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At least 667 records · Page 37

Virtual Battery Aggregator (Virtual Battery Aggregator for Distributed Energy Resource Management Systems)

Distributed energy resource management systems (DERMS) are being deployed in feeders with high distributed energy resource (DER) penetration to provide visibility of DERs and enable DER control strategies for grid operators. DERMS can support centralized grid controls by aggregating individual DER information into a single virtual DER model. This codebase creates algorithms for a DERMS platform that are able to aggregate a set of DERs that can be modeled as batteries, create a virtual battery model for centralized grid controls, and dispatch power setpoints to the individual DERs based on a desired virtual power setpoint received from the centralized grid control. It integrates with existing co-simulation frameworks and models for buildings, DERs, and distribution systems. While the DERMS is designed to work with batteries, it can be used with any DER that can be defined by a generalized battery model.

Blonsky, Michael↗

AdCyDER Attack Simulator

SF-25-117 A framework for simulating various cyber attacks on industrial control systems and SCADA environments.

Blakely, Benjamin↗

White Box Access to Quantum Testbeds for Co-Design

At Lawrence Livermore National Laboratory (LLNL), we operate and maintain the Quantum Device and Integration Testbed (QuDIT) facility, a small quantum testbed that supports about 10 active research teams (including our own) and over 50 internal and external collaborators. This testbed is designed to give remote white box access to users for research, training, and outreach. A guiding principle behind the development of our testbed infrastructure, software and user interfaces is to empower users to perform experiments at the cutting edge of quantum information science at any level of abstraction, from materials studies, device physics and control and characterization techniques to algorithm development and quantum operating system design. Our testbed targets a multilevel quantum system (qudit) to expand the accessible Hilbert space of a simple-to-manufacture quantum device and focuses on quantum simulation, typically implemented through custom gates designed with quantum optimal control methods, rather than on a universal computing framework with a fixed gate set. We leverage the Lab’s high-performance computing (HPC) program and related expertise to simulate quantum systems, develop hybrid algorithms, and generate gates optimized for given simulations. Additionally, we have adopted a co-design philosophy from the HPC community in designing new hardware, so that the systems we develop are optimized for the specific physics simulations we plan to use them for.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Status Report on Regulatory Criteria Applicable to the Use of Artificial Intelligence (AI) and Machine Learning (ML)

Although the interest in the use of artificial intelligence (AI) and machine learning (ML) in nuclear energy is increasing rapidly, at present their implementation is limited. This rapid increase in interest is not surprising considering that implementing AI and ML technology would allow for continuous monitoring, facilitate the implementation of predictive maintenance with optimized staffing plans, enable automation and autonomy opportunities that could drastically reduce fixed operation and maintenance costs, and provide training for operations and maintenance. Other industries are using AI for construction, and in the nuclear arena AI could provide great benefit in decommissioning activities. The ability of AI and ML to operate in real time vastly increases their potential impact. Before AI can be used in design, operations, or as a regulatory tool, the specifics on the regulations applicable to the use of AI for nuclear power applications need to be established. The difficulty is that the specific use cases will dictate the applicability of regulations. For example, even within the application domain associated with operations, the regulations might vary if the AI is used to create a virtual reference for plant operations or is used for training, optimization of maintenance intervals, prioritization of maintenance activities, etc. Different still is if the AI is to be used for design or setting technical specifications, which will introduce additional requirements. US Nuclear Regulatory Commission (NRC) licensing reviews are based on an applicant’s design meeting its performance assessment based on (1) safety goals and objectives, (2) deterministic and/or probabilistic analysis of accident scenarios, and (3) quantitative assessment of design alternatives against the safety goals and objectives using accepted engineering tools, methodologies, and performance criteria. The current regulatory framework does not explicitly address AI or autonomous control. However, as implementing AI technology will require the use of a digital platform, it must meet the requirements of an instrumentation and control (I&C) system. The regulatory requirements for AI, which will be incorporated into the I&C system, will be very dependent on how it is used (i.e., its functionality, safety classification, etc.). The licensing process is primarily risk-based with the identification of components and systems as nonsafety, important to safety, or safety related. A risk-informed approach allows further gradation of components and systems based on risk metrics such as core damage frequency or large early release fractions. Thus, the use cases and the risk categorization of impacted systems and components will determine the regulatory requirements. Regardless of how AI is used it presents new opportunities for risk-informing operating, maintenance, and regulatory decisions. Trustworthiness, transparency, and the ability to validate and verify the results will be paramount in showing that the systems and plant still meet their performance requirements. This report describes the results of research to identify regulatory implications of AI technologies and their uses. Specifically, this report reviews current regulatory guidance relevant to the application of AI for design (including design changes or new designs including advanced reactors), construction, operations, training, maintenance, research, testing, and as a regulatory tool. AI can be automated at different levels from purely informative purposes to autonomous controls. The focus of this review included determination of constraints on the application of AI technology, identification of any regulatory gaps or uncertainties, and clarification of anticipated technical basis information likely to be important for regulatory acceptance of these technologies. Currently, any use of AI at nuclear power plants is focused on nonsafety-related applications. The NRC and other regulatory bodies are evaluating providing guidance to address gaps rather than create new regulations to address the use of AI and ML. This approach seems to be the best to encourage AI development without adding regulatory uncertainty.

97 MATHEMATICS AND COMPUTING↗

Assessment of Cloud-Based Applications Enabling a Scalable Risk-Informed Predictive Maintenance Strategy Across the Nuclear Fleet

The current light water reactor fleet uses time-based or failure-based maintenance strategies to achieve high-capacity factors. But to make nuclear more competitive in the energy market, these reactors could utilize emerging technologies in terms of artificial intelligence (AI) and cloud computing to enable a cost-effective, predictive maintenance strategy. This report examines the feasibility of cloud computing for the nuclear industry’s needs in terms of the cloud’s computing capabilities, feasibility, and regulatory concerns. The technical viability of cloud computing was analyzed using one year worth of data from a boiling water reactor’s safety relief valve. Models were hosted on a local desktop, Idaho National Laboratory’s high-performance computer, and Microsoft Azure. Data was loaded, processed, and two types of models were trained in an A/B fashion. Based on the speed at which these actions were completed, it was used to determined that cloud computing has adequate computing resources. Additionally, the computing power can scale with the demanded load. To enable cloud computing in the existing fleet, additional sensors, networks, and other requirements must be implemented to ensure a smooth transition from current maintenance strategies. However, there is a benefit as the plant no longer needs manage their own servers, software, cybersecurity, and IT support staff. Many of these features can be offloaded on to the cloud provider. A comprehensive analysis was completed that showed the current annual cost of operating is more expensive than using cloud computing resources. Lastly, the regulatory framework does not explicitly address AI or autonomous control. Currently, the NRC and other regulatory bodies are evaluating providing guidance to address gaps rather than new regulations to address the use of AI and ML. But since many of the AI applications are focused on non-safety related applications, such as balance-of-plant components, they will likely have little or no regulatory restrictions or necessary approvals. Demonstrating how AI can improve maintenance and operation of these non-safety related systems seems like the likely path forward for implementing AI and cloud computing resources inside nuclear power plants (NPPs).

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Heteroatom-Modified and Compacted Zeolite-Templated Carbons for Gas Storage

Methane, the primary component of natural gas, is an energy-rich fuel by weight but exhibits lower energy density by volume than diesel and gasoline; efforts to increase its “volumetric” energy density have been focused on the design and synthesis of a porous scaffold that can bind the methane favorably. Novel approaches typically invoke the highly designable class of materials known as metal-organic frameworks (MOFs) owing to the relative difficulty of controlling carbon structure and composition precisely, without the use of a metal-based node. In this project, we instead explore the concept of carbon templating to achieve a porous scaffold with atomistically thin walls separated at a distance of ~1.2 nm, ideal for the formation of precisely two layers of methane per pore. This bottom-up templating approach permits the use of any small molecular precursor to build up the carbon scaffold, begging the question: which other elements (besides carbon) can be used to tune the surface for optimal methane binding without compromising the structure of the overall material? Boron and nitrogen were both explored and nitrogen was identified as the ideal agent for increasing methane binding to the optimal strength for use at near room temperature. Densification of the resulting materials by mechanical compaction was then explored to produce free-standing pellets with the highest methane “delivery” capacities of any known material. Here we define the amount “delivered” as the amount stored minus the amount remaining in the tank at 73 psi, the lowest useful pressure for vehicular transportation applications. The key features of the resulting methane storage system are rapid discharging and refueling speeds, extremely long cycle life (infinite cycle life for high-purity methane), a near-constant heat of refueling (making the heat generated upon refueling easier to manage), and a low maximum pressure of operation (<1500 psi), enabling the use of all-metal Type I cylinders and significantly reducing the costs of conversion of existing vehicles to cleaner burning, abundantly available natural gas). The technical effectiveness of this approach was further improved by exploring several cost-reduction strategies and investigating the reliability of such storage systems in the presence of “real” natural gas mixtures which contain a mixture of gaseous species.

03 NATURAL GAS↗

Machine Learning for Predictive Performance Analysis in Charged Particle Beam Tools

Imaging methods driven by probes, electrons, and ions have played a dominant role in modern science and engineering. Opportunities for machine vision and AI that focus on consumer problems like driving and feature recognition, are now presenting themselves for automating aspects of the scientific processes. This proposal aims to enable and drive discovery in ultra-low energy implantation by taking advantage of faster processing, flexible control and detection methods, and architecture-agnostic workflows that will result in higher efficiency and shorter scientific development cycles. Custom microscope control, collection and analysis hardware will provide a framework for conducting novel in situ experiments revealing unprecedented insight into surface dynamics at the nanoscale. Ion implantation is a key capability for the semiconductor industry. As devices shrink, novel materials enter the manufacturing line, and quantum technologies transition to being more mainstream. Traditional implantation methods fall short in terms of energy, ion species, and positional precision. Here we demonstrate 1 keV focused ion beam Au implantation into Si and validate the results via atom probe tomography. We show the Au implant depth at 1 keV is 0.8 nm and that identical results for low energy ion implants can be achieved by either lowering the column voltage, or decelerating ions using bias – while maintaining a sub-micron beam focus. We compare our experimental results to static calculations using SRIM and dynamic calculations using binary collision approximation codes TRIDYN and IMSIL. A large discrepancy between the static and dynamic simulation is found that is due to lattice enrichment with high stopping power Au and surface sputtering. Additionally, we demonstrate how model details are particularly important to the simulation of these low-energy heavy-ion implantations. Finally, we discuss how our results pave a way to much lower implantation energies, while maintaining high spatial resolution.

47 OTHER INSTRUMENTATION↗

Model Parameter Development for Complex Materials: Species-Specific Diffusion Barriers in 316 Stainless Steel from Systematic DFT Calculations

Vacancy-mediated diffusion barriers in 316 stainless steel have been systematically calculated using density functional theory to provide essential parameters for mesoscale microstructure evolution models. A statistical sampling approach employing 210 nudged elastic band calculations across multiple special quasi-random structures captures the effects of local chemical environments in this concentrated alloy. The computational methodology addresses challenges specific to chemically disordered systems, including proper magnetic treatment throughout multi-step calculations and validation against experimental structural properties. The calculated activation barriers reveal clear species-dependent diffusion behavior with the hierarchy Ni >> Fe ˜ Cr >> Mo. Nickel exhibits the highest barriers (0.74–1.31 eV, mean 1.045 eV), confirming its role as the slowest-diffusing major component. Iron and chromium show similar moderate barriers averaging 0.587 eV and 0.522 eV, respectively. Remarkably, molybdenum demonstrates exceptionally low barriers (0.12–0.28 eV, mean 0.194 eV), suggesting much higher mobility than previously recognized and potentially significant implications for precipitation kinetics and microstructure evolution. The barrier ranges remain consistent across different 316 SS compositions, supporting parameter transferability for modeling applications. The overall mean barrier of 0.64 eV provides a practical approximation for phase field simulations, while species-specific values enable detailed treatments of diffusion-controlled processes. This systematic approach establishes a validated framework for generating diffusion parameters in other concentrated alloys where experimental data are limited, while providing the first systematic set of species-specific barriers for predictive modeling of 316 stainless steel microstructure evolution.

36 MATERIALS SCIENCE↗

An Accuracy-Maximization Approach for Claims Classifiers in Document Content Analytics for Cybersecurity

This paper presents our research approach and findings towards maximizing the accuracy of our classifier of feature claims for cybersecurity literature analytics, and introduces the resulting model ClaimsBERT. Its architecture, after extensive evaluations of different approaches, introduces a feature map concatenated with a Bidirectional Encoder Representation from Transformers (BERT) model. We discuss deployment of this new concept and the research insights that resulted in the selection of Convolution Neural Networks for its feature mapping aspects. We also present our results showing ClaimsBERT to outperform all other evaluated approaches. This new claims classifier represents an essential processing stage within our vetting framework aiming to improve the cybersecurity of industrial control systems (ICS). Furthermore, in order to maximize the accuracy of our new ClaimsBERT classifier, we propose an approach for optimal architecture selection and determination of optimized hyperparameters, in particular the best learning rate, number of convolutions, filter sizes, activation function, the number of dense layers, as well as the number of neurons and the drop-out rate for each layer. Fine-tuning these hyperparameters within our model led to an increase in classification accuracy from 76% obtained with BertForSequenceClassification’s original model to a 97% accuracy obtained with ClaimsBERT.

Ameri, Kimia (ORCID:0000000328791871)↗

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗

Intra-Molecular Isotope Study of Light Hydrocarbons

Light hydrocarbons (C 1 -C 10 ) are the largest fraction of petroleum hydrocarbons and some of the most ubiquitous and mobile fluids within sedimentary basins. It has been increasingly recognized that hydrocarbons of varying chain-lengths can be stable even under mantle conditions and that their fluxes may play a key role in the carbon dynamics of the Earth. Major formation mechanisms of these light hydrocarbons include microbial, thermogenic, and abiogenic origins. Despite their proven utility, conventional approaches using the bulk or global stable isotopes of light hydrocarbons are often not sufficient to distinguish their sources (particularly, biogenic vs. abiogenic), maturation stages/temperatures, and migration-degradation processes. Most natural compounds, including light hydrocarbons, are composed of a set of diverse isotopic molecules that differ in the number of isotopic substitutions and/or positions of isotopic substitution within a given molecules. Many of light hydrocarbon molecules contain hydrogen and carbon in energetically non-equivalent positions: isotopomers or position-specific (intra-molecular) isotope fractionation. Position-specific isotopic compositions can differ due either to equilibrium or to path-dependent kinetic or biological processes. Thus, the position-specific isotopic fractionation between different carbon and hydrogen positions within a single molecular compound could be used regardless of their reactants and other products. We hypothesize that the formation, transport and degradation processes of light hydrocarbons in the subsurface induce and control significant, perhaps unique position-specific 13 C/ 12 C and 2 H/ 1 H isotope fractionation. In this proposal, we propose to develop a new dimension in stable isotope geochemistry of light hydrocarbons: intra-molecular isotope study of light hydrocarbons. The specific objectives of our proposal include: (a) develop robust and routine quantitative nuclear magnetic resonance (NMR) methods for high-precision/high-accuracy isotopomer analysis of propane and other light hydrocarbons (C 3 -C 10 ), (b) gain a first clear picture on position-specific δ 2 H and δ 13 C values of select light hydrocarbons of both natural and industrial sources, including samples of natural gases (C 3 and possibly C 4 -C 5 ) collected from select sedimentary basins with conventional and unconventional reservoirs, (c) acquire information on position-specific 13 C/ 12 C and 2 H/ 1 H isotope fractionation of light hydrocarbons in key natural processes (thermogenic formation and oxidative degradation) based on well-controlled laboratory experiments, and (d) establish a general framework for interpreting/modeling position-specific 13 C/ 12 C and 2 H/ 1 H isotope compositions of light hydrocarbons. Intra-molecular isotope study of light hydrocarbons is expected to open up great potentials that the bulk and position-specific isotope fractionation of light hydrocarbons, in combination with mathematical/theoretical kinetic models, could provide unprecedented wealth of information on the sources, transport, and sinks of light hydrocarbons in sedimentary basins and deep Earth.

03 NATURAL GAS↗

Transactive Energy Systems: The Market-based Coordination of Distributed Energy Resources

This paper synthesizes a unifying framework that captures a large class of transactive energy systems studied in the literature. The framework consists of four key elements: agent preferences, control decisions, information structure, and solution concept. Among them, agent preference specifies the preferred outcome by each agent and models the conflict of interest in decision making. Control decision specifies the set of decisions for each agent to maximize its payoff. Information structure describes the information available to each agent before it makes a decision. Solution concept encodes the rationality assumptions of each agent in the system. These elements are important in identifying and distinguishing different transactive energy systems. In this paper, we use them to analyze a number of important ones, including the competitive equilibrium, Stackelberg game, reverse Stackelberg game, and mechanism design. Each class of these problems is formulated as a special case of the proposed transactive energy systems. Their connections and differences are discussed. Available tools and results for each category of problems are surveyed.

Li, Sen↗

CityLearn v2: energy-flexible, resilient, occupant-centric, and carbon-aware management of grid-interactive communities

As more distributed energy resources become part of the demand-side infrastructure, quantifying their energy flexibility on a community scale is crucial. CityLearn v1 provided an environment for benchmarking control algorithms. However, there is no standardized environment utilizing realistic building-stock datasets for distributed energy resource control benchmarking without co-simulation or third-party frameworks. CityLearn v2 extends CityLearn v1 by providing a stand-alone simulation environment that leverages the End-Use Load Profiles for the U.S. Building Stock dataset to create grid-interactive communities for resilient, multi-agent, and objective control of distributed energy resources with dynamic occupant feedback. While the v1 environment used pre-simulated building thermal loads, the v2 environment uses data-driven thermal dynamics and eliminates the need for co-simulation with building energy performance software. This work details the v2 environment and provides application examples that use reinforcement learning control to manage battery energy storage system, vehicle-to-grid control, and thermal comfort during heat pump power modulation.

Nweye, Kingsley↗

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

Allowing third-party applications on Radio Access Network (RAN) Intelligent Controllers (RICs) within the OpenRAN (O-RAN) framework introduces conflicting interactions that are often difficult to detect in advance. These conflicts, occurring between third-party applications in the Near RealTime RIC (Near-RT RIC), known as xApps, can lead to performance degradation and instability in O-RAN if not identified early. Existing conflict detection and mitigation solutions in the literature assume that the conflicts are known beforehand, which is not always accurate due to the complex and often hidden relationships between control parameters and Key Performance Indicators (KPIs). In this paper, we propose a novel Recurrent Neural Network (RNN) to detect both known and unknown conflicts in O-RAN xApps as specified in the O-RAN standards. We model the xApps, control parameters, and KPIs with nodes and edges to create graph structures and use the hidden nonEuclidean geometric properties of the Riemannian manifold to train the RNN model. The performance of this proposed model is validated using evaluation metrics and compared with benchmarks. Results demonstrate that the proposed RNN model, leveraging Riemannian geometric properties, can achieve 100% of the F1-score provided by an optimal solution in just 20 iterations.

5G↗

Conflict Detection in Open RAN with Recurrent Neural Networks Using Geometric Manifolds

Allowing third-party applications on Radio Access Network (RAN) Intelligent Controllers (RICs) within the OpenRAN (O-RAN) framework introduces conflicting interactions that are often difficult to detect in advance. These conflicts, occurring between third-party applications in the Near RealTime RIC (Near-RT RIC), known as xApps, can lead to performance degradation and instability in O-RAN if not identified early. Existing conflict detection and mitigation solutions in the literature assume that the conflicts are known beforehand, which is not always accurate due to the complex and often hidden relationships between control parameters and Key Performance Indicators (KPIs). In this paper, we propose a novel Recurrent Neural Network (RNN) to detect both known and unknown conflicts in O-RAN xApps as specified in the O-RAN standards. We model the xApps, control parameters, and KPIs with nodes and edges to create graph structures and use the hidden nonEuclidean geometric properties of the Riemannian manifold to train the RNN model. The performance of this proposed model is validated using evaluation metrics and compared with benchmarks. Results demonstrate that the proposed RNN model, leveraging Riemannian geometric properties, can achieve 100% of the F1-score provided by an optimal solution in just 20 iterations.

5G↗

Digital twin framework for PIP-II linac: AI-driven multi-scale modeling from ion source to 800 MeV

The PIP-II superconducting linac at Fermilab is designed to deliver multi-megawatt proton beams for neutrino physics and other high-intensity applications. To expedite commissioning and enhance operational reliability, we have developed an EPICS-based data flow framework that seamlessly integrates digital twins (DT) with physical twins (PT). These digital twins comprise high-fidelity beam dynamics models or data-driven surrogate models connected to their physical counterparts through real-time diagnostics and advanced machine-learning algorithms.Central to this framework is Linac_Gen, an accelerated simulation tool that incorporates convolutional neural networks, random forests, and genetic algorithms to provide up to a tenfold speedup in optimizing the accelerator geometry model. An EPICS translator layer ensures interoperability by efficiently mapping lattice parameters across diverse simulation platforms.Our EPICS-based framework supports multiple operational modes—monitoring, passive learning, closed-loop control, and online learning—covering the entire machine lifecycle. By leveraging HPC resources and multi-objective optimization techniques, the digital twin enables adaptive trajectory correction, real-time fault detection, and predictive modeling of beam stability. This comprehensive approach paves the way for robust, high-intensity operation and data-driven accelerator R&D at Fermilab.

Pathak, Abhishek [Fermilab]↗

Within-Host Phenotypic Evolution and the Population-Level Control of Chronic Viral Infections by Treatment and Prophylaxis

Chronic viral infections can persist for decades spanning thousands of viral generations, leading to a highly diverse population of viruses with its own complex evolutionary history. We propose an expandable mathematical framework for understanding how the emergence of genetic and phenotypic diversity affects the population-level control of those infections by both non-curative treatment and chemo-prophylactic measures. Our frameworks allows both neutral and phenotypic evolution, and we consider the specific evolution of contagiousness, resistance to therapy, and efficacy of prophylaxis. We compute both the controlled and uncontrolled, population-level basic reproduction number accounting for the within-host evolutionary process where new phenotypes emerge and are lost in infected persons, which we also extend to include both treatment and prophylactic control efforts. We used these results to discuss the conditions under which the relative efficacy of prophylactic versus therapeutic methods of control are superior. Finally, we give expressions for the endemic equilibrium of these models for certain constrained versions of the within-host evolutionary model providing a potential method for estimating within-host evolutionary parameters from population-level genetic sequence data.

sensitivity analysis↗

Paralleling of LLC Resonant Converters

The LLC resonant converter is a popular, variable switching frequency DC-DC converter that may be controlled using two methods: charge and frequency control. In this paper, the application of LLC resonant converters to input-parallel, output-parallel system is studied. In this respect, the models of output-port I-V characteristics and small-signal output impedance of the charge controlled LLC converter are proposed. In addition, a mathematical framework is developed for droop-based paralleled DC-DC systems. Here, it distinctly identifies the output DC voltage and circulating current modes of stability, even in systems comprising of non-identical converters.

42 ENGINEERING↗