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Mathematical Optimization Techniques

The papers collected in this volume were presented at the Symposium on Mathematical Optimization Techniques held in the Santa Monica Civic Auditorium, Santa Monica, California, on October 18-20, 1960. The objective of the symposium was to bring together, for the purpose of mutual education, mathematicians, scientists, and engineers interested in modern optimization techniques. Some 250 persons attended. The techniques discussed included recent developments in linear, integer, convex, and dynamic programming as well as the variational processes surrounding optimal guidance, flight trajectories, statistical decisions, structural configurations, and adaptive control systems. The symposium was sponsored jointly by the University of California, with assistance from the National Science Foundation, the Office of Naval Research, the National Aeronautics and Space Administration, and The RAND Corporation, through Air Force Project RAND.

Bellman, R.↗

Co-developing a SAR for Disasters Reference Guide for the International Applications Community

Synthetic Aperture Radar (SAR) data are widely applicable for disaster monitoring, especially in Central and South America where atmospheric effects are a frequent obstacle for disaster monitoring. There is a growing interest in the application of SAR data to diverse disasters, ranging from landslides to volcanic eruptions and floods. With this interest comes a growing need for user-friendly guides that facilitate the integration of SAR into existing workflows. A joint effort between AmeriGEO, university networks in the Americas, NASA SERVIR’s Science Coordination Office (SCO), and the NASA Earth Science Disasters Program, culminated in the “SAR for Disasters” Guide. The guide is modeled after the one-page informational sheets created for SERVIR’s SAR Handbook, with the aim to succinctly communicate the key considerations needed to apply relevant analyses using SAR. Developed with contributors from diverse backgrounds, this guide is designed to be a useful reference for experienced technical users and beginners alike.

SAR↗

Application of Earth Observation Data for Improved Environmental and Disaster Monitoring in Central America

Since its establishment in 1991, the Central American Integration System (SICA, in Spanish) has served as a force for integrating the eight countries of Central America and the Dominican Republic, and in recent years, SICA’s General Secretariat and its various technical secretariats have focused on integrating Earth observations into various regional and national processes. In 2019, for instance, a joint statement was signed between SICA’s General Secretariat and NASA, toward strengthening the region’s use of Earth observations. SICA has also pursued cooperation with the Group on Earth Observations’ AmeriGEO regional initiative, the Japanese Aerospace Agency (JAXA), the United Nations Office of Outer Space Affairs (UNOOSA), and the Copernicus program, among others. Just in the framework of the NASA-SICA Joint Statement, and towards the goal of strengthening the region’s use of Earth observations across sectors, a large number of training webinars has been conducted, particularly benefiting national institutions, non-governmental organizations, and universities. Additionally, targeted support has been provided in the areas of environmental monitoring and disaster management. From 2019 through 2021, for instance, a number of feasibility studies were implemented by NASA’s DEVELOP program in collaboration with SICA technical secretariats. In 2020, in response to devastating Hurricanes Eta and Iota, the SERVIR program also provided support for extending the HYDRAFloods algorithm which had been originally developed for the Mekong to Central America. Support is also being provided toward monitoring land cover change across the Mesoamerican Biological Corridor. In the framework of the “observing the Earth for the benefit of all” theme, this presentation will also focus on how Central America can serve as a case study for the development of Earth observation capacity, applicable to other regions of the world.

applied sciences↗

Joint AFOSR/ONR/NASA HTP Boundary Layer Transition Workshop Summary for RAeS

A workshop hosted by three US government entities (the Air Force Office of Scientific Research, the Office of Naval Research, and the National Aeronautics and Space Administration Hypersonic Technology Project) was held in June 2023. This workshop focused on high supersonic and hypersonic boundary layer transition. The purpose of the workshop was to gather subject matter experts in the nation to determine the current state of the art in the field, any gaps or areas that require more studies, and the future of the field. Participants of the workshop were drawn from industry, academia, and government agencies. Prior to the workshop they were provided a questionnaire to spark discussion during the workshop. Roadmaps for six different areas were created as one of the final end products of the workshop.

boundary layer transition↗

Results of the Simulation and Assimilation of Doppler Wind Lidar Observations in Preparation for European Space Agency's Aeolus Mission

With the launch of the European Space Agency's Aeolus Mission in 2013, direct spaceborne measurements of vertical wind profiles are imminent via Doppler wind lidar technology. Part of the preparedness for such missions is the development of the proper data assimilation methodology for handling such observations. Since no heritage measurements exist in space, the Joint Observing System Simulation Experiment (Joint OSSE) framework has been utilized to generate a realistic proxy dataset as a precursor to flight. These data are being used for the development of the Gridpoint Statistical Interpolation (GSI) data assimilation system utilized at a number of centers through the United States including the Global Modeling and Assimilation Office (GMAO) at NASA/Goddard Space Flight Center and at the National Centers for Environmental Prediction (NOAA/NWS/NCEP) as an activity through the Joint Center for Satellite Data Assimilation. An update of this ongoing effort will be presented, including the methodology of proxy data generation, the limitations of the proxy data, the handling of line-of-sight wind measurements within the GSI, and the impact on both analyses and forecasts with the addition of the new data type.

McCarty, Will↗

Improved Fuel Cycle Capability of Griffin for Fast Reactor Applications

Griffin is a MOOSE based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, the fuel cycle capability has been significantly extended by improving the assembly shuffling option to allow flexible fuel reloading in the multi-cycle depletion calculation and incorporating decay between cycles. An equilibrium core calculation capability was also implemented to find an equilibrium core. Additionally, an enrichment search capability was added to determine the enrichment condition that allows a core to reach an equilibrium cycle with the end-of-cycle k-effective meeting a user-specified target value. The updated fuel management capability has been extensively tested using the three-dimensional ABTR problem with different batch schemes, exhibiting reasonable solutions in terms of manual shuffling, equilibrium cycle, and enrichment search calculations. The cross section generation workflow capability for fast reactors was further verified to produce microscopic cross sections as well as Griffin core inputs for an ring-heterogeneous configuration. Rigorous verification tests using the ABTR problem demonstrated that the RH core calculations, with cross sections and Griffin inputs generated from the cross section workflow of Griffin, produced accurate solution for fast reactor problems. In addition, an option to convert delay neutron parameter data generated from MC 2 -3 in the DLAYXS format into XML format was added to support transient calculations using MC 2 -3-generated data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Safe Response to Renewable Energy Hazards

The International Association of Fire Fighters (IAFF) and Underwriters Laboratories, LLC (UL) in conjunction with UL Solutions initiated a joint project in 2022 under an agreement with the United States Department of Energy-Office of Energy Efficiency and Renewable Energy (DOE-EERE). This project focused on two separate and important initiatives related to energy efficiency in residential buildings. Initiative 1: Fire Performance on Energy Efficient Exterior Walls. Initiative 2: Firefighting Tactics in Residential Properties with Building Energy Storage Systems (BESS). The project’s first initiative addresses concerns surrounding new technologies with enhanced, energy-efficient exterior walls installed on residential properties. The concerns of fire rapidly traveling vertically up the exterior of these walls were examined. This addressed a growing concern from the first responder community that many times, the fires on the exterior of residential buildings have already evolved into an attic fire by the time of arrival – making it problematic to address the fire scenario. The test plan for Initiative 1 incorporated a modified version of an American Society for Testing and Materials (ASTM) test method, ASTM E2707, Standard Test Method for Determining Fire Penetration of Exterior Wall Assemblies Using a Direct Flame Impingement Exposure, as the foundation of the research. The test method involved a wall structure intended to represent retrofit construction to evaluate how fire would spread vertically or laterally. The second aspect of the UL-IAFF Project focuses on the fire service response to Residential Battery Energy Storage System (RBESS) incidents. These simulation tests were constructed in the large-scale fire test facility at UL Solutions’ Northbrook, IL campus. A baseline test was conducted that involved a test structure with no batteries—shelving units populated with standardized commodities, representing a typical garage with cellulosic and plastic contents. Three additional tests have been conducted to generate data with the contribution of energy storage system (ESS) batteries to compare fire and explosion hazards against the baseline test. Through this work, fire service tactical considerations can be explored. From the data, the team can determine 1) the visual indicators of a residential fire that has involved an RBESS (or, potentially, other large batteries) and 2) the impact of fire service-initiated ventilation of the structure on the fire conditions and explosion risks.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Aerospace Technology Innovation

Whether finding new applications for existing NASA technologies or developing unique marketing strategies to demonstrate them, NASA's offices are committed to identifying unique partnering opportunities. Through their efforts NASA leverages resources through joint research and development, and gains new insight into the core areas relevant to all NASA field centers. One of the most satisfying aspects of my job comes when I learn of a mission-driven technology that can be spun-off to touch the lives of everyday people. NASA's New Partnerships in Medical Diagnostic Imaging is one such initiative. Not only does it promise to provide greater dividends for the country's investment in aerospace research, but also to enhance the American quality of life. This issue of Innovation highlights the new NASA-sponsored initiative in medical imaging. Early in 2001, NASA announced the launch of the New Partnerships in Medical Diagnostic Imaging initiative to promote the partnership and commercialization of NASA technologies in the medical imaging industry. NASA and the medical imaging industry share a number of crosscutting technologies in areas such as high-performance detectors and image-processing tools. Many of the opportunities for joint development and technology transfer to the medical imaging market also hold the promise for future spin back to NASA.

Turner, Janelle↗

NASA safety program activities in support of the Space Exploration Initiatives Nuclear Propulsion program

The activities of the joint NASA/DOE/DOD Nuclear Propulsion Program Technical Panels have been used as the basis for the current development of safety policies and requirements for the Space Exploration Initiatives (SEI) Nuclear Propulsion Technology development program. The Safety Division of the NASA Office of Safety and Mission Quality has initiated efforts to develop policies for the safe use of nuclear propulsion in space through involvement in the joint agency Nuclear Safety Policy Working Group (NSPWG), encouraged expansion of the initial policy development into proposed programmatic requirements, and suggested further expansion into the overall risk assessment and risk management process for the NASA Exploration Program. Similar efforts are underway within the Department of Energy to ensure the safe development and testing of nuclear propulsion systems on Earth. This paper describes the NASA safety policy related to requirements for the design of systems that may operate where Earth re-entry is a possibility. The expected plan of action is to support and oversee activities related to the technology development of nuclear propulsion in space, and support the overall safety and risk management program being developed for the NASA Exploration Program.

Sawyer, J. C., Jr.↗

Space Station Freedom Evolution Symposium

Information on the Space Station Freedom Evolution Symposium is given in viewgraph form. Topics covered include industry development needs and the Office of Commercial Programs strategy, the three-phase program to develop commercial space, Centers for the Commercial Development of Space (CCDS), key provisions of the Joint Endeavor agreement, current commercial flight experiment requirements, the CCDS expendable launch vehicle program, the Commercial Experiment Transporter (COMET) program, commercial launch dates, payload sponsors, the commercial roles of the Space Station Freedom, and a listing of the Office of Commercial Programs Space Station Freedom payloads.

Ott, Richard H.↗

Generating synthetic occupants for use in building performance simulation

Occupant behaviour simulation frameworks can employ synthetic populations to characterize occupancy and behavioural patterns in buildings based on observed demographic data at a certain geographical location. For buildings, very few synthetic occupant populations have been generated. This paper uses a Bayesian Networks (BN) structural learning approach to synthesize populations of occupants in a multi-family housing case study. Two additional cases of office occupants and senior housing residents are considered as a cross-case comparison. Furthermore, we draw upon the extended version of drivers-needs-actions-systems (DNAS) framework to guide the selection of variables and data imputation. Our results show that the BN approach is powerful in learning the structure of data sets. The synthetic data sets successfully match the joint distributions of the underlying combined data sets. Experiments on the multi-family housing particularly show better performance than the office and senior housing cases.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

AMS / BARC Joint Survey Addendum Technical Report

This report details the data analysis results from data collected during the September-October 2019 joint survey series between the Department of Energy (DOE) National Nuclear Security Administration (NNSA) Aerial Measuring System (AMS) asset, and the Government of India’s Department of Atomic Energy (DAE) Bhabha Atomic Research Centre (BARC). This joint survey series took place at the Nevada National Security Site (NNSS), areas of public land in Southern Nevada, and at the DOE Office of Legacy Management (LM) Large Area Calibration Pads (LACP) at the Grand Junction Regional Airport in Grand Junction, CO. The data detailed in this report were gathered at the LACP. More details regarding the setup of these surveys and personnel involvement can be found in the AMS / BARC Joint Survey Summary Report. The data from the LACP collected by AMS are consistent with past data collection campaigns at the LACP. The AMS Bell 412 (B412) helicopter, equipped with both the standard AMS thallium-doped sodium iodide (NaI(Tl)) 2"x4"x16" 12-detector system and a subset of the BARC Aerial Gamma Spectroscopy System (AGSS) consisting of two independent 3"x3"cylindrical NaI(Tl) detectors, measured each of the five calibration pads for a minimum of 10 minutes. After the helicopter measurements, a pressurized ion chamber (PIC) was used to directly measure radiation exposure rates on each of the pads for a period 5 minutes. The geophysical calibration procedure published by the International Atomic Energy Agency (IAEA) (Erdi-Krausz et al. 2003) was used to determine the spectral stripping sensitivity matrix for naturally occurring radiological material (NORM). The sensitivity matrix is consistent with the AMS long term average. Additionally, the PIC data was used to calibrate the AMS system for exposure rate. The results of the exposure rate analysis are also consistent with AMS long-term averages.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

National Security & International Studies (Q1 FY2021 Newsletter)

Happy New Year to everyone. Activity in the office continues to be at a high pace with the addition of the Strategic Analyses and Assessments (SAA) Office from ALDX, and the Mission Integration (MI) Office (formerly known as Nuclear and Military [NMA] Office) from DDW. We are working closely to optimize the impact of our combined offices. In this issue of our newsletter, we will highlight programs from the SAA Office portfolio, delve into our interactions with the Project on Nuclear Issues (PONI) program from CSIS, introduce you to new staff in NSIS and review a new joint postdoc program with the UC Institute on Global Conflict and Cooperation and the Center for Global Security Research at LLNL. I also encourage you to take a look at the new NSIS website for more information on the office. Finally, the NSIS office will soon be kicking off a webinar series on starting with topics of interest to the Director’s Strategic Resilience Initiative and will grow beyond that. Stay tuned for more information. --John Scott, Acting Office Director, NSIS

99 GENERAL AND MISCELLANEOUS↗

Bion-11 Spaceflight Mission

The Sensors 2000! Program, in support of the Space Life Sciences Payloads Office at NASA Ames Research Center developed a suite of bioinstrumentation hardware for use on the Joint US/Russian Bion I I Biosatellite Mission (December 24, 1996 - January 7, 1997). This spaceflight included 20 separate experiments that were organized into a complimentary and interrelated whole, and performed by teams of US, Russian, and French investigators. Over 40 separate parameters were recorded in-flight on both analog and digital recording media for later analysis. These parameters included; Electromyogram (7 ch), Electrogastrogram, Electrooculogram (2 ch), ECG/EKG, Electroencephlogram (2 ch), single fiber firing of Neurovestibular afferent nerves (7 ch), Tendon Force, Head Motion Velocity (pitch & yaw), P02 (in vivo & ambient), temperature (deep body, skin, & ambient), and multiple animal and spacecraft performance parameters for a total of 45 channels of recorded data. Building on the close cooperation of previous missions, US and Russian engineers jointly developed, integrated, and tested the physiologic instrumentation and data recording system. For the first time US developed hardware replaced elements of the Russian systems resulting in a US/Russian hybrid instrumentation and data system that functioned flawlessly during the 14 day mission.

Skidmore, M.↗

Report of the Interagency Optical Network Testbeds Workshop 2, NASA Ames Research Center, September 12-14, 2005

The Optical Network Testbeds Workshop 2 (ONT2), held on September 12-14, 2005, was cosponsored by the Department of Energy Office of Science (DOE/SC) and the National Aeronautics and Space Administration (NASA), in cooperation with the Joint Engineering Team (JET) of the Federal Networking and Information Technology Research and Development (NITRD) Program's Large Scale Networking (LSN) Coordinating Group. The ONT2 workshop was a follow-on to an August 2004 Workshop on Optical Network Testbeds (ONT1). ONT1 recommended actions by the Federal agencies to assure timely development and implementation of optical networking technologies and infrastructure. Hosted by the NASA Ames Research Center in Mountain View, California, the ONT2 workshop brought together representatives of the U.S. advanced research and education (R&E) networks, regional optical networks (RONs), service providers, international networking organizations, and senior engineering and R&D managers from Federal agencies and national research laboratories. Its purpose was to develop a common vision of the optical network technologies, services, infrastructure, and organizations needed to enable widespread use of optical networks; recommend activities for transitioning the optical networking research community and its current infrastructure to leading-edge optical networks over the next three to five years; and present information enabling commercial network infrastructure providers to plan for and use leading-edge optical network services in that time frame.

OEP(Open Exchange Points)↗

Position Papers for the ASCR Workshop on Reimagining Codesign

On behalf of the Advanced Scientific Computing Research (ASCR) program in the US Department of Energy (DOE) Office of Science, we are organizing a Workshop on Reimagining Codesign (ReCoDe). Codesign is the process of jointly designing interoperating components of a computing system—in particular: applications, algorithms, system software, programming models, and the hardware on which they run. The goal is to maximize the overall performance, efficiency, and other desirable qualities of the system as a whole. Codesign is a standard methodology in the embedded-systems community, where space, power, and cost constraints are commonly pitted against execution speed for a tightly constrained feature set. Over the last decade, the DOE has invested in codesign efforts to foster the development of exascale computing systems for broad classes of scientific and engineering applications. The ReCoDe workshop hopes to explore how scientific applications of interest to the DOE can be accelerated through close interactions with hardware designers and software-stack developers, in which all components adapt to each other’s requirements and constraints. We want to answer the question of what are the key tools and methodologies for accomplishing codesign in today’s computing landscape, and what will be the highest impact targets for meeting DOE’s emerging mission requirements. This workshop aims to bring together DOE, industry, and academia to identify opportunities to build on past codesign successes and identify new areas that are either emerging or that may need reimagining for the future. We want to continue to find opportunities that can be pursued as a joint effort and continue to break down the traditional customer/vendor dichotomy with true partnerships. From this work, DOE will benefit from increased application performance relative to what stock hardware or existing general-purpose roadmaps can provide, and vendors will benefit from expanding their hardware’s capabilities to address needs they might have not otherwise anticipated and thereby create more widespread interest in their products. The workshop will be structured around a set of breakout sessions, with every attendee expected to participate actively in the discussions. Afterward, workshop attendees—from DOE, industry, and academia—will produce a report for ASCR that summarizes the findings made during the workshop.

97 MATHEMATICS AND COMPUTING↗

The Transactive Energy Network Template Metamodel

While transactive energy, which is defined as an allocation of electricity based on dynamically discovered values or prices, has been extensively studied, its uptake and use has been slow. This report describes a tool, the transactive network template, which should hasten the creation and uptake of transactive energy networks. Some basic principles of transactive energy are familiar from existing wholesale electricity markets. Locational prices are calculated today for zones within bulk electric transmission systems. Locational prices differ while accounting for the locational costs of electricity generation and the losses and constraints incurred when electricity is transmitted from generators and distributed to consumers. A transactive energy network might include these transmission zones. However, current research strives to apply transactive energy also in electricity distribution circuits, buildings, and even for individual generating and consuming devices. At the same time, researchers explore how to apply transactive energy in real time during increasingly shorter time intervals. Automated computational agents become necessary as transactive energy becomes applied to smaller circuit zones and at faster dynamic timescales. A transactive energy network is an example of a multi-agent system. Each zone in the network is represented by its transactive agent, which makes decisions for and acts on behalf of a business entity that is responsible for and manages one of the circuit regions. A transactive energy network is also an example of a decentralized, distributed control system. Control decisions and responsibilities are distributed among the network’s transactive agents. The transactive agents are independent; that is, there typically is no centralized authority or oversight function. Instead, transactive agents exchange transactive signals and thereby negotiate the prices and quantities of electricity that they will exchange. Initially, the circuit regions and responsibilities of transactive agents appear to be very dissimilar. Each circuit region may comprise transmission, distribution, or building-level circuits. Each has a unique position and electrical connectivity within the transactive energy network. Each possesses unique assets that either generate or consume electricity, and these (e.g., renewable energy generator, diesel generator, aggregate utility load, building load, space conditioning, refrigerator, etc.) may further differ in their price flexibility and in their strategies for responding to dynamic electricity prices. Given such diversity, an implementer’s first inclination might be to start from scratch to define all these devices and to engineer their seemingly unique interactions. Given that each implementer’s perspective may be narrow within a transactive energy network, it is unlikely that uniquely engineered systems would interact well. This is where the transactive network template is applicable. The transactive network template is a metamodel that has been developed to guide implementers as they configure their own transactive agent within a network of such agents. The object-oriented design of the transactive network template provides basic code object types that may be used and extended by implementers to represent each of the assets in their circuit region. These objects further facilitate the transactive agent’s necessary computations, which are divided among responsibilities to schedule power usage, balance electric supply and demand, and coordinate the exchange of electricity with the other transactive agents. This report addresses the conceptual transactive network template design. Implementers are directed to more formal design documents and reference implementations. A Python™-based1 reference implementation of the transactive network template has been coded, and three implementations have been configured to represent a national laboratory and two university campuses. Version 2 of the transactive node template generalizes the market class and its methods to facilitate multiple, and more diverse market coordination mechanisms than were facilitated by and demonstrated using Version 1. Version 3 includes new Appendix B, which addresses the designs of methods that would make dynamic prices track approved electricity rates. In the future, the author wishes to make the transactive network template more generally applicable to networks that require more accurate power flow. Development of the transactive network template is jointly funded by the U.S. Department of Energy (DOE) Energy Efficiency and Renewable Energy and the DOE Office of Electricity. In late 2015, one of the first projects to be funded by the DOE Grid Laboratory Modernization Laboratory Consortium was the Clean Energy and Transactive Campus project, led by Pacific Northwest National Laboratory. DOE funds were matched by an investment by the Washington Department of Commerce through its Clean Energy Fund. The transactive network template was developed to guide the implementation of transactive energy networks within this project’s scope.

24 POWER TRANSMISSION AND DISTRIBUTION↗