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At least 1,531 records · Page 85

Evaluacion del potencial solar fotovoltaico en Brownfields y embalses de Puerto Rico: analisis y modelaje [Assessing the Solar Photovoltaic Potential in Puerto Rican Brownfields and Reservoirs: Analysis and Modeling] [Slides]

Este estudio del Laboratorio Nacional de Energia Renovable (NREL, por sus siglas en ingles) evalua el potencial de desarrollo de energia solar fotovoltaica (FV) en zonas industriales abandonadas y embalses de Puerto Rico. La rehabilitacion de estos sitios ofrece importantes beneficios, como la ampliacion de la infraestructura energetica, el apoyo al saneamiento ambiental y el mejoramiento de la revitalizacion de las comunidades. El estudio identifica hasta 3.3 gigavatios (GW) de capacidad solar fotovoltaica, incluidos 213 megavatios (MW) en vertederos cerrados, 1-2.5 GW en sitios contaminados, 78 MW en plantas desmanteladas, 21-50 MW en derechos de paso de lineas de transmision y 636 MW en masas de agua para energia fotovoltaica flotante. Esta investigacion pone de relieve la importancia estrategica de las inversiones y el apoyo normativo para alcanzar el objetivo de Puerto Rico de un 100% de energia limpia para 2050.

14 SOLAR ENERGY↗

Is Clean Hydrogen Production a Good Fit for Questa? (Final Economic Impact Results) [Slides]

The Village of Questa, New Mexico is aiming to become a regional clean energy hub with robust and diverse employment opportunities for the local community supported by the energy sector and by other businesses inspired or attracted by abundant clean energy, outdoor recreation, and cultural opportunities. A coalition of stakeholders in the Village of Questa, comprising the Village, Kit Carson Electric Cooperative (KCEC), Questa Economic Development Fund, and Chevron, is exploring options to develop hydrogen production facilities as an opportunity to create jobs, provide reliable clean energy, and utilize former mine resources. Questa is home to a molybdenum mine owned by Chevron that closed in 2014. Several residents in Questa and surrounding communities lost their jobs when the mine closed and transitioned from active operations into environmental remediation. Although remediation efforts have been ongoing since 2014 and are expected to continue for at least 16 more years, the number of jobs with Chevron is much smaller now than it was before the closure. Between available workforce, brownfield land, and water rights formerly supporting mine operations but now in a transition period, there are considerable local resources that could be directed toward clean energy generation. Questa's electricity supply is already 100% solar during daylight hours thanks to Kit Carson Electric Cooperative's (KCEC's) strategic decision-making and partnering over the last decade. Now, Questa, KCEC, and Chevron are exploring the potential costs and benefits of siting an electrolytic hydrogen production facility and additional solar photovoltaic (PV) capacity in Questa to further advance the region's clean energy economy. In this report, we estimated the potential economic impacts (i.e., jobs, value added, gross output, tax revenue) of constructing and operating a combined hydrogen (32 MW polymer electrolyte membrane electrolizer + 7.5 MW fuel cell) and solar facility (22.5 MW) in the Village of Questa, as well as the resulting economic spillovers to Taos County and the state of New Mexico. We employ an input-output model that leverages IMPLAN's economic data for the region complemented by construction and operating expenses estimated by NREL and feedback from the local coalition to evaluate the direct, indirect and induced effects of the project construction (transient impacts) and operation (more permanent impacts). Based on the area's average trade profile, feedback from the coalition and current market conditions, these projects are expected to support 487 full-time equivalent jobs during construction, generating $\$24$ million in income for those workers and $\$82$ million in local economic activity in the state. Of those jobs, 106 are expected to be construction sector jobs. These investments are also estimated to add $\$36.5$ million to New Mexico's gross state product (GSP). In the Village of Questa, we estimate 16 jobs will be supported in construction and transportation industries, generating $\$0.9$ million in earnings. In Taos County, the construction phase is expected to support 285 jobs primarily in construction and professional services, while manufacturing jobs dominate the results for the Rest of New Mexico. The Village is also estimated to receive $\$0.9$ million in tax revenue from the construction phase alone. Once in operation, the project continues to impact the state and Questa. Around 20 jobs (full-time equivalent for each year of operation) are supported across New Mexico, with approximately 11 directly employed in Questa by both facilities. The total annual local economic activity supported by ongoing operations is just over $\$1.3$ million/yr, generating $\$1.6$ million/yr in additional income in the state. Annual operations are estimated to add $\$2.1$ million to the state's GSP. The Village is expected to receive around $\$43,000$/yr in tax revenue. Impacts vary significantly depending on which businesses are supplying materials, equipment and services, and where construction workers reside. Choosing local suppliers will most benefit Questa and the New Mexico economy, adding up to 500 jobs during construction and 13 long-term jobs. Local and state governments may consider ways to incentivize local businesses in order to maximize economic benefits.

08 HYDROGEN↗

Is Clean Hydrogen Production a Good Fit for Questa? Final Economic Impact Results

The Village of Questa, New Mexico is aiming to become a regional clean energy hub with robust and diverse employment opportunities for the local community supported by the energy sector and by other businesses inspired or attracted by abundant clean energy, outdoor recreation, and cultural opportunities. A coalition of stakeholders in the Village of Questa, comprising the Village, Kit Carson Electric Cooperative (KCEC), Questa Economic Development Fund, and Chevron, is exploring options to develop hydrogen production facilities as an opportunity to create jobs, provide reliable clean energy, and utilize former mine resources. Questa is home to a molybdenum mine owned by Chevron that closed in 2014. Several residents in Questa and surrounding communities lost their jobs when the mine closed and transitioned from active operations into environmental remediation. Although remediation efforts have been ongoing since 2014 and are expected to continue for at least 16 more years, the number of jobs with Chevron is much smaller now than it was before the closure. Between available workforce, brownfield land, and water rights formerly supporting mine operations but now in a transition period, there are considerable local resources that could be directed toward clean energy generation. Questa's electricity supply is already 100% solar during daylight hours thanks to Kit Carson Electric Cooperative's (KCEC's) strategic decision-making and partnering over the last decade. Now, Questa, KCEC, and Chevron are exploring the potential costs and benefits of siting an electrolytic hydrogen production facility and additional solar photovoltaic (PV) capacity in Questa to further advance the region's clean energy economy. In this report, we estimated the potential economic impacts (i.e., jobs, value added, gross output, tax revenue) of constructing and operating a combined hydrogen (32 MW polymer electrolyte membrane electrolizer + 7.5 MW fuel cell) and solar facility (22.5 MW) in the Village of Questa, as well as the resulting economic spillovers to Taos County and the state of New Mexico. We employ an input-output model that leverages IMPLAN's economic data for the region complemented by construction and operating expenses estimated by NREL and feedback from the local coalition to evaluate the direct, indirect and induced effects of the project construction (transient impacts) and operation (more permanent impacts). Based on the area's average trade profile, feedback from the coalition and current market conditions, these projects are expected to support 487 full-time equivalent jobs during construction, generating $\$24$ million in income for those workers and $\$82$ million in local economic activity in the state. Of those jobs, 106 are expected to be construction sector jobs. These investments are also estimated to add $\$36.5$ million to New Mexico's gross state product (GSP). In the Village of Questa, we estimate 16 jobs will be supported in construction and transportation industries, generating $\$0.9$ million in earnings. In Taos County, the construction phase is expected to support 285 jobs primarily in construction and professional services, while manufacturing jobs dominate the results for the Rest of New Mexico. The Village is also estimated to receive $\$0.9$ million in tax revenue from the construction phase alone. Once in operation, the project continues to impact the state and Questa. Around 20 jobs (full-time equivalent for each year of operation) are supported across New Mexico, with approximately 11 directly employed in Questa by both facilities. The total annual local economic activity supported by ongoing operations is just over $\$1.3$ million/yr, generating $\$1.6$ million/yr in additional income in the state. Annual operations are estimated to add $\$2.1$ million to the state's GSP. The Village is expected to receive around $\$43,000$/yr in tax revenue. Impacts vary significantly depending on which businesses are supplying materials, equipment and services, and where construction workers reside. Choosing local suppliers will most benefit Questa and the New Mexico economy, adding up to 500 jobs during construction and 13 long-term jobs. Local and state governments may consider ways to incentivize local businesses in order to maximize economic benefits.

08 HYDROGEN↗

Supporting ARPA-E Power Grid Optimization (Final Report)

Pacific Northwest National Laboratory (PNNL), Arizona State University (ASU), Georgia Institute of Technology (Georgia Tech), Los Alamos National Laboratory (LANL), National Renewable Energy Laboratory (NREL), Texas A&M University (TAMU), The University of Texas at Austin (UT), and the University of Wisconsin-Madison (UW-M) supported the ARPA-E Grid Optimization (GO) Competition by providing a common problem formulation, data format, datasets, evaluation mechanism, scoring, rules, and results that resulted in the awarding of $\$9.24$ million dollars to teams from academia, industry, and national labs for solving three sets of increasingly difficult non-linear, security- constrained AC Optimal Powerflow (AC-OPF) optimization problems in order to increase the efficiency of the US Electric Grid. It is estimated that a 1% increase in efficiency can save $\$1$ billion. Current industry practices typically use a linear DC model (DC-OPF) in order solve the OPF problem within the time constraints of the operation schedule. The GO Competition challenges the best power engineers, mathematicians, and computer scientists to make possible operational decisions based on accurate physical models. To accomplish this, the GO Competition created a series of Challenges and funded teams to produce the best solver. Challenge 1 was to solve the security constrained Alternating Current Optimal Power Flow (ACOPF) problem. Challenge 2 extended that to by adding adjustable transformer tap ratios, phase shifting transformers, switchable shunts, price-responsive demand, ramp rate constrained generators and loads, and fast-start unit commitment (UC). Furthermore, Challenge 2 was a maximization problem while Challenge 1 was a minimization problem. While Challenge 3 was being developed, the entrants were invited to find better solutions to the Challenge 2 synthetic datasets with no restrictions on time, hardware, or algorithms. The Challenge 2 solutions turned out to be very good. Challenge 3 expanded the Challenge 2 problem further by using multiperiod dynamic markets, including advisory models for extreme weather events, day-ahead markets, and the real-time markets with an extended look-ahead. These problems included active bid-in demand and topology optimization. Together the Challenges used nearly 30 million CPU hours. Since each team was working on the same problem, using the same data, and running on the same hardware, fair comparisons could be drawn as to the best solver. The datasets were varied enough, however, that the best solver for one dataset was not necessarily the best at another, so cumulative scores were used. The process was managed by the PNNL maintained website https://GOCompetition.energy.gov, where Entrants could find information about the problem, the data, the rules, submit their solver for evaluation, and see the scores of all the competing teams on a Leaderboard. Interest was world-wide but only American teams were eligible for prizes. The Competition has produced 34 journal articles 115 papers and been cited over 500 times in the literature, including 12 dissertations (4 from foreign countries; Columbia (2), Germany, and Italy) and 3 from the DOE ExaScale project. Software developed by Pearl Street Technologies for Challenges 1 and 2 is now deployed by Southwest Power Pool (SPP) and Midcontinent Independent Service Operator (MISO). Other teams have received inquiries from venture capitalists. Google DeepMind has thanked the Competition for making the datasets developed for the Competition public. They are using it to train machine learning models. The larger datasets have billions of unknowns to be solved for, but only a small percent matter in the final solution. Knowing what unknowns are important can dramatically speedup the solution.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Assessment of BQ-9000 Biodiesel Properties for 2023

This is the seventh in a series of reports documenting the quality of biodiesel from U.S.- and Canadian-based producers that participate in the BQ-9000 program, the biodiesel industry’s voluntary quality assurance program. Participants provided monthly data on critical quality parameters for calendar year 2023 with quality data provided to a team of experts, who removed any identifying company information and provided anonymized data to the National Renewable Energy Laboratory (NREL) for statistical analysis. New for 2023, data on kinematic viscosity, sulfated ash, distillation temperature, carbon residue, and cetane were collected, as well as individual levels of sodium, potassium, calcium, and magnesium. Critical quality parameters analyzed are listed in Table ES-1 with descriptive statistics.

09 BIOMASS FUELS↗

OPTOM: Optimization of Parabolic Trough - Operations & Maintenance

The US Department of Energy’s SunShot goals look to reduce the cost of Concentrating Solar Power (CSP) technology to 5¢/kWh for baseload plants. This is about a 50% reduction from current costs. To achieve this cost target, a significant reduction in operation and maintenance (O&M) costs of 40 to 50% is likely needed. Advances are needed in the O&M practices of CSP plants if the technology is to achieve the SunShot cost goals. Digitization of plant performance and O&M data has become a new best practice in the world of renewable energy asset management. Owners and operators of large photovoltaic and wind power plants are working to digitize performance and O&M data at their existing assets, to improve their management of the facilities, to increase performance, reduce O&M costs, and lower the overall life cycle cost of ownership. CSP power plants are behind the curve of other technologies on the digitization of plant information to aid in the plant asset management. This project directly addresses the objective of digitizing the O&M data of the solar field, focusing on three areas: 1) creating a framework for sharing data and information, 2) creating a system for monitoring and managing the maintenance of the solar field collectors, and 3) developing analytic tools to identify issues in the solar field. According to the NREL CSP Best Practices Study, the current practice at many CSP plants is to rely on paper lists, spreadsheets, and email for monitoring and managing problems and maintenance in the solar field. The key element to digitize solar field O&M is the creation of a centralized data archive that all users and systems can interface with. This project developed a centralized relational database framework that allows users and applications to access and share data. Conventional power plants utilize Computerized Maintenance Management Systems (CMMSs) to track the corrective, preventive (scheduled), and predictive maintenance of equipment and subsystems in the power plant. CSP plants use these systems in the power block, but while these systems specialize at tracking maintenance on up to thousands of pieces of equipment, they are not well suited for tracking the tens or hundreds of thousands of components in large commercial CSP or photovoltaic solar fields. In this project we developed a new software application referred to as FieldStatus (TM). This is a specialized database program that is used to track the status of each collector and its components. This application is designed to complement the existing CMMS to enable improved tracking and management of maintenance activities in the solar field. One of the major maintenance tasks for solar fields is maintaining the cleanliness of the mirrors. Although seemingly a relatively straight forward task, it has often proven challenging to maintain high levels of cleanliness in an efficient and cost-effective manner. This project developed new tools and metrics for monitoring and optimizing solar field cleaning resources and overall solar field cleanliness.

14 SOLAR ENERGY↗

Floating PV Potential and Technology Validation [Slides]

This presentation covers, at a high-level, the potential for floating solar PV (FPV) in the United States as well as technology validation approaches and research capabilities at the U.S. Department of Energy's National Renewable Energy Laboratory (NREL).

14 SOLAR ENERGY↗

Solar Energy Innovation Network 2017-2024: Abbreviated Final Technical Report

This material is based upon work supported by the U.S. Department of Energy's (DOE) Office of Energy Efficiency and Renewable Energy (EERE) Solar Energy Technologies Office under the Agreement/Award Number 32954 for Solar Energy Innovation Network (SEIN) Project, 2017-2024. SEIN is a dynamic program that assembles diverse teams of stakeholders to research solutions to real-world challenges associated with solar energy adoption. In conjunction with its partner organizations, NREL implemented the program by providing research, analysis, and technical expertise directly to project teams and groups of teams (cohorts), by facilitating networked learning through cohorts and peer exchange, and by facilitating dissemination and replication of solutions and lessons learned among stakeholders across the U.S. with similar challenges.

14 SOLAR ENERGY↗

Impact of Electric Vehicle Charging Station Reliability, Resilience, and Location on Electric Vehicle Adoption

While the majority of electric vehicle (EV) charging events in the United States occur at home, issues with public charging stations are consistently found to be a top reason that potential EV buyers do not purchase an EV, demonstrating that both EVSE reliability and availability impacts EV adoption. This report explores multiple parameters that impact EVSE reliability and deployment, which in turn impact EV sales. These include extreme weather, codes and standards, region (urban vs. rural), and grid network type. Grid reliability was not found to impact EV adoption. The relationships between EV station reliability, station resilience, grid resilience, and EV adoption are largely outside the scope of the National Renewable Energy Laboratory's (NREL's) Automotive Deployment Options Projection Tool (ADOPT) and other vehicle adoption models, so the methodology of this report is varied. Section 2 sets the baseline for infrastructure reliability, user satisfaction, and maintenance practices. Section 3 explores the ways that electric vehicle supply equipment (EVSE) reliability impacts the relationship between EVSE and EV adoption. Section 4 shows how geographical categories such as urban, rural, large grid, off-grid, or microgrid can be helpful in EVSE deployment strategies, as well as how the relationship between EVSE and EV adoption differs among these categories. Section 5 investigates the impacts of grid reliability and infrastructure resilience on EV adoption. Finally, Section 6 reverses the perspective to examine the impact that EVs and EVSE have on grid resilience and reliability. As recent funding initiatives result in an expansion of public chargers across the United States, as well as an increase in the uptime of existing chargers, EV adoption will likely grow.

33 ADVANCED PROPULSION SYSTEMS↗

An Analysis of High Opportunity Geothermal Leasing Areas on BLM and USFS Lands

This analysis, conducted by the National Renewable Energy Laboratory (NREL) with support from the U.S. Department of Energy (DOE) Geothermal Technologies Office (GTO), models potential geothermal deployment on BLM and USFS land for the years 2025, 2030, 2035, and 2050 under various scenarios using the Renewable Energy Potential (reV) model and the Regional Energy Deployment System (ReEDS) model. This report identifies potential future high opportunity geothermal leasing areas (i.e., Best, Middle, and Least identified opportunities) based on available data for geothermal resource potential, natural resource conflicts, and transmission access. In addition, this analysis considers the impacts of the Energy Policy Act of 2005's (EPAct 2005's) default competitive leasing provisions, specifically the impact this may have had on geothermal resource discovery outside of known geothermal resource areas.

15 GEOTHERMAL ENERGY↗

Workshop Summary: Bridging the Gap Between Atmospheric Science and Grid Integration

The need for dedicated, accurate, expertly curated weather data is increasingly important as the share of variable renewable energy increases on the power system. Projections for futures with very high (50+% annual energy) shares of variable generation require ongoing assessment of data requirements from industry stakeholders in their power system operation and planning contexts. In March 2024, NREL organized a workshop entitled "Bridging the Gap Between Atmospheric Science and Grid Integration Workshop", which brought atmospheric scientists and power system experts together to refine the requirements of atmospheric datasets for grid integration, and to describe a holistic approach to creating new and regularly updated national scale wind datasets for power system planning and operations. The results of this workshop are being used to inform the near-term development and a longer-term strategy for DOE to produce relevant wind resource datasets and inform wider use of wind/solar/load data sets in power system planning. This presentation provides an overview of a preworkshop survey, an assessment of current state of the art of national-scale datasets for wind resource assessment and grid integration, insights on appropriate uses of the WTK-LED, power system perspectives on data needs, as well as recommended next steps as discussed in the workshop and how these steps support longer-term strategies.

17 WIND ENERGY↗

Residential Home Repairs, Energy Efficiency, and Electrification in the Hill District of Pittsburgh [Slides]

Through Communities LEAP, a community coalition focused on the Hill District neighborhood of Pittsburgh is working with a technical assistance provider network led by the National Renewable Energy Laboratory (NREL). The coalition includes community organizations, nonprofits, the city government, and the utility. Technical assistance provides analysis and information to support Hill District stakeholders in their goals to create informed residential energy efficiency and renewable energy transition strategies. This report summarizes the insights from stakeholder engagement with organizations that provide home repair services, weatherization, and residential energy efficiency in the Hill District as well as from a building analysis to characterize Hill District housing stock and the potential costs and benefits of energy efficiency and electrification measures.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Nonsteady Load Responses of Wind Turbines to Atmospheric and Mountain-Generated Turbulence Eddies, With Impacts on the Main Bearing: A Validation Study

Previous computational and field experiments identify three characteristic time scales in the aerodynamic responses of utility-scale wind turbine loads to atmospheric boundary layer (ABL) turbulence: a 30-90 second time scale for the passage of high/low speed "streaks" through the rotor plane, the blade and rotor rotation time scales (approximately 1 to 5 seconds), and a sub-second time scale created by blade rotation through gradients within eddy coherent structure. In the current study we compare aerodynamic load responses from daytime ABL turbulence quantified with large-eddy simulation and a actuator line model of the NREL 5 MW wind turbine with analysis of field data from the NREL/GE 1.5 MW wind turbine 5 kilometers east of the Rocky Mountain Front Range in Colorado. In addition, we contrast the responses to the passage of the mountain-generated eddies embedded within the westerly winds with the ABL eddies embedded within northerly/southerly winds. These analyses are in context with the nonsteady forcing of the main bearing by the aerodynamic generation of nontorque bending moments on the main shaft. Potentially relevant to main bearing failure mechanisms, both computational and field data show that the magnitudes of turbulence-generated nontorque bending moments, that we show generate nonsteady force on the main bearing, are of order, and often larger than, torque (which underlies power). However, the temporal variations in these two responses are uncorrelated, implying that the aerodynamic mechanisms that drive power and main bearing response are fundamentally different. We find this to be the case in the field with both mountain-generated eddies (westerly winds) and ABL-generated eddies (northerly/southerly winds). Whereas the time and length scales are comparable, the mountain eddies were somewhat more energetic than the northerly/southerly ABL eddies. Interestingly, however, the fluctuations in nontorque bending moment that force the main bearing were found to be stronger when forced by the ABL eddies than the mountain eddies. The field studies validate the key results from the computational study and show even stronger response in the nontorque bending moment than in the computer simulations. In all cases, the torque and nontorque bending moments are temporally uncorrelated, torque and power are driven by time variations in rotor-averaged horizontal wind velocity and nontorque bending moments are driven by time changes in the degree of nonuniformity in the distribution of velocity over the rotor plane. Thus the results generalize the mechanisms underlying nonsteady aerodynamic forcing to classes of turbulence eddy types with strength of order or stronger than ABL eddies with transverse scale of order the wind turbine rotor. These include atmospheric turbulence eddies, topography-generated turbulence eddies and, by extension, impacts of turbine-wake-scale turbulence eddies on downstream wind turbine rotors.

17 WIND ENERGY↗

Cambium Datasets [Slides]

This is a presentation deck used in the "Powered By Cambium" webinar, given on August 13th 2024, in which Pieter Gagnon gave an overview of NREL's Cambium datasets.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Representative Project Design Envelope for Floating Offshore Wind Energy: A Focus on the California 2023 Federal Leases

NREL developed recommendations for a representative project design envelope (RPDE) for floating offshore wind energy projects in the California lease areas, considering industry feedback from offshore wind farm developers. The RPDE provides estimates of minimum and maximum values for project design parameters that are relevant for assessing environmental impacts. The design envelope considers the practical range of technology options that may be deployed and accounts for major physical constraints, technology feasibility, and supply chain readiness. In addition to the RPDE, this report presents four scenarios that illustrate some of the differences between technologies that could be used offshore California, as well as descriptions of the typical installation processes that are expected to be used for floating offshore wind farms.

17 WIND ENERGY↗

Vehicle Data for Analysis of Medium- and Heavy-Duty Electrification [Slides]

Medium- and heavy-duty vehicles (MHDVs) are a major source of greenhouse gases and local criteria air pollutants. Electrifying MHDVs may reduce these harmful emissions, but understanding MHDV operations is a necessary first step to decarbonizing them. In February 2024, NREL released a public dataset and accompanying technical report describing the subset of MHDV operating patterns that may originate from a consistent depot each day and rely on the same depot for charging if electrified (NREL/TP-5400-88241). This presentation provides a brief overview of that dataset and technical report.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

An Atlas of Current Customer-Facing Utility Program Designs and Pricing

The National Renewable Energy Laboratory (NREL) and Kevala conducted a targeted literature review and leveraged extensive expertise, including team members with four decades of experience in the utility sector, to characterize utility programs and rate designs. This analysis delves into the motivations behind these programs and the various hurdles they face. Through this in-depth study, the team provides critical insights into the operational dynamics of utility programs, identifying key drivers and barriers that influence their effectiveness and implementation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Overview of Tools to Provide Support for State Energy Programs [Slides]

This "Overview of Tools to Provide Support for State Energy Programs?" is a resource to support technical assistance programs, specifically motivated by the State Energy Program Direct TA program under SCEP at the Department of Energy. It provides a general description of seven unique tools - six by NREL, one by Argonne National Lab - which may be used to benefit state energy offices either through direct use (by state offices) or through contracted support (by national lab staff via TA programs).

97 MATHEMATICS AND COMPUTING↗