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DOE OSTI2026

FY25 Electric Grid Security Annual Report

Sandia’s Electric Grid Security program advances a national vision of energy dominance and accessibility, while applying our national security -emphasis on ensuring of a secure, resilient, and affordable electric system for all users. Our achievements reflect a strategic approach combining technology development; modeling, simulation, and data analytics; and partnered demonstrations and outreach to further the adoption of advanced grid and storage technologies. Our FY25 efforts leverage the strengths of our partnerships—spanning Sandia’s core science and technology competencies as well as external technology leaders—to develop the solutions today which enable the grid of tomorrow. Key accomplishments in this report that support our strategy span our technical program areas and include: • New open-source analytical tools for systems -level planning and optimization, including significant advances to the QuESt analytical environment; • Further advancement of artificial intelligence and machine learning to enhanced grid operations and planning as we rise to the challenge of new large loads; • Development of solid-state power conversion technologies and a new medium-voltage research lab; • New technologies to assess wildfire vulnerabilities and mitigate potential impacts; • Advanced applications of new cybersecurity technologies with industry partners; • Contributions to understanding the impacts of electromagnetic pulses and geomagnetic disturbances on grid components; and • Digital twin development for hybrid microgrids with multiple generators, storage, and loads. This report indicates key areas of research and engagement and summarizes the impact of Sandia’s contributions through notable accomplishments, journal publications, patents, and technical conferences and presentations. It is provided with the hope that readers discover ways we can further team to create our modern grid and apply the outcomes of our efforts. The bulk of work described herein is funded by several offices within the U.S. Department of Energy (USDOE), including the Office of Electricity (OE); Cybersecurity, Energy Security, and Emergency Response (CESER); former offices such as the Office of Energy Efficiency and Renewable Energy (EERE), the Grid Deployment Office (GDO), the Office of Clean Energy Demonstrations (OCED), and other key programs at USDOE. As we continue to state in these annual reports, the contributors to our successes are too numerous to name here, though our team wishes to express our deep gratitude to the numerous program and project sponsors at the US Department of Energy, who often function equally as technical collaborators; our many partners in industry, academia, utilities, and other national labs; and fellow researchers and business partners at Sandia whose leadership and creativity have enabled the accomplishments described herein.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Real-Time Modal Analysis of Electric Power Grids - The Need for Dynamic State Estimation: Preprint

We articulate the reason why dynamic state estimation is needed to push the boundaries of the modal analysis of electric power grids in real-time operation. Then, we demonstrate how to unravel linear and nonlinear modes by using the extended dynamic mode decomposition along with estimates of the synchronous generators' rotor angles and rotor speed deviations from nominal speed. The estimated modes are associated with electromechanical oscillations that take place continuously in electric power grids because of imbalances between power generation and demand. The numerical simulations are performed on a synthetic, albeit realistic, 2,000-bus network that was designed to resemble the electric power grid of Texas.

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2025

Time correlations from steady-state expectation values

Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a control parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to experimentally characterize ultrafast systems, and to theoretically analyze many-body models with dynamics that are analytically or numerically hard.

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2025

Time correlations from steady-state expectation values

Górecki, Wojciech [INFN, Pavia]↗

DOE OSTI2023

Closed Loop Geothermal Working Group: GeoCLUSTER App, Subsurface Simulation Results, and Publications

To better understand the heat production, electricity generation performance, and economic viability of closed-loop geothermal systems in hot-dry rock, the Closed-Loop Geothermal Working Group -- a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed-loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and supercritical CO2) while varying seven continuous independent parameters of interest (mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying Python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the techno-economic analysis script are provided. This data submission will contain results from the Closed Loop Geothermal Working Group study that are within the public domain, including publications, simulation results, databases, and computer codes. GeoCLUSTER is a Python-based web application created using Dash, an open-source framework built on top of Flask that streamlines the building of data dashboards. GeoCLUSTER provides users with a collection of interactive methods for streamlining the exploration and visualization of an HDF5 dataset. The GeoCluster app and database are contained in the compressed file geocluster_vx.zip, where the "x" refers to the version number. For example, geocluster_v1.zip is Version 1 of the app. This zip file also contains installation instructions. **To use the GeoCLUSTER app in the cloud, click the link to "GeoCLUSTER on AWS" in the Resources section below. To use the GeoCLUSTER app locally, download the geocluster_vx.zip to your computer and uncompress this file. When uncompressed this file comprises two directories and the geocluster_installation.pdf file. The geo-data app contains the HDF5 database in condensed format, and the GeoCLUSTER directory contains the GeoCLUSTER app in the subdirectory dash_app, as app.py. The geocluster_installation.pdf file provides instructions on installing Python, the needed Python modules, and then executing the app.

15 GEOTHERMAL ENERGY↗

DOE OSTI2025

A bilevel multistage stochastic self-scheduling model with indivisibilities for trading in the continuous intraday electricity market

In this paper, we study the profit maximization problem of a virtual power plant trading in the continuous intraday electricity market. Our virtual power plant model is compatible with renewable, and thermal assets, covering a range of virtual power plants currently participating in energy markets. We model the trading problem as a bilevel multistage stochastic program. The upper level of the problem accounts for the profit maximization of the virtual power plant with explicit modeling of the technical constraints of the operational status of the thermal power plant including minimum start-up and shut-down times, ramp-up and ramp-down rates, and minimum generation level. The upper level also decides which continuous and indivisible (fill-or-kill) orders are submitted to the market. The lower-level problem accounts for the clearing of the continuous intraday market, i.e., matching of buy and sell orders. Because of the presence of fill-or-kill orders, the lower-level problem is mixed-integer, which prevents its direct conversion to a single-level problem using duality. In order to solve this challenging problem, we develop a convex-hull extended formulation for the lower-level problem, apply duality theory to obtain a single-level stochastic equivalent formulation, and employ McCormick envelopes to turn the problem into a multistage stochastic mixed-integer linear problem, which we solve using the stochastic dual dynamic integer programming algorithm. We conduct numerical experiments and analyze the optimal trading behavior of a virtual power plant trading in an ideal continuous market without arbitrage.

Bilevel multistage stochastic programming problem↗

DOE OSTI2021

A review of modelling techniques for floating offshore wind turbines

Modelling floating offshore wind turbines (FOWTs) is challenging due to the strong coupling between the aerodynamics of the turbine and the hydrodynamics of the floating platform. Physical testing at scale is faced with the additional challenge of the scaling mismatch between Froude number and Reynolds number due to working in the two fluid domains, air and water. In the drive for cost-reduction of floating wind energy, designers may be seeking to move towards high-fidelity numerical modelling as a substitute for physical testing. However, the numerical engineering tools typically used for FOWT modelling are considered as mid-fidelity to low-fidelity tools, and currently lack the level of accuracy required to do so. Furthermore, there is a lack of operational FOWT data available for further development and validation. High-fidelity tools, such as CFD, have greater accuracy but are cumbersome tools and still require validation. Physical scale model testing therefore continues to play an essential role in the development of FOWTs both as a source of validation data for numerical models and as an important development step along the path to commercialization of all platform concepts. The aim of this paper is to provide an overview of both numerical modelling and physical FOWT scale model testing approaches and to provide guidance on the selection of the most appropriate approach (or combination of approaches). The current state-of-the-art will be discussed along with current research trends and areas for further investigation.

17 WIND ENERGY↗

DOE OSTI2022

Tree hydrodynamic modelling of the soil–plant–atmosphere continuum using FETCH3

Modelling the water transport along the soil–plant–atmosphere continuum is fundamental to estimating and predicting transpiration fluxes. A Finite-difference Ecosystem-scale Tree Crown Hydrodynamics model (FETCH3) for the water fluxes across the soil–plant–atmosphere continuum is presented here. The model combines the water transport pathways into one vertical dimension, and assumes that the water flow through the soil, roots, and above-ground xylem can be approximated as flow in porous media. This results in a system of three partial differential equations, resembling the Richardson–Richards equation, describing the transport of water through the plant system and with additional terms representing sinks and sources for the transfer of water from the soil to the roots and from the leaves to the atmosphere. The numerical scheme, developed in Python 3, was tested against exact analytical solutions for steady state and transient conditions using simplified but realistic model parameterizations. The model was also used to simulate a previously published case study, where observed transpiration rates were available, to evaluate model performance. With the same model setup as the published case study, FETCH3 results were in agreement with observations. Through a rigorous coupling of soil, root xylem, and stem xylem, FETCH3 can account for variable water capacitance, while conserving mass and the continuity of the water potential between these three layers. FETCH3 provides a ready-to-use open access numerical model for the simulation of water fluxes across the soil–plant–atmosphere continuum.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Leading-color two-loop QCD corrections for three-jet production at hadron colliders

We present the complete set of leading-color two-loop contributions required to obtain next-to-next-to-leading-order (NNLO) QCD corrections to three-jet production at hadron colliders. We obtain analytic expressions for a generating set of finite remainders, valid in the physical region for three-jet production. The analytic continuation of the known Euclidean-region results is determined from a small set of numerical evaluations of the amplitudes. We obtain analytic expressions that are suitable for phenomenological applications and we present a C++ library for their efficient and stable numerical evaluation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

DOE OSTI2025

On the discretization error of the discrete generalized quantum master equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 112 , 110401 (2014)] can be considered a discrete-time formulation of the Nakajima–Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 21 , 5037 (2025)] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time t = 0. Here, this work presents a detailed analysis of the discretization structure of the TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel K N and the continuous-time NZ-QME kernel $\mathscr{K}$( N Δ t ). This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as Δ t → 0. While the TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri’s work. The relative performance of various schemes for either computing accurate $\mathscr{K}$( N Δ t ) from exact dynamics or obtaining accurate dynamics from exact $\mathscr{K}$( N Δ t ) warrants further investigation.

Density-matrix↗

DOE OSTI2026

Radial oscillations of viscous neutron stars: Zero diffusion case

In this article, the spectrum of radial oscillations of neutron stars is systematically studied within two frameworks of viscous relativistic hydrodynamics: the relativistic Navier-Stokes and Israel-Stewart theories. A correspondence is established between the discrete stellar eigenmodes and the continuous dispersion relation of perturbations around a homogeneous fluid, providing a basis for interpreting our numerical results. We analyze the Newtonian limit and assess the impact of relativistic corrections, such as the gravitational redshifting of microscopic relaxation timescales. We show that bulk viscosity can significantly affect the behavior of both hydrodynamic and nonhydrodynamic fundamental modes, and that, depending on the magnitude of the viscous effects, it is the nonhydrodynamic mode that becomes unstable beyond the turning point in a sequence of equilibrium configurations. These results provide a useful step toward systematic studies of neutron star quasinormal modes in the presence of viscosity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Journal paper

Laser technology is being widely studied for controlled energy deposition for a range of applications, including flow control, ignition, combustion, and diagnostics. The absorption and scattering of laser radiation by liquid droplets in aerosols affects propagation of the laser beam in the atmosphere, while the ignition and combustion characteristics in combustion chambers are influenced by the evaporation rate of the sprayed fuel. In this work, we present a mathematical model built on OpenFOAM for laser heating and evaporation of a single droplet in the diffusion-dominated regime taking into account absorption of the laser radiation, evaporation process, and vapor flow dynamics. The developed solver is validated against available experimental and numerical data for heating and evaporation of ethanol and water droplets. The two main regimes—continuous and pulsed laser heating—are explored. For continuous laser heating, the peak temperature is higher for larger droplets. For pulsed laser heating, when the peak irradiance is close to transition to the boiling regime, the temporal dynamics of the droplet temperature does not depend on the droplet size. With the empirical normalization of time, the dynamics of the droplet shrinkage and cooling are found to be independent of droplet sizes and peak laser intensities.

42 ENGINEERING↗

DOE OSTI2026

Data Center Market Report

The data center market is poised to explode in the coming decade due to undeniable drivers such as continued adoption of generative AI, increased data storage needs, and enterprise integration of AI in numerous industries [1] [2] [3]. Scalable power and increased computational capacity are at the forefront of considerations for hyperscalers, the major cloud service providers in this space. Lawrence Livermore National Laboratory is uniquely poised to help with informed decision making for data center market leaders during this phase of explosive expansion. National grid modeling expertise and cutting edge innovations in computer cooling systems place LLNL in an enviable position for creating economic impact in the data center industry by leveraging its expertise in these areas which can help the data center market keep up with growing demand.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Numerical Modeling of Laser Heating and Evaporation of a Single Droplet

42 ENGINEERING↗

DOE OSTI2025

Super-Resolution for Renewable Energy Resource Data with Wind from Reanalysis Data and Application to Ukraine

With a potentially increasing share of the electricity grid relying on wind to provide generating capacity and energy, there is an expanding global need for historically accurate, spatiotemporally continuous, high-resolution wind data. Conventional downscaling methods for generating these data based on numerical weather prediction have a high computational burden and require extensive tuning for historical accuracy. In this work, we present a novel deep learning-based spatiotemporal downscaling method using generative adversarial networks (GANs) for generating historically accurate high-resolution wind resource data from the European Centre for Medium-Range Weather Forecasting Reanalysis version 5 data (ERA5). In contrast to previous approaches, which used coarsened high-resolution data as low-resolution training data, we use true low-resolution simulation outputs. We show that by training a GAN model with ERA5 as the low-resolution input and Wind Integration National Dataset Toolkit (WTK) data as the high-resolution target, we achieved results comparable in historical accuracy and spatiotemporal variability to conventional dynamical downscaling. This GAN-based downscaling method additionally reduces computational costs over dynamical downscaling by two orders of magnitude. We applied this approach to downscale 30 km, hourly ERA5 data to 2 km, 5 min wind data for January 2000 through December 2023 at multiple hub heights over Ukraine, Moldova, and part of Romania. With WTK coverage limited to North America from 2007–2013, this is a significant spatiotemporal generalization. The geographic extent centered on Ukraine was motivated by stakeholders and energy-planning needs to rebuild the Ukrainian power grid in a decentralized manner. This 24-year data record is the first member of the super-resolution for renewable energy resource data with wind from the reanalysis data dataset (Sup3rWind).

17 WIND ENERGY↗

DOE OSTI2023

Tabulated Database of Closed-Loop Geothermal Systems Performance for Cloud-Based Technical and Economic Modeling of Heat Production and Electricity Generation: Preprint

To better understand the heat production, electricity generation performance and economic viability of closed loop geothermal systems in hot-dry-rock, the Closed Loop Geothermal Group, a consortium of several national labs and academic institutions has tabulated time-dependent numerical solutions and levelized cost results of two popular closed loop heat exchanger designs (u-tube and co-axial). The heat exchanger designs were evaluated for two working fluids (water and super-critical CO2) while varying seven continuous independent parameters of interest (i.e., mass flow rate, vertical depth, horizontal extent, borehole diameter, formation gradient, formation conductivity, and injection temperature). The corresponding numerical solutions (approximately 1.2 million per heat exchanger design) are stored as multi-dimensional HDF5 datasets and can be queried at off-grid points using multi-dimensional linear interpolation. A Python script was developed to query this database and estimate time-dependent electricity generation using an Organic Rankine cycle (for water) or direct turbine expansion cycle (for CO2) and perform a cost assessment. This document aims to give an overview of the HDF5 database file and highlights how to read, visualize, and query quantities of interest (e.g., levelized cost of electricity, levelized cost of heat) using the accompanying python scripts. Details regarding the capital, operation, and maintenance and levelized cost calculation using the TEA (techno-economic analysis) script are provided.

co-axial↗

DOE OSTI2024

Continuous-wave GaAs/AlGaAs quantum cascade laser at 5.7 THz

Design strategies for improving terahertz (THz) quantum cascade lasers (QCLs) in the 5–6 THz range are investigated numerically and experimentally, with the goal of overcoming the degradation in performance that occurs as the laser frequency approaches the Reststrahlen band. Two designs aimed at 5.4 THz were selected: one optimized for lower power dissipation and one optimized for better temperature performance. The active regions exhibited broadband gain, with the strongest modes lasing in the 5.3–5.6 THz range, but with other various modes observed ranging from 4.76 to 6.03 THz. Pulsed and continuous-wave (cw) operation is observed up to temperatures of 117 K and 68 K, respectively. In cw mode, the ridge laser has modes up to 5.71 THz – the highest reported frequency for a THz QCL in cw mode. The waveguide loss associated with the doped contact layers and metallization is identified as a critical limitation to performance above 5 THz.

47 OTHER INSTRUMENTATION↗