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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 181 records · Page 10
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DOE OSTI2025

Adaptive PID Gain Scheduling Control for Hydropower Turbine Using Neural CDE and Stochastic Distribution Shaping

This paper introduces a gain-scheduling PID controller design strategy for hydroturbine frequency control mode. This scheme first uses real data to learn the nonlinear dynamics of the hydroturbine using neural controlled differential equations and then perturbs the obtained nonlinear system at different equilibrium points, based on which a static output feedback adaptive dynamic programming algorithm is then used to optimize the PID gains for each equilibrium point. Moreover, a continuous-time version of stochastic distribution control is proposed to further fine-tune the optimized PID gains. Finally, the controller is obtained by implementing linear interpolation between the optimized PID control gains. The simulation results show that the proposed gain-scheduling PID controller can control a larger range of operation points compared with the given fixed PID controller and the baseline method. Compared with the given fixed PID controller, the proposed gain-scheduling PID controller can regulate hydroturbine frequency against disturbances induced by power-load variation with over 50% less overshoot for some operation points.

13 HYDRO ENERGY↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Deterministic modeling of hybrid nonlinear effects in epsilon-near-zero thin films

In nonlinear optics, significant effort is concentrated on improving the strength and efficiency of interactions; however, experimentally investigating nonlinear materials is a complex, time-consuming, and costly investment. Moreover, it is often challenging to isolate, study, and optimize material parameters in an experiment due to complexities in the growth process. Recently, epsilon-near-zero materials have received a great deal of attention as promising nonlinear optical materials, but like many up-and-coming materials, the ability to explore and optimize their properties has been challenging. Here, we establish a framework to rapidly evaluate the performance of nonlinear epsilon-near-zero materials for both inter- and intraband effects in silico, requiring only an energy-momentum (E-k) diagram, linear optical properties, and experimental conditions. Measured nonlinear reflection and transmission in gallium-doped zinc oxide films are compared to the numerical framework for both intra- and interband excitation to verify accuracy across wavelength and irradiance while two figures of merit (FoMs) are introduced to quickly evaluate the performance of films without a full numerical framework. This capability is used to predict the performance of highly doped gallium nitride, cadmium oxide, zinc oxide, and indium tin oxide films, and efficient intra- and interband operation conditions are identified. Through this numerical framework and the FoMs, the exploration of unstudied epsilon-near-zero materials is enabled without the need for a nonlinear experiment, thereby accelerating the search for more efficient nonlinear materials and excitation conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition

In “Recent Developments in Security-Constrained AC Optimal Power Flow: Overview of Challenge 1 in the ARPA-E Grid Optimization Competition,” we review the state of the art in practical algorithms for scheduling power-systems operations in the short term and the results of the recent competition organized by the U.S. Advanced Research Projects Agency–Energy. We explain the mixed-integer nonlinear formulation used in the competition for nonspecialists in electrical engineering, the context and organization of the competition, and the performance of competitors. We find that the collective approaches and results of competitors provide support for efforts to move nonlinear optimization techniques into industrial applications, as they have proven to be a robust and efficient alternative to current linear approximation techniques.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ 2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

17 WIND ENERGY↗
DOE OSTI2022

Using a Grid-Forming Inverter to Stabilize a Low-Inertia Power System - Maui Hawaiian Island

As power systems around the world integrate greater amounts of wind and solar photovoltaic power, periods of very high instantaneous power shares of inverters, the primary interfacing technology for these generation sources, are complicating system stability and control. The contemporary, primary mode of inverter operation, grid-following, which explicitly assumes the presence of a local, stable voltage waveform, yields operational inadequacy at high instantaneous power shares potentially leading to instability due to the low-inertia conditions, as well as the correlated reduced voltage forming capacity on the respective system. Parallel connected grid-forming inverters, which directly regulate the local voltage, are a solution that is expected to bolster system stability and mitigate the shortcomings of the grid-following technology. In this paper, grid-following and two types of grid-forming inverter control, the traditional linear droop and the recently introduced nonlinear exponential droop (Droop-e), are simulated on a low-inertia, H = 0.48s, high inverter-based resource scenario, 97%, with a validated electromagentic transient domain model of the Hawaiian island of Maui power system. The benefit of a single grid-forming device over its grid-following counterpart is significant, both in terms frequency deviation and voltage stability. Further, the superiority of the Droop-e and the associated secondary power sharing control over both grid-following and linear droop grid-forming technologies is displayed, with improved nadir and rate of change of frequency over the linear droop control.

droop control↗
DOE OSTI2021

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Ultrasound Characterization of Plastic Bonded Explosives With Varied Binder Content and Density

Advanced explosive formulations and methods of production require rapid characterization for both processes and materials. Here, we present results for ultrasound characterization of a plastic bonded explosive (PBX) formulation as a function of binder weight percent and pressing density using through-transmission sound speed measurements. The explosive in this study was composed of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) combined with the fluoropolymer binder Kynar Ultraflex B. Binder content ranged from 2.6 wt.% to 11.5 wt.% with associated explosive formulation densities from 1.69 g/cc to 1.89 g/cc. We find linear and nonlinear changes in longitudinal and shear sound speeds, peak frequencies, and measured elastic properties for the different PBX formulations. These measured changes can differentiate the tested formulations, highlighting the potential for ultrasound as a nondestructive characterization method for newly-formulated PBXs. We also demonstrate through-transmission measurements using different coupling media and present results from an ultrasound technique called resonant ultrasound spectroscopy (RUS). Both transmission and RUS approaches may allow for rapid and even automated characterization of PBX components suitable for high-throughput manufacturing operations.

Engineering↗
DOE OSTI2023

Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks

Abstract Anticipating qualitative changes in the rheological response of complex fluids (e.g., a gelation or vitrification transition) is an important capability for processing operations that utilize such materials in real-world environments. One class of complex fluids that exhibits distinct rheological states are soft glassy materials such as colloidal gels and clay dispersions, which can be well characterized by the soft glassy rheology (SGR) model. We first solve the model equations for the time-dependent, weakly nonlinear response of the SGR model. With this analytical solution, we show that the weak nonlinearities measured via medium amplitude parallel superposition (MAPS) rheology can be used to anticipate the rheological aging transitions in the linear response of soft glassy materials. This is a rheological version of a technique called structural health monitoring used widely in civil and aerospace engineering. We design and train artificial neural networks (ANNs) that are capable of quickly inferring the parameters of the SGR model from the results of sequential MAPS experiments. The combination of these data-rich experiments and machine learning tools to provide a surrogate for computationally expensive viscoelastic constitutive equations allows for rapid experimental characterization of the rheological state of soft glassy materials. We apply this technique to an aging dispersion of Laponite ® clay particles approaching the gel point and demonstrate that a trained ANN can provide real-time detection of transitions in the nonlinear response well in advance of incipient changes in the linear viscoelastic response of the system.

Lennon, Kyle R. (ORCID:0000000212515461)↗
DOE OSTI2020

Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

Here, we present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker–Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In particular, we focus on an operator often known as the ‘Lenard–Bernstein’ or ‘Dougherty’ operator. Several novel algorithmic innovations, based on the concept of weak equality, are reported. These weak equalities are used to define weak operators that compute primitive moments, and are also used to determine a reconstruction procedure that allows an efficient and accurate discretization of the diffusion term. We show that when two integrations by parts are used to construct the discrete weak form, and finite velocity-space extents are accounted for, a scheme that conserves density, momentum and energy exactly is obtained. One novel feature is that the requirements of momentum and energy conservation lead to unique formulas to compute primitive moments. Careful definition of discretized moments also ensure that energy is conserved in the piecewise linear case, even though the kinetic-energy term, $v^2$ is not included in the basis set used in the discretization. A series of benchmark problems is presented and shows that the scheme conserves momentum and energy to machine precision. Empirical evidence also indicates that entropy is a non-decreasing function. The collision terms are combined with the Vlasov equation to study collisional Landau damping and plasma heating via magnetic pumping.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Joint Estimation of Topology and Injection Statistics in Distribution Grids with Missing Nodes

Optimal operation of distribution grid resources relies on accurate estimation of its state and topology. Practical estimation of such quantities is complicated by the limited presence of real-time meters. This article discusses a theoretical framework to jointly estimate the operational topology and statistics of injections in radial distribution grids under limited availability of nodal voltage measurements. In particular, we show that our proposed algorithms are able to provably learn the exact grid topology and injection statistics at all unobserved nodes as long as they are not adjacent. The algorithm design is based on novel ordered trends in voltage magnitude fluctuations at node groups, that are independently of interest for radial physical flow networks. The complexity of the designed algorithms is theoretically analyzed and their performance is validated using both linearized and nonlinear ac power flow samples in test distribution grids.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2022

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A review of active probing-based system identification techniques with applications in power systems

System identification is becoming a relevant research area for numerous applications in power grids due to the increasing complexity of the system. A paradigm shift in power system infrastructure driven by renewable energy resources, controllable loads, and new power electronics technologies have given rise to new challenges in power systems operation and control. This increased complexity of power systems and unavailability of physics-based models of most inverter-based resources requires that traditional modeling of power systems approaches be complemented by system identification-based black or grey box modeling techniques. In light of the importance of system identification and little attention paid to the applications of these techniques in transforming power systems, this paper provides a comprehensive review of active probing-based system identification methods in the context of power system applications. It reviews applications of both linear and nonlinear system identification with discussion on their potential and key takeaways. To motivate a further practical use in power systems, the paper provides an example of system identification, to develop a state space model of an unknown plant with step-by-step details. The paper highlights the advantages of using modern power electronics-based sources in the identification process and discusses the emerging research directions for future.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

A new and alternative look at nonlinear Alfvénic states

The formulation for studying nonlinear Alfvenic states, sustainable in Hall Magnetohydrodynamics (HMHD), becomes considerably simpler and more tractable when circularly polarized Beltrami vectors (the eigenstates of linear HMHD) are used as the basis functions. Nonlinear HMHD is, then, reduced to a rather simple looking set of scalar equations from which a model problem of three interacting Beltrami modes is formulated and analytically solved. The triplet interactions span a variety of familiar nonlinear processes leading to a redistribution as well as periodic exchange of energy. The energy exchange processes (whose strength is measured by an energy exchange/depletion time) will, perhaps, play a dominant role in determining the spectral content of an eventual Alfvenic state. All nonlinearities (sensitive functions of the interacting wave vectors) operate at par, and none is dominant over any substantial region of k-space; their intricate interplay prevents a “universal” picture from emerging; few generalizations on the processes that may, for instance, lead to a turbulent state, are possible. However, the theory can definitely claim: (1) the energy tends to flow from lower to higher k and (2) the higher k z (in the direction of the ambient magnetic field) components of a mode with a given k are depleted/oscillate faster—in some cases much faster. It is noteworthy that the mode coupling is the strongest (with the shortest depletion time) when the participating wave vectors are nearly perpendicular; perhaps, an expected consequence of the curl (cross product) nonlinearities. Numerical simulations will be necessary to help create a fully reliable picture.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Turbulence simulations of drift-Alfvén wave effects on edge-localized modes and divertor target heat flux width

A series of BOUT++ turbulence simulations are performed for two Pre-Fusion Power Operation (PFPO-1,2) phases of the ITER Research plan proclaimed in 2019. Linear simulation results show that PFPO-1 is unstable to Peeling-ballooning modes (PB), while the PFPO-2 is unstable to the coupling of PB and Drift-Alfvén wave (DAW) instabilities. The linear results are qualitatively consistent with the dispersion relation of DAW. To study the influence of the DAW on the edge-localized mode (ELM) crash, the PFPO-2 is adopted in this section. Different from the grassy ELM in [Li et al 2022 Nucl. Fusion 62, 096030], nonlinear simulations show that the ELM size of PFPO-2 is almost one-third of the grassy ELM, representing a distinct small ELM. However, simulations then show that if the PB instability is removed, the fluctuation amplitude drops by an order of magnitude and the ELM crash disappears, which is in accord with the theory in [Xu et al 2010 Physical Review Letters, Vol. 105, 175005] and the results in [Li et al 2022 Nucl. Fusion 62, 096030], confirming that the PB instability is a necessary condition for an ELM crash. Furthermore, removing the DAW drive also suppresses ELM crashes, implying that PB instability is necessary but insufficient for PFPO-2 ELM and that DAW could amplify PB-driven turbulence. In addition, by integrating results of both PFPO phases by BOUT++ turbulence analysis with heat flux width (λ q ) and electron thermal diffusivity (χ e ), these simulations establish a predictive framework for heat flux width and its dominant mechanisms, thereby providing a comprehensive scheme for the prediction of the heat flux width. Moreover, simulations indicate that DAW driving can increase the transport coefficient by enhancing the turbulent transport, leading to a broadened heat flux width once the transport coefficient exceeds

Drift-Alfvén wave↗
DOE OSTI2023

Machine-learning-based spectral methods for partial differential equations

Spectral methods are an important part of scientific computing’s arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the solution of a PDE. The last decade has seen the emergence of deep learning as a strong contender in providing efficient representations of complex functions. In the current work, we present an approach for combining deep neural networks with spectral methods to solve PDEs. In particular, we use a deep learning technique known as the Deep Operator Network (DeepONet) to identify candidate functions on which to expand the solution of PDEs. We have devised an approach that uses the candidate functions provided by the DeepONet as a starting point to construct a set of functions that have the following properties: (1) they constitute a basis, (2) they are orthonormal, and (3) they are hierarchical, i.e., akin to Fourier series or orthogonal polynomials. We have exploited the favorable properties of our custom-made basis functions to both study their approximation capability and use them to expand the solution of linear and nonlinear time-dependent PDEs. The proposed approach advances the state of the art and versatility of spectral methods and, more generally, promotes the synergy between traditional scientific computing and machine learning.

97 MATHEMATICS AND COMPUTING↗