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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 1,639 records · Page 91
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Workability Characteristics and Deformation Mechanisms of Die-Cast AM60 and AZ91 Magnesium Alloys: Correlation with Processing Maps

Thermo-mechanical deformation behavior of the die-cast AM60 and AZ91 alloys was assessed by performing uniaxial compression tests on Gleeble 3800 simulator under different temperatures and strain rate conditions. Low-temperature deformation behavior of both alloys was accessed at 25, 100, and 150 °C, at the strain rates of 0.1 and 1 s{sup −1}. Processing maps at a true strain of 0.5 were generated to study the intrinsic hot workability of AM60 and AZ91 alloys. Optimum processing windows were identified, and the evolution of microstructures and textures was correlated with the imposed deformation conditions. The processing map for the AM60 alloy exhibited three dynamic recrystallization (DRX) domains in the ranges: (1) 320-400 °C and 0.2-1.5 s{sup −1}, (1A) 300-325 °C and 0.1-0.2 s{sup −1}, and (2) 360-400 °C and 3-5 s{sup −1}. In Domain 1, DRX occurred predominantly by pyramidal slip and recovery mechanisms by cross-slip as confirmed by the randomized textures. Deformation in Domain 1A is by the combination of basal and prismatic slip. In Domain 2, dynamic recovery was a softening mechanism controlled by the climb. The processing map for AZ91 alloy exhibited two DRX domains in the ranges: (1) 260-310 °C and 0.1-0.5 s{sup −1} and (2) 325-350 °C and 0.8-3 s{sup −1}. The rate-controlling mechanism was climb by lattice self-diffusion in Domain 1 and by grain boundary self-diffusion in Domain 2. Both alloys exhibited flow instability at 200 and 250 °C, and therefore, they were unsuitable for processing at these temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Stochastic inverse problems: Models and metrics

In past work, we introduced model-based inverse methods, and applied them to problems in which the anomaly could be reasonably modeled by simple canonical shapes, such as rectangular solids. In these cases the parameters to be inverted would be length, width and height, as well as the occasional probe lift-off or rotation. We are now developing a formulation that allows more flexibility in modeling complex flaws. The idea consists of expanding the flaw in a sequence of basis functions, and then solving for the expansion coefficients of this sequence, which are modeled as independent random variables, uniformly distributed over their range of values. There are a number of applications of such modeling: 1. Connected cracks and multiple half-moons, which we have noted in a POD set. Ideally we would like to distinguish connected cracks from one long shallow crack. 2. Cracks of irregular profile and shape which have appeared in cold work holes during bolt-hole eddy-current inspection. One side of such cracks is much deeper than other. 3. L or C shaped crack profiles at the surface, examples of which have been seen in bolt-hole cracks. By formulating problems in a stochastic sense, we are able to leverage the stochastic global optimization algorithms in NLSE, which is resident in VIC-3D®, to answer questions of global minimization and to compute confidence bounds using the sensitivity coefficient that we get from NLSE. We will also address the issue of surrogate functions which are used during the inversion process, and how they contribute to the quality of the estimation of the bounds.

36 MATERIALS SCIENCE↗
DOE OSTI2016

CHIRP-Like Signals: Estimation, Detection and Processing A Sequential Model-Based Approach

Chirp signals have evolved primarily from radar/sonar signal processing applications specifically attempting to estimate the location of a target in surveillance/tracking volume. The chirp, which is essentially a sinusoidal signal whose phase changes instantaneously at each time sample, has an interesting property in that its correlation approximates an impulse function. It is well-known that a matched-filter detector in radar/sonar estimates the target range by cross-correlating a replicant of the transmitted chirp with the measurement data reflected from the target back to the radar/sonar receiver yielding a maximum peak corresponding to the echo time and therefore enabling the desired range estimate. In this application, we perform the same operation as a radar or sonar system, that is, we transmit a “chirp-like pulse” into the target medium and attempt to first detect its presence and second estimate its location or range. Our problem is complicated by the presence of disturbance signals from surrounding broadcast stations as well as extraneous sources of interference in our frequency bands and of course the ever present random noise from instrumentation. First, we discuss the chirp signal itself and illustrate its inherent properties and then develop a model-based processing scheme enabling both the detection and estimation of the signal from noisy measurement data.

42 ENGINEERING↗
DOE OSTI2022

Random quasi-phase-matching for pulse characterization from the near to the long wavelength infrared

Experiments requiring ultrafast laser pulses require a full characterization of the electric field to glean meaning from the experimental data. Such characterization typically requires a separate parametric optical process. As the central wavelength range of new sources continues to increase so too does the need for nonlinear crystals suited for characterizing these wavelengths. Here we report on the use of poly-crystalline zinc selenide as a universal nonlinear crystal in the frequency resolved optical gating characterization technique from the near to long-wavelength infrared. Due to its property of random quasi-phase-matching it’s capable of phase matching second-harmonic and sum-frequency generation of ultra-broadband pulses in the near and long wavelength infrared, while being crystal orientation independent. With the majority of ultra-fast laser sources being in this span of wavelengths, this work demonstrates a greatly simplified approach towards ultra-fast pulse characterization spanning from the near to the long-wavelength infrared. To our knowledge there is no single optical technique capable of such flexible capabilities.

Davis, Brandin (ORCID:0000000166964548)↗
DOE OSTI2026

Paradigm for universal quantum information processing with integrated acousto-optic frequency beamsplitters

Frequency-bin encoding offers tremendous potential in quantum photonic information processing, in which a single waveguide can support hundreds of lightpaths in a naturally phase-stable fashion. This stability, however, comes at a cost: arbitrary unitary operations can be realized by cascaded electro-optic phase modulators and pulse shapers, but require nontrivial numerical optimization for design and have thus far been limited to discrete tabletop components. In this article, we propose, formalize, and computationally evaluate a new paradigm for universal frequency-bin quantum information processing using acousto-optic scattering processes between distinct transverse modes. We show that controllable phase matching in intermodal processes enables 2 × 2 frequency beamsplitters and transverse-mode-dependent phase shifters, which together comprise cascadable FRequency-transverse-mODe Operations (FRODOs) that can synthesize any unitary via analytical decomposition procedures. Modeling the performance of both random gates and discrete Fourier transforms, we demonstrate the feasibility of high-fidelity quantum operations with existing integrated photonics technology, highlighting prospects of parallelizable operations achieving 100% bandwidth utilization. Our approach is realizable with CMOS technology, opening the door to scalable on-chip quantum information processing in the frequency domain.

Lukens, Joseph M. [Purdue Univ., West Lafayette, I↗
DOE OSTI2021

Development of a Random-Forest Cloud-Regime Classification Model Based on Surface Radiation and Cloud Products

Various methods have been developed to characterize cloud type, otherwise referred to as cloud regime. These include manual sky observations, combining radiative and cloud vertical properties observed from satellite, surface-based remote sensing, and digital processing of sky imagers. While each method has inherent advantages and disadvantages, none of these cloud-typing methods actually includes measurements of surface shortwave or longwave radiative fluxes. Here, a method that relies upon detailed, surface-based radiation and cloud measurements and derived data products to train a random-forest machine-learning cloud classification model is introduced. Measurements from five years of data from the ARM Southern Great Plains site were compiled to train and independently evaluate the model classification performance. A cloud-type accuracy of approximately 80% using the random-forest classifier reveals that the model is well suited to predict climatological cloud properties. Furthermore, an analysis of the cloud-type misclassifications is performed. While physical cloud types may be misreported, the shortwave radiative signatures are similar between misclassified cloud types. From this, we assert that the cloud-regime model has the capacity to successfully differentiate clouds with comparable cloud–radiative interactions. Therefore, we conclude that the model can provide useful cloud-property information for fundamental cloud studies, inform renewable energy studies, and be a tool for numerical model evaluation and parameterization improvement, among many other applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A dictionary learning algorithm for compression and reconstruction of streaming data in preset order

There has been an emerging interest in developing and applying dictionary learning (DL) to process massive datasets in the last decade. Many of these efforts, however, focus on employing DL to compress and extract a set of important features from data, while considering restoring the original data from this set a secondary goal. On the other hand, although several methods are able to process streaming data by updating the dictionary incrementally as new snapshots pass by, most of those algorithms are designed for the setting where the snapshots are randomly drawn from a probability distribution. In this paper, we present a new DL approach to compress and denoise massive dataset in real time, in which the data are streamed through in a preset order (instances are videos and temporal experimental data), so at any time, we can only observe a biased sample set of the whole data. Here, our approach incrementally builds up the dictionary in a relatively simple manner: if the new snapshot is adequately explained by the current dictionary, we perform a sparse coding to find its sparse representation; otherwise, we add the new snapshot to the dictionary, with a Gram-Schmidt process to maintain the orthogonality. To compress and denoise noisy datasets, we apply the denoising to the snapshot directly before sparse coding, which deviates from traditional dictionary learning approach that achieves denoising via sparse coding. Compared to full-batch matrix decomposition methods, where the whole data is kept in memory, and other mini-batch approaches, where unbiased sampling is often assumed, our approach has minimal requirement in data sampling and storage: i) each snapshot is only seen once then discarded, and ii) the snapshots are drawn in a preset order, so can be highly biased. Through experiments on climate simulations and scanning transmission electron microscopy (STEM) data, we demonstrate that the proposed approach performs competitively to those methods in data reconstruction and denoising.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A Quick Overview of the Extended Feynman Project

The low natural background rates and the penetrating nature of neutron radiation makes neutron detection a good method for quantifying and accounting for large amounts of special nuclear material capable of neutron induced fission and fission chains. Fission is one of the few natural processes that produces time-correlated neutrons, the others are spallation-type processes (e.g. (n,Xn), cosmic induced background, etc) which have low but measurable rates in common terrestrial material. The high rates of most transuranic spontaneous fission sources of even a gram or less usually swamp any cosmic induced background rate but even Kilogram quantities of natural uranium produce neutrons only on the same order as that of the cosmic generated background flux. However the primary characteristic of special nuclear material is its ability to fission and to support fission chains through neutron induced fission. This means that neutrons produced from fission are not produced randomly singly but rather in time-correlated bursts. Almost from the beginning of the atomic age, the measurement of time-correlated neutrons has been used to detect and quantify fission and fission processes. Feynman himself proposed a method, the grandfather of what is used today, to compare correlation rates of neutron flux in a fixed time to that which would be expected of a random neutron source. The larger variance (broader distribution) as compared to a random distribution is a tell-tale sign of correlated production and commonly used as signature of fission and more importantly fission chains, the broader the distribution (and its departure from a random distribution) the higher the multiplication. Feynman’s original method was used to determine the criticality of the first reactor and other critical or near critical systems. We at LLNL have been developing this concept over the past decade and a half and have employed it for the detection and assessment of nuclear materials. Our method for doing this involved generating a theoretical prediction of what we might expect to see, given a neutron source (spontaneous fission with a nubar, or alpha-n) and a possibly multiplying material (Plutonium or Uranium) and comparing it to a measured result and deducing from this what it is we are measuring. We first developed these methods for portable (low efficiency) thermal neutron detectors that were used predominantly for emergency response situations and we have applied some of these techniques with thermal neutron detectors to arms control verification and authentication, for example verifying that there are multiplying quantities of plutonium in an unknown object. In recent years we have been exploring the use of fast neutrons using liquid scintillator cells with Pulse Shape Discrimination (PSD) and in this project we developing both the theory of fast particle production from fission and fission chains and the use of fast particle detection methods primarily for arms control verification and authentication, but for other uses. We have found that fast detection has many advantages, primarily because the speed of the detection (nanoseconds) preserves the original time scale of the particles produced by fission (and more importantly from induced fission) but also because the fast time scales allow for considering much shorter measurement times (binning) that greatly reduce the pollution of random correlations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Convective effects on directional solidification of a simulated metal alloy

The first significant results of a ground-based experimental program which supports a low gravity space processing Spacelab experiment are reported. The phenomena which precipitate pluming and thus freckling in a metal alloy analog (ammonium chloride and water) are studied in detail and the sequential events leading to massive channeling and convection are optically documented. The pluming is shown to be other than a random burst of unstable fluid from a preferred channel but rather a natural occurrence resulting from a fundamental (Rayleigh-Benard) fluid dynamic instability at the density inversion interface. This extrapolates to critical size parameters appropriate to processing of actual metal alloys.

Mccay, T. D.↗
NASA NTRS2009

Physical Principle for Generation of Randomness

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Zak, Michail↗
DOE OSTI2023

Modulating the Mixing Gibbs Free Energy to Enhance Solid–Liquid Phase Separation for High–Performance Organic Solar Cells

Organic solar cells (OSC) feature a hierarchical structure with the electron donor/acceptor layer sandwiched by anode and cathode, which raises the importance of controlling the molecular crystal orientation, domain size, and vertical distribution to facilitate the charge collection at electrodes. However, the similar conjugated backbone of donor/acceptor material and fast film–formation kinetics have led to spinodal–decomposition–orientated phase separation that result in the film presenting an intimately mixed morphology and random molecular orientation. To solve the issue, the mixing Gibbs free energy–triggered solid–liquid phase separation during the film formation process is enhanced by solidifying one component and solvating the other based on a liquid additive. Following the liquid evaporation process, a favorable vertical distribution is obtained. Meanwhile, the prolonged solvation process enlarges the domain size and assists the molecules to diffuse and orient properly, enabling better exciton/charge dynamics during the power conversion processes. As a result, the fabricated devices exhibit a fill factor over 80% and an efficiency of 18.72%, which is one of the top efficiencies for binary OSCs. In conclusion, insights and a methodology is provided here to manipulate the organic donor/acceptor phase separation in terms of mixing Gibbs free energy.

14 SOLAR ENERGY↗
DOE OSTI2016

Enhanced Optical Head Tracking for Cranial Radiation Therapy: Supporting Surface Registration by Cutaneous Structures

Purpose: To support surface registration in cranial radiation therapy by structural information. The risk for spatial ambiguities is minimized by using tissue thickness variations predicted from backscattered near-infrared (NIR) light from the forehead. Methods and Materials: In a pilot study we recorded NIR surface scans by laser triangulation from 30 volunteers of different skin type. A ground truth for the soft-tissue thickness was segmented from MR scans. After initially matching the NIR scans to the MR reference, Gaussian processes were trained to predict tissue thicknesses from NIR backscatter. Moreover, motion starting from this initial registration was simulated by 5000 random transformations of the NIR scan away from the MR reference. Re-registration to the MR scan was compared with and without tissue thickness support. Results: By adding prior knowledge to the backscatter features, such as incident angle and neighborhood information in the scanning grid, we showed that tissue thickness can be predicted with mean errors of <0.2 mm, irrespective of the skin type. With this additional information, the average registration error improved from 3.4 mm to 0.48 mm by a factor of 7. Misalignments of more than 1 mm were almost thoroughly (98.9%) pushed below 1 mm. Conclusions: For almost all cases tissue-enhanced matching achieved better results than purely spatial registration. Ambiguities can be minimized if the cutaneous structures do not agree. This valuable support for surface registration increases tracking robustness and avoids misalignment of tumor targets far from the registration site.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2022

A Differentiable Hydrology Approach for Modeling With Time-Varying Parameters

In the analysis of observational data with mathematical models, it is often desirable to let one or more model parameters vary with time to account for changing environmental conditions or to offer more flexibility. A standard approach for dynamic models is to allow for the number of parameters to grow as a function of time, leading to a high-dimensional inference problem for long data records. We propose using Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo (MCMC) method, to perform Bayesian inference for time-varying parameters (TVP) in hydrology models. As derivatives of model error functions with regard to parameters are not available in closed form, we implemented the GR4J rainfall-runoff models in Theano/PyMC3, and Jax/NumPyro, allowing for the application of automatic differentiation techniques. A simulation experiment assessing the viability of these methods for recovering underlying temporal variation in parameters indicates that a discrete Gaussian random walk-based prior appears to be best suited across a range of scenarios while the continuous-time Gaussian process compares relatively poorly. In an analysis of 20 years of daily real-world streamflow records from the Model Parameter Estimation Experiment (MOPEX) hydrology data set with increasing data sparsity and at multiple temporal resolutions, we find that TVP inference with gradient-based MCMC is a flexible and reliable approach for analyzing hydrology models with dynamic parameter sets.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Accumulation of Pb and Cu heavy metals in sea water, sediment, and leaf and root tissue of Enhalus sp. in the seagrass bed of Banten Bay

Banten Bay in Indonesia is a coastal area which has been highly affected by human activity. Previous studies have reported the presence of lead (Pb) and copper (Cu) heavy metals in the seawater of this area. This study was conducted to measure the accumulation of Pb and Cu in seawater, sediment, leaf tissue, and root tissue of the seagrass species Enhalus sp. Sampling was conducted at two observation stations in Banten Bay: Station 1 (St.1) was located closer to the coastline and to industrial plants as source of pollution, while Station 2 (St.2) was located farther away offshore. At each station, three sampling points were established by random sampling. Field sampling was conducted at two different dates, i.e., on 29 May 2012 and 30 June 2012. Samples were processed by wet ashing using concentrated HNO{sub 3} acid and measured using Atomic Absorption Spectrometry (AAS). Accumulation of Pb was only detected in sediment samples in St.1, while Cu was detected in all samples. Average concentrations of Cu in May were as follows: sediment St.1 = 0.731 ppm, sediment St.2 = 0.383 ppm, seawater St.1 = 0.163 ppm, seawater St.2 = 0.174 ppm, leaf St.1 = 0.102 ppm, leaf St.2 = 0.132 ppm, root St.1= 0.139 ppm, and root St.2 = 0.075 ppm. Average measurements of Cu in June were: sediment St.1 = 0.260 ppm, leaf St.1 = 0.335 ppm, leaf St.2 = 0.301 ppm, root St.1= 0.047 ppm, and root St.2 = 0.060 ppm. In June, Cu was undetected in St.2 sediment and seawater at both stations. In May, Cu concentration in seawater exceeded the maximum allowable threshold for water as determined by the Ministry of the Environment. Spatial and temporal variation in Pb and Cu accumulation were most probably affected by distance from source and physical conditions of the environment (e.g., water current and mixing)

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Modeling generic aspects of ideal fibril formation

Many different proteins self-aggregate into insoluble fibrils growing apically by reversible addition of elementary building blocks. But beyond this common principle, the modalities of fibril formation are very disparate, with various intermediate forms which can be reshuffled by minor modifications of physico-chemical conditions or amino-acid sequences. To bypass this complexity, the multifaceted phenomenon of fibril formation is reduced here to its most elementary principles defined for a linear prototype of fibril. Selected generic features, including nucleation, elongation, and conformational recruitment, are modeled using minimalist hypotheses and tools, by separating equilibrium from kinetic aspects and in vitro from in vivo conditions. These reductionist approaches allow to bring out known and new rudiments, including the kinetic and equilibrium effects of nucleation, the dual influence of elongation on nucleation, the kinetic limitations on nucleation and fibril numbers, and the accumulation of complexes in vivo by rescue from degradation. Overlooked aspects of these processes are also pointed: the exponential distribution of fibril lengths can be recovered using various models because it is attributable to randomness only. It is also suggested that the same term “critical concentration” is used for different things, involved in either nucleation or elongation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quantifying nitrogen loss hotspots and mitigation potential for individual fields in the US Corn Belt with a metamodeling approach

The high productivity in the US Corn Belt is largely enabled by the consumption of millions of tons of manufactured fertilizer. Excessive application of nitrogen (N) fertilizer has been pervasive in this region, and the unrecovered N eventually escaped from croplands in forms of nitrous oxide (N 2 O) emission and N leaching. Mitigating these negative impacts is hindered by a lack of practical information on where to focus and how much mitigation potential to expect. At a large scale, process-based crop models are the primary tools for predicting variables required by decision making, but their applications are prohibited by expensive computational and data storage costs. To overcome these challenges, we built a series of metamodels to learn the key mechanisms regarding the carbon (C) and N cycle from a well-validated process-based biogeochemical model, ecosys. The trained metamodel captures over 98% of the variability of the ecosys simulated outputs for 99 randomly selected counties in Iowa, Illinois, and Indiana. To identify hotspots with high mitigation potential, we introduce net societal benefit (NSB) as an indicator for synthesizing the loss in yield and social benefits through emissions and pollutants avoided. Our results show that reducing N fertilizer by 10% leads to 9.8% less N 2 O emissions and 9.6% less N leaching at the cost of 4.9% more SOC depletion and 0.6% yield reduction over the study region. The estimated total annual NSB is $\$395$ M (uncertainty ranges from $\$114$ M to $\$1271$ M), including $\$334$ from social benefits (uncertainty ranges from $\$46$ M to $\$1076$ M), $\$100$ M from saving fertilizer (uncertainty ranges from $\$13$ M to $\$455$ M), and –$\$40$ M due to yield changes (uncertainty ranges from –$\$261$ M to $\$69$ M). For the median scenario, we noted that 20% of the study area accounts for nearly 50% of the NSB, and thus represent hotspot locations for targeted mitigation. Although the uncertainty range suggests that developing such a high-resolution framework is not yet settled and the scenario based estimations are not appropriate to inform the management practices for individual farmers, our efforts shed light on the new generation of analytical tools for life cycle assessment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Cas3-Mediated Genome Reduction: Demonstration in Cupriavidus Necator H16 Improves Growth on Heterotrophic and Autotrophic Carbon Sources

Genome reduction is widely used to improve microbial bioprocessing hosts by reducing the burden of inessential physiology. Rationally identifying genomic regions that are dispensable or even detrimental to bioprocessing is challenged by our inability to map genome sequence to function across complex regulation and physiology. Thus, there is a need for tools that rapidly generate reduced genome strains with improved performance in process-relevant conditions. Here, we report a Cascade-Cas3-enabled method called TRIM3 that generates large deletions by targeting a randomly integrated transposon, enabling facile generation of a genome-reduced mutant library. Mutants with improved performance were isolated following growth-coupled selection and analyzed by long-read DNA sequencing to identify deletions in their genomes. We deploy this system iteratively in the industrial host Cupriavidus necator H16 on fructose and on formate. After two rounds of TRIM3, we isolate a strain containing a total reduction of 1.4 Mb (18.4% of the genome) that grows 25% faster in a bioreactor on fructose and a strain with a total reduction of 0.5 Mb (7.3% of the genome) that grows 14% faster on formate. This work demonstrates a method for random, iterative, growth-selectable genome reduction that represents a new avenue for large-scale genome modifications and the development of improved bioprocessing hosts.

09 BIOMASS FUELS↗
DOE OSTI2018

Analytic Analysis for Dynamic System Frequency in Power Systems Under Uncertain Variability

In this paper, a new systematic method is proposed to analyze the system frequency in power systems under uncertain variability (UV). UV gradually increases in power systems, which originates from the renewable energy generation, random loads, frequency measurement, and communication channels, exerting noteworthy impacts on dynamic system frequency. The UV is modeled as a stochastic process in this paper. Then, the stochastic differential equations are used to describe the dynamic system frequency response (SFR) of a power system under UV, which is based on the SFR model. To assess system frequency dynamics under UV, an index of intra-range probability is put forward. Based on stochastic analysis theory, an analytic method is proposed to analyze the system frequency under UV, by which the intra-range probability can be analytically solved. Compared with Monte Carlo simulation in a typical SFR case and the Iceland electricity transmission network, the proposed method shows almost the same results using much less computation resource. Finally, insights for improving the SFR under UV are provided. The proposed method can be used to quickly verify whether the system frequency could withstand the UV and stay in the security range.

42 ENGINEERING↗