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DOE OSTI2023

Large Angle Deviation in Grid-Following IBRs Upon Grid Voltage Dip

In the 2021 Texas Odessa large-scale solar PV tripping events, phase-locked-loop (PLL) loss of synchronism is identified as a major cause of solar PV tripping. When solar PVs detected a large phase angle deviation (e.g., 10 degrees), tripping commands were initiated. Here, the large phase angle deviation was triggered by a transmission line fault 200 miles away, which in turn led to approximately 30% voltage drop in the 345-kV system. This paper offers a plausible reason why grid-following inverter-based resources (IBRs) may experience a large angle deviation upon grid voltage dip. Critical operating conditions contributing to such phenomena are identified via analysis and their effects are demonstrated using electromagnetic transient (EMT) simulation. Furthermore, the effect of converter control, e.g., grid-following control vs. grid-forming control, is examined. It is found from EMT simulation results that frequency and voltage control are helpful in mitigating angle deviation. Furthermore, linear block diagrams are derived to examine why frequency control can effectively suppress large angle deviation.

14 SOLAR ENERGY↗

DOE OSTI2025

Spectral distortions to momentum and scalar exchanges by non-turbulent motion and patchy landscape variability

Modifications to the spectra of turbulent velocity and scalars and co-spectra of vertical fluxes of momentum and scalars due to patchy landscape heterogeneity and non-stationarity are explored for a Mediterranean ecosystem. About 9 months of high frequency measurements of the three velocity components, water vapor concentration, carbon dioxide concentration, and air temperature were analyzed for different seasons (spring/summer) and prevalent wind directions (southeast/northwest). The two wind directions sampled a contrast of clumped and patchy landscape comprised of olive trees (southeast) and wall bounded flow disturbed by the presence of few upwind trees (northwest). The measured spectra and co-spectra were also compared to theoretical scaling forms from stationary, planar homogeneous flow, in the absence of subsidence as derived from the Kansas experiment. To assess the role of low frequency non-turbulent motion on the spectral and co-spectral content, a 5-min Fourier cutoff was introduced and the analysis was limited to near-neutral conditions where the boundary layer depth is shallow compared to its unstable counterpart. It was shown that the velocity statistics were not appreciably impacted by the low-frequency motion causing non-stationarity. Moreover, the turbulent scalar fluxes were also shown not to be significantly impacted by such low frequency motion. The scalar variances were impacted, especially the water vapor variance and its concomitant spectral shape. When the non-turbulent motion was filtered, the scalar spectra at low wavenumbers followed expectations from the so-called attached eddy hypothesis (i.e. exhibited a $k^{-1}_x$ scaling with $k_x$ defining the longitudinal wavenumber) applicable for near-neutral conditions. For momentum co-spectra, the canonical shapes from the Kansas experiment appear to describe well the measurements here and in both dominant directions and seasons with some adjustment to the integral time scales based on wind direction. For the scalar co-spectra, deviations from the Kansas experiment were prevalent. The most noticeable and surprising deviations were their slow decay with increased sampling frequency at inertial subrange scales. This slow decay was shown not to contribute appreciably to the overall scalar fluxes. At those fine scales, predictions from local isotropy were expected to hold. The scalar co-spectral deviations from local isotropy were then discussed using a simplified co-spectral budget model where scalar–scalar co-spectra naturally emerged and the interplay between landscape heterogeneity and a scale-dependent pressure-scalar de-correlation time was postulated. It is also envisaged that the findings here offer a preliminary template for analyzing eddy-covariance data in situations that deviate from ideal conditions, especially regarding low-frequency modulations of scalar spectra and vertical scalar flux co-spectra.

Canopy turbulence↗

DOE OSTI2021

Reflectivity and spectrum of relativistic flying plasma mirrors

Flying plasma mirrors induced by intense lasers via laser wake field acceleration scheme have been proposed as a promising way to generate few-cycle EUV or x-ray lasers. In addition, if such a relativistic plasma mirror can accelerate, then it would serve as an analog black hole to investigate the information loss paradox associated with the black hole Hawking evaporation. Among these applications, the reflectivity, which is usually frequency-dependent, would affect the outgoing photon spectrum and, therefore, impact on the analysis of the physics under investigation. In this paper, these two issues are investigated analytically and numerically with one-dimensional particle-in-cell simulations. Based on our simulation results, we propose a new model that provides a better estimate of the reflectivity than those studied previously. Moreover, we found that the peak frequency of the reflected spectrum of a Gaussian incident wave deviates from the expected value, 4γ 2 ω, due to the dependence of reflectivity on the frequency of the incident wave.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Concordant Mode Approach (CMA): Vibrational Analysis of New and Upgraded Intermolecular Benchmarks for Noncovalent Bonding

The Concordant Mode Approach (CMA) is a novel method that offers tremendous potential for increasing the system size and the level of theory attainable in quantum chemical computations of molecular vibrational frequencies. To investigate the extension of CMA to intermolecular vibrations, computations with coupled cluster singles and doubles with perturbative triples theory [CCSD(T)] using two augmented correlation-consistent polarized-valence triple-ζ basis sets (aug-cc-pVTZ or h-aug-ccpVTZ) were performed on 17 prototypical loosely bound complexes of hydrogen-bonded, dispersion, and mixed character. These Level A results provide new and upgraded benchmarks for noncovalent bonding and a severe test for CMA vibrational analyses. The Level A target frequencies were recovered remarkably well using second-order Møller−Plesset perturbation theory (MP2) with h-aug-cc-pVTZ for generating the underlying (Level B) normal modes of the CMA scheme. Employing this Level B within the lowest-rung CMA-0A method reproduces the 435 benchmark frequencies with a mean absolute error (MAE) of 0.23 cm −1 and a corresponding standard deviation (σ) of 0.84 cm −1 ; strikingly, the corresponding subset of 106 interfragment frequencies exhibits MAE = 0.34 cm −1 and σ = 0.90 cm −1 . Subsequent application of the higher-rung CMA-2A scheme eliminates all outliers and reduces the overall MAE to a minuscule 0.08 cm −1 with the inclusion of only 3.0% of the off-diagonal couplings not accounted for by CMA-0A. Accordingly, the highly efficient CMA methodology proves to be robust even for vibrations on flat potential energy surfaces.

Aromatic compounds↗

DOE OSTI2021

Isotopic dependence of the frequency of optical vibrations in molybdenum monohydride

We show that it is currently known that three hydrides – PdH x , MoH x , and TiH x – exhibit an inverse isotope effect in superconductivity. Namely, the phase with a heavier hydrogen isotope, deuterium, has a higher critical temperature. Hydrides and deuterides of palladium have intensively been studied both experimentally and theoretically, but the origin of the isotope effect has not been established with certainty. The commonly accepted explanation is that the effect is likely to be due to the strong anharmonicity of the optical hydrogen vibrations, which was considered to be responsible for the large deviation of the ratio of the fundamental optical frequencies ω H /ω D = 1.51 from the harmonic value $\sqrt{2}$ ≈ 1.41. In the present paper, powder samples of MoH 1.1(1) and MoD 1.07(3) were synthesized under a hydrogen / deuterium pressure of several gigapascals and studied by inelastic neutron scattering (INS) at ambient pressure and T = 10 K. The INS study demonstrated that optical vibrations of H atoms in MoH 1.1 and D atoms in MoD 1.07 are harmonic and the ratio of fundamental optical frequencies ω H /ω D = 1.44 is close to the harmonic value $\sqrt{2}$ ≈ 1.41. This shows that anharmonicity is not a necessary condition for the presence of the inverse isotope effect. The MoD 1.07 sample was additionally studied by neutron diffraction (ND) at ambient pressure and T = 100 K. In agreement with previous ND results for MoH 1.2 , the ND study of MoD 1.07 showed that deuterium atoms occupied almost all octahedral interstitial sites in its hexagonal close-packed metal lattice and formed a NiAs-type crystal structure with the composition close to MoD. The overstoichiometric composition MoD 1.07 of the deuteride is likely to result from a small fraction D/Mo ~ 0.07 of deuterium atoms partially occupying the tetrahedral interstices.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Importance of Considering Near-Surface Attenuation in Earthquake Source Parameter Estimation: Insights from Kappa at a Dense Array in Oklahoma

ABSTRACT Separating earthquake source spectra from propagation effects is challenging. The propagation effect contains a site-dependent term related to the high attenuation of shallow sediments. Neglecting the site-dependent attenuation can cause large biases and scattering in the corner-frequency (fc) estimates, resulting in significant stress-drop deviations. In this study, we investigate shallow attenuation at the LArge-n Seismic Survey in Oklahoma (LASSO) and site-related biases and scattering in source parameter measurements due to simplified attenuation models. We measure the high-frequency spectral decay parameter kappa on the vertical acceleration spectra of regional earthquakes (125 km away). The site-dependent kappa (κ0,acc) suggests that attenuation increases rapidly at shallow depth and is highly site-dependent. 10%–75% of the attenuation is site-dependent for S waves and even larger for P waves. The quality factor for S waves (QS) ranges from 10 to 100 in the upper 400 m. QP for P waves is mostly below 10 within the same depth. The Quaternary sediments tend to be more attenuating (QS<30), but the Permian rocks also can have high attenuation. We demonstrate that using a non-site-dependent attenuation model in single-spectra fitting leads to large scattering in fc estimates among stations with apparent good fits. The apparent fc can significantly deviate when the range of site-dependent kappa is large or with a higher assumed source spectral fall-off rate n. The biases in apparent fc depend on site condition and distance; however, the correlation between fc and these factors might not be obvious, depending on model assumptions. An apparent increase of stress drop with magnitude in a previous study for local microearthquakes (1.3

Chang, Hilary↗

DOE OSTI2021

Signatures of deconfined quark phases in binary neutron star mergers

We investigate the quark deconfinement phase transition in the context of binary neutron star (BNS) mergers. We employ a new finite-temperature composition-dependent equation of state (EOS) with a first order phase transition between hadrons and deconfined quarks to perform numerical relativity simulations of BNS mergers. Here, the softening of the EOS due to the phase transition causes the merger remnants to be more compact and to collapse to a black hole (BH) at earlier times. The phase transition is imprinted on the postmerger gravitational wave (GW) signal duration, amplitude, and peak frequency. However, this imprint is only detectable for binaries with sufficiently long-lived remnants. Moreover, the phase transition does not result in significant deviations from quasi-universal relations for the postmerger GW peak frequency. We also study the impact of the phase transition on dynamical ejecta, remnant accretion disk masses, r-process nucleosynthetic yields and associated electromagnetic (EM) counterparts. While there are differences in the EM counterparts and nucleosynthesis yields between the purely hadronic models and the models with phase transitions, these can be primarily ascribed to the difference in remnant collapse time between the two. An exception is the non-thermal afterglow caused by the interaction of the fastest component of the dynamical ejecta and the interstellar medium, which is systematically boosted in the binaries with phase transition as a consequence of the more violent merger they experience.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Cosmological evolution of ultralight axionlike scalar fields

In this paper, we examine the cosmological evolution of ultralight axionlike (ULA) scalar fields with potentials of the form V(Φ)=m 2 f 2 [1–cos(Φ/f)] n , with particular emphasis on the deviation in their behavior from the corresponding small–Φ power-law approximations to these potentials: V(Φ)∝Φ 2n . We show that in the slow-roll regime, when Φ ˙2 /2 $\ll$ V(Φ), the full ULA potentials yield a more interesting range of possibilities for quintessence than do the corresponding power law approximations. For rapidly oscillating scalar fields, we derive the equation of state parameter and oscillation frequency for the ULA potentials and show how they deviate from the corresponding power-law values. We derive an analytic expression for the equation of state parameter that better approximates the ULA value than does the pure power-law approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Infrared spectroscopy of the syn -methyl-substituted Criegee intermediate: A combined experimental and theoretical study

An IR–vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR–VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081 cm−1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Chemistry↗

DOE OSTI2022

Impact of Open Communication Networks on Load Frequency Control with Plug-in Electric Vehicles by Cyber-Physical Dynamic Co-Simulation: Preprint

With the increasing electrification of the transportation sector, vehicle to grid (V2G) control technologies are promising to improving system frequency stability. However, these control technologies might require non-traditional communication supports. This paper investigates the impacts of electric vehicles (EVs) V2G on power system frequency regulation considering communication variations through transmission-distribution-communication (TDC) dynamic simulation. The simulation model is built based on our previously developed open-source transmission-and-distribution (T&D) dynamic co-simulation framework. Here, we add the communication variation functions (i.e. delay and packet loss) to complete the TDC simulation framework. In the case studies, practical communication variation scenarios are considered when the system experiencing an N-1 generation trip contingency. The considered scenarios include communication delay and packet loss using both homogeneous and heterogeneous assumptions. The delay and packet loss rate are the same in all communication channels in the homogeneous case but varies in the heterogeneous case. The results show the communication delay has an obvious impact on the frequency recovery compared to the communication packet drop. The impacts of the standard deviations of communication delay time and packet drop rate are not significant. The outcomes of this work can help improve the EV frequency regulation services and provide robust and effect supports to the grid.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2021

Direct driving of electronic and phononic degrees of freedom in a honeycomb bilayer with infrared light

Here, we study theoretically AB-stacked honeycomb bilayers driven by light in resonance with an infrared phonon within a tight-binding description. We characterize the phonon properties of honeycomb bilayers with group theory and construct an electronic time-dependent tight-binding model for the system following photoexcitation in resonance with an infrared phonon. We adopt an atomically adiabatic approximation [V. Mohanty and E. J. Heller, Proc. Natl. Acad. Sci. 116, 18316 (2019)] to describe classically vibrating nuclei, but obtain the Floquet quasienergy spectrum associated with the time-dependent model exactly. We introduce a general scheme to disentangle the complex low-frequency Floquet spectrum to elucidate the relevant Floquet bands. As a prototypical example, we consider bilayer graphene. We find that light in the low-frequency regime can induce a band gap in the quasienergy spectrum in the vicinity of the $K$ points even if it is linearly polarized, in contrast with the expectations within the Born-Oppenheimer approximation and the high-frequency regime. Finally, we analyze the diabaticity of the driven electron and driven phonon processes and find contrasting effects on the autocorrelation functions at the same driving frequency: Driven phonons preserve the character of the initial state while driven electrons exhibit strong deviations within a few drive cycles. The procedure outlined here can be applied to other materials to describe the combined effects of low-frequency light on phonons and electrons.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2024

Convergent Concordant Mode Approach for Molecular Vibrations: CMA-2

The concordant mode approach (CMA) is a promising new scheme for dramatically increasing the system size and level of theory achievable in quantum chemical computations of molecular vibrational frequencies. Here, we achieve advances in the CMA hierarchy by computations targeting CCSD(T)/cc-pVTZ (coupled cluster singles and doubles with perturbative triples using a correlation-consistent polarized-valence triple-ζ basis set) benchmarks within the G2 molecular test set, executing a statistical analysis for 1501 frequencies from 111 compounds and then separately solving the refractory case of pyridine. First, MP2/cc-pVTZ (second-order Møller–Plesset perturbation theory with the same basis set) proves to be an excellent and preferred choice for generating the underlying (Level B) normal modes of the CMA scheme. Utilizing this Level B within the CMA-0A method reproduces the 1501 benchmark frequencies with a mean absolute error (MAE) of only 0.11 cm –1 and an attendant standard deviation of 0.49 cm –1 . Second, a convergent CMA-2 method is constituted that allows efficient computation of higher level (Level A) frequencies to any reasonable accuracy threshold by using only Hartree–Fock (HF) and MP2 or density functional theory (DFT) data to generate ξ parameters, which select the sparse off-diagonal force field elements for explicit evaluation at Level A. When Level B = MP2/cc-pVTZ, a cutoff of ξ = 0.02 provides an average maximum absolute error per molecule of only 0.17 cm –1 by incurring merely a 33% increase in average cost over CMA-0A. This CMA-2 method also eradicates the 4 problematic CMA-0A outliers of pyridine with even less effort (ξ = 0.04, 22% increase). Finally, the newly developed CMA procedures are shown to be highly successful when applied to 1-(1H-pyrrol-3-yl)ethanol, a new test molecule with diverse types of vibration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Factors That Influence Variability in Stress-Drop Measurements Using Spectral Decomposition and Spectral-Ratio Methods for the 2019 Ridgecrest Earthquake Sequence

Stress drop is a fundamental parameter related to earthquake source physics, but is hard to measure accurately. To better understand how different factors influence stress-drop measurements, we compare two different methods using the Ridgecrest stress-drop validation data set: spectral decomposition (SD) and spectral ratio (SR), each with different processing options. Here, we also examine the influence of spectral complexity on source parameter measurement. Applying the SD method, we find that frequency bandwidth and time-window length could influence spectral magnitude calibration, while depth-dependent attenuation is important to correctly map stress-drop variations. For the SR method, we find that the selected source model has limited influence on the measurements; however, the Boatwright model tends to produce smaller standard deviation and larger magnitude dependence than the Brune model. Variance reduction threshold, frequency bandwidth, and time-window length, if chosen within an appropriate parameter range, have limited influence on source parameter measurement. For both methods, wave type, attenuation correction, and spectral complexity strongly influence the result. The scale factor that quantifies the magnitude dependence of stress drop show large variations with different processing options, and earthquakes with complex source spectra deviating from the Brune-type source models tend to have larger scale factor than earthquakes without complexity. Based on these detailed comparisons, we make a few specific suggestions for data processing workflows that could help future studies of source parameters and interpretations.

58 GEOSCIENCES↗

DOE OSTI2025

Molecular-Level Insights into the NMR Relaxivity of Gadobutrol Using Quantum and Classical Molecular Simulations

MRI is an indispensable diagnostic tool in modern medicine; however, understanding the molecular-level processes governing NMR relaxation of water in the presence of MRI contrast agents remains a challenge, hindering the molecular-guided development of more effective contrast agents. By using quantum-based polarizable force fields, the first-of-its-kind molecular dynamics (MD) simulations of Gadobutrol are reported where the 1 H NMR longitudinal relaxivity r 1 of the aqueous phase is determined without any adjustable parameters. The MD simulations of r 1 dispersion (i.e., frequency dependence) show good agreement with measurements at frequencies of interest in clinical MRI. Importantly, the simulations reveal key insights into the molecular level processes leading to r 1 dispersion by decomposing the NMR dipole–dipole autocorrelation function G(t) into a discrete set of molecular modes, analogous to the eigenmodes of a quantum harmonic oscillator. The molecular modes reveal important aspects of the underlying mechanisms governing r 1 , such as its multiexponential nature and the importance of the second eigenmodal decay. By simply analyzing the MD trajectories on a parameter-free approach, the Gadobutrol simulations show that the outer-shell water contributes ∼50% of the total relaxivity r 1 compared to the inner-shell water, in contrast to simulations of (nonchelated) gadolinium-aqua where the outer shell contributes only ∼15% of r 1 . The deviation between simulations and measurements of r 1 below clinical MRI frequencies is used to determine the low-frequency electron-spin relaxation time for Gadobutrol, in good agreement with independent studies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Uncertainty Analysis and Software Verification

Uncertainty analyses are an important part of calibrations and testing. They allow researchers insight on how to reduce and mitigate errors in testing. Each device used in testing introduces error in a system, as well as other sources such as environmental conditions, electronics, analog to digital, and random errors. Each source is carefully examined to identify how much error it introduces to a system. These sources are then combined using various methods of uncertainty calculations. To verify and validate software, a manual calculation is required to ensure the software is performing as intended. Using Excel to verify the calculations, we can identify discrepancies within the software. The root of the sum of the squares uncertainty (RSS) is used to find the combined uncertainty of a device at one and two standard deviations of the mean. Calibrations on accelerometers are performed using a vibration system along with a back-toback reference accelerometer. The vibration system takes a reference point at 100Hz frequency at 10g amplitude. The sensitivities are collected at each dialed in frequency. The sensitivity of the device represents the electrical output of the UUT (mV, pC, etc.) per unit of acceleration (g). The full history of sensitivities of selected accelerometers are used to find the averaged, standard deviation, and uncertainty of the device at each frequency tested. The uncertainty calculations from excel and the software are then compared.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Tropical Oceanic Influences on Observed Global Tropical Cyclone Frequency

Abstract The global tropical cyclone (TC) number has historically been relatively constant from year‐to‐year, however, the reason remains unknown. Furthermore, climate projections are inconclusive regarding future global TC frequency changes. Here, we investigated years in which observed global TC activity deviated from the mean and potential links to ocean drivers from 1980 to 2021. We found that the annual global number of named storm days and accumulated cyclone energy (ACE) were significantly linked with El Niño–Southern Oscillation (ENSO) and the Atlantic Meridional Mode (AMM). La Niña and positive AMM are associated with the bottom percentiles of both TC metrics, and vice versa for El Niño and negative AMM. The ENSO Longitude Index explains variability in annual global named storm days and ACE as well as the Niño 3.4 index. This research reveals that reliable future projections of ENSO are necessary, but not sufficient, to understand future changes in global TC frequency.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2025

Weather and climate extremes in a changing Arctic

Weather and climate extremes are increasingly occurring in the Arctic. Here, in this Review, we evaluate historical and projected changes in rare Arctic extremes across the atmosphere, cryosphere and ocean and elucidate their driving mechanisms. Clear shifts occur in mean and extreme distributions after ~2000. For instance, pre-2000 to post-2000 observational probabilities of 1.5 standard deviation events increase by 20% for atmospheric heat waves, 76.7% for Atlantic layer warm events, 83.5% for Arctic sea ice loss and 62.9% for Greenland Ice Sheet melt extent — in many cases, low probability, rare extreme events in the early period become the norm in the latter period. These observed changes can be explained using a ‘pushing and triggering’ concept, representing interplay between external forcing and internal variability: long-term warming destabilizes the climate system and ‘pushes’ it to a new state, allowing subsequent variability associated with large-scale atmosphere–ocean–ice interactions and synoptic systems to ‘trigger’ extreme events over different timescales. Ongoing anthropogenic warming is expected to further increase the frequency and magnitude of extremes, such that simulated probabilities of 1.5 standard deviation events increase by 72.6% for atmospheric heat waves, 68.7% for Atlantic layer warm events and 93.3% for Greenland Ice Sheet melt rate between historic (1984–2014) and future (2069–2099) periods under a very high emission scenario. Future research should prioritize the development of physically based metrics, enhance high-resolution observation and modelling capabilities and improve understanding of multiscale Arctic climate drivers.

atmospheric dynamics↗

DOE OSTI2024

Towards the Flexibility of HVDC-Interconnected Systems: A Novel Emergency Freqeuncy Response Model

In this paper, we propose a novel multi-time scale emergency frequency response model by unlocking the flexibility of High Voltage Direct Current (HVDC) systems. Unlike assigning power ramping rates for FACTS to regulate frequency in traditional methods, this paper designs a step-change electromagnetic power frequency response (EPFR) scheme, by leveraging the temporal over/under DC voltage capability of HVDC. Wherein the Kullback-Leibler Divergence is adopted to convexify the modified swing equation after integrating the step-change power. Further, to avoid the complicated differential equations, we equivalently reformulate the duration limits of DC voltage deviation into the HVDC decreasing power ramping rates, which participate in the system primary frequency response. Finally, the new steady-state operation level of HVDC is involved with the secondary frequency response. As a result, an improved three-level algorithm is developed to solve the model, wherein the instant step-change, primary, and secondary frequency response are coordinated together. After applying the proposed frequency response scheme on the test system, the EPFR is validated to effectively provide the most instantaneous supports when faced with bulk power loss due to extreme contingencies, and the resilience is ensured within acceptable expenditures.

Jiang, Sufan↗