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DOE OSTI2024

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. Furthermore, the comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Probing Signal-Based Inertia and Frequency Response Estimation for Power Systems with High Penetration of Inverter-Based Resources: Preprint

Power system inertia is the inherent capability of a power system to resist changes in its frequency during disturbances. Real-time inertia estimation technology has become more important due to the low-inertia issues caused by the increasing integration levels of inverter-based resources (IBRs) from renewable energy; however, existing inertia estimation methods hardly consider multiple frequency response controls that act within the same time frame as conventional inertial response, thus making measured inertia values vary under different testing conditions. To resolve this issue, this paper proposes a novel real-time estimation method to simultaneously estimate a power system's inertia constant and frequency response droop constant using a well-designed probing signal. First, we formulate the inertia and frequency response model of a power system with IBRs. Second, through the integration and manipulation of the developed model, we propose a multivariate linear regression- based estimation method that is resilient to measurement noise. Third, we design a probing signal that can be injected by IBRs to incite the required transients for estimation. Finally, we validate the proposed estimation method through comprehensive power- hardware-in-the-loop experiments using inverter hardware and a realistic island power system model. The results demonstrate that the proposed method can accurately estimate the inertia and droop value of the power system with grid-following IBRs and grid-forming IBRs with virtual synchronous machine control.

frequency response↗

DOE OSTI2025

Slender-body approach for computing second-order wave loads in the frequency domain

This work presents a slender-body approach to evaluate the second-order wave loads acting on a floating structure in the frequency domain. The approach is in the same spirit as the common use of Morison’s equation to approximate the wave loads without solving the radiation/diffraction problem. To do so, we employ Rainey’s equation, which can be seen as an extension of the inertial part of Morison’s equation to include nonlinear effects. We introduce modifications to Rainey’s formulation in order to evaluate wave kinematics at the mean body position instead of the original approach of considering instantaneous displacements. We also propose a simple approximation to partially account for wave scattering effects on the second-order loads based on the analytical solution of a surface-piercing bottom-mounted vertical circular cylinder. Though limited to structures composed of cylinders, this slender-body approach is orders of magnitude faster than computing second-order wave coefficients with a radiation/diffraction code. We implemented this approach for difference-frequency (slow drift) loads in an open-source frequency-domain floating wind turbine model. We present comparisons against results obtained with radiation/diffraction theory for three reference floating wind turbine designs: the OC3-Hywind spar, the OC4-DeepCwind semisubmersible, and the VolturnUS-S semisubmersible. In general, the results show that the proposed slender-body approach with the correction to approximate wave scattering effects provides useful estimations of the difference-frequency wave loads and the resulting motions of the floater.

17 WIND ENERGY↗

DOE OSTI2026

Joint Optimization of Multimodal Transit Frequency and Shared Autonomous Vehicle Fleet Size with Hybrid Metaheuristic and Nonlinear Programming

Shared autonomous vehicles (SAVs) bring competition to traditional transit services but redesigning multimodal transit network can utilize SAVs as feeders to enhance service efficiency and coverage. This paper presents an optimization framework for the joint multimodal transit frequency and SAV fleet size problem, a variant of the transit network frequency setting problem. The objective is to maximize total transit ridership (including SAV-fed trips and subtracting boarding rejections) across multiple time periods under budget constraints, considering endogenous mode choice (transit, point-to-point SAVs, driving) and route selection, while allowing for strategic route removal by setting frequencies to zero. Due to the problem’s non-linear, non-convex nature and the computational challenges of large-scale networks, we develop a hybrid solution approach that combines a metaheuristic approach (particle swarm optimization) with nonlinear programming for local solution refinement. To ensure computational tractability, the framework integrates analytical approximation models for SAV waiting times based on fleet utilization, multimodal network assignment for route choice, and multinomial logit mode choice behavior, bypassing the need for computationally intensive simulations within the main optimization loop. Applied to the Chicago metropolitan area’s multimodal network, our method illustrates a 33.3% increase in transit ridership through optimized transit route frequencies and SAV integration, particularly enhancing off-peak service accessibility and strategically reallocating resources.

Ng, Max↗

DOE OSTI2025

Low Frequency Vibrational Modes of Two-Dimensional Lead-Free Metal Halide Double Perovskites

2D layered double perovskites of (S-MPA) 4 AgBiI 8 (MPA-AgBiI 8 ) and (S-MPA) 4 CuBiI 8 (MPA-CuBiI 8 ) (S-MPA, S-β-methylphenethylammonium) were synthesized with a hydrothermal method. The crystal structure of MPA-AgBiI 8 was determined using single-crystal X-ray diffraction (scXRD). Powder XRD (pXRD) data suggest that the crystal structure of MPA-CuBiI 8 is more complex than that of MPA-AgBiI 8 . UV-Vis electronic absorption spectra of these perovskites reveal a bandgap of 2.03 eV for both. Short exciton lifetime from time-resolved photoluminescence (TRPL) results and low PL intensity of the Cu-based perovskite suggest a high density of trap states within the bandgap. Low frequency Raman spectra of both materials show distinct peaks and a slightly higher frequency for the Cu-based perovskite than the Ag-based perovskite. Density functional theory (DFT) calculations were conducted to simulate the low frequency Raman spectra and help explain the different phonon modes, which are collective vibrations of metal halide bond bending and stretching within the Ag- and Cu-centered octahedra coupled with MPA libration and twisting within the inorganic layer. The DFT theory also quantified octahedral distortions in the two perovskites. Furthermore, this combined experimental and computational study provides new insights into the low frequency vibrations of 2D perovskites.

Halogens↗

DOE OSTI2024

Integrated optical frequency division for microwave and mmWave generation

Abstract The generation of ultra-low-noise microwave and mmWave in miniaturized, chip-based platforms can transform communication, radar and sensing systems 1–3 . Optical frequency division that leverages optical references and optical frequency combs has emerged as a powerful technique to generate microwaves with superior spectral purity than any other approaches 4–7 . Here we demonstrate a miniaturized optical frequency division system that can potentially transfer the approach to a complementary metal-oxide-semiconductor-compatible integrated photonic platform. Phase stability is provided by a large mode volume, planar-waveguide-based optical reference coil cavity 8,9 and is divided down from optical to mmWave frequency by using soliton microcombs generated in a waveguide-coupled microresonator 10–12 . Besides achieving record-low phase noise for integrated photonic mmWave oscillators, these devices can be heterogeneously integrated with semiconductor lasers, amplifiers and photodiodes, holding the potential of large-volume, low-cost manufacturing for fundamental and mass-market applications 13 .

Science & Technology - Other Topics↗

DOE OSTI2026

Frequency reproducibility of solid-state thorium-229 nuclear clocks

Solid-state thorium-229 ( 229 Th) nuclear clocks are set to provide new opportunities for precision metrology and fundamental physics. Taking advantage of inherent low sensitivity of a nuclear transition to its environment, orders of magnitude more emitters can be hosted in a solid-state crystal compared with current optical lattice atomic clocks. Furthermore, solid-state systems needing only simple thermal control are key to the development of field-deployable compact clocks. Here we explore and characterize the frequency reproducibility of the 229 Th:CaF 2 nuclear clock transition, a key performance metric for all clocks. We measure the transition linewidth and centre frequency as a function of the doping concentration, temperature and time. We report the concentration-dependent inhomogeneous linewidth of the nuclear transition, limited by the intrinsic host crystal properties. We determine an optimal working temperature for the 229 Th:CaF 2 nuclear clock at 196(5) K, at which the first-order thermal sensitivity vanishes. This would enable in situ temperature co-sensing using different quadrupole-split lines, reducing the temperature-induced systematic shift below the 10 −18 fractional frequency uncertainty level. At 195 K, the reproducibility of the nuclear transition frequency is 220 Hz (fractionally 1.1 × 10 −13 ) for two differently doped 229 Th:CaF 2 crystals over 7 months. Furthermore, these results form the foundation for understanding, controlling and harnessing the coherent nuclear excitation of 229 Th in solid-state hosts and for their applications in constraining temporal variations of fundamental constants.

Atomic and molecular physics↗

DOE OSTI2025

Investigating the Impact of Temporal and Directional Traffic Distribution on Crash Frequencies

Safety Performance Functions (SPFs) are mathematical models that establish relationships between the frequency of various crash types and site-specific characteristics, serving as essential tools for traffic safety analysis and roadway design. Traditional SPFs, however, often overlook the temporal fluctuations in traffic flow (such as peak-hour surges) and directional imbalances between opposing traffic streams. These traffic patterns can exacerbate congestion, disrupt driver behavior, and create unexpected conflict points, potentially leading to increased crash frequencies and more severe accidents. In light of this gap, this study aims to explore the potential of incorporating K-factors (representing peak-hour traffic proportions) and D-factors (reflecting the imbalance of directional traffic) into the development of SPFs to assess whether these factors can effectively represent the impact of temporal and spatial traffic distribution on roadway safety. Using crash data from Pennsylvania urban-suburban collector roadways, it is found that the D-factor plays a significant role in predicting the frequency of total crashes, fatal + injury crashes, and angle crashes, with positive coefficient signs indicating that higher directional imbalances correspond to increased crash risks. Similarly, the K-factor emerges as a critical predictor for fatal + injury crashes and rear-end crashes, with negative coefficients suggesting that a more pronounced traffic peak is associated with a reduction in expected crash frequencies. These results highlight the importance of accounting for uneven traffic distribution in both time and direction when developing SPFs, offering deeper insights into crash patterns and supporting more effective safety interventions and roadway designs.

Xu, Guanhao [ORNL] (ORCID:0000000214326357)↗

DOE OSTI2026

Implementation of heterodyne detection of radio frequency waves using phase contrast imaging

An upgrade to the DIII–D phase contrast imaging (PCI) diagnostic for detection of radio frequency waves has been implemented using low-noise optical heterodyning. Electro-optical modulation allows detection of waves with frequencies up to 500 MHz with wide flexibility restricted only by the driver electronics, with continuous adjustability up to 100 MHz and fixed frequency drivers needed for higher frequencies. The PCI diagnostic images the line-integrated plasma density fluctuations and provides absolutely calibrated measurements with good wavenumber resolution.

Rost, J. C. [Massachusetts Institute of Technology↗

DOE OSTI2025

Expanded Accident Scenarios and Frequency Characteristics for a Fast Spectrum Molten Salt Reactor in an Integrated Energy System

Integration of advanced nuclear reactors to industrial processes in an integrated energy system (IES) has many potential advantages. The coupling of nuclear power to varied industrial processes introduces additional accident scenarios unique to the specific systems included in the IES. Similarly, noise in one system of the IES could potentially create negative effects in the other systems. Because of the limited amount of comparable nuclear IES operating experience, there is added value in scoping the inherent behavior of these systems in response to these transients. Here, this paper investigates the safety-related behavior of an open-source IES dynamic model of a fast spectrum molten salt reactor (MSR) powering a regenerative Rankine cycle for electricity production and a hybrid sulfur (HyS) cycle for hydrogen production. The simulations include a loss of cooling water to the Rankine cycle, a loss of sulfur in the HyS cycle, and the frequency characteristics of the entire IES across six orders of magnitude of frequency. The results show safe behavior in response to the two accident scenarios, wherein a disruption in heat transfer leads to increased salt temperatures and a decrease in reactor power. The frequency analysis shows that at higher frequencies, temperature changes propagating through an IES are increasingly damped to the point of negligibility.

Dunkle, Nicholas [Univ. of Tennessee, Knoxville, T↗

DOE OSTI2025

The effect of blue and infrared laser melting frequency on oxide morphology in 304L

Continuous Wave Laser Beam (LB) melting offers control over the localised heating and cooling of melt pools for welding, brazing, additive manufacturing and solidification. Research into laserliquid metal interactions has primarily focused on the heat and mass transport under large thermal gradients imposed by the localised melting conditions. Recent commercial availability of blue (450 nm) wavelength lasers has enabled the printing of material with poor IR (1064) nm attenuation like Cu. However, little research has been conducted into varying input laser frequency and scan rate at fixed absorption to understand the effects of laser light on surface oxide formation and the underlying liquid metal thermodynamic response. Here, this article conducts laser melting of 304L under Blue (450 nm) and Infrared (IR, 1064 nm) laser frequencies and examines their impact on laser oxide thickness, chemistry and coloration. We find that laser frequencies induce changes in the oxide layer thickness and chemistry that cannot be explained using conventional thermal absorption shifts and fluid dynamics. We suggest that light coupling may have thermodynamic implications for the chemical potential of the liquid metal, which may drive the observed phase behaviour. Identifying mechanisms for the tuning of the chemical potential via laser frequency control could enable the ability to control solidification microstructure and atomic ordering in laser welding and additive manufacturing processes.

304L↗

DOE OSTI2024

Frequency-domain computing using nonlinear acoustic-wave device on lithium niobate

Abstract Multiply-accumulation are crucial computing operations in signal processing, numerical simulations, and machine learning. In recent years, optical analog approaches have demonstrated higher computing performance and better power efficiency than their digital counterparts. However, analog computing chips usually need large areas and complex structures for parallel computing, as a single device element only executes one computing operation at a single time. Here, we demonstrate frequency-domain computing using the nonlinear acoustic-wave devices on lithium niobate, featuring a normalized external second-harmonic generation conversion efficiency of ~ 5.7 × 10-4 W-1. The second-order sum-frequency nonlinear process of lithium niobate enables multiplication of inputs encoded in the frequency domain. Compared to the analog schemes, our device features a notably simpler design, and nanofabrication requires only one lift-off. Using a single acoustic-wave device within an area of 0.03 mm2, we can simultaneously conduct over 130,000 multiply-accumulation operations. Our acoustic-wave device shows applications in real and complex vector convolutions and image processing. This demonstration sets the stage for experimental realizations into frequency-domain integrated nonlinear acoustic computing systems, potentially shaping future developments in acoustic neural networks and quantum computing.

chai, mingzhao (ORCID:0009000466226341)↗

DOE OSTI2025

Dependence of ion-cyclotron range of frequencies instabilities on species mix and fast-ion distribution: III. Novel sub-cyclotron modes

Dedicated DIII-D experiments studied instabilities above and below the ion cyclotron frequency by injecting thirteen different neutral beam populations into L-mode plasmas with different thermal compositions of H, D, and 3 He at five different values of toroidal field. Two companion papers describe the results of these experiments in detail. This paper focuses on data and analysis of two instabilities that occur at ${\sim}0.6$ of the deuterium and hydrogen cyclotron frequencies $f_\mathrm {cD}$ and $f_\mathrm {cH}$ in mixed hydrogen and deuterium plasmas. The modes below $f_\mathrm {cD}$ are often driven unstable by deuterium beams but are rarely destabilized by hydrogen beams. The modes below $f_\mathrm {CD}$ are reported here for the first time in a fusion plasma. These $\mathrm{sub-}f_\mathrm {cH}$ modes are only driven by deuterium beams but, unlike the $\mathrm{sub-}f_\mathrm {cD}$ modes, they are only unstable in plasmas with deuterium concentrations that are ${\lesssim}20\%$; they also have a smaller amplitude than the sub-deuterium modes. Addition of fully-ionized 3 He to the plasma has little effect on the sub-cyclotron deuterium modes but is stabilizing for the sub-cyclotron hydrogen modes. The modes are excited in the core and have toroidal mode numbers around 20. These trends are compared with calculations of the growth rate in a simplified model. The theory successfully predicts global Alfvén eigenmode instability with frequencies and mode numbers close to experimental values, the stronger amplitude of the sub-deuterium modes, and the species-mix dependence of the sub-hydrogen modes. Increased damping associated with the ion-ion hybrid, cutoff, and crossover frequencies plausibly accounts for the stabilization of the $\mathrm{sub-}f_\mathrm {cH}$ modes when 3 He is puffed. However, the relative stability of $\mathrm{sub-}f_\mathrm {cH}$ modes during hydrogen injection remains unexplained.

electromagnetic ion cyclotron instability↗

DOE OSTI2026

Radiation modeling and experimental validation of sub-cyclotron frequency microwave synchrotron radiation as a diagnostic tool for runaway electrons in present and future tokamaks

The microwave synchrotron radiation in the sub-cyclotron frequency region has been systematically validated as a diagnostic method for runaway electrons (>1 MeV) with radiation modeling and experiments on the DIII-D tokamak. Experimental observations reveal that sub-cyclotron frequency microwave radiation emerges only after runaway electrons are excited during plasma disruptions. Electron gyro-magnetic radiation modeling confirms that only runaway electrons with energies exceeding 1 MeV can emit radiation in the observed sub-cyclotron frequency band on DIII-D. The synchrotron Razin and Beaming effects are modeled in both the sub-cyclotron and standard Electron Cyclotron Emission (ECE) frequency region. Due to the pronounced beaming effect, the modeling supports that a standard ECE system is insensitive to synchrotron radiation from beamed runaway electrons (p ∥ >> p ⟂ ), but very sensitive to ECE radiation from isotropic suprathermal electrons (100 keV or less). DIII-D experiments further show that combining ECE and sub-cyclotron receivers reveals new insights into transient runaway dynamics during the plateau phase. Certain transient crash events appear only in the sub-cyclotron band or lead to opposite changes on the sub-cyclotron and standard ECE signals, supporting models where transient MHD events can exert a different effect on electrons of different energy levels. This novel diagnostic technique offers a powerful tool for studying and detecting runaway electron dynamics in both present-day and high-field future tokamaks. The diagnostic approach has been extrapolated to the SPARC tokamak, where sub-cyclotron radiation is predicted to respond sensitively and solely to runaway electrons during SPARC’s L-mode startup phase.

Yu, Guanying [Hefei Comprehensive National Science↗

DOE OSTI2025

The Frequency Shift and $Q$ of Disordered Superconducting RF Cavities

Niobium superconducting radio-frequency (SRF) cavities for high-energy accelerator applications have been greatly improved in terms of the quality factor $Q$ by techniques such as Nitrogen doping. However, the mechanisms leading to improvement in $Q$ are still not fully understood. Quite recently the SRF group at Fermilab measured anomalies in the frequency shift of N-doped SRF Niobium cavities near the transition temperature. Here we report our theoretical analysis of these results based on the microscopic theory of superconductivity that incorporates anisotropy of the superconducting gap and inhomogeneous disorder in the screening region of the SRF cavities. We are able to account for frequency shift anomalies very close to $T_c$ on the order of fractions of 1 kHz. Our results for the frequency shift and Q are in good agreement with the experimental data reported for all four N-doped Nb SRF cavities by Bafia et al. We also compare our theory with an earlier report on a Nb sample measured at 60 GHz. In addition, we show that the quality factor calculated theoretically has a peak of upper convexity with the largest $Q$ at intermediate levels of disorder. For strong disorder, i.e. the dirty limit, pair breaking in the presence of disorder and screening currents limits the $Q$.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Digital Filter Design for Point-on-Wave Sensors: Highlighting Frequency Response Limitations and Enhancing Grid Simulation Accuracy

Data is proving to be the backbone of today's and, more importantly, tomorrow's grid. As the system changes and introduces fast-acting devices like power electronics, overall observability tends to decrease from the utility point-of-view. This can be mitigated by adding more high-fidelity sensors onto the grid, although this incurs a cost. These sensors are never ideal, and each have unique frequency responses that may influence the data produced. This may, in turn, impact the protection and control of the power grid. This paper presents a methodology of representing these point-on-wave sensors digitally by estimating digital-filter representations of them, thereby introducing means of improving the sensor models used in electromagnetic-transient (EMT) simulations. This may help with identifying potential high-frequency, sensor-induced distortions, and system resonance compensation. Three commercial-grade medium-voltage point-on-wave sensors are utilized in a lab environment to obtain experimental frequency responses with a frequency sweep, and it is shown that both Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) filter representations may approximate these responses with varying degrees of accuracy, though each has their own strengths and weaknesses. It is found that, in general, FIR estimation better approximates these sensors than IIR estimation does.

Wilson, Aaron [ORNL] (ORCID:0000000327331697)↗

DOE OSTI2024

Polarization–frequency hyperentangled photons: generation, characterization, and manipulation

Frequency-bin encoding is massively parallelizable and robust for optical fiber transmission. When coupled with an additional degree of freedom (DoF), the expansion of the Hilbert space allows for deterministic controlled operations between two DoFs within a single photon. Such capabilities, when combined with photonic hyperentanglement, are of great value for quantum communication protocols, including dense coding and single-copy entanglement distillation. In this talk, we present an all-fiber-coupled, ultrabroadband polarization–frequency hyperentangled source and conduct comprehensive quantum state tomography across multiple dense wavelength division multiplexing channels spanning the optical C+L-band (1530–1625 nm). In addition, we design and implement a high-fidelity controlled-NOT (cnot) operation between polarization and frequency DoFs by exploiting electro-optic phase modulation within a fiber Sagnac loop. Collectively, our hyperentangled source and two-qubit gate should unlock new opportunities for harnessing polarization–frequency resources in established telecommunication fiber networks for future quantum applications.

Lu, Hsuan-Hao↗

DOE OSTI2025

Improved Calculation of the Young’s Modulus of Rectangular Prisms from Their Resonant Frequency Overtones by Identifying Appropriate Shear Constants

Young’s modulus is an important parameter for characterizing the strength of, and wave propagation through, a given material. This study improves the estimation of Young’s modulus using the impulse excitation technique based on an experimental analysis of 19 borosilicate glass bars. Analysis of the frequency equations relating Young’s modulus to the out-of-plane and in-plane flexural resonant frequencies of rectangular prisms has been conducted for both the fundamental frequency and its overtones at higher orders of vibration. Furthermore, the Young’s moduli of three novaculite rocks with various porosities were then measured up to the seventh order of vibration to validate the optimum shear constant equation for estimating Young’s modulus. Young’s modulus was found to be nearly frequency independent for these rock samples.

Impulse excitation↗