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Complexity growth in integrable and chaotic models

We use the SYK family of models with N Majorana fermions to study the complexity of time evolution, formulated as the shortest geodesic length on the unitary group manifold between the identity and the time evolution operator, in free, integrable, and chaotic systems. Initially, the shortest geodesic follows the time evolution trajectory, and hence complexity grows linearly in time. We study how this linear growth is eventually truncated by the appearance and accumulation of conjugate points, which signal the presence of shorter geodesics intersecting the time evolution trajectory. By explicitly locating such “shortcuts” through analytical and numerical methods, we demonstrate that: (a) in the free theory, time evolution encounters conjugate points at a polynomial time; consequently complexity growth truncates at O($\sqrt{N}$), and we find an explicit operator which “fast-forwards” the free N-fermion time evolution with this complexity, (b) in a class of interacting integrable theories, the complexity is upper bounded by O(poly(N)), and (c) in chaotic theories, we argue that conjugate points do not occur until exponential times O(e N ), after which it becomes possible to find infinitesimally nearby geodesics which approximate the time evolution operator. Finally, we explore the notion of eigenstate complexity in free, integrable, and chaotic models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Integrated modeling for assessing climate change impacts on water resources and hydropower potential in the Himalayas

Regional hydroclimatic variability and change can affect water resources and hydropower generation. It is essential to assess hydropower potential under current and future climatic conditions to inform the design and operation of hydropower infrastructures. Here, we employ an integrated modeling framework to assess the impact of projected hydroclimatic conditions on water resource systems and hydropower generation. The integrated framework samples climate model outputs under different scenarios to force a hydrologic model and produces streamflow projections. The projected streamflows are inputs for the future hydropower potential assessment. We implement the framework in the central Himalayan river basin. Our results demonstrate substantial spatiotemporal variability in different water balance components (precipitation, evapotranspiration, and water yield) under current and future climatic conditions. For the Himalayan Tila river basin, the annual average energy production is expected to increase under future hydroclimatic conditions (up to 39% in Tila-2 hydropower project, suggested by ensemble mean). Furthermore, this increase in energy is driven mainly by the increased streamflow projections, particularly during the dry season and in the late century. Our results highlight the impacts of hydroclimatic variability in hydropower productions and are of practical use to provide decision-relevant information for designing and operating hydropower infrastructures. The integrated modeling framework presented here is region-specific; however, the approach is reproducible, and the overall insights are generalizable across the Himalayan region.

54 ENVIRONMENTAL SCIENCES↗

Path-Integrated Stereo X-Ray Digital Image Correlation: Resolving the Violation of Conservation of Intensity

In this study, x-ray imaging addresses many challenges with visible light imaging in extreme environments, where optical diagnostics such as digital image correlation (DIC) and particle image velocimetry (PIV) suffer biases from index of refraction changes and/or cannot penetrate visibly occluded objects. However, conservation of intensity—the fundamental principle of optical image correlation algorithms—may be violated if ancillary components in the X-ray path besides the surface or fluid of interest move during the test. The test series treated in this work sought to characterize the safe use of fiber-epoxy composites in aerospace and aviation industries during fire accident scenarios. Stereo X-ray DIC was employed to measure test unit deformation in an extreme thermal environment involving a visibly occluded test unit, incident surface heating to temperatures above 600°C, and flames and soot from combusting epoxy decomposition gasses. The objective of the current work is to evaluate two solutions to resolve the violation of conservation of intensity that resulted from both the test unit and the thermal chamber deforming during the test. The first solution recovered conservation of intensity by pre-processing the path-integrated X-ray images to isolate the DIC pattern of the test unit from the thermal chamber components. These images were then correlated with standard, optical DIC software. The second solution, called Path-Integrated Digital Image Correlation (PI-DIC), modified the fundamental matching criterion of DIC to account for multiple, independently-moving components contributing to the final image intensity. The PI-DIC algorithm was extended from a 2D framework to a stereo framework and implemented in a custom DIC software. Both solutions accurately measured the cylindrical shape of the undeformed test unit, recovering radii values of R = 76.20±0.12 mm compared to the theoretical radius of R theor = 76.20 mm. During the test, the test unit bulged asymmetrically as decomposition gasses pressurized the interior and eventually burned in a localized jet. Both solutions measured the heterogeneous radius of this bulge, which reached a maximum of approximately R = 91 mm, with a discrepancy of 2–3% between the two solutions. Two solutions that resolve the violation of conservation of intensity for path-integrated X-ray images were developed. Both were successfully employed in a stereo X-ray DIC configuration to measure deformation of an aluminum-skinned, fiber-epoxy composite test unit in a fire accident scenario.

47 OTHER INSTRUMENTATION↗

Path-Integrated X-Ray Digital Image Correlation using Synthetic Reference Images

X-rays can provide images when an object is visibly obstructed, allowing for motion measurements via x-ray digital image correlation (DIC). However, x-ray images are path-integrated and contain data for all objects between the source and detector. If multiple objects are present in the x-ray path, conventional DIC algorithms may fail to correlate the x-ray images. A new DIC algorithm called path-integrated (PI)-DIC addresses this issue by reformulating the matching criterion for DIC to account for multiple, independently-moving objects. PI-DIC requires a set of reference x-ray images of each independent object. However, due to experimental constraints, such reference images might not be obtainable from the experiment. Here, this work focuses on the reliability of synthetically-generated reference images, in such cases. A simplified exemplar is used for demonstration purposes, consisting of two aluminum plates with tantalum x-ray DIC patterns undergoing independent rigid translations. Synthetic reference images based on the “as-designed” DIC patterns were generated. However, PI-DIC with the synthetic images suffered some biases due to manufacturing defects of the patterns. A systematic study of seven identified defect types found that an incorrect feature diameter was the most influential defect. Synthetic images were re-generated with the corrected feature diameter, and PI-DIC errors were improved by a factor of 3-4. Final biases ranged from 0.00-0.04 px, and standard uncertainties ranged from 0.06-0.11 px. In conclusion, PI-DIC accurately measured the independent displacement of two plates from a single series of path-integrated x-ray images using synthetically-generated reference images, and the methods and conclusions derived here can be extended to more generalized cases involving stereo PI-DIC for arbitrary specimen geometry and motion. This work thus extends the application space of x-ray imaging for full-field DIC measurements of multiple surfaces or objects in extreme environments where optical DIC is not possible.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Extended convex hull-based distributed optimal energy flow of integrated electricity-gas systems

Integrated electricity and gas systems are constructed to facilitate the gas-fired generation, and the distributed operation of these integrated systems have received much attention due to the increased emphasis on data security and privacy between different agencies. This paper proposes an extended convex hull based method to address optimal energy flow problems for the integrated electricity and gas systems in a distributed manner. First, a multi-block electricity-gas system model is constructed by dividing the whole system into N blocks considering both physical and regional differences. This multi-block model is then convexified by replacing the nonconvex gas transmission equation with the extended convex hull-based constraints. The Jacobi-Proximal alternating direction method of multipliers algorithm is adopted to solve the convexified model and minimize its operation cost. Finally, the feasibility of the optimal solution for the convexified model is checked, and a sufficient condition is developed. If the sufficient condition is satisfied, the optimal solution for the original nonconvex problem can be recovered from that for the convexified problem. Simulation results demonstrate that the proposed method is tractable and effective in obtaining feasible optimal solutions for multi-block optimal energy flow problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Framework for optimization of long-term, multi-period investment planning of integrated urban energy systems

In order to achieve stringent greenhouse gas emission reductions, a transition of our entire energy system from fossil to renewable resources needs to be designed. Such an energy transition brings two main challenges: most renewables generate variable electric energy, yet most demand is currently not electric (carrier mismatch) and does not always manifest at the same time as supply (temporal mismatch). Integrating multiple energy infrastructures can address both challenges by using the synergy between different energy carriers; building on existing infrastructure, while allowing a robust and flexible integration of the new. This paper proposes an optimization framework for long-term, multi-period investment planning of urban energy systems in an integrated manner. We formulate it as a mixed-integer linear program, combining a capacitated facility location with a multi-dimensional, capacitated network design problem. It includes generation and network expansion planning as well as interconnections between networks and storage infrastructure for each energy system. It can incorporate pathway effects like techno-economic developments, policy measures, and weather variations. The intended use is to support urban decision makers with long-term investment planning, though it can be tailored to fit other geographical or temporal scales. We demonstrate the model using two cases based on an average city in The Netherlands, which wants to reduce its CO 2 -emissions with 95% by 2050. In the first case, we include explicit carbon-emission constraints to study the effects of the carrier mismatch. In the second case, we implement interannual weather variations to analyze the temporal mismatch. The results give valuable insights into the energy transition design strategy for urban decision makers. They also show the future potential, as well as the computational challenges of the optimization framework.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Analysis of controls for integrated energy storage system in energy arbitrage configuration with concrete thermal energy storage

Novel highly detailed NuScale reactor and turbo-generator models have been built in Modelica to analyze potential controls for an integrated energy system (IES) configuration combining a nuclear reactor and concrete thermal energy storage (CTES) operating in energy arbitrage. A shakedown test demonstrates the viability of the control schemes to operate across expected operating conditions while maintaining safety limits and buffers. A five-day data set from Idaho is used to show a load-following application of this system that increases the average reactor power level by 20% over the data set and matching demand at nearly all points. Here, by integrating these models, feedback mechanisms across the primary and secondary sides of the nuclear reactor are integrated, and realistic control evaluation is done. All models are consistent with the Hybrid repository, a suite of Modelica models, maintained at Idaho National Laboratory.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Deep reinforcement learning based optimization for a tightly coupled nuclear renewable integrated energy system

New ways to integrate energy systems to maximize efficiency are being sought to meet carbon emissions goals. Nuclear-renewable integrated energy system (NR-IES) concepts are a leading solution that couples a nuclear power plant with renewable energy, hydrogen generation plants, and energy storage systems, such that thermal and electrical power are dispatchable to fulfill grid-flexibility requirements while also producing hydrogen and maximizing revenue. Here, this paper introduces a deep reinforcement learning (DRL)-based framework to address the complex decision-making tasks for NR-IES. The objective is to maximize revenue by generating and selling hydrogen and electricity simultaneously according to their time-varying prices while keeping the energy flow in the subsystems in balance. A Python-based simulator for a NR-IES concept has been developed to integrate with OpenAI Gym and Ray/RLlib to enable an efficient and flexible computational framework for DRL research and development. Three state-of-the-art DRL algorithms have been investigated, including two-delayed deep deterministic policy gradient (TD3), soft-actor critic (SAC), proximal policy optimization (PPO), to illustrate DRL’s superiority for controlling NR-IES by comparing it with a conventional control approach, particle swarm optimization (PSO). In this effort, PPO has shown more-stable performance and also better generalization capability than SAC and TD3. Comparisons with PSO have demonstrated that, on average, PPO can achieve 13.9% more mean episode returns from the training process and 29.4% more mean episode returns from the testing process when different hydrogen-production targets are applied.

08 HYDROGEN↗

ARPIST: Provably accurate and stable numerical integration over spherical triangles

Numerical integration on spherical triangles, including the computation of their areas, is a core computation in geomathematics. The commonly used techniques sometimes suffer from instabilities and significant loss of accuracy. We describe a new algorithm, called ARPIST, for accurate and stable integration of functions on spherical triangles. ARPIST is based on an easy-to-implement transformation to the spherical triangle from its corresponding linear triangle via radial projection to achieve high accuracy and efficiency. More importantly, ARPIST overcomes potential instabilities in computing the Jacobian of the transformation, even for poorly shaped triangles that may occur at poles in regular longitude-latitude meshes, by avoiding potential catastrophic rounding errors. We compare our proposed technique with L’Huilier’s Theorem for computing the area of spherical triangles, and also compare it with the recently developed LSQST method (Beckmann et al., 2014) and a radial-basis-function-based technique (Reeger and Fornberg, 2016) for integration of smooth functions on spherical triangulations. In conclusion, our results show that ARPIST enables better or comparable accuracy over previous methods while being easier to implement, significantly faster, and more tolerant of poor element shapes.

97 MATHEMATICS AND COMPUTING↗

Integrating tactical planning, operational planning and scheduling using data-driven feasibility analysis

Supply chain operations and scheduling are well-studied problems in the literature. Although these problems are related, they are often solved sequentially. This uncoordinated approach usually leads to sub-optimal solutions. Here this paper proposes a methodology for integrating scheduling operations into the supply chain network, motivated by the available enterprise data, and feasibility analysis. Existing literature on integrated models for addressing the supply chain is reviewed and classified. Then the mathematical model formulation for each level is discussed, after which the proposed data-driven integrated framework is described. The methodology is tested on two different case studies of varying dimensions. For each case study, the solution solves a multi-objective problem with the overall aim of an optimal solution that is robust towards achieving optimal cost while keeping customer satisfaction in mind.

42 ENGINEERING↗

Capacity optimization of nuclear power integration to meet dynamic industrial demand

To decarbonize their industrial facilities, The Dow Chemical Company has collaborated with Idaho National Laboratory (INL) to study the integration of nuclear power with an industrial chemical facility. Using Holistic Energy and Resource Optimization Network developed at INL for optimizing and analyzing integrated energy systems, a nuclear microreactor system was sized and evaluated for dynamic dispatch to Dow Silicones Corporation’s Carrollton, KY (USA) site for iloxane production. It was found that a 180 MW th system (12 × 15MW th ) with 75.1 MWh th of thermal energy storage could provide heat and power to the chemical facilities. In the process, this would reduce electricity imports by 99.9 % and reduce the Scope 1 and 2 emissions of the site by 292,100 tonnes CO 2 /yr (98.8 %). The primary novelty of this work is a first of a kind design and optimization of a microreactor powered integrated energy system to provide heat and power to a chemical plant using real plant data. This analysis will pave the way for future studies using dispatchable clean energy sources to reduce carbon emissions and commodity industries’ reliance on fossil fuels.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

Evaluation of integrated daylighting and electric lighting design projects: Lessons learned from international case studies

This article presents and discusses the lessons learned from the monitoring of 25 integrated daylighting and electric lighting international case study projects. The case studies consist of real occupied buildings that have been monitored as part of the International Energy Agency (IEA) SHC Task 61/EBC Annex 77 Programme. The general goal of the case studies was to balance lighting energy use with occupants’ visual and non-visual requirements. This was achieved using innovative solutions for daylighting and electric lighting with advanced controls, but also implementing simple and out-of-the-box strategies. The findings suggest that energy demands for lighting can significantly be reduced by combining sensible daylight provision, efficient lighting sources, and advances in controls. Yet, the effective achievement of project goals requires adequate monitoring, fine-tuning, and verification. The findings also suggest that the adoption of “integrative” lighting – that is, lighting systems that address both visual and non-visual responses – is getting increasingly popular. Catering to non-visual requirements will likely drive further innovation in lighting technology. Currently, there is limited investment available for developing daylighting systems for integrative lighting, and the current related electric strategies often come at the risk of energy rebound effects. Overall, providing daylighting and understanding user requirements are fundamental steps towards achieving quality projects, with potential benefits beyond saving energy.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Rapid Load Transition for Integrated Solid Oxide Fuel Cell - Gas Turbine (SOFC-GT) Energy Systems: A Demonstration of the Potential for Grid Response

Rapid load transition is an essential requirement for integrated energy systems to maintain grid resilience as more renewable resources are added to the grid. Integrated solid oxide fuel cell - gas turbine (SOFC-GT) systems can provide high efficiency and low carbon emissions over a broad range of turndown. These hybrids also have the potential to enable rapid grid response. The challenge has been to demonstrate effective control strategies to manage load transitions. In the present study, a load transition of ~50% was achieved in 10 s using a novel but simple strategy. Power demand on the SOFC and the GT were ramped down concurrently. During this transition, the SOFC anode fuel was manipulated to maintain SOFC fuel utilization while the cathode inlet air flow and temperature were also manipulated to thermally protect the SOFC. This study was conducted using the Hybrid Performance (Hyper) facility at the National Energy Technology Laboratory (NETL) in a co-simulation environment with the Idaho National Laboratory (INL)'s grid-simulation. The load ramping strategy was tested using a hardware-based cyber-physical simulation methodology. The results demonstrate a high-fidelity representation of SOFC-GT hybrid dynamics and validation of the control strategy. Thermal and electrochemical transients indicated that the SOFC was well protected during rapid load turndown without violating operability constraints. This demonstration revealed the non-linear nature of tightly coupled SOFC-GT system components, especially the non-linear response of SOFC cathode air flow and inlet temperature controls. These results highlight the needs and challenges in developing adaptive automatic controls for autonomous rapid load transitions. This work demonstrates that SOFC-GT hybrids are a viable option to provide the fast-ramping characteristics essential to accommodate high levels of variable renewable power while maintaining grid resilience, reliability, and environmental performance. The results also demonstrate the utility of co-simulation in advancing the tightly-coupled integrated energy systems needed to meet goals for zero-carbon power generation.

DIRECT ENERGY CONVERSION,POWER TRANSMISSION AND DI↗

Integration of cryogenic energy storage with renewables and power plants: Optimal strategies and cost analysis

Energy storage is critical for overcoming challenges associated with the intermittency and the variable availability of renewable sources for decarbonizing the energy sector. Cryogenic energy storage (CES) is of interest due to its high technology readiness level, no geographical limitations, and moderate round-trip efficiency. The time-varying nature of demands and renewable availability needs to be considered at the design and integration stages of energy storage. We develop a mixed-integer nonlinear program (MINLP) model to obtain the energy storage costs on a daily basis for different scenarios that typically arise over an entire year. Using this optimization-based framework, we address key decision-making questions towards energy transition: What is the energy cost when CES is integrated with renewables and power plants? How does each scenario affect the overall energy cost? How much storage is needed for complete transition to renewables? What is the optimal integration towards 100% renewable energy? What are the optimal storage designs for both renewables and fossil-based power generation with current and future energy demands? Here, we discuss different scenarios and solutions to these questions.

25 ENERGY STORAGE↗

A systematic solution to quantify economic values of vehicle grid integration

We report Vehicle-Grid-Integration (VGI) supplies one of the potential benefit extensions for electric vehicles (EVs) to make use of their parking time, which enables the EVs to provide grid services while still meeting consumer driving needs. However, the costs, benefits and risks of VGI still remain unclear, which limits the development of the VGI to promote the interaction between the EV and grid. In this study, we propose an integrated framework to quantify and utilize the aggregate flexibility of the EVs to supply the grid services in electricity markets. The integrated solution includes five sub-modules that cover end-to-end functionalities from individual EV energy consumption estimation to final monetary values calculation of providing grid services. Both wholesale market and local level charging management are formulated in the optimization module. A predictive control algorithm is proposed to allocate power to individual vehicles in real time, considering uncertainties from dispatch signal and travel behavior. Simulation results from 10,000 EVs indicate that the proposed optimization methods can significantly reduce the system cost in both wholesale market and retail market. Local tariff optimization reduces the electricity cost by 24.4% compared to uncontrolled charging. Wholesale market optimization results show that $\$$691 and $\$$255 revenues can be captured by each EV in ERCOT and CAISO markets per year, although with a conservative assumption on battery throughput cost at 0.16$\$$/kWh.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Watershed Workflow: A toolset for parameterizing data-intensive, integrated hydrologic models

Integrated, distributed hydrologic models leverage advances in computational power and data accessibility to improve predictive understanding of the water cycle. While impressive advances in this area of environmental modeling have been accomplished, such models are still rarely used, partially because of difficulty integrating model and data. This research describes the release of Watershed Workflow version 1.2, a new library aiming to automate and enable complex workflows defining inputs to high resolution, integrated, distributed hydrologic models. Watershed Workflow provides tools enabling the discovery, acquisition, mapping, and coordination of watershed geometry, land cover, soil properties, and meteorological data. It enables the construction of unstructured meshes that incorporate this data, and provides tools for automating a “first” simulation on any watershed in the United States. We present the design of the workflow tool, and describe best practices for its usage, culminating in a final example from watershed specification to simulation at the Coweeta Hydrologic Laboratory.

Integrated hydrologic modeling↗

Enhancing building resilience in cold climates: Integrating heat pump technologies with renewable energy

As electrification advances and Cold Climate Heat Pump technology progresses, ensuring grid stability becomes increasingly critical for effective heating in cold climates. However, natural disasters, especially during winter, pose significant threats to grid stability, impacting the reliability of air-source heat pumps. Despite these challenges, the integration of renewable energy sources and storage solutions in heating systems has not been extensively studied within the context of resilience. Here, this paper delves into the literature on renewable-powered heat pumps to assess their potential in enhancing building resilience in U.S. cold climate zones, which are particularly susceptible to extreme weather and grid disruptions. By leveraging renewable sources—solar, geothermal, and water—in conjunction with heat pump technology and supported by thermal or battery storage, this approach aims to provide a dependable solution for maintaining indoor heating during grid failures. Our analysis begins with a review of various renewable energy sources suitable for heat pumps, followed by an exploration of their application in cold climate regions across the U.S., and discussions on potential integration strategies with heat pump systems. This study highlights the advantages and suitability of solar irradiance and geothermal resources, emphasizing the importance of tailored, site-specific assessments to maximize energy efficiency and resilience. Additionally, it outlines the economic and environmental considerations necessary for implementing such systems and identifies potential challenges and areas for future research to facilitate the broader integration of renewable energy in heating solutions for enhanced resilience.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Revenue prediction for integrated renewable energy and energy storage system using machine learning techniques

Revenue estimation for integrated renewable energy and energy storage systems is important to support plant owners or operators’ decisions in battery sizing selection that leads to maximized financial performances. A common approach to optimizing revenues of a hybrid hydro and energy storage system is using mixed-integer linear programming (MILP). Although MILP models can provide accurate production cost estimations, they are typically very computationally expensive. To provide a fast yet accurate first-step information to hydropower plant owners or operators who consider integrating energy storage systems, we propose an innovative approach to predicting optimal revenues of an integrated energy generation and storage system. In this study, we examined the performance of two prediction techniques: Generalized Additive Models (GAMs) and machine learning (ML) models developed based on artificial neural networks (ANN). Predictive equations and models are generated based on optimized solutions from a market participation optimization model, the Conventional Hydropower Energy and Environmental Resource System (CHEERS) model. The two predicting techniques reduce the computational time to evaluate annual revenue for one set of battery configurations from 3 h to 1 to 4 min per run while also being implementable with significantly less data. The model validation prediction errors of developed GAMs and ML models are generally below 5%; for model testing predictions, the ML models consistently outperform the regression equations in terms of root mean square errors. This new approach allows plant owners, operators, or potential investors to quickly access multiple battery configurations under different energy generation and market scenarios. This new revenue prediction method will therefore help reduce the barriers, and thereby promoting the deployment of battery hybridization with existing renewable energy sources.

13 HYDRO ENERGY↗