scale injection projects. This report is part of a series of reports prepared under the Midwestern Regional Carbon Sequestration Partnership (MRCSP) Phase III (Development Phase). These reports summarize and detail the findings of the work conducted under the Phase III project. A key activity of the MRCSP monitoring program was to continuously monitor the CO 2 injection and bottom-hole reservoir pressure in the injection wells and selected monitoring wells in the study reefs from 2013 through 2019. During the monitoring period, which varied from reef to reef, the reefs were undergoing one or more phases of development, such as CO 2 injection without hydrocarbon production, CO 2 injection with production Enhanced Oil Recovery (EOR), production without CO 2 injection, and idle (no injection or production) in pressure depleted condition. A multi-year record of reservoir pressure and injection rate data are available for one or more wells for each reef for analysis. This report discusses the methodology and results of various types of analyses performed with this data, with the primary objective of characterizing the in-situ permeability of the formation of interest.

01 COAL, LIGNITE, AND PEAT↗

Theoretical study of the CO 2 –O 2 van der Waals complex: potential energy surface and applications

A four-dimensional-potential energy surface (4D-PES) of the atmospherically relevant carbon dioxide–oxygen molecule (CO 2 –O 2 ) van der Waals complex is mapped using the ab initio explicitly correlated coupled cluster method with single, double, and perturbative triple excitations (UCCSD(T)-F12b), and extrapolation to the complete basis set (CBS) limit using the cc-pVTZ-F12/cc-pVQZ-F12 bases and the l –3 formula. An analytic representation of the 4D-PES was fitted using the method of interpolating moving least squares (IMLS). These calculations predict that the most stable configuration of CO 2 –O 2 complex corresponds to a planar slipped-parallel structure with a binding energy of V ~ –243 cm –1 . Another isomer is found on the PES, corresponding to a non-planar cross-shaped structure, with V ~ –218 cm –1 . The transition structure connecting the two minima is found at V ~ –211 cm –1 . We also performed comparisons with some CO 2 –X van der Waals complexes. Moreover, we provide a SAPT analysis of this molecular system. Then, we discuss the complexation induced shifts of CO 2 and O 2 . Afterwards, this new 4D-PES is employed to compute the second virial coefficient including temperature dependence. A comparison between quantities obtained in our calculations and those from experiments found close agreement attesting to the high quality of the PES and to the importance of considering a full description of the anisotropic potential for the derivation of thermophysical properties of CO 2 –O 2 mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Topological structure of complex predictions

Abstract Current complex prediction models are the result of fitting deep neural networks, graph convolutional networks or transducers to a set of training data. A key challenge with these models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into a simplified topological view of the prediction landscape. The result is a map of the predictions that enables inspection of the model results with more specificity than dimensionality-reduction methods such as tSNE and UMAP. The methods scale up to large datasets across different domains. We present a case study of a transformer-based model previously designed to predict expression levels of a piece of DNA in thousands of genomic tracks. When the model is used to study mutations in the BRCA1 gene, our topological analysis shows that it is sensitive to the location of a mutation and the exon structure of BRCA1 in ways that cannot be found with tools based on dimensionality reduction. Moreover, the topological framework offers multiple ways to inspect results, including an error estimate that is more accurate than model uncertainty. Further studies show how these ideas produce useful results in graph-based learning and image classification.

Computer Science↗

Mechanistic Studies of a Primitive Homolog of Nitrogenase Involved in Coenzyme F430 Biosynthesis (Final Report)

Methyl-coenzyme M reductase (MCR) is the key enzyme in the biological formation and anaerobic oxidation of methane (AOM). Methane is a potent greenhouse gas and the major component of natural gas. Given the abundance of natural gas reserves in remote areas, there is great current interest in a scalable bio-based process for the conversion of methane to liquid fuel and other high-value chemicals. MCR holds much promise for use in such a methane bioconversion strategy. However, MCR cannot currently be produced in an active form in a heterologous host, due in large part to the lack of genetic and biochemical information about the production of holo MCR. In an effort to overcome this deficiency, our laboratory recently elucidated the biosynthetic pathway of the unique nickel-containing coenzyme of MCR, F430. The key step in coenzyme F430 biosynthesis (Cfb) was found to involve an unprecedented reductive cyclization reaction. This remarkable transformation, which involves a 6-electron reduction, the formation of a γ-lactam ring, and the generation of 7 stereocenters, is catalyzed by a primitive homolog of nitrogenase (CfbCD). Nitrogenase is a two-component metalloenzyme that catalyzes the adenosine triphosphate (ATP)-dependent reduction of dinitrogen to ammonia (nitrogen fixation). Homologs of nitrogenase are also involved in the biosynthesis of the photosynthetic pigments chlorophyll and bacteriochlorophyll. Phylogenetic analysis of the CfbCD complex suggests that it is representative of a more ancient lineage of the nitrogenase superfamily, and a thorough investigation of its structure and function is likely to shed light on the mechanisms and evolution of these important metalloenzymes. Moreover, a detailed understanding of the mechanism of the CfbCD complex may aid in the development of specific inhibitors to help reduce natural greenhouse gas emissions and can be exploited for the heterologous production of MCR for methane bioconversion. Towards these goals, specific aims were pursued for the 1) identification of physiological electron donors and in vivo coenzyme F430 synthesis, 2) analysis of the iron sulfur centers, structure, and oligomerization state changes, and 3) characterization of transient intermediates and the intercomponent electron transfer.

03 NATURAL GAS↗

A deep learning approach for semantic segmentation of unbalanced data in electron tomography of catalytic materials

In computed TEM tomography, image segmentation represents one of the most basic tasks with implications not only for 3D volume visualization, but more importantly for quantitative 3D analysis. In case of large and complex 3D data sets, segmentation can be an extremely difficult and laborious task, and thus has been one of the biggest hurdles for comprehensive 3D analysis. Heterogeneous catalysts have complex surface and bulk structures, and often sparse distribution of catalytic particles with relatively poor intrinsic contrast, which possess a unique challenge for image segmentation, including the current state-of-the-art deep learning methods. To tackle this problem, we apply a deep learning-based approach for the multi-class semantic segmentation of a γ-Alumina/Pt catalytic material in a class imbalance situation. Specifically, we used the weighted focal loss as a loss function and attached it to the U-Net’s fully convolutional network architecture. We assessed the accuracy of our results using Dice similarity coefficient (DSC), recall, precision, and Hausdorff distance (HD) metrics on the overlap between the ground-truth and predicted segmentations. Our adopted U-Net model with the weighted focal loss function achieved an average DSC score of 0.96 ± 0.003 in the γ-Alumina support material and 0.84 ± 0.03 in the Pt NPs segmentation tasks. We report an average boundary-overlap error of less than 2 nm at the 90th percentile of HD for γ-Alumina and Pt NPs segmentations. The complex surface morphology of γ-Alumina and its relation to the Pt NPs were visualized in 3D by the deep learning-assisted automatic segmentation of a large data set of high-angle annular dark-field (HAADF) scanning transmission electron microscopy (STEM) tomography reconstructions.

36 MATERIALS SCIENCE↗

Report on FY 2021 testing in support of integrating Alloy 800H and 2.25Cr-1Mo for EPP analysis

The use of simplified Elastic-Perfectly Plastic (EPP) design methods avoids the complexities and limitations of the elastic analysis approach in evaluating strain limits and creep-fatigue damage for Class A metallic coolant boundary components in ASME Boiler and Pressure Vessel Code, Section III, Division 5, Subsection HB, Subpart B. No stress classification and linearization are required in the EPP methods. Further, the strain limits and creep-fatigue damage evaluation procedures based on elastic analysis results were developed for the reactor operating conditions where uncoupled, rate-independent plasticity and stationary creep can be used to approximate the deformation in the component adequately. But at very high temperatures, the deformation is rate-dependent, and it can only be approximated adequately by unified viscoplastic model. Thus, for example, the elastic analysis approach cannot be used to evaluate strain limits and creep-fatigue damage for Alloy 617 above 650 °C. The EPP methods remove the temperature restriction. They can be used to evaluate strain limits and creep-fatigue damage for the full range of temperatures.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Graph characterization of higher-order structure in atmospheric chemical reaction mechanisms

Atmospheric chemical reactions play an important role in air quality and climate change. While the structure and dynamics of individual chemical reactions are fairly well understood, the emergent properties of the entire atmospheric chemical system, which can involve many different species that participate in many different reactions, are not well described. In this work, we leverage graph-theoretic techniques to characterize patterns of interaction (“motifs”) in three different representations of gas-phase atmospheric chemistry, termed “chemical mechanisms.” These widely used mechanisms, the master chemical mechanism, the GEOS-Chem mechanism, and the Super-Fast mechanism, vary dramatically in scale and application, but they all generally aim to simulate the abundance and variability of chemical species in the atmosphere. This motif analysis quantifies the fundamental patterns of interaction within the mechanisms, which are directly related to their construction. For example, the gas-phase chemistry in the very small Super-Fast mechanism is entirely composed of bimolecular reactions, and its motif distribution matches that of an individual bimolecular reaction well. The larger and more complex mechanisms show emergent motif distributions that differ strongly from any specific reaction type, consistent with their complexity. The proposed motif analysis demonstrates that while these mechanisms all have a similar design goal, their higher-order structure of interactions differs strongly and thus provides a novel set of tools for exploring differences across chemical mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Deciphering Distinct Overpotential-Dependent Pathways for Electrochemical CO 2 Reduction Catalyzed by an Iron–Terpyridine Complex

[Fe(tpyPY2Me)] 2+ ([Fe] 2+ ) is a homogeneous electrocatalyst for converting CO 2 into CO featuring low overpotentials of <100 mV, near-unity selectivity, and high activity with turnover frequencies faster than 100 000 s -1 . To identify the origins of its exceptional performance and inform future catalyst design, we report a combined computational and experimental study that establishes two distinct mechanistic pathways for electrochemical CO 2 reduction catalyzed by [Fe] 2+ as a function of applied overpotential. Electrochemical data shows the formation of two catalytic regimes at low (η TOF/2 of 160 mV) and high (η TOF/2 of 590 mV) overpotential plateaus. We propose that at low overpotentials [Fe] 2+ undergoes a two-electron reduction, two-proton-transfer mechanism (electrochemical-electrochemical-chemical-chemical, EECC), where turnover occurs through the dicationic iron complex, [Fe] 2+ . Computational analysis supports the importance of the singlet ground-state electronic structure for CO 2 binding and that the rate-limiting step is the second protonation in this low-overpotential regime. When more negative potentials are applied, an additional electron-transfer event occurs through either a stepwise or proton-coupled electron-transfer (PCET) pathway, enabling catalytic turnover from the monocationic iron complex ([Fe] + ) via an electrochemical-chemical-electrochemical-chemical (ECEC) mechanism. Comparison of experimental kinetic data obtained from variable controlled potential electrolysis (CPE) experiments with direct product detection with calculated rates obtained from the energetic span model supports the PCET pathway as the most likely mechanism. Moreover, we build upon this mechanistic understanding to propose the design of an improved ligand framework that is predicted to stabilize the key transition states identified in our study and explore their electronic structures using an energy decomposition analysis. Finally, taken together, this work highlights the value of synergistic computational/experimental approaches to decipher mechanisms of new electrocatalysts and direct the rational design of improved platforms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

AUTOMATIC GENERATION OF EVENT TREES AND FAULT TREES: A MODEL-BASED APPROACH

In the past few decades, increasing complexity in modern engineering systems has been driven by the integration of a large number of components and by the fact that the system operations involve many disciplines (e.g., thermal-hydraulics, plant operations, cyber-security). Current safety/reliability modeling approaches to such systems are labor intensive, difficult to learn, and rely heavily on simplistic Boolean logic to depict failure propagation and accident progression. While these methods serve well for simple systems (i.e., linear causal systems with limited small inter- and intra-system interactions), their results are difficult to verify when modeling complex systems (typically performed through the extensive use of modeling assumptions). The development of new methods is addressed to meet these challenges through a model-based system engineering (MBSE) lens. Under MBSE philosophy, every aspect of the system (form or function) is represented by a model that completely characterizes its architecture or behavior. MBSE approach greatly improves the management of design, analysis and verification of complex systems. An integration of Dynamic Probabilistic Risk Assessment (DPRA) methods with MBSE models is proposed to perform safety/reliability analyses of engineering systems. In particular, MBSE representation of the system (performed using Systems Modeling Language [SysML]) is coupled with DPRA methods to automatically generate event trees and fault trees.

97 - MATHEMATICS AND COMPUTING↗

Synthesis, Structure, and Redox Reactivity of Ni Complexes Bearing a Redox and Acid–Base Non-innocent Ligand with Ni II , Ni III , and Ni IV Formal Oxidation States

Here, a series of Ni complexes bearing a redox and acid–base noninnocent tetraamido macrocyclic ligand, H 4 -(TAML-4) {H 4 -(TAML-4) = 15,15-dimethyl-5,8,13,17-tetrahydro-5,8,13,17-tetraaza-dibenzo[a,g]cyclotridecene-6,7,14,16-tetraone}, with formal oxidation states of Ni II , Ni III , and Ni IV were synthesized and characterized structurally and spectroscopically. The X-ray crystallographic analysis of the Ni complexes revealed a square planar geometry, and the [Ni(TAML-4)] complex with the formal oxidation state of Ni IV was characterized to be [Ni III (TAML-4 •+ )] with the oxidation state of the Ni III ion and the one-electron oxidized TAML-4 ligand, TAML-4 •+ . The Ni III oxidation state and the TAML-4 radical cation ligand, TAML-4 •+ , were supported by X-ray absorption spectroscopy and density functional theory calculations. The reversible interconversions between [Ni II (TAML-4)] 2– and [Ni III (TAML-4)] − and between [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were demonstrated in spectroelectrochemical measurements as well as in chemical oxidation and reduction reactions. The reactivities of [Ni III (TAML-4)] − and [Ni III (TAML-4 •+ )] were then investigated in hydride transfer reactions using NADH analogs. Hydride transfer from 9,10-dihydro-10-methylacridine (AcrH 2 ) to [Ni III (TAML-4 •+ )] was found to proceed via electron transfer (ET) from AcrH 2 to [Ni III (TAML-4 •+ )] with no deuterium kinetic isotope effect (k H /k D = 1.0(2)). In contrast, hydride transfer from AcrH 2 to [NiIII(TAML-4)] − proceeded much more slowly via a concerted proton-coupled electron transfer (PCET) process with k H /k D = 7.0(5). In the latter reaction, an electron and a proton were transferred to the Ni III center and the TAML-4 ligand, respectively. The mechanisms of the ET by [Ni III (TAML-4 •+ )] and the concerted PCET by [Ni III (TAML-4)] − were ascribed to the different redox potentials of the Ni complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hardware-Efficient Quantum Phase Estimation via Local Control

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

Schiffer, Benjamin F. [Max Planck Institute of Qua↗

Statistically-driven Experimental Design to Improve Reference-free Quantification of Small Molecules by Liquid Chromatography-Mass Spectrometry

Non-targeted analysis of small molecules and metabolites in unknown, complex samples using liquid chromatography-tandem mass spectrometry remains challenging. One of the main bottlenecks is the extensive unannotated regions of metabolomics mass spectrometry data, resulting in knowledge gaps. Small molecule annotation in mass spectrometry data has conventionally relied on reference standards and libraries for compound identification and confirmation, which can constrain compound identification to those molecules already known, thus limiting the ability to discover new knowledge and new markers. Retention time prediction can facilitate and expedite unknown compound identification in non-targeted analysis of complex metabolomics samples. Additionally, accurate retention time predictions can also inform sample mixture design for LC-MS/MS analyses. However, current machine learning-based methods for retention time prediction are typically developed for specific chromatographic platforms and are not generalizable across scales. And while technologies and methods to improve reference-free metabolite identification for more comprehensive annotation of unknowns has received much attention, development of the same for quantitation without reference standards has been much more limited, despite its importance in toxicological, environmental, food safety, forensics, and clinical applications. We believe that a reference-free quantitation strategy that exploits mass spectrometry data already collected for reference-free identification can provide much more insight on unknowns, and move the metabolomics field for more complete unknowns characterization. As such, we pursue two efforts to improve upon current state-of-the-art methods in non-targeted analysis: (1) machine learning-based retention time prediction and (2) statistical design of experiments framework for reference-free quantitation. In this work, we develop and demonstrate (1) a generalizable retention time prediction capability across chromatographic conditions and scales, and (2) a statistical design-based framework for response factor contribution elucidation and reference-free quantitation. Evaluation of our retention time prediction model, PrediToR, showed approximately 24% improvement over current models, and we observed approximately 10X improvement in concentration estimation accuracy from our statistical design-based response factor model over a primarily ionization efficiency-based model. We expect that future efforts to improve upon these new capabilities will further advance non-targeted analysis of small molecules towards truly reference-free metabolomics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Contingency Analysis Based on Partitioned and Parallel Holomorphic Embedding

In the steady-state contingency analysis, the traditional Newton-Raphson method suffers from non-convergence issues when solving post-outage power flow problems, which hinders the integrity and accuracy of security assessment. In this paper, we propose a novel robust contingency analysis approach based on holomorphic embedding (HE). Here, the HE-based simulator provides theoretical convergence guarantee, which is desirable because it avoids the influence of numerical issues and provides a credible security assessment conclusion. In addition, based on the multi-area characteristics of real-world power systems, a partitioned HE (PHE) method is proposed with an interfacebased partitioning of HE formulation. The PHE method does not undermine the numerical robustness of HE and significantly reduces the computation burden in large-scale contingency analysis. The PHE method is further enhanced by parallel or distributed computation to become parallel PHE (P2HE). Tests on a 458-bus system, a synthetic 419-bus system and a large-scale 21447-bus system demonstrate the advantages of the proposed methods in robustness and efficiency.

42 ENGINEERING↗