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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Optimal Network Reconfiguration and Scheduling With Hardware-in-the-Loop Validation for Improved Microgrid Resilience

With the increased occurrence of various major extreme weather events, power outages and prompt power system restorations have recently drawn more attention to the resilience and recovery of power systems. From the perspective of a more resilient power delivery at the distribution grid, system restoration using network topology reconfiguration together with optimal scheduling of distributed energy resources are adopted in this paper. The proposed optimization model aims at minimizing the total load shedding cost and other operational costs, in which linearized topological constraints borrowed from graph theory and linearized DistFlow models are respectively used to maintain the radial network topology and power flow balance after system contingencies. To demonstrate the applicability of the proposed strategy, a real-world case study of a networked three-microgrid system in Adjuntas, Puerto Rico, is used with the consideration of different independent/interconnected microgrid scenarios, contingencies, and fairness settings. Furthermore, hardware-in-the-loop testing is conducted for the same three-microgrid network, where the closely matched results with the simulated ones have validated the effectiveness of the proposed restoration strategy, which is now ready to move one step forward towards field deployment. Finally, to test the proposed restoration strategy in a larger networked system, the modified IEEE-33 bus test distribution system is considered, and the results show a more resilient power delivery for critical loads under three and four line outages.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Advanced Sensors and Instrumentation (ASI) Program Plan. Nuclear Energy Enabling Technologies (NEET)

The U.S. Department of Energy Office of Nuclear Energy (DOE-NE) sponsors a crosscutting technology development (CTD) program addressing common instrumentation & controls (I&C) needs in all DOE-NE sponsored programs. In 2012, DOE-NE initiated the Nuclear Energy Enabling Technology (NEET) Program to conduct research, development, and demonstration (RD&D) in crosscutting technologies that directly support and enable the development of existing, new and advanced reactor designs, and fuel cycle technologies. These technologies will advance the state of nuclear technology, improve its competitiveness, and promote continued contribution to meeting our Nation’s energy and environmental challenges. The NEET Program has spurred innovation in the field of sensors and instrumentation, advanced methods for manufacturing, and cyber security. The Advanced Sensors and Instrumentation (ASI) program is one element of the NEET CTD that has spurred innovation in the measurement science field by funding research on sensors, instrumentation and controls, communication, and advanced analytics that measure system parameters, gauge component control input, and provide power plant owners and operators critical awareness so they can plan and safely manage operational evolutions. The NEET ASI Program has carried out research and development (R&D) required to develop and deploy innovative and advanced sensors, and instrumentation and control capabilities for current and future nuclear energy systems, and to enable the advanced technologies essential to NE’s R&D efforts needed to realize mission goals. The concept of technology readiness assessment is helpful for the classification of instrumentation technology as part of the program strategy. A technology readiness assessment evaluates technology maturity using the Technology Readiness Level (TRL) scale and was pioneered by the National Aeronautics and Space Administration in the 1980s for space technology. It has recently been adopted to advance fuels and materials. The NEET ASI program objective is to mature instruments technology to TRL 6, which is “demonstration of the technology in relevant environment.” While there may be instances in which a different strategy is justified, the aim of the program is to respond to DOE program and stakeholder needs for nuclear instrumentation then hand off the technology after demonstration for integration in a more complex system, for example an irradiation test, experimental loop or a plant component such as the core, primary system or heat exchanger. A mechanism to continue some level of support from NEET ASI during and after the adoption (for example, to maintain fabrication and calibration capabilities) will be defined as the first example of technology hand off comes to fruition. In addition, several paths exist within DOE to complement NEET ASI activities to extend the maturity beyond TRL, for example through GAIN, technology commercialization funding, and small-business programs. Role of NEET ASI CINR projects in the TRL space, and integration with direct funded demonstration.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Multicriterion Benefit Evaluation of Deploying New Battery Technology with Increased Capacity at a Generic Nuclear Power Plant

This presentation is prepared for the DOE LWRS RISA Pathway Stakeholder Engagement Meeting on October 13-14, 2021. Nuclear power plant (NPP) safety improvements are routinely made by plant licensees and regulators. Examples of plant improvements include accident-tolerant fuel, diverse and flexible coping strategies, passive cooling systems, and increased battery capacity. A combined use of these plant improvements could lead to plant designs with enhanced resilience, allowing NPPs to better cope with both internal and external hazards and keep the plant operating safely, efficiently, and economically. This presentation focuses on increased battery capacity and evaluates the potential costs and benefits of deploying batteries with increased capacities at a generic boiling water reactor (BWR) NPP. A multicriterion benefit evaluation methodology is used for the cost-benefit analysis. Ten alternatives for extending battery capacity are developed, including eight alternatives to provide additional direct-current power and one alternative to provide additional alternating-current power. Potential benefits of reducing plant risk are quantified through incorporating the alternatives into loss-of-offsite-power scenarios of the generic BWR probabilistic risk assessment model. Potential costs of implementing the alternatives are qualitatively discussed and ranked. The alternatives are then compared based on their impacts on plant risk and economics.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2024

Integrated Renewable Combined Heat and Power for Ethanol

Conference presentation at 48th International Technical Conference on Clean Energy (Clearwater Clean Energy Conference), Clearwater, Florida, June 16–19, 2024. This project evaluates the technical and economic feasibility of small‑scale combined heat and power (CHP) systems using corn stover to support bioenergy with carbon capture and storage (BECCS) at ethanol facilities. The work includes resource characterization, pilot‑scale gasification and CO 2 capture testing to support techno‑economic analysis, economic evaluation of CHP deployment and potential carbon revenue, and life‑cycle assessment of gasification‑based CHP systems.

09 BIOMASS FUELS↗
DOE OSTI2021

Hamilton: Flexible, Open Source $10 Wireless Sensor System for Energy Efficient Building Operation

Sensors for improving building performance are rapidly populating the market, driven in part by the drive to reduce greenhouse gas emissions resulting from energy production as well as improve the interior environment for healthy and more productive spaces. UC Berkeley has led wireless sensor development over the past 25 years (e.g., Telos mote), with the Hamilton (named after Alexander Hamilton on the US $10 bill) as the most recent. The Hamilton sensor was designed as a low-cost high-performance sensor that is modular and interoperable. The objective of the Hamilton project was to create, evaluate and establish the technological foundations for secure and easy to deploy building energy efficiency applications utilizing pervasive, low-cost wireless sensors integrated with traditional Building Management Systems (BMS), consumer-sector building components, and powerful data analytics. The project included iterative hardware design, incorporating a high-performance database (BTrDb, http://btrdb.io/), creating and iterating the development of secure data middleware (BOSSwave, WAVE/WAVEMQ), working with and pushing the development of an open-source tiny operating system RiotOS, and implementing and improving protocols such as Thread/OpenThread and TCP/IP. The hardware benefited from careful design to drive down the cost; the design included a System-on-a-Chip (SoC), chip antenna, single crystal and five passive components. Careful design of the operating system created a low-power design to enable a long life with small batteries. The hardware included several sensors: temperature, radiant temperature, relative humidity, magnetometer, accelerometer, and light, with an optional occupancy (Passive InfraRed) sensor. The project was the basis of several applications, both internal to the research team and other researchers and professionals at other institutions. Several applications used the sensor hardware as the basis for other complex devices. Other applications used the sensors to improve building performance through interoperating with the building Heating Ventilation and Air-Conditioning (HVAC) system, such as using occupancy and/or distributed temperature sensing to reduce HVAC zone energy while still providing thermal comfort and to reduce peak loads in small commercial buildings. We demonstrated cloud-based energy analytics, implemented a schedule and a Model Predictive Controller in a small commercial building to optimize HVAC energy, occupancy and electricity price. Initial integration of these technological innovations was performed through the creation of execution containers containing the WAVE agent and various driver, proxy, or building system function logic. The research added to the understanding of efficient sensor hardware, secure middleware, time-series data management (high performance database), efficient communication protocols, and interoperating with applications and building systems. The project showed the technical effectiveness and economic feasibility of creating a low-cost, modular, and easy-to-deploy sensor. Through conversations with multiple end users, the research team discovered that many customers wanted data management and services in addition to the sensors. HamiltonIOT developed packages of sensors, border router, and data services to provide a seamless “plug-and-play” sensor deployment. Some customers were willing to pay for higher quality sensors (such as light); some customers wanted a robust enclosure (waterproof).

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Implementation and Demonstration of the Digital Twin Certification System Remote Operations Framework

Microreactors are one promising advanced-reactor concept being pursued by the nuclear industry. They are distinguished by a relatively low power output of 20 MWth or less. These microreactors are intended for deployment in applications where conventional small-capacity power solutions, such as diesel generators, are either economically unfeasible or logistically challenging. Such applications include providing electric power and/or heat for remote communities, mining sites, defense installations, and humanitarian and disaster-relief missions. An important feature for the successful deployment of microreactors is their capability to be operated remotely. This capability can significantly reduce staffing costs by eliminating the need for licensed operators to be physically present at each reactor site. Instead, operators can be centralized in a single remote operations center placed in an economically advantageous location, thereby optimizing resources by consolidating expertise and enhancing operational efficiency. However, the implementation of a remote operation system for nuclear reactors raises new concerns regarding the security, reliability, and resilience of such a system. One way in which remote operations can be supported in a manner that maintains system security, reliability, and resilience is through the use of digital twins in a novel framework designed to verify and validate sensor data and commands communicated between the remote operations center and reactor. This framework, known as the Digital Twin Certification System (DTCS), has previously been proposed as an operations architecture that can bring security and resiliency levels of remote nuclear-reactor operations to a level acceptable for commercial deployment. This paper moves the proposed DTCS architecture from concept to reality by presenting the implementation and testing of the system. The rationale and implementation of the DTCS using tools such as DeepLynx and Apache Airflow, is covered in-depth. This is followed by a demonstration of the DTCS by applying the implemented system architecture to the Single Primary Heat Extraction and Removal Emulator, a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The demonstration includes both normal and abnormal operating scenarios to highlight how the DTCS can increase the security, reliability, and resilience of a remote operations system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Implementation and Demonstration of the Digital Twin Certification System Remote Operations Framework

Microreactors are one promising advanced-reactor concept being pursued by the nuclear industry. They are distinguished by a relatively low power output of 20 MWth or less. These microreactors are intended for deployment in applications where conventional small-capacity power solutions, such as diesel generators, are either economically unfeasible or logistically challenging. Such applications include providing electric power and/or heat for remote communities, mining sites, defense installations, and humanitarian and disaster-relief missions. An important feature for the successful deployment of microreactors is their capability to be operated remotely. This capability can significantly reduce staffing costs by eliminating the need for licensed operators to be physically present at each reactor site. Instead, operators can be centralized in a single remote operations center placed in an economically advantageous location, thereby optimizing resources by consolidating expertise and enhancing operational efficiency. However, the implementation of a remote operation system for nuclear reactors raises new concerns regarding the security, reliability, and resilience of such a system. One way in which remote operations can be supported in a manner that maintains system security, reliability, and resilience is through the use of digital twins in a novel framework designed to verify and validate sensor data and commands communicated between the remote operations center and reactor. This framework, known as the Digital Twin Certification System (DTCS), has previously been proposed as an operations architecture that can bring security and resiliency levels of remote nuclear-reactor operations to a level acceptable for commercial deployment. This paper moves the proposed DTCS architecture from concept to reality by presenting the implementation and testing of the system. The rationale and implementation of the DTCS using tools such as DeepLynx and Apache Airflow, is covered in-depth. This is followed by a demonstration of the DTCS by applying the implemented system architecture to the Single Primary Heat Extraction and Removal Emulator, a small-scale non-nuclear test bed that emulates thermal behavior of a microreactor. The demonstration includes both normal and abnormal operating scenarios to highlight how the DTCS can increase the security, reliability, and resilience of a remote operations system.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Cyber–Physical System Security of Distribution Systems

The Information and Communications Technology (ICT) for control and monitoring of power systems is a layer on top of the physical power system infrastructure. The cyber system and physical power system components form a tightly coupled Cyber–Physical System (CPS). Sources of vulnerabilities arise from the computing and communication systems of the cyber–power grid. Cyber intrusions targeting the power grid are serious threats to the reliability of electricity supply that is critical to society and the economy. In a typical Information Technology environment, numerous attack scenarios have shown how unauthorized users can access and manipulate protected information from a network domain. The need for cyber security has led to industry standards that power grids must meet to ensure that the monitoring, operation, and control functions are not disrupted by cyber intrusions. Cyber security technologies such as encryption and authentication have been deployed on the CPS. Intrusion or anomaly detection and mitigation tools developed for power grids are emerging. Furthermore, this survey paper provides the basic concepts of cyber vulnerabilities of distribution systems and CPS security. The important ICT subjects for distribution systems covered in this paper include Supervisory Control And Data Acquisition, Distributed Energy Resources, including renewable energy and smart meters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

EQC: Ensembled Quantum Computing for Variational Quantum Algorithms

Variational quantum algorithms (VQA), which are comprised of a classical optimizer and a parameterized quantum circuit, emerges as one of the most promising approaches of harvesting quantum power in the noisy-intermediate-scale-quantum (NISQ) era. However, the deployment of VQAs on today's NISQ devices often faces considerable system noise and prohibitively slow training speeds. On the other hand, the expensive supporting sources and infrastructure make quantum computers extremely keen on high utilization. In this paper, we propose a novel way of thinking about a quantum backend: rather than relying on one physical device which tends to introduce platform-specific noise and bias, a quantum ensemble, which distributes quantum tasks across parallel devices, can serve as a virtualized quantum computer for offering reduced noise levels through an adaptive mixture and also provide significantly improved training speeds through parallelization. With this idea, we build a distributive VQA optimization framework called DVQA, serving as the first effort in adopting parallel quantum devices for cooperative VQA training. To further constraint noise and speed-up convergence, we design a model for individual NISQ devices concerning their properties and running conditions, and propose a weighting mechanism for regularizing the returned gradients. Extensive evaluations on 10 IBM-Q quantum devices using the VQE example show that the distributive VQA training framework can substantially boost the training speed by 10.5x on average (up to 86x and at least 5.2x) with improved training accuracy.

Stein, Samuel A.↗
DOE OSTI2025

Virtual Agents-Based Attack-Resilient Distributed Control for Islanded AC Microgrid

Due to its dependence on a communication network, distributed secondary control of microgrids is susceptible to denial-of-service (DoS) attacks in channel shutdown mode, which may negatively impact the network connectivity and thus deteriorate the coordination and power sharing among distributed generators (DGs). Honeypot is a common method for cyber deception by introducing fake targets. However, in the context of microgrid, the misleading information spread by honeypots will also impact the system performance. This paper proposes an attack-resilient distributed control for AC microgrids utilizing virtual agents (VAs) to counteract both DoS edge and node attacks. The VAs are designed to not impact the system’s steady state during normal operation but to share information among neighboring real agents and serve as dummy targets for DoS attacks. The control with VAs is implemented by a primal-dual gradient based distributed algorithm to efficiently obtain a practical solution for voltage/frequency regulation and power sharing. The simulation results on a 4-DG test system and a modified IEEE 34-bus system show that 1) VAs do not impact the normal functionality of the test system, and 2) deploying VAs can enhance the resilience of the microgrid control against DoS edge and node attacks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Peak load reduction and load shaping in HVAC and refrigeration systems in commercial buildings by using a novel lightweight dynamic priority-based control strategy

Reducing peak power demand in a building can reduce electricity expenses for the building owner and contribute to the efficiency and reliability of the electrical power grid. For the building owner, reduced expenses come from the reduction or elimination of peak power charges on electricity bills. For the power system operator, reducing peak power demand leads to a more predictable load profile and reduces stress on the electric grid system. Herein we present a computationally inexpensive, dynamic, and retrofit-deployable control strategy to effect peak load reduction and load shaping. The effectiveness of the control strategy is examined in a simulation with 80 air-conditioning units and 40 refrigeration units. The results show that a peak demand reduction of 60 kW can be achieved relative to peak demand in a typical set point–based approach. The proposed strategy was deployed in a gymnasium building with four rooftop HVAC units, where it showed over 15% peak demand (kW) reduction savings while maintaining or lowering energy consumption (in kilowatt-hours) relative to the set point–based thermostat controls.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Recent Advances in Precision Clock Synchronization Protocols for Power Grid Control Systems

With the advent of a new Precision Time Protocol specification, new opportunities abound for clock synchronization possibilities within power grid control systems. The third iteration of the Institute of Electrical and Electronics Engineers Standard 1588 specification provides several new features specifically aimed at complex, wide-area deployments in which situational awareness and control require precise time agreement. This paper describes the challenges faced by existing technology, introduces the new time distribution specification, and provides examples to explain how it represents a game-changing innovation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Techno-Economic Optimization of Advanced Energy Plants with Integrated Thermal, Mechanical, and Electro-Chemical Storage (Final Report)

The increasing use of renewable energy sources is leading to increased cycling of fossil-fueled power plants (FFPP) that are designed to operate at base-loaded conditions. Integrating energy storage facilities with the FFPPs can be helpful in reducing load-following operation of FFPPs. Decentralized deployment of energy storage facilities at the FFPP level has considerable advantages due to possibilities of smaller storage capacities, immediate benefits realized by the host power plant due to the increase in the efficiency, cleaner emission and higher plant life to name a few. Most importantly, deployment at the FFPP level can exploit the existing equipment items and facilities at the host power plant, thus reducing the CAPEX and reducing the storage capacity. However, realization of these benefits will critically depend on novel configuration/integration strategies with the least impact on the power plant operation and its configuration. Furthermore, dynamics of the entire integrated system including both the FFPP and the storage technologies must be taken into account to obtain the cost-optimal solution. With these motivations, the objective of this project was to complete a focused evaluation of decentralized deployments of energy storage facilities at the FFPP level. Promising thermal, chemical, mechanical, and electro-chemical storage technologies were evaluated with due consideration of their transient response to obtain various optimal system concepts that can minimize the levelized cost of storage. For thermal storage, cryogenic energy storage along with high temperature heat storage in molten salt as well as phase change material were evaluated. For mechanical storage, cryogenic air storage and pumped hydro storages were evaluated. For chemical storage, hydrogen storage was evaluated. For electrochemical storage, the team evaluated sodium sulfur, vanadium redox flow battery as well as Li-ion batteries. Integration of these storage technologies with the natural gas combined cycle (NGCC) and supercritical pulverized coal (SCPC) plants was considered. Six technologies, namely molten salt, cryogenics, compressed air, pumped hydro, H2 storage and Li-ion battery storage, were downselected based on their levelized cost of storage. It was observed that the ranking of the optimal storage technology can differ based on the host power plant technology even when same demand/supply/price profile for electricity are considered. It was also observed that as the variability in power demand varies, the ranking of the optimal storage technologies vary. However, for the same demand and LMP profile, top six optimal storage technologies for NGCC vs SCPC plants did not differ much even though LCOS for the same technology and optimal size of a given storage technology did differ. Detailed techno-economic assessment of these six technologies was undertaken.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2026

Applying Particle Swarm Optimization and Extended Kalman Filtering to Model Kaplan Generation Dynamics for Hydropower Systems

Variable renewable generation is increasing the need for hydropower plants to provide fast and flexible grid support, which places new demands on plant-level dynamic models used for monitoring, control, and operational decision-making. This need is especially important for hydroelectric systems, where turbine and generator dynamics are strongly coupled, nonlinear, and time-varying, making accurate real-time representation difficult. To address this problem, this paper develops a digital twin (DT) framework for a synchronous generator–Kaplan turbine system using an explicit separation of slow turbine dynamics and fast generator dynamics. The turbine subsystem is represented by a six-coefficient model, whose parameters are identified offline using particle swarm optimization, while the generator subsystem is updated online through an extended Kalman filter for real-time state and parameter estimation. These models are integrated within a closed-loop simulation that includes a proportional–integral–derivative–double-derivative governor and excitation system, allowing the DT to track plant behavior under realistic operating conditions. Unlike prior studies that treat turbine and generator modeling separately or rely mainly on simulated inputs, the proposed framework is validated using real operational data from a hydropower plant. Results show that the DT reproduces terminal voltage, active power, and reactive power with a normalized root mean square error of approximately 5%. This hybrid offline–online formulation constitutes the main contribution of the work, providing an adaptive and practically deployable DT for hydropower systems with direct relevance to control improvement, performance monitoring, and grid-support applications under high renewable penetration.

13 HYDRO ENERGY↗
DOE OSTI2024

A Cast of Thousands: How the IDEAS Productivity Project Has Advanced Software Productivity and Sustainability

Computational and data-enabled science and engineering are revolutionizing advances throughout science and society, at all scales of computing. For example, teams in the U.S. Department of Energy’s Exascale Computing Project have been tackling new frontiers in modeling, simulation, and analysis by exploiting unprecedented exascale computing capabilities—building an advanced software ecosystem that supports next-generation applications and addresses disruptive changes in computer architectures. However, concerns are growing about the productivity of the developers of scientific software. Members of the Interoperable Design of Extreme-scale Application Software project serve as catalysts to address these challenges through fostering software communities, incubating and curating methodologies and resources, and disseminating knowledge to advance developer productivity and software sustainability. This article discusses how these synergistic activities are advancing scientific discovery—mitigating technical risks by building a firmer foundation for reproducible, sustainable science at all scales of computing, from laptops to clusters to exascale and beyond.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Frontier: Exploring Exascale

As the US Department of Energy (DOE) computing facilities began deploying petascale systems in 2008, DOE was already setting its sights on exascale. In that year, DARPA published a report on the feasibility of reaching exascale. The report authors identified several key challenges in the pursuit of exascale including power, memory, concurrency, and resiliency. That report informed the DOE's computing strategy for reaching exascale. With the deployment of Oak Ridge National Laboratory's Frontier supercomputer, we have officially entered the exascale era. In this paper, we discuss Frontier's architecture, how it addresses those challenges, and describe some early application results from Oak Ridge Leadership Computing Facility's Center of Excellence and the Exascale Computing Project.

Atchley, Scott {Leadership Computing}↗
DOE OSTI2023

Volt/VAR Optimization (VVO) Application on GridAPPS-D Platform

There is a large increment in the distributed energy resources (DERs) installation and deployments of smart sensing devices and communication infrastructure; hence, the power distribution network is swiftly evolving from a passive network to an active network. This motivates the development of advanced applications to operate power distribution systems for higher efficiency and reliability. These advanced applications are model-based and data-driven. This requires an advanced distribution management system (ADMS) to provide required data for the optimal operation of the distribution systems by coordinating various grid controllable devices. In this paper a Volt-VAR optimization (VVO) application to coordinate the grid’s legacy and new voltage control devices for conservation voltage reduction (CVR) is deployed on the GridAPPS-D platform (an open-source platform ) for ADMS application development. The VVO application is validated for various operating conditions on using modified IEEE 8500-node distribution test feeders. Further, the application is successfully deployed on the GridAPPS-D platform.

Jha, Rahul↗
DOE OSTI2023

The Potential Role for New Nuclear in the U.S. Power System: A View from Electricity System Modelers

There are diverse views on the role nuclear power might play in a decarbonized energy system, with some vocal viewpoints suggesting nuclear should either have no role or that nuclear should be a key pillar. Here we present a perspective on the role of nuclear power based on our collective experience in modeling nuclear power within the decarbonized U.S. power systems. We summarize the costs of current reactor development projects, and compare their stated costs with the costs that our models indicate is necessary in order to see deployment of new nuclear. We also discuss aspects of new nuclear deployment that are not included in our models but can influence decisions about whether to invest in new nuclear capacity.

decarbonization↗