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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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Power and Natural Gas Systems Interface Study

Power systems worldwide are becoming more reliant on energy from natural gas, wind, and solar, posing potential reliability and coordination challenges from the tighter coupling of these infrastructure systems. This paper proposes a framework for the market-based coordination of electricity and natural gas system operations. The proposed framework includes a power system model that accounts for flexibility in the commitment of power plants with short start-up and shut-down times, coupled with a dynamic gas model that simulates when gas cannot be delivered to generators. The capabilities of the framework are illustrated using real-world electric power and gas systems, including scenarios around wind and solar penetrations and the analysis of time-variant, “shaped flow” gas nominations. Our results indicate that coordination between power and gas systems improves total gas delivery and reduces out-of-merit order dispatch in the electricity system, and that shaped flows may reduce unserved gas in systems with high penetrations of wind and solar.

coordinated operation↗
DOE OSTI2023

The Hidden Flexibility of the Natural Gas Network for Electric Power Operations: A Case Study of a Near-Miss Winter Event

The U.S. power sector has become increasingly reliant on gas pipeline networks to deliver fuel to natural gas power plants. In addition to supplying relatively low-cost fuel, gas networks offer generators flexibility in their operations through the ability to deliver fuel when needed by using gas storage facilities or linepack if the gas network is at an operating point below its design capacity. However, disruptions or stress events on the gas network - like those occurring in the Northeast and Texas in recent years - can result in limitations on gas availability to generators at times when generation is in short supply. Here we examine a period of stress that occurred in the winter of 2022 in the Western United States. Using data on the region's natural gas pipeline network and electric generators, we build an integrated gas and electric model that closely replicates the actual dispatch of the period. We then evaluate the implications of removing flexibility employed by the gas network operator, which during that period curtailed scheduled gas deliveries to other parties to increase deliveries to natural gas power plants, which requested more gas than initially forecasted. We find that without the flexibility supplied by the gas network operator, there would have been curtailment of gas generation due to gas offtake constraints, requiring the power system operator to redispatch relying on more expensive generation or to potentially shed load. A sensitivity exploring a wind drought further exacerbates the strain, illustrating the potential challenge of managing gas and grid interactions as systems move to higher shares of variable renewable electricity. Based on this example, we discuss potential coordination strategies between the two system operators to ensure that the power system can successfully utilize and rely on the flexibility offered by natural gas networks.

03 NATURAL GAS↗
DOE OSTI2020

Microgrid Power Flow Control with Integrated Battery Management Functions

This paper presents a microgrid power flow control for islanded microgrids consisting of photovoltaic (PV) system, battery energy storage system (BESS) and diesel generator. The proposed control ensures automatic coordination among the microgrid units. To achieve the coordination, the local control of PV system and BESS are configured to regulate power flow without relying on communications. The generator is controlled as the back-up source and its connection depends on battery state of charge (SOC). A state machine with hysteresis settings is used to trigger smooth transition among operation modes. Not only does the proposed controller consider battery SOC and power limits, but also integrates three-stage charging control as battery charging mechanism, which is not considered in the existing literature. The proposed control is validated for an islanded hybrid microgrid using an OPAL-RT real-time simulator.

Long, Qian↗
DOE OSTI2023

Modeling and control of nuclear–renewable integrated energy systems: Dynamic system model for green electricity and hydrogen production

The need for decarbonization and diversification of energy resources has led to the development of integrated energy systems (IESs), where multiple resources supply more than one energy sector. Here, one such IES with small modular nuclear reactors and renewables (wind and solar) as generating resources, catering to the demand of the electric grid while producing hydrogen for industries, is modeled in this paper. The physics-based component models are represented using the Modelica language and interconnected to form the IES. The control and coordination of the overall system are ensured by designing a suitable control architecture composed of individual subsystem-level controls and supervisory control. The dynamic performance and the load-following capability of the IES are evaluated, while satisfying the safe operational limits of the components. Different configurations and modes of IES operation are considered, where the adaptability of the control system in the presence of varying demands and renewable generations is validated. The simulation results indicate that hydrogen as a flexible load facilitates the supply of varying grid demand. Additionally, the renewables are also accommodated into the IES owing to the flexibility of the balance of plant associated with the nuclear reactors.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Developing a PSCAD Model of the Reduced 240-Bus WECC Test System: Preprint

Fast-acting controls of inverter-based resources (IBR) introduce unprecedented dynamics to bulk power systems and island power grids, especially the high-frequency dynamics ranging from $>5$ Hz to hundreds of Hz. These oscillatory stability problems cannot be captured by the phasor domain simulations, e.g., in PSS/E, Powerworld and TSAT, due to insufficient modeling. Instead, they should be studied by electromagnetic transient (EMT) simulations by using proper EMT dynamic models. This paper develops and validates the PSCAD model of the reduced 240-bus Western Electricity Coordinating Council (WECC) test system. The PSCAD model will be released to the public, which can be used by both academia and power industry practitioners for studying the fast dynamic problems without any Critical Energy/Electric Infrastructure Information (CEII).

240-bus WECC test system↗
DOE OSTI2026

Cooperative Agreement To Analyze variabiLity, change and predictabilitY in the earth SysTem (CATALYST)

CATALYST proposes to perform foundational coordinated research in a team-oriented collaborative effort aimed at advancing a robust understanding of modes of Earth system variability and change using models, observations and process studies. The proposed research will address the DOE/BER mission by exploring the limits to predictability, identifying fundamental underlying mechanisms, quantifying interactions among modes of variability, and discovering tipping points in the Earth system to understand the current and future impacts of these phenomena on regional and global climate. Four fundamental gaps are identified in our knowledge of the Earth system: 1) What are the limits to predictability on various timescales? 2) What are the interactions among modes of Earth system variability? 3) How may modes of Earth system variability change in response to changes in external forcing, and what are the tipping points involved with those changes? 4) How are high impact events connected to modes of Earth system variability and how may they change in the future? Related to those gaps in our knowledge, we formulate four research objectives to address those gaps using a combination of Earth system models (ESMs) and machine learning (ML) methods. Research Objective 1 (RO1) addresses the first gap above and proposes to understand modes of variability and their limits of predictability on subseasonal to decadal timescales using ESMs and ML. Research Objective 2 (RO2) addresses the second gap and proposes to use a hierarchy of models to understand relevant processes and feedbacks related to how modes of variability interact with each other. Research Objective 3 (RO3) is designed to study the third gap and proposes to examine the role of external forcings in changes of modes of Earth system variability and their interactions, and the likelihood and predictability of tipping points and irreversible changes. Research Objective 4 (RO4) will address the fourth gap and proposes to use high resolution ESMs, regionally refined models (RRMs), and ML methods to investigate the relationships between high impact events (e.g. flash droughts and precipitation extremes, atmospheric rivers (ARs), tropical cyclones (TCs), storm surge/sea level rise), the synoptic systems that produce them, and their changes related to modes of Earth system variability. The research will involve the use of the Community Earth System Model (CESM), Energy Exascale Earth System Model (E3SM), CMIP multi-model data sets, a hierarchy of simpler models, and numerous observational data sets. In the course of the proposed research, CATALYST will contribute to metrics and diagnostics that will be integrated in Coordinated Model Evaluation Capabilities (CMEC), particularly with regards to the Quasi-biennial Oscillation (QBO) and its interactions with the Madden-Julian Oscillation (MJO), high atmospheric pressure blocking, and new precipitation metrics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

TrustDER: Trusted, Private and Scalable Coordination of Distributed Energy Resources

In this project, the Stanford and SLAC Teams have developed a Trusted, Private and Scalable platform for coordinating Coordination of Distributed Energy Resources (TrustDER). This is a layered system that ensures private, trusted and scalable coordination and monitoring of DERs. It accommodates a variety of resources, such as solar generation, gensets and loads, with a particular focus on battery systems-based resources, as they are a transformational technology experiencing fast growth in adoption by large critical facilities. The platform can be used as standalone or added to existing aggregation systems to enable trust, privacy and resilience. TrustDER consists of layers that address each of the shortcomings of the existing state of the art. Each layer in the platform can operate independently but provides information to the layers above it to enable a novel form of overall coordination architecture. The project consists of several tasks, with each task dedicated to the design of each layer. Task 2 Resource Virtualization defined a software abstraction layer for distributed energy resources (DERs). The goal of this abstraction was to simplify the implementation of algorithms utilizing cooperation of DERs resources in a variety of use cases. Task 3 is on Secure ID for Asset Authentication. Identity Management Systems (IDMS) are a foundational infrastructure for interactions between entities (organizations, users, devices, and services). Secure ID is blockchain-based a distributed identity management system allowing (1) identity provisioning, (2) authentication, (3) authorization, and (4) identity data sharing for IoT-enabled assets on the electricity grid. In this project, the SLAC team focused on designing and testing Keymaker, a protocol for authenticating device identity managed by Secure ID. Task 5 Private and Safe Integration is focused on the design and evaluation of a DER cooperation scheme which allows for the aggregation of DERs without impacting network reliability. The approach is designed based on realistic assumptions regarding data availability, communication infrastructure limitations, and privacy. Task 6 Scalable Distributed Privacy for Information explored how virtualized batteries could be managed privately. Specifically, it examined the case in which a principal provides a partitioned battery to multiple clients. Task 7 Use Cases was to ensure that this technology was applied in relevant situations and scenarios. Primarily, this means that virtualization needed to be employed in a manner that either improved flexibility, bolstered security or privacy, or decreased costs.

25 ENERGY STORAGE↗
DOE OSTI2022

Modeling Distributed Energy Resources for Analyzing Distribution Systems with High Renewable Penetration: Preprint

Increasing levels of inverter-based distributed energy resources (IBDERs) impact the legacy overcurrent distribution protection systems. The fault current injections of IBDERs are limited to between 1-2 p.u. of the rated current. The combination of the limited fault current and varying system load makes it increasingly difficult to reliably set the overcurrent protection. To address this challenge, researchers are proposing adaptive overcurrent protection mechanisms that can adapt to changing system conditions. Accurate modeling of IBDERs is required to develop reliable protection schemes. This paper presents a photovoltaics-based IBDER model in OpenDSS for adaptive overcurrent protection. The paper presents the validation of the proposed IBDER model against a detailed model in electromagnetic transient programs. Protection analysis of the Electric Power Research Institute J1 feeder with the proposed IBDER model is also presented.

adaptive↗
DOE OSTI2024

Hydropower Black Start: A Guidebook for Retrofitting Grid Dependent Hydropower

Not all United States (US) hydropower plants were designed to provide black start, but they are increasingly needed to uphold resilience in the evolving electric grid. This guidance is designed to help understand the minimal retrofits required for grid dependent hydropower (GDH) plants behind the point of interconnection (POI). For distribution connected hydropower plants or those with dedicated cranking paths, such upgrades can be sufficient for the plant to provide black start. For others, more coordination with the transmission system operator will be needed. This guidebook answers a number of questions relevant to retrofitting hydropower plants with black start capabilities. For example, the guidebook answers: • How flexible do the wicket gate controls need to be? • Who needs to do hydro governor model validation, why, and how? • How robust and flexible do the excitation and AVR controls need to be? • What protection settings need to be adjusted? • What relay(s) will need to be bypassed or overridden and at what risk? • What is the electrical energy demand of the station load or auxiliary power systems? • What should the strategy to energize transformer(s) along cranking path to address inrush currents be? • How should the critical load restoration be sequenced? In addition to outlining the specifications that hydropower plants need to meet for each component to be able to perform black start, this guidebook provides a set of case studies for specific upgrades needed at actual plants. Between the case studies of plants that have already performed black start retrofits and the examples of how this guidebook can be applied to scope future retrofits, five key themes have been identified for retrofit needs. 1. Protection needs “black start” mode: hydropower plants that are not designed with black start capabilities will have protections that prevent them from interconnecting to a “dead bus.” These protections will need to be overridden in every retrofit case and a separate black start mode should be established so that operators can safely switch between black start and grid connected modes, minimizing the risk to the plant. 2. Wicket gates need modern controls: digital governors accelerate the parameter tuning process and gate position sensors improve controllability, so plants with mechanical governors should be upgraded. Furthermore, a black start and islanding mode should be established for controls to maximize plant performance. 3. Robust excitation support: the DC system or excitation generator needs to be reliable enough to form and sustain the rotor electromagnetic field. These systems are typically undersized in plants that were not designed for black start, so they will need to be upgraded. 4. Turbine-governor model validation and operator training: validation of a standard hydro governor model is needed to characterize the dynamic response (i.e., inertial and primary frequency response) of the GDH. This is required for control development and old hydropower plants often have outdated or incorrect models. Operator training is also typically required to ensure the hardware retrofits are utilized correctly during the black start process. 5. Transformer and cranking path energization: any upgradation and control adjustment in front of the POI will depend upon the existing interconnection. Coordination with the transmission or distribution operator may be required.

13 HYDRO ENERGY↗
DOE OSTI2026

Coarse-grained resource allocation modeling for decoding and rewiring microbial metabolism

Microbial metabolism is a complex, emergent system driven by the coordinated interplay of intricate and dynamic molecular processes. To elucidate cellular behavior and enable biotechnological applications, quantitative models that address the inherent complexity of metabolism have been developed from a resource allocation perspective. Here, we synthesize recent advances in coarse-grained resource allocation frameworks and their applications in understanding microbial physiology and guiding gene circuit design. Here, these frameworks reveal global regulatory constraints and predict cellular adaptation to nutrient and environmental changes. In addition, they enable the quantification of metabolic costs, the dissection of circuit–host interactions, and the development of strategies for burden mitigation. Collectively, these modeling frameworks provide a powerful platform for uncovering quantitative principles of microbial growth and engineering robust synthetic biological systems.

coarse-grained modeling↗
DOE OSTI2022

Materials research and development needs to enable efficient and electrified buildings

Because of the complexity of modern buildings—with many interconnected materials, components, and systems—fully electrifying buildings will require targeted R&D and efficient coordination across those material, component, and system levels. Because buildings that consume the smallest amount of energy are easier to electrify, energy efficiency is a crucial step toward fully electrified buildings. Materials advances will play an important role in both reducing the energy intensity of buildings and electrifying their remaining energy use. Materials are currently being explored, discovered, synthesized, evaluated, optimized, and implemented across many building components, including solid-state lighting; dynamic windows and opaque envelopes; cold climate heat pumps; thermal energy storage; heating, ventilating, and air conditioning (HVAC); refrigeration; non-vapor compression HVAC; and more. In this article, we review the current state-of-the-art of materials for various buildings end uses and discuss R&D challenges and opportunities for both efficiency and electrification.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Networked HIL Simulation System for Modeling Large-scale Power Systems

This paper presents a network hardware-in-the-loop (HIL) simulation system for modeling large-scale power systems. Researchers have developed many HIL test systems for power systems in recent years. Those test systems can model both microsecond-level dynamic responses of power electronic systems and millisecond-level transients of transmission and distribution grids. By integrating individual HIL test systems into a network of HIL test systems, we can create large-scale power grid digital twins with flexible structures at required modeling resolution that fits for a wide range of system operating conditions. This will not only significantly reduce the need for field tests when developing new technologies but also greatly shorten the model development cycle. In this paper, we present a networked OPAL-RT based HIL test system for developing transmission-distribution coordinative Volt-VAR regulation technologies as an example to illustrate system setups, communication requirements among different HIL test systems, and connection mechanisms. Impacts of communication delays, information exchange cycles, and computing delays are illustrated. Simulation results show that the performance of a networked HIL test system is satisfactory.

digital twin, distribution system, co-simulation, ↗
DOE OSTI2025

Characterization of Pinhole Collimators for High-Resolution Gamma Imaging of Irradiated Fuel

Post-irradiation examination (PIE) of nuclear fuels requires imaging tools capable of resolving isotopic and spatial features with high throughput. This project contributes to a proof-of-concept effort aimed at advancing gamma emission tomography (GET) by evaluating novel fine-aperture pinhole collimators. Two Rose’s metal collimators, 100 µm (20° acceptance angle) and 350 µm (30° acceptance angle), were prototyped and characterized for their effectiveness in transporting gamma rays through the pinhole aperture. To support data collection, a Python-based data acquisition system was developed to coordinate a rotation stage, linear stage, and CZT detector, reducing latency in high-rate gamma event logging to one second per acquisition. Queue-based file writing enabled seamless real-time data capture for count rates up to 35,000 counts per second (cps). List-mode parsing algorithms were implemented to differentiate single and simultaneous gamma interactions for future tomographic reconstruction. Detector response was evaluated in both spectroscopy and list mode acquisition methods across varying source distances to confirm absolute and collimator efficiencies. Preliminary efficiency figures suggest effective collimation of gamma-rays with energies below 700 keV, with ~4% residual intensity through the aperture for Cs-137. The impact of collimator geometry on image quality is currently being evaluated. This groundwork supports the ongoing development of a sub mm resolution cone-beam CT system for imaging fuel phantoms, an essential step toward improving GET efficiency and accelerating nuclear fuel qualification efforts.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗
DOE OSTI2026

Integrated System Planning: Emerging Software Requirements in the Power Industry

Power system planning software remains fragmented across organizational boundaries, with specialized tools for capacity expansion, production cost modeling, power flow, and dynamic analysis operating on incompatible data models and assumptions. This article argues that the fragmentation is not merely a technical problem but a predictable consequence of Conway's law: software architectures mirror the departmental structures within which they are developed. Regulatory milestones like Federal Energy Regulatory Commission (FERC) Order 888 formalized these divisions, but the roots trace back to the distinct engineering disciplines-mechanical, chemical, and electrical-that staffed generation and transmission planning departments in vertically integrated utilities. As the industry moves toward integrated system planning (ISP) that coordinates generation, transmission, and distribution investment decisions, the software ecosystem must evolve accordingly. We identify five categories of software requirements to enable this transition: coherent data inputs decoupled from individual applications, unified and extensible data schemas, modular component representations that support multiple abstraction levels, lifecycle management of planning datasets, and well-defined application programming interface (API) contracts that separate data exchange from algorithmic control. We examine how these requirements interact with three common workflow patterns-serial gate clearing, sequential multiapplication, and convergence oriented-and discuss the interface design principles each demands. We then outline a vision for platform-based planning architectures where specialized analytical services compose through standardized interfaces and where artificial intelligence (AI)/machine learning (ML) tools augment decision support within a disciplined software infrastructure. The practices proposed here offer a path from today's siloed tool collections toward collaborative planning ecosystems capable of handling the complexity of modern power system transformation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Bundling measures for food systems transformation: a global, multimodel assessment

Background Current food systems leave one in ten individuals at risk of hunger while driving unsustainable environmental impacts. Inaction risks further exacerbating negative impacts on both human and planetary health. These challenges emerge from complex system interactions, requiring approaches that engage with this complexity and consider how transformation measures interact across food systems. We aimed to quantify the magnitude and uncertainty of the impacts of key food systems transformation measures both individually and in a bundle using an ensemble of global economic models. Methods In this global multimodel assessment, we applied an ensemble of ten state-of-the-art global economic models to evaluate the potential of four key measures in transforming food systems: increasing agricultural productivity, halving food loss and waste, shifting towards healthier diets, and economy-wide climate mitigation policies aligned with limiting warming to 1·5°C. The scenarios used a middle-of-the-road shared socioeconomic pathway for population and gross domestic product growth, climate impact data from Jägermeyr and colleagues, Thornton and colleagues, and Nelson and colleagues, and dietary targets based on the EAT–Lancet healthy reference diet, with model simulations conducted from 2020 to 2050. We then assessed the effect of these measures in isolation and in combination in a bundled scenario. To further understand the interactions between these measures, we conducted a decomposition analysis that distinguishes between the individual effects of a measure (effect when implemented alone), total effects (its contribution within the bundle), and interaction effects (the difference between total and individual effects). This approach aimed to show complementarities and trade-offs that emerge when multiple measures are implemented simultaneously. Findings Our analysis showed that individual measures in isolation are insufficient to achieve high-level environmental objectives and might generate unintended consequences. In contrast, bundling measures produces co-benefits: avoiding 50% of projected agricultural greenhouse gas emissions by 2050 and almost 20% of anticipated land conversion, while moderating food price increases associated with ambitious climate change mitigation policies. Our decomposition analysis further shows that measures can have varying effects across different dimensions. Although dietary shifts and climate mitigation policies are the largest drivers of environmental benefits (each contributing to a median decline of >10 percentage points in non-CO 2 emissions and 5 percentage points in agricultural land use globally), productivity improvements and reducing food loss and waste play essential roles in moderating price increases (each contributing to a median decline of >5 percentage points in average prices). Interpretation This study highlights the importance of implementing coordinated approaches to food system transformation and climate change mitigation rather than relying on isolated interventions. Comprehensive transformation requires understanding how supply-side and demand-side changes can interact with climate mitigation policies, enabling policy makers to design intervention packages that maximise benefits while minimising trade-offs across environmental, economic, and social dimensions.

Sundiang, Marina [Cornell Univ., Ithaca, NY (Unite↗
DOE OSTI2023

Photothermally Activated Artificial Neuromorphic Synapses

Biological nervous systems rely on the coordination of billions of neurons with complex, dynamic connectivity to enable the ability to process information and form memories. In turn, artificial intelligence and neuromorphic computing platforms have sought to mimic biological cognition through software-based neural networks and hardware demonstrations utilizing memristive circuitry with fixed dynamics. Here, to incorporate the advantages of tunable dynamic software implementations of neural networks into hardware, we develop a proof-of-concept artificial synapse with adaptable resistivity. This synapse leverages the photothermally induced local phase transition of VO 2 thin films by temporally modulated laser pulses. Such a process quickly modifies the conductivity of the film site-selectively by a factor of 500 to “activate” these neurons and store “memory” by applying varying bias voltages to induce self-sustained Joule heating between electrodes after activation with a laser. These synapses are demonstrated to undergo a complete heating and cooling cycle in less than 120 ns.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Quantifying the Correlation between Coordination Chemistry, Interfacial Formation, and Electrochemical Performances for Mg Battery Electrolytes

Here, the rise of magnesium batteries as promising post-Li-ion energy storage technologies has sparked considerable attention toward understanding the fundamental aspects of coordination chemistry concerning Mg cations in multivalent electrolytes. This exploration includes investigating how coordination influences crucial electrolyte properties like solubility, electroreduction stability, and the formation of the interphase, all of which are pivotal for practical battery applications. Despite recent progress in developing a few functional electrolytes, a comprehensive understanding of the solvation structure that can facilitate efficient Mg deposition performance and the formulation of general design rules based on the solvation structure is still lacking. In our study, we endeavor to establish a connection between solvent and anion interactions with Mg 2+ , interface formation, and cycling performance through a series of organic ether solvents (tetrahydrofuran, glyme, diglyme, and triglyme) and amine solvents (dimethylamine, 3-methoxypropylamine, and dimethoxyethylamine). Our findings reveal a distinct coordination trend for solvent/Mg 2+ and (Mg-TFSI):solvent across various solvents, which dictates the extent of ion pairing for TFSI salts with increasing solvent molecule size and denticity. The solvated species in the bulk electrolyte across different solvents lead to diverse interfacial chemistries with varying decomposition components. We also explore the cycling efficiency as well as Mg deposition overpotentials for different solvents. A correlation analysis was conducted to assess the interplay between the structure and performance. Lastly, we apply the insights gained from these results to tailor the relative anion/Mg 2+ coordination structures using cosolvent systems, aiming for improved cell performance.

25 ENERGY STORAGE↗
DOE OSTI2021

Stability of trapped solutions of a nonlinear Schrödinger equation with a nonlocal nonlinear self-interaction potential

This work focuses on the study of the stability of trapped soliton-like solutions of a (1 + 1)-dimensional nonlinear Schrödinger equation (NLSE) in a nonlocal, nonlinear, self-interaction potential of the form [|Ψ(x,t)| 2 +|Ψ(-x,t)| 2 ] κ where κ is an arbitrary nonlinearity parameter. Although the system with κ = 1 (i.e. fully integrable case) was first reported by Yang (2018 Phys. Rev. E 98 042202), here in the present work, we extend this model to the one in which κ is arbitrary. This allows us to compare the stability properties of the now trapped solutions to previously found solutions of the more usual NLSE with κ ≠ 1 which are moving soliton solutions. We show that there is a simple, one-component, nonlocal Lagrangian and corresponding action governing the dynamics of the system. Using a collective coordinate method derived from the action as well as assuming the validity of Derrick's theorem, we find that these trapped solutions are stable for 0 < κ < 2 and unstable when κ > 2. At the critical value of κ, i.e. κ = 2, the solution can either collapse or blowup linearly in time when q 0 = 0, where q 0 is the center of the initial density ρ(x, t = 0) = ψ*ψ of the solution. For q 0 ≠ 0 the displaced solution collapses. When κ > 2 initial small displacements from the origin also lead to collapse of the wave function. This phenomenon is not seen in the usual NLSE.

collective coordinates↗