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DOE OSTI2021

The development of a Sustained High Power Density (SHPD) facility

A Sustained High Power Density (SHPD) facility is being planned within the U.S. as a non DT device which can be a bridge to a Compact Fusion Pilot Plant (CFPP) DT operated facility with the future capacity to produce a levelised cost of electricity at a rate competitive with current power generating systems. To accomplish this a review of ITER cost data and recent next step physics/engineering studies that promoted technology development, physics enhancements and innovated configuration improvements that increase operating availability have been injected into a proposed PPPL SHPD design. Much of the physics and engineering design basis for this effort centers on a series of ST studies carried out in recent years attempting to maximize the low aspect ratio (AR) ST performance within realistic engineering constraints of this compact fusion device. One issue found in the low AR design is the lack of volt-seconds generated by a small central solenoid that resides in the available space left after sizing the TF structure to support the high current density/HTS TF coil. Although not required in a larger pilot plant device, a solenoid wrapped around the plasma side of the SC TF coil was considered for the small low aspect ratio SHPD device. Adding a solenoid to the plasma side of the TF imposes a major change to the device configuration – a change which has been found to have cost and assembly issues when compared with an OH solenoid located at the machine center. Finally, the inclusion of a liquid metal first wall divertor system, the integration of local pairs of outboard DCLL blanket segments and a summary of physics performance conditions will be presented.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

CO 2 electroreduction favors carbon isotope 12 C over 13 C and facilitates isotope separation

We discovered that CO 2 electroreduction strongly favors the conversion of the dominant isotope of carbon ( 12 C) and discriminates against the less abundant, stable carbon 13 C isotope. Both absorption of CO 2 in the alkaline electrolyte and CO 2 electrochemical reduction favor the lighter isotopologue. As a result, the stream of unreacted CO 2 leaving the electrolyzer has an increased 13 C content, and the depletion of 13 C in the product is several times greater than that of photosynthesis. Using a natural abundance feed, we demonstrate enriching of the 13 C fraction to ~1.3% (i.e., +18%) in a single-pass reactor and propose a scalable and economically attractive process to yield isotopes of a commercial purity. Our finding opens pathways to both cheaper and less energy-intensive production of stable isotopes ( 13 C, 15 N) essential to the healthcare and chemistry research, and to an economically viable, disruptive application of electrolysis technologies developed in the context of sustainability transition.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

The Science of Scientific Software Development and Use

Increasingly powerful and affordable computing has revolutionized scientific and scholarly discovery across a broad range of fields. Computing relies on software, which has been rapidly growing in scope, diversity, and complexity. At the same time, the methods, processes, and tools used to produce and utilize this essential software are often ad hoc, and the study and improvement of them is often done without the benefit of direct funding or prioritization. Consequently, concerns are growing about the productivity of the developers and users of scientific software, its sustainability, and the trustworthiness of the results that it produces. The US Department of Energy Office of Science (DOE-SC) is at the forefront of modern software-enabled scientific discovery across numerous areas of computational, experimental, and observational science, including major investments in national user facilities that support these activities. In December 2021, the DOE-SC Office of Advanced Scientific Computing Research (ASCR) convened a workshop on basic research needs for the Science of Scientific Software Development and Use (SSSDU). Through keynote presentations, lightning talks, and breakout groups, participants discussed the current practice of software development, maintenance, evolution, and use, and considered how the scientific method could be used to examine these practices and develop more evidence-based approaches to enhance the impact of software and computing on all areas of science. Workshop participants identified three priority research directions (PRDs) and three important crosscutting themes that center on the following overarching insight: software has become an essential part of modern science that impacts new discovery, policy, and technological development. To have full confidence in science delivered via software, we must improve the processes and tools that help us create and use it, and this enhancement requires a deep understanding of the diverse array of teams and individuals doing the work. The full workshop report will be available at https://doi.org/10.2172/1846009.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Recovery and Refining of Rare Earth Elements from Lignite Mine Wastes

The University of North Dakota (UND), in collaboration with a comprehensive team of technical, business and host-site partners, built on prior technology development to complete a front-end engineering and design (FEED) and business planning study to recover and refine rare earth elements (REE) and critical minerals (CM) from North Dakota (ND) lignite mine wastes. The end of project goal was to have an investment quality project and a committed team ready to commercialize the proposed technologies in a future construction and operations phase.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2022

Technology Enablers for Advanced Gasoline Compression Ignition Engines

To meet current emission regulations and increasingly demanding global fleet CO2 standards on fuel economy and future trends towards life cycle GHG emissions, advanced combustion engines remain significant in the passenger vehicle sector to achieve high efficiency and low emissions over the full operating range. Lean burn gasoline compression ignition (GCI) technology has shown to have the most potential in reaching these goals, although it faces challenges in the operating range. In this study, an advanced GCI engine is considered with the capability to operate under two combustion modes, namely low temperature combustion (LTC) and GCI. They are enabled with the use of two Hyundai in-house developed technologies; an advanced valve control mechanism known as continuously variable valve duration (CVVD) and a high-pressure gasoline injection system. At low load, the engine utilizes dual CVVD and dual CVVT (continuously variable valve timing) mechanisms for both intake and exhaust valvetrains to enable NVO (negative valve overlap) to trap hot residuals. The hot residuals enable low load auto-ignition, and the phasing control of that auto-ignition is achieved by varying the degrees of NVO, and in turn, the amount of hot residuals. This is done in real time with respect to the changes in engine loads or operating conditions, significantly improving cylinder-phasing control in LTC mode, and subsequently is able to realize a fuel economy gain and reduced emission benefits. Early direct injection during NVO or intake stroke is used to form homogenous or quasi-homogenous air-fuel mixture for LTC. At mid to high loads, late direct injection of gasoline or GCI mode is employed to take advantage of the high volatility and high resistance to auto-ignition of gasoline fuel, so that diesel-engine like high combustion efficiency can be achieved with lower soot emissions for the same NOx level as diesel combustion. In this paper, the key control and fueling technologies that enable this multiple mode combustion are introduced, and the resultant analysis on engine test and CFD simulation at LTC and GCI operating conditions are presented in detail.

Gasoline compression ignition, low temperature com↗

DOE OSTI2022

High Yield, Economical and Environmentally Benign Production of Rare Earth Elements from Coal Ash (Phase II Final Summary Report)

Fly ash stored in landfills and ponds across the United States is an attractive, abundant domestic resource for the cost-effective recovery of rare earth elements (REE) and other critical minerals (CM). Physical Sciences Inc. (PSI) and its team members, Winner Water Services (WWS) and University of Kentucky/Center for Applied Energy Research (UK/CAER) successfully executed a multiphase program that developed technologies and their implementation in a pilot plant. We demonstrated plant operations for cost-effective and environmentally-friendly production of rare earth element oxide (REO) concentrates, and the critical minerals scandium and aluminum (in the forms of salts or oxide products), from coal ash. We also constructed and demonstrated a research-scale (0.5 kg/day) micropilot facility to validate the key physical and chemical processing operations, predict yields, and troubleshoot process bottlenecks. The project team then designed, constructed and operated two decoupled pilot plants: (1) an operational pilot plant for physical separation processes with capacity of 0.4 metric tons per day (tpd), where we optimized processes to produce selected ash fractions as the feedstock for chemical processing and as valuable byproducts such as cenospheres, magnetic ash, and secondary fuel carbon, and (2) an operational pilot plant for chemical ash processing with a capacity of 0.5 tpd that developed optimized processes for the production of: (a) REO concentrates, (b) critical minerals (Sc, Al), and (c) beneficiated ash as a valuable byproduct suitable for cement applications. In Phase I, the project team (with Equinox Chemicals in place of WWS) developed and demonstrated the feasibility of the physical and chemical separation processes, developed the design of a pilot plant, and began the development of a preliminary techno-economic model. In the baseline (initial) Phase II program, the project team developed and demonstrated the above pilot scale plant, producing salable REE concentrates, including Y and Sc (REYSc), plus commercially viable byproducts, using environmentally safe and high-yield physical and chemical enrichment processes. The team successfully demonstrated chemical pilot design, construction, shakedown, and operations of the plant. We produced the Phase II deliverable REYSc concentrate ((50 g of >60 wt.% purity REYSc salts on elemental basis), generated the feed for the Phase II follow-on program, identified processing challenges for future optimizations, and refined the techno-economic model. In the Phase II follow-on program, the project team: (1) developed and demonstrated processes to increase the REE amount by 3X (content basis) and convert the Phase II REE salt mixture to an oxide mixture, (2) produced/delivered >38 g of REO mixture with >85 wt.% purity (elemental basis); (3) developed processes to recover critical minerals scandium and aluminum from intermediate streams; (4) produced/delivered > 1 g of scandium salt mixture with >85 wt. % purity (elemental basis); (5) produced/delivered > 100 g of aluminum oxide type material with >70% wt. purity (elemental basis); and (6) updated the techno-economic model from the baseline Phase II program to assess CAPEX and OPEX of a commercial operation. This program has developed extensive databases on process chemistry, unit operations, plant engineering, and techno-economics that will enable further scale-up toward commercial plant design. Specific future developments will be focused on achieving dramatic savings in energy, reagent usage, and operating costs. The combined results will contribute significantly for maturing the technologies of REE recovery from coal byproducts and promote the establishment of domestic REE and CM supply chains.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2019

Correlated Neutron Interrogation Source in the Active Well [Slides]

The Active Well Coincidence Counter (AWCC) is a technology developed by Los Alamos National Laboratories for the use of non-destructive assay of Uranium materials for international nuclear inspectorates such as the IAEA.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Cyber-Informed Engineering Guidance—Implementing CIE in Early Systems Engineering Lifecycle Stages

Traditionally, cybersecurity is not considered in the design process. Design engineers typically focus on building safety and reliability into their products and applications. Security against malicious cyber incidents is often an afterthought, resulting in deployment of security solutions during installation or operation. Unfortunately, waiting to consider cybersecurity until later in the systems engineering lifecycle often results in less effective and more expense security. Idaho National Laboratory (INL) developed the concept of Cyber-Informed Engineering (CIE) in 2015 to provide a framework that enables cybersecurity to be built into systems beginning at the conceptual design stage. In addition to ongoing research by INL, the U.S. Department of Energy (DOE) Office of Cybersecurity, Energy Security, and Emergency Response has recently developed a National CIE Strategy document for incorporating CIE into the design and operation of infrastructure systems reliant on digital monitoring or controls. This paper provides a brief review of this National CIE Strategy as well as a roadmap to historical, current, and future CIE research by INL through the U.S. DOE Office of Nuclear Energy (NE) Cybersecurity Crosscutting Technology Development Program. A near-term focus of the DOE-NE’s research and development is to extend the foundational CIE work into detailed guidance for implementation during initial systems engineering stages in nuclear digital instrumentation and control projects and to demonstrate use of the guidance in an integrated energy systems project.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2022

Review of the gas breakdown physics and nanomaterial-based ionization gas sensors and their applications

Ionization gas sensors are ubiquitous tools that can monitor desired gases or detect abnormalities in real time to protect the environment of living organisms or to maintain clean and/or safe environment in industries. The sensors’ working principle is based on the fingerprinting of the breakdown voltage of one or more target gases using nanostructured materials. Fundamentally, nanomaterial-based ionization-gas sensors operate within a large framework of gas breakdown physics; signifying that an overall understanding of the gas breakdown mechanism is a crucial factor in the technological development of ionization gas sensors. Moreover, many studies have revealed that physical properties of nanomaterials play decisive roles in the gas breakdown physics and the performance of plasma-based gas sensors. Based on this insight, this review provides a comprehensive description of the foundation of both the gas breakdown physics and the nanomaterial-based ionization-gas-sensor technology, as well as introduces research trends on nanomaterial-based ionization gas sensors. The gas breakdown is reviewed, including the classical Townsend discharge theory and modified Paschen curves; and nanomaterial-based-electrodes proposed to improve the performance of ionization gas sensors are introduced. The secondary electron emission at the electrode surface is the key plasma–surface process that affects the performance of ionization gas sensors. Finally, we present our perspectives on possible future directions.

nanomaterial-based gas breakdown characteristics↗

DOE OSTI2024

Design, Control and Application of Next Generation Qubits

Design, Control and Application of Next Generation Qubits Arun Bansil, Northeastern University (Principal Investigator) Claudio Chamon, Boston University (Co-Investigator) Adrian Feiguin, Northeastern University (Co-Investigator) Liang Fu, MIT (Co-Investigator) Eduardo Mucciolo, Univ. of Central Florida (Co-Investigator) Qimin Yan, Temple University (Co-Investigator) The quest for developing technologies for manipulating and storing information quantum mechanically is currently led by approaches that include Josephson-junctions, ion-traps, and qubits generated by defect spins in solids. Topological qubits, however, are inherently more robust to decoherence by environmental effects, and should be able to sprint ahead once practical barriers have been overcome. At the present stage of the development of the field, it is important to explore a variety of architectures and materials beyond the conventional paradigms in order to seed breakthroughs toward building a scalable quantum computer. Our comprehensive theoretical research program involved four interconnected thrusts as follows. • A materials discovery effort in two-dimensional compounds in search of materials to support Majorana zero modes and defect structures suitable as qubits. • Exploration of architectures for topological quantum computation by investigating both superconducting Majorana qubits, and robust platforms for braiding with new “meta-materials” built of arrays of Majorana qubits. • Investigation of properties of hybrid metal-organic qubits based on transition-metal centers in graphene, and molecular crystals of polyaromatic complexes with embedded transition-metal atoms. • Development of tensor-network and semiclassical approaches to study decoherence in the presence of random and dispersive spin baths, and NV centers in diamond. The full spectrum of theoretical and numerical approaches was used to address the goals of this project including first-principles, density-matrix-renormalization group, tensor networks, and data-driven high-throughput approaches using materials database and machine-learning.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Performance of Embedded Sensors in 3D Printed SiC

This report summarizes recent advances in embedding sensors in 3D printed silicon carbide (SiC) ceramic components under the Transformational Challenge Reactor (TCR) program. The additive manufacturing technologies developed under this program will enable fabrication of complex structures with embedded fuels and sensors. The sensors will be capable of characterizing fuel performance using spatially distributed measurements at the most strategic locations that would be otherwise inaccessible using conventional manufacturing techniques. While previous programmatic updates describe initial concepts for embedding sensors, materials selection, and initial characterization of the embedded sensors, the technology requires further demonstration, and quality-significant procedures must be established before the embedding technology is ready for adoption by industry. To this end, this report describes the most effective techniques that have been used to embed functional sensors in 3D printed components using a combination of binder-jet additive manufacturing and chemical vapor infiltration (CVI). A detailed procedure describes each step in the process and is available upon request. Molybdenum (Mo)-sheathed thermocouples have been successfully embedded in complex SiC components, and temperatures were monitored in situ during the embedding process. Post-embedding measurements showed no significant hysteresis, and characterization of the interface revealed qualitatively strong bonding around the entire perimeter of the sensor sheath. Distributed fiber-optic temperature sensors were able to briefly measure temperature profiles during CVI, but they ultimately failed prior to completion of the CVI run. The failure appears to be related to the fiber coating at temperatures close to 1,000°C. Future work will focus on irradiation testing of embedded thermocouples and other sheathed electrical sensors, as well as the identification of fiber-optic sensor coatings that can survive CVI.

42 ENGINEERING↗

DOE OSTI2022

Competitiveness and Commercialization of Energy Technologies: Supply Chain Deep Dive Assessment

The report “America’s Strategy to Secure the Supply Chain for a Robust Clean Energy Transition” lays out the challenges and opportunities faced by the United States in the energy supply chain as well as the federal government plans to address these challenges and opportunities. It is accompanied by several issue-specific deep dive assessments, including this one, in response to Executive Order 14017 “America’s Supply Chains,” which directs the Secretary of Energy to submit a report on supply chains for the energy sector industrial base. The Executive Order is helping the federal government to build more secure and diverse U.S. supply chains, including energy supply chains. Competitive U.S.-based clean energy manufacturers and rapid commercialization of U.S.-developed technologies are critical to secure energy supply chains, generate high quality jobs, and meet the United States’ national security, energy and climate objectives. The February 2021 “Executive Order on America’s Supply Chains” (E.O. 14017) directs the U.S. Department of Energy (DOE) to evaluate supply chains that encompass the energy industrial base, focusing on technologies that are critical to meet U.S. decarbonization goals by 2050. Understanding and analyzing the end-to-end supply chain through economic analysis is crucial to mitigating risks and identifying opportunities to enhance U.S. competitiveness in the clean energy industry. This insight will allow the Department of Energy (DOE) to leverage its research, development, demonstration and deployment (RDD&D) capabilities to most fully realize the objectives of E.O. 14017.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Safeguards Considerations for Salt Fuel Fabrication

Molten salt reactors (MSR) with liquid fuel present a unique safeguards challenge whereby the current verification techniques have not been evaluated for effectiveness and applicability. While MSR operations have been the subject of prior studies, the front-end liquid fuel preparation activities have not been extensively evaluated. Reviewing the existing resources on fuel fabrication and evaluating the range of fuel fabrication process options available will allow safeguards analysts to identify the applicability of existing safeguards practices, identify gaps in capability, and identify opportunities where safeguards may be applied. There is no existing supplier of fuel salt for MSRs. In an extensive review of MSR technology, the International Atomic Energy Agency’s (IAEA's) Nuclear Power Technology Development Section acknowledges the gap in existing capabilities for fuel salt fabrication, noting, simply, “if demand exists, supply will appear.” Salt reactor fuel has not been previously produced on an industrial scale in a non-nuclear weapon state. These characteristics of MSR fuel fabrication present high levels of uncertainty, but they also represent an opportunity to mature safeguards techniques alongside liquid fuel preparation technologies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Using Digital and Web-Based Platforms to Enhance Nuclear Power Plant Knowledge Transfer - 20203

As the workforce ages, the loss of experienced personnel can result in a loss of important knowledge. Updating Electric Power Research Institute (EPRI) research and guidance with the latest technology developments and operating experience is an important method to transfer knowledge between the retiring and incoming workforce. Studies suggest that the incoming workforce is accustomed to using digital and/or internet-based platforms to find information and may have a higher comfort with these types of platforms than they have with static, written reports. Additionally, the ease and speed of updating and delivering content through digital formats may offer an effective method for knowledge transfer and combining information from multiple reports into a single access point. EPRI has recently produced an online Decommissioning Hub available to members and is working on replicating the effort in the area of radioactive waste management called the Radwaste Web References. EPRI has extensive guidance in both disciplines. The Decommissioning Hub uses a wiki format to provide a platform that allows for both the updating of that guidance resulting from new research and new operating experiences, and combining related topical information from multiple reports. It also allows users to access the information based on key words and topical searches, and can be a tool for users to input experience to share with others. The Decommissioning Hub is accessed via a web-based portal and includes topical pages; experience summaries; a question and answer capability; and a smart search function of all EPRI decommissioning reports. Use of a wiki format allows users to input new experiences or modify existing experience summaries to add additional detail. EPRI moderates all content. The experience data base has been initially populated with information available in published EPRI reports and unpublished information currently available within EPRI. Moving forward, population of the database will continue with information available within the open literature, new information developed from current decommissioning projects, and user inputs. The web site became active in late 2017, and a major update will be issued in early 2020. Larger scale updates are planned biannually, and smaller-scale updates will occur continuously. Capturing and applying lessons learned from industry experiences is a hallmark of the global nuclear industry. This is even more important in the decommissioning technology area since very few plant staff have relevant experience and thus there is a steep learning curve. Moreover, decommissioning involves a number of complex, non-routine and specialized tasks. The web-accessible and searchable experience database provides an easy-to-use resource for capturing and disseminating practical experiences from completed and ongoing decommissioning projects. The EPRI Radwaste Web References will build upon the philosophy and objectives of the Radwaste Desk References that were published in the 1990's. The purpose of the original Radwaste Desk References was to provide nuclear power plant professionals with a how-to manual for managing radioactive waste. The Radwaste Web References will adopt this original purpose and will be a wiki type web site that provide fundamental practical and theoretical information, operating experience (OE), and information about advanced technologies and methods. As much as practicable, features that allow for interaction between users to share OE, best practices, and benchmarking will be added. Where they exist and are appropriate, the various EPRI Guidelines documents on radwaste topics will be updated and incorporated into the Radwaste Web References. The first Radwaste Web Reference will be on Low Level Waste Characterization and will build upon the EPRI Low Level Waste Characterization Guidelines (EPRI Report TR-107201, 1996) and will be available in 2020. The next Radwaste Web Reference will be on the topic of liquid radioactive waste processing and management, tentatively set for unveiling in 2021. This paper summarizes the EPRI's previous experiences with web-based platforms and future plans in this area. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2021

Woody Feedstocks 2021 State of Technology Report

The U.S. Department of Energy promotes production of advanced liquid transportation fuels from lignocellulosic biomass by funding fundamental and applied research that advances the state of technology (SOT). As part of its involvement with this overall mission, Idaho National Laboratory completes annual SOT reports for n th -plant biomass feedstock logistics. The purpose of the SOTs is to provide the status of feedstock supply system technology development for biomass to biofuels, based on actual data and experimental results relative to technical targets and cost goals from specific design cases.

09 BIOMASS FUELS↗

DOE OSTI2024

Enabling Extreme Fast Charging with Energy Storage Final Report

The objective of this project was to develop and demonstrate an extreme fast charging (XFC) station with three 350 kW charging ports that operate at a combined power exceeding 1 MW and mitigate the grid impact by employing smart charging algorithms, using an energy storage system, and connecting directly to a medium-voltage (15 kV-class three-phase) distribution feeder. This final report describes the team's achievements in all aspects of the technology development.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Key Drivers for Offshore Wind Deployment in the Western United States

The western coast of the United States has abundant natural resources, including wind, sun, and water. Despite strong ocean winds, offshore wind energy (OSW) in the Western United States is in the early stages of technology development due largely to the deep water off the coast, which requires floating platforms rather than fixed‐bottom turbines. Floating OSW increases the technical difficulty of installation and thus the cost relative to both fixed‐bottom OSW and land‐based turbines. OSW is a potential generation option to help meet increasing demand on the west coast of the United States because it likely has fewer land‐use conflicts than other technologies and complements sources in the existing electricity supply by providing energy during times of high system stress. This paper examines the possible drivers and barriers to OSW deployment on the West Coast using the National Laboratory of the Rockies' state‐of‐the‐art capacity expansion model and the Regional Energy Deployment System (ReEDS) model. We use ReEDS to explore a multitude of future scenarios looking at key drivers for OSW deployment, including variations on the cost of OSW, electricity demand growth, and the availability of competing technologies to examine the factors that may play a role in OSW growth. Assuming coastal state policies such as renewable portfolio and clean energy standards remain in place, we find that OSW can play a role in meeting electricity demand and provide energy during stressful grid conditions and find that deployment from the least‐cost investment model ranges from 7.6 to 38 GW by 2045.

17 WIND ENERGY↗

DOE OSTI2020

Networked Microgrid Operations: Supporting a Resilient Electric Power Infrastructure

Modern electric power systems operate using large generating units managed with a centralized control structure. The current systems are the result of over a hundred years of technological development and consolidation to leverage economies of scale. While the existing systems have proven cost effective and reliable, modern systems are experiencing a wide range of operational challenges that are causing a reexamination of the centralized control structure. Despite the nearly universal adoption of centralized control, electric power systems are fractal in their operational requirements. Specifically, the fundamental operational requirements are the same, regardless of the system size. While past technologies have not allowed for exploitation of this fractal behavior, emerging technologies are making it possible; these technologies include grid-forming inverters, modern telecommunications systems, and distributed control architectures. Here we show emerging technologies that allow the fractal operational requirements of electric power systems to be exploited as networked microgrids to increase the resiliency of the world’s critical electrical infrastructure.

Schneider, Kevin P.↗