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Quantum computing for finance

Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. Here, we present a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modelling, optimization and machine learning. This Review is aimed at physicists, so it outlines the classical techniques used by the financial industry and discusses the potential advantages and limitations of quantum techniques. Finally, we look at the challenges that physicists could help tackle. Quantum computers are expected to surpass classical computers and transform industries. This Review focuses on quantum computing for financial applications and provides a summary for physicists on potential advantages and limitations of quantum techniques, as well as challenges that physicists could help tackle.

97 MATHEMATICS AND COMPUTING↗

A Recipe for ABC Multifamily Retrofits: Technologies, Financing, and Project Delivery

This report documents the final technical accomplishments and outcomes of Rocky Mountain Institute’s project under the U.S. Department of Energy (DOE) Award DE-EE0009064. The project aimed to develop, validate, and scale whole building retrofit solutions for multifamily buildings, including two configurations of Integrated Mechanical System Pods (IMSP-C and IMSP-U), in alignment with DOE Advanced Building Construction (ABC) initiative's decarbonization and energy efficiency goals. While the project made significant progress in Budget Period 1 (Phase 1) and throughout Budget Period 2 (Phase 2), activities were discontinued as of March 26, 2025, following a Stop Work Order issued by DOE. As such, this report reflects all completed work through that date. The project did not enter Budget Periods 3 and 4 (Phase 2), and demonstration site implementation, field M&V, and final commercialization execution were not conducted.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Entropy-Assisted Quality Pattern Identification in Finance

Short-term patterns in financial time series form the cornerstone of many algorithmic trading strategies, yet extracting these patterns reliably from noisy market data remains a formidable challenge. In this paper, we propose an entropy-assisted framework for identifying high-quality, non-overlapping patterns that exhibit consistent behavior over time. We ground our approach in the premise that historical patterns, when accurately clustered and pruned, can yield substantial predictive power for short-term price movements. To achieve this, we incorporate an entropy-based measure as a proxy for information gain: patterns that lead to high one-sided movements in historical data yet retain low local entropy are more “informative” in signaling future market direction. Compared to conventional clustering techniques such as K-means and Gaussian Mixture Models (GMMs), which often yield biased or unbalanced groupings, our approach emphasizes balance over a forced visual boundary, ensuring that quality patterns are not lost due to over-segmentation. By emphasizing both predictive purity (low local entropy) and historical profitability, our method achieves a balanced representation of Buy and Sell patterns, making it better suited for short-term algorithmic trading strategies. This paper offers an in-depth illustration of our entropy-assisted framework through two case studies on Gold vs. USD and GBPUSD. While these examples demonstrate the method’s potential for extracting high-quality patterns, they do not constitute an exhaustive survey of all possible asset classes.

Physics↗

Kickstart Your Federal Microgrid Resiliency Project: Financing Opportunities and Best Practices

Recent high-impact events such as hurricanes and wildfires have resulted in the loss of utility grid power to federal sites, highlighting the need for energy system resilience. To sustain critical functions, site loads may need to operate during an electric grid outage or at least have power restored quickly after the event. A microgrid can provide reliable backup power to critical loads when electric utility power is interrupted, and may also provide value during normal operations.

DER↗

Feasibility and strategic implications of deploying nuclear power reactors in Africa

This report assesses the feasibility and strategic implications of deploying nuclear power reactors, including large-scale plants, advanced small modular reactors (SMRs), and microreactors, in African countries. Case studies focus on South Africa, Egypt, Kenya, Ghana, and Nigeria, examining nuclear energy’s role in Africa’s rapidly evolving energy landscape, marked by fast-growing demand, significant electricity access gaps, increasing renewable penetration, and strong policy commitments to industrialization and energy security. Several U.S. reactor technologies and designs are considered based on their development status and readiness for deployment. The analysis finds that nuclear power can provide reliable, clean baseload and flexible generation, as well as high-temperature process heat for desalination, hydrogen production, and industrial applications. However, suitability is highly country-specific, depending on grid size and stability, transmission capacity, cooling water availability, regulatory readiness, and fuel supply chains. Near-term deployment opportunities are strongest for light-water reactors (such as NuScale, BWRX-300, AP300, and SMR-300) that use low-enriched uranium and build on proven technology. More advanced concepts, including gas-cooled, sodium-cooled, molten-salt cooled reactors, and microreactors, will likely be relevant for African deployment in the 2030s or later, contingent on demonstration projects, high-assay low-enriched uranium (HALEU) fuel availability, and mature international licensing frameworks. Economic analysis shows that SMRs are capital-intensive, with projected overnight costs for 300 MWe units in 2025 ranging from approximately 1.4 to 2.6 billion USD per module. The levelized cost of electricity (LCOE) is highly sensitive to the weighted average cost of capital (WACC). Given typically higher financing costs and utility balance-sheet weaknesses in many African countries, bankable project structures will require sovereign guarantees, robust offtake arrangements, and layered financing from export credit agencies, development finance institutions, and vendor nations. Comparisons with recent large nuclear projects in the United Arab Emirates (UAE) and Egypt underscore the central role of state-backed loans, long tenors, and concessional terms. Country case studies illustrate a spectrum of readiness and opportunity. South Africa operates two 920 MWe pressurized light water reactors (totaling 1,840 MWe) at Koeberg and has the most mature regulatory and industrial base, positioning it as a prime candidate for both large reactors and SMRs to replace coal, support desalination, and anchor industrial hubs. Egypt is constructing four VVER-1200 units at El Dabaa with strong state leadership and could later complement this fleet with SMRs for coastal and industrial applications. Kenya and Ghana are advancing through IAEA Milestones with growing institutional capacity and clear interest in SMRs that match their smaller grids and industrialization plans. Nigeria has the largest demand potential but faces acute constraints in grid reliability, project bankability, and regulatory capacity; targeted deployments of large reactors and SMRs near coastal or industrial sites could have high impact if accompanied by major grid upgrades and institutional reforms. The report identifies cross-cutting challenges such as financing, political continuity, public acceptance, nonproliferation and security, waste and back-end management, regulatory capacity, grid adequacy, and long deployment timelines for first-of-a-kind designs, and ANL/NSE-26/3 ii proposes broad directions for resolution. These include stronger multifaceted financing for nuclear, long-term national energy strategies that transcend electoral cycles, proactive stakeholder engagement, strengthened regional and national regulators, and systematic workforce development through centers of excellence and expanded training. The United States should develop partnerships with African countries and offer end-to-end nuclear package similar to those used effectively by competitors: coordinated project development, state-backed financing, long-term fuel services, and durable in-country support through regional offices and sustained workforce/regulatory training. With timely planning, sustained political commitment, and appropriate financing and institutional support, nuclear energy, both large reactors and advanced SMRs, can become a meaningful, though not dominant, pillar of Africa’s future power mix, enhancing energy security, enabling industrial growth, and supporting climate goals.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

2022 Product Commercialization and Market Development Awardee: Bergey Windpower

In 2023, consumers will finance more than 80% of the residential solar energy systems they purchase, which they use as collateral (called "non-recourse loans"). Similar loans are not yet offered to fund distributed wind energy systems. To accelerate deployment of small wind systems, which power individual rural homes and farms, the United States will need to make consumer loans available at reasonable rates with modest downpayments and collateral requirements. A team led by Bergey Windpower Co. is creating new consumer financing options to reduce or eliminate the upfront cash needed to buy distributed wind energy systems. This new financing structure would decrease purchase costs for small wind turbines produced by Bergey Windpower and possibly other manufacturers. Product financing is instrumental in growing wind power market share, clean energy manufacturing, and installation jobs while reducing greenhouse gas emissions. Bergey Windpower's previous Competitiveness Improvement Project (CIP) awards have led to the development of affordable, high-performance wind turbines, microgrids, and components.

CIP↗

Achieving Cooperative Community Equitable Solar Sources (ACCESS) (Final Technical Report)

Since 2011, solar has grown from a niche technology to a widely accessible source of power for homes and businesses across the United States and has become a fundamental part of the modern grid. There are still challenges, however, in learning how to integrate and use PV most effectively and how to make PV universally available. Most low- and moderate-income (LMI) customers cannot currently afford PV; capital costs and financing costs are too high to drive significant penetration. Providing access to LMI individuals and communities is a critical and immediate priority, and the focus of this project. The overall objective of the Achieving Cooperative Community Equitable Solar Sources (ACCESS) project is to explore and amplify the use of innovative, cost-effective energy access programs to serve co-ops’ LMI members1. ACCESS will research at least three financing mechanisms and at least six LMI program designs including LMI engagement strategies to maximize participation for these hard-to-reach audiences. ACCESS evaluated the financial mechanisms and program designs from field tests sited at diverse co-ops that provide recognizable models for the broader co-op community to identify optimal solutions for small utilities. The research with these cooperatives allowed testing of concepts and development of models and tools for other utilities to adapt to their own program designs and expansions. ACCESS published results and developed an “ACCESS Solar Access Toolkit” consisting of program designs, LMI engagement strategies, how-to guidance, and other tools to facilitate replication at small utilities across the country. Through the dissemination practices of the ACCESS project team, all NRECA member co-ops (~900) were made aware of the “ACCESS Solar Access Toolkit” and all other ACCESS resources. NRECA and its partners developed innovations to expand co-ops’ solar energy offerings to provide all of a co-op’s members—especially those who struggle to pay their bills—with cost-effective options that meet their needs. ACCESS specifically explored utility financing mechanisms and program designs that, independently or used in combination, increase solar access for rural electric cooperatives’ LMI members/ratepayers and that reduce LMI member/ratepayers’ electricity costs by at least 10%. LMI engagement strategies focused on maximizing the number of members who receive benefits and on the cost savings to LMI participants.

14 SOLAR ENERGY↗

Transforming Public Housing with Deep Energy Retrofits

Open Market ESCO’s (OME) Transforming Public Housing through Deep Energy Retrofits project demonstrated new design and financing solutions for implementing deep energy retrofits (DERs) in occupied low-income multifamily housing. The Project performed an integrated project delivery process, including designing low-carbon retrofit solution packages, construction pricing, and financing. The Project developed a constructible and financeable DER scope for a 102-unit extremely low-income multifamily property in Boston. This Project demonstrated a replicable approach for streamlining and implementing DER projects in occupied housing, including real solutions for overcoming design complexities and cost barriers.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Clean Energy Revolving Loan Funds: International Experience [Slides]

Tunisia’s Energy Transition Fund (FTE), created in 2013, was established to promote energy efficiency and renewable energy projects in the public and private sectors. To overcome financing challenges related to the energy transition, Tunisia’s National Agency for Energy Conservation (ANME) seeks both to strengthen available financial resources and to develop innovative financing structures. Revolving Loan Funds (RLFs) are one such innovative financing structure, used by countries around the world to foster the development of distributed clean energy projects. This report aims to inform policy makers and various stakeholders on the opportunity to design an RLF by drawing on successful experiences from other countries. Specifically, this report provides analytical support for discussions with ANME and its partners to develop an RLF in the context of Tunisia. It outlines the 12 essential steps for establishing a RLF and includes detailed case studies demonstrating successful RLF implementation across various contexts.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Coalition for Community-Supported Affordable Geothermal Energy Systems (C2SAGES)

The C2SAGES project evaluated the feasibility of a community geothermal system for the planned Windy Ridge affordable housing development in Hinesburg, Vermont. Led by GTI Energy with Vermont Gas Systems, LN Consulting, NREL, and Frontier Energy, the work assessed technical design, energy performance, costs, business models, community engagement, maintenance, workforce development, and permitting. The proposed system was designed to serve 100% of the development’s heating, cooling, and domestic hot water loads. Compared with a baseline using air-source heat pumps and natural gas water heating, the geothermal system was estimated to reduce HVAC and domestic hot water energy use by about 45% to 48%, lower operating and maintenance costs, and reduce 30-year life-cycle costs by 37% for Phase 1 and 10% for Phase 2. Technical testing and modeling indicated that the Windy Ridge site is suitable for a community-scale geothermal system. The project also developed borehole field layouts, piping concepts, pump house designs, controls, maintenance plans, and supporting engineering drawings. The business model analysis found that first cost, ownership structure, and customer affordability remain major deployment challenges. Utility-led maintenance and operation were viewed favorably, but traditional utility cost-recovery models may require subsidy or revised financing structures to be practical for affordable housing. Community engagement highlighted the need for clear public education, transparent financing, reliable long-term maintenance, trained technicians, and the potential to pair geothermal systems with weatherization. Overall, the report concludes that community geothermal is technically feasible and offers meaningful energy, emissions, and life-cycle cost benefits, but broader deployment will depend on workable financing models and workforce readiness.

15 GEOTHERMAL ENERGY↗

Advancing Clean Energy Equity

This year’s Financial Innovations Roundtable (June 16-17, 2022) focused on advancing clean energy equity and was co-hosted by the University of New Hampshire's Carsey School of Public Policy and the Federal Reserve Bank of New York. Clean energy technologies are better than ever, with costs continuing to decline. Yet the low-income and under-resourced communities – particularly communities of color, Native communities, and other traditionally marginalized populations – that are disproportionately impacted by climate and severe weather-related events lag in clean energy investments. Community Development Financial Institutions (CDFIs) have a long track record of providing access to capital to low- and moderate-income communities nationwide. Green Banks, established at state and local levels, use innovative financing to attract private capital and incentivize investments in clean and renewable energy. Together, the nation's network of more than 1,300 CDFIs and 21 Green Banks have the financing expertise and deep market understanding and relationships to finance a transition to clean energy. This event explored how Green Banks and CDFIs can funnel creditworthy projects to market and efficiently raise capital for them. Building on the Carsey School White Paper, Clean Energy Project Development for Low-Income Communities: Strengthening the Ecosystem for Delivering Solar Energy and Deep Efficiency Retrofits (Hangen, 2022), the FIR sought to identify options and create opportunities for Green Banks, CDFIs, and impact investors to collaborate in offering a range of products, approaches, and tools to better serve communities and individuals who have thus far been left out of the transition to clean energy. The event had 101 participants from a variety of sectors including CDFIs, Green Banks, mission-driven clean energy organizations, government agencies, banks, and impact investment professionals.

14 SOLAR ENERGY↗

The enduring role of contracts for difference in risk management and market creation for renewables

Governments procure renewables through a variety of mechanisms. Contracts for difference (CfDs) have been used for more than 50% of the global offshore wind supply. The payments awarded through CfDs are sometimes labelled subsidies, suggesting that they support uneconomic activity. Here, in this study, we argue that the primary role of CfDs is rather risk management by creating a market for electricity supply at stable long-term prices. Similar to its use in other sectors of the economy, this contract type transforms a variable to a fixed price to reallocate volatility risks. Such long-term contracts are often necessary for renewables financing due to limited hedging options in existing markets. Our perspective could imply a shift in perception towards CfDs as a fundamental and lasting market feature. We hope to stimulate a timely discussion about the impact of greater CfD diffusion on electricity market mechanisms, risk allocation and the potential for combining fragmented streams of energy finance, market and policy research.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Roadmap to reach global net-zero emissions for developing regions by 2085

As climate change intensifies, determining a developing region’s role in achieving net-zero emissions worldwide is crucial. However, regional efforts, considering historical emissions, remain underexplored. Here, we assess energy system changes, technology adoption, and investments needed for developing regions, including five major- and minor-emitting nations. Our analysis, using an integrated assessment model, shows a large gap in regional efforts toward global net-zero emissions, stemming from the necessary shift of energy systems to low-carbon resources. The use of new technologies, like electric vehicles, hydrogen, and carbon capture, varies by region, with the highest adoption required between 2020 and 2030. Financing this shift needs an average gross domestic product (GDP) investment rise of 0.464% in minor-emitting regions and up to 2.1% in major-emitting regions by 2085. Our results could guide policies and support setting quantifiable targets for developing nations. The findings are key to facilitating strategic technology use and finance mobilization to achieve a carbon-neutral future.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Incorporating energy justice into utility-scale photovoltaic deployment: A policy framework

Utility-scale photovoltaic (PV) installations made up 77 GW (6%) of installed capacity in the United States, as of the end of 2021. This will grow to more than 500 GW by 2050 under a mid-case projection or more than 800 GW if solar costs decline more rapidly. While utility-scale PV is projected to grow rapidly, to date, unlike energy efficiency or distributed PV, utility-scale PV has not been used to provide substantial financial benefits to underserved communities, either through ownership, financing of assets, or direct electricity bill reduction. We assess two mechanisms through which utility-scale PV could benefit underserved communities. We find that while a framework for direct electricity bill reduction can be meaningful to customers, this mechanism falls short of providing restorative justice via wealth creation for minority-owned businesses. In contrast, we find that a framework for procurement of utility-scale PV by public and private entities from PV projects that are financed, owned, and/or developed by minority-owned businesses can provide this restorative justice benefit, and thereby facilitate an equitable energy transition. We conclude with concrete recommendations for new policies and programs to ensure that the benefits of utility-scale PV systems are distributed to underserved communities.

14 SOLAR ENERGY↗

An Economics-by-Design Approach Applied to a Heat Pipe Microreactor Concept

Microreactors present a potential paradigm shift in the nuclear industry. Emphasis thus far has been on large-scale multi-billion-dollar projects that cater solely to grid electricity market. These projects can be challenging to finance and execute. On the other hand, microreactors are intended to target a wide variety of smaller niche markets and are expected to be factory-fabricated and more readily deployable. While diseconomies of scale for microreactors may tend to raise their costs per energy output (MWh) relative to large nuclear plants, offsetting gains can be expected from standardization, simplification, passive safety, lower radionuclide inventories, factory fabrication, fast installation, and low financing costs. To adequately assess these contributions, designers should have a different perspective on cost drivers than for large nuclear plants and can utilize novel approaches for systematic cost reduction. To account for these important aspects of microreactors, this report proposes an economics-by-design approach that places economic considerations at the center of the design process. The methodology builds on existing frameworks such as design-to-cost and value engineering, expanding them to new markets (beyond the grid), new attributes (beyond costs alone), and introducing the approach at earlier points in the design cycle. Design parameters and technical specifications are systematically evaluated until costs meet market entry points, while also providing the high-priority performance attributes of the particular use case. Determining first-order estimates for different components early in the process enables designers to focus R&D efforts on the biggest overall cost contributors and components with the most cost uncertainty. The analysis is always guided by market needs and threshold prices. In addition to microreactors, the approach is expected to be useful for other classes of nuclear reactors as well. The analysis was applied to a concept found in the open literature (the Design A heat-pipe reactor). A comprehensive bottom-up estimate was generated by leveraging a new microreactor-specific code of accounts and a range of cost equations. The initial estimate for levelized cost of electricity (LCOE) unsurprisingly exceeded market ranges since the use case had prioritized technological readiness over economic considerations in design choices. An alternate concept was then proposed, with various assumptions/targets made to reduce the largest cost contributors. Changes in the neutron spectrum, the power output, and building structures were found to make even the first-of-a-kind of this modified concept competitive with diesel generation in some remote communities. Learning rate (LR) assumptions indicated cost reductions achieved from sequential unit deployments could expand the range of competitiveness to include additional markets as deployments proceed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Practices for Demonstrating Energy Savings from Commercial PACE Projects

Nearly three-fourths of U.S. states have authorized local governments to use voluntary special assessments on commercial properties to finance energy improvements that boost economic development, create jobs, increase property values and advance energy goals. Commercial Property Assessed Clean Energy (C-PACE) financing allows building owners to repay the borrowed capital — from private or public sources — over time using their property as security. Berkeley Lab is supporting the Department of Energy’s Commercial PACE Working Group by developing a series of C-PACE issue briefs. The second brief in this series, Practices for Demonstrating Energy Savings from Commercial PACE Projects, looks at common practices for demonstrating energy savings to support state and local governments that sponsor C-PACE programs and want to track their energy impacts. This brief reviews: -The value proposition and trade-offs of conducting energy impact assessments for C-PACE programs; -Methods to quantify energy savings impacts from energy efficiency building improvements; and -Available resources and tools to support energy impact assessments. C-PACE programs may benefit from energy impact assessments for many reasons, including: -Validating the public benefits of the programs -Demonstrating that C-PACE can deliver participant benefits -Illustrating program impacts on public policy goals -Generating data to help improve program performance Many C-PACE programs are collecting data on project energy savings impacts, and these data can be leveraged to further support decision making and program implementation. Potential drawbacks to energy impact assessments may include added cost and burdens on property owners (e.g., the need to collect building energy consumption data). Where these burdens are considerable, they might slow program uptake. State and local governments can balance the benefits of energy impact assessments with the range of costs and accuracy inherent to available assessment methodologies. Additionally, depending on the policy context in the state or local government, a C-PACE program may be able to leverage existing efforts (e.g., building energy benchmarking programs) to reduce impact assessment costs, align with building owner practices and expectations, and efficiently assess program impact.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗