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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Total Measurement Uncertainty in Neutron Coincidence Multiplicity Analysis

Neutron multiplicity counting is the most commonly used nondestructive assay technique for determining the plutonium mass within containers of scrap PuO 2 or mixed oxide (MOX). In multiplicity analysis, the 240 Pu eff mass, leakage multiplication, and alpha ratio (the ratio of [α, n]-to-spontaneous fission neutron production) are the three primary unknown sample properties. They must be determined simultaneously. To solve for these three unknowns in a multiplicity assay, three measured values are needed: the singles, doubles, and triples neutron count rates. While the analysis is limited to solving for three unknowns, there are many additional factors that impact the observed count rates and contribute to the measurement uncertainty. In this study we investigate the various uncertainty contributors for the multiplicity analysis through a combination of traditional uncertainty propagation techniques supplemented by Monte Carlo simulations to address the dependences not explicitly expressed by the point source model. Uncertainties arising from counting statistics, calibration parameters, calibration method, nuclear data, and various material characteristics (isotopic abundances, chemical form, density, and impurities) are considered. A Total Measurement Uncertainty (TMU) estimate is then developed from these uncertainty contributors. This study is confined to multiplicity analysis of items commonly encountered in international safeguards applications. That is, the study focused on Pu oxides and MOX materials for the masses ranging up to 4000 grams total Pu. Multiplicity measurements were simulated using MCNP V6 based on the Plutonium Scrap Multiplicity Counter (PSMC), Epithermal Multiplicity Counter (ENMC), Pyrochemical Multiplicity Counter, and Large Epithermal Multiplicity Counter (LEMC) for this study; however, this report focuses on the parameterization of the uncertainties for the PSMC. The performance differences between the PSMC and the other multiplicity counting systems are relatively small, primarily manifesting in the impact on measurement precision so that the evaluation developed for the PSMC can be applied to the other multiplicity counting systems. Finally an analysis tool, the Multiplicity TMU Estimator, was developed from this study to serve as an aid for evaluation of the total measurement uncertainty of multiplicity assay results obtained from the commonly used INCC acquisition and analysis software.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Core Mass Estimates in Strong Lensing Galaxy Clusters: A Comparison between Masses Obtained from Detailed Lens Models, Single-halo Lens Models, and Einstein Radii

The core mass of galaxy clusters is both an important anchor of the radial mass distribution profile and probe of structure formation. With thousands of strong lensing galaxy clusters being discovered by current and upcoming surveys, timely, efficient, and accurate core mass estimates are needed. Here, we assess the results of two efficient methods to estimate the core mass of strong lensing clusters: the mass enclosed by the Einstein radius (M(<θ E ) where θ E is approximated from arc positions; Remolina González et al. 2020), and single-halo lens model (M SHM ; Remolina González et al. 2021), against measurements from publicly available detailed lens models (M DLM ) of the same clusters. We use data from the Sloan Giant Arc Survey, the Reionization Lensing Cluster Survey, the Hubble Frontier Fields, and the Cluster Lensing and Supernova Survey with Hubble. We find a scatter of 18.2% (8.2%) with a bias of -7.1% (1.0%) between M corr (<θ arcs ) (M SHM ) and M DLM . Last, we compare the statistical uncertainties measured in this work to those from simulations. This work demonstrates the successful application of these methods to observational data. As the effort to efficiently model the mass distribution of strong lensing galaxy clusters continues, we need fast, reliable methods to advance the field.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Joint inference of multiplicative and additive systematics in galaxy density fluctuations and clustering measurements

Galaxy clustering measurements are a key probe of the matter density field in the Universe. With the era of precision cosmology upon us, surveys rely on precise measurements of the clustering signal for meaningful cosmological analysis. However, the presence of systematic contaminants can bias the observed galaxy number density, and thereby bias the galaxy two-point statistics. As the statistical uncertainties get smaller, correcting for these systematic contaminants becomes increasingly important for unbiased cosmological analysis. We present and validate a new method for understanding and mitigating both additive and multiplicative systematics in galaxy clustering measurements (two-point function) by joint inference of contaminants in the galaxy overdensity field (one-point function) using a maximum-likelihood estimator (MLE). We test this methodology with Kilo-Degree Survey-like mock galaxy catalogues and synthetic systematic template maps. We estimate the cosmological impact of such mitigation by quantifying uncertainties and possible biases in the inferred relationship between the observed and the true galaxy clustering signal. Our method robustly corrects the clustering signal to the sub-percent level and reduces numerous additive and multiplicative systematics from 1.5σ to less than 0.1σ for the scenarios we tested. In addition, we provide an empirical approach to identifying the functional form (additive, multiplicative, or other) by which specific systematics contaminate the galaxy number density. Even though this approach is tested and geared towards systematics contaminating the galaxy number density, the methods can be extended to systematics mitigation for other two-point correlation measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

An Evaluation of a Neutron Time Correlated Interrogation Method for Measurement of Fissile Content in Research Reactor Spent Fuel Assemblies

There are many research reactors worldwide that have been, or are being converted from the use of high enrichment uranium (HEU) to low enrichment uranium (LEU, < 20% enriched). The verification of fissile content and initial enrichment of the spent fuel is needed for the effective safeguards of the fuel. The advanced experimental fuel counter (AEFC) was developed for the measurement of spent fuel rods and assemblies from research reactors for safeguards verification. This measurement system contains components for active neutron interrogation, passive neutron totals counting, neutron coincidence counting, and gross gamma-ray counting. This report presents the first application of the time correlated interrogation technique for the measurement of the 235 U content in research reactor spent fuel assemblies. The technique, called time correlated induced fission (TCIF), uses a 252 Cf neutron source to irradiate the fuel assembly, and the subsequent induced fission events in the fissile material are measured by coincidence counting. The doubles rates are enhanced by having the neutron trigger events from both the 252 Cf source and the induced fission neutrons in the same time gate in the coincidence analysis. The average neutrons per fission of the 252 Cf source is 3.76 and the induced fission neutrons for 235 U is 2.44, so the number of neutrons that are produced is higher than for random neutron interrogation. This high effective neutron number increases the multiplicity counting rates and reduces the statistical error. The background coincidence counts from the 252 Cf are reduced by the water in the sample cavity and the polyethylene surrounding the 3 He detector tubes. This method of active neutron interrogation has been applied to the measurement of spent research reactor (IRT) fuel assemblies. The advanced experimental fuel counter (AEFC) was used to compare the TCIF method with the typically used AmLi neutron interrogation source that emits neutrons that are random in time. The statistical uncertainty for the use of the random neutron source (AmLi) and the time correlated source ( 252 Cf) for spent fuel interrogations was evaluated.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Performance of borated scintillator screens for high-resolution neutron imaging

The most commonly used screens for neutron imaging consist of 6 LiF + ZnS. This type of screen yields the highest light output per detected neutron. For high resolution, gadolinium oxysulfide (GOS, Gadox) screens are employed, which have a much higher detection efficiency, but a light output so much lower than LiF + ZnS that measurements are often limited by photon statistics. Historically, screens using boron as a neutron-sensitive material have not been very successful. However, a new preparation method was introduced recently that produces light output higher than Gadox with detection efficiency greater than LiF + ZnS. Measurements of these new borated screens were performed at the NeXT facility at ILL, Grenoble, in comparison to a high resolution Gadox screen.

10B↗
DOE OSTI2024

Determining the tilt of the Raman laser beam using an optical method for atom gravimeters

The tilt of a Raman laser beam is a major systematic error in precision gravity measurement using atom interferometry. The conventional approach to evaluating this tilt error involves modulating the direction of the Raman laser beam and conducting time-consuming gravity measurements to identify the error minimum. In this work, we demonstrate a method to expediently determine the tilt of the Raman laser beam by transforming the tilt angle measurement into characterization of parallelism, which integrates the optical method of aligning the laser direction, commonly used in freely falling corner-cube gravimeters, into an atom gravimeter. A position-sensing detector (PSD) is utilized to quantitatively characterize the parallelism between the test beam and the reference beam, thus measuring the tilt precisely and rapidly. After carefully positioning the PSD and calibrating the relationship between the distance measured by the PSD and the tilt angle measured by the tiltmeter, we achieved a statistical uncertainty of less than 30 µrad in the tilt measurement. Furthermore, we compared the results obtained through this optical method with those from the conventional tilt modulation method for gravity measurement. The comparison validates that our optical method can achieve tilt determination with an accuracy level of better than 200 µrad, corresponding to a systematic error of 20 µGal in g measurement. This work has practical implications for real-world applications of atom gravimeters.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

Bayesian calibration of a physics-based crystal plasticity and damage model

In this work, we present a model parameter calibration procedure for a physics-based crystal plasticity model. The calibration process utilizes a powerful statistics-based Bayesian calibration method. Calibration of the crystal plasticity parameters makes use of experimentally-measured data, i.e. compressive stress–strain response, from $\langle$100$\rangle$ and $\langle$123$\rangle$ single crystal copper dynamically loaded via Kolsky bar tests. The calibration of damage parameters is achieved using experimentally-measured free-surface velocity history data from plate impact test on $\langle$100$\rangle$ and $\langle$110$\rangle$ single crystal copper, which generates shock compression followed by dynamic tensile failure. A validation assessment is then carried out by comparing the calibrated model predictions and experimental measurements of the dynamic tensile damage generated in an impacted bicrystal copper plate. Lastly, a model-informed rationale for the experimentally-observed dependence of the spatial distribution of ductile damage (porosity) on crystallography is provided.

42 ENGINEERING↗
DOE OSTI2025

Stochastic frequency fluctuation super-resolution imaging

The inherent non-linearity of intensity correlation functions can be used to spatially distinguish identical emitters beyond the diffraction limit, as achieved, for example, in super-resolution optical fluctuation imaging (SOFI). Here, we propose a complementary concept based on spectral correlation functions, termed spectral fluctuation super-resolution (SFSR) imaging. Through theoretical and computational analysis, we show that spatially resolving time-frequency correlation functions in the image plane can improve the imaging resolution by a factor of $\sqrt2$ in most cases and up to twofold for strictly two emitters. This improvement is achieved by quantifying the degree of correlation in spectral fluctuations across the spatial domain. Experimentally, SFSR can be implemented using a combination of interferometry and photon-correlation measurements. The method works for non-blinking emitters and stochastic spectral fluctuations with arbitrary temporal statistics. This suggests its utility in super-resolution microscopy of quantum emitters at low temperatures, where spectral diffusion is often more pronounced than emitter blinking.

47 OTHER INSTRUMENTATION↗
DOE OSTI2022

Toward Better Understanding of Microphysical Processes and Resulting Precipitation Physics: A Merger Of Observations and Cloud Models (Final Report)

A large database of global disdrometer observations and a diverse set of simulations from the Regional Atmospheric Modeling System (RAMS) were compared using principal component analysis (PCA) in order to better understand warm and ice-based precipitation processes. The analysis demonstrated that six distinct precipitation groups (PGs) with common characteristics were revealed in both the observations and model simulations. These PGs were defined by similar co-variability of rain parameters. However, the model showed large concentrations of drops with a given size compared to the observations. Detailed investigations determined the parameterization of drop breakup was forcing the drops to an equilibrium size with a stronger constraint than was indicated by the observations. A series of sensitivity studies permutating the rain shape parameter in the RAMS 2-moment bulk scheme demonstrated how the assumed shape of the rain distribution influences the microphysics as well as precipitation characteristics. Results were compared to the same simulations performed with a bin microphysics scheme where the rain shape parameter is freely evolving. In the bin scheme, a wide range of shape parameters were found, with horizontal and vertical variability, in addition to being a function of storm lifetime. The results of this study highlight the limitations of a fixed assumed rain distribution in 2-moment microphysics schemes. Model simulations were used to probe the microphysical origins of the six PGs. Rain budgets from a supercell case showed that several of the groups hypothesized to be associated with strong ice microphysical processes had significant contributions from melting hail, but the complexity of ice and warm-rain processes in the supercell precluded definitive determination of microphysical origins for many of the PGs. A case study from the Mid-latitude Continental Convection and Clouds Experiment (MC3E) compared the model PGs to disdrometer observations, and demonstrated the spatial and temporal variability of the PGs which is not possible from disdrometer point measurements alone. The analyses performed during this project demonstrated how statistical analysis can provide a robust method for comparing model simulations and observations, which ultimately resulted identification of limitations in some current microphysics parameterizations as well as insights into precipitation variability which ultimately benefits both observations and modeling efforts.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Risk Ratio and Risk Difference Estimation in Case-cohort Studies

Background: In case-cohort studies with binary outcomes, ordinary logistic regression analyses have been widely used because of their computational simplicity. However, the resultant odds ratio estimates cannot be interpreted as relative risk measures unless the event rate is low. The risk ratio and risk difference are more favorable outcome measures that are directly interpreted as effect measures without the rare disease assumption. Methods: We provide pseudo-Poisson and pseudo-normal linear regression methods for estimating risk ratios and risk differences in analyses of case-cohort studies. These multivariate regression models are fitted by weighting the inverses of sampling probabilities. Also, the precisions of the risk ratio and risk difference estimators can be improved using auxiliary variable information, specifically by adapting the calibrated or estimated weights, which are readily measured on all samples from the whole cohort. Finally, we provide computational code in R (R Foundation for Statistical Computing, Vienna, Austria) that can easily perform these methods. Results: Through numerical analyses of artificially simulated data and the National Wilms Tumor Study data, accurate risk ratio and risk difference estimates were obtained using the pseudo-Poisson and pseudo-normal linear regression methods. Also, using the auxiliary variable information from the whole cohort, precisions of these estimators were markedly improved. Conclusion: The ordinary logistic regression analyses may provide uninterpretable effect measure estimates, and the risk ratio and risk difference estimation methods are effective alternative approaches for case-cohort studies. These methods are especially recommended under situations in which the event rate is not low.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Systematic and statistical uncertainties of the hilbert-transform based high-precision FID frequency extraction method

Pulsed nuclear magnetic resonance (NMR) is widely used in high-precision magnetic field measurements. The absolute value of the magnetic field is determined from the precession frequency of nuclear magnetic moments. The Hilbert transform is widely used to extract the phase function from the observed free induction decay (FID) signal and then its frequency. In this paper, a detailed implementation of a Hilbert-transform based FID frequency extraction method is described. How artifacts and noise level in the FID signal affect the extracted phase function are derived analytically. A method of mitigating the artifacts in the extracted phase function of an FID is discussed. Correlations between noises of the phase function samples are studied for different noise spectra. We discovered that the error covariance matrix for the extracted phase function is nearly singular and improper for constructing the $\chi^2$ used in the fitting routine. A down-sampling method for fixing the singular covariance matrix has been developed, so that the minimum $\chi^2$-fit yields properly the statistical uncertainty of the extracted frequency. Other practical methods of obtaining the statistical uncertainty are also discussed.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Characterizing and Mitigating Intraday Variability: Reconstructing Source Structure in Accreting Black Holes with mm-VLBI

The extraordinary physical resolution afforded by the Event Horizon Telescope has opened a window onto the astrophysical phenomena unfolding on horizon scales in two known black holes, M87* and Sgr A*. However, with this leap in resolution has come a new set of practical complications. Sgr A* exhibits intraday variability that violates the assumptions underlying Earth aperture synthesis, limiting traditional image reconstruction methods to short timescales and data sets with very sparse (u, v) coverage. We present a new set of tools to detect and mitigate this variability. We develop a data-driven, model-agnostic procedure to detect and characterize the spatial structure of intraday variability. This method is calibrated against a large set of mock data sets, producing an empirical estimator of the spatial power spectrum of the brightness fluctuations. We present a novel Bayesian noise modeling algorithm that simultaneously reconstructs an average image and statistical measure of the fluctuations about it using a parameterized form for the excess variance in the complex visibilities not otherwise explained by the statistical errors. These methods are validated using a variety of simulated data, including general relativistic magnetohydrodynamic simulations appropriate for Sgr A* and M87*. We find that the reconstructed source structure and variability are robust to changes in the underlying image model. We apply these methods to the 2017 EHT observations of M87*, finding evidence for variability across the EHT observing campaign. The variability mitigation strategies presented are widely applicable to very long baseline interferometry observations of variable sources generally, for which they provide a data-informed averaging procedure and natural characterization of inter-epoch image consistency.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Explicit simulation of the Brownian rotation of arbitrary shaped aerosol particles using quaternions

The shape of an aerosol particle strongly influences its mass and momentum transfer cross-sections, charging properties, and other physical properties. Here, we present an explicit time-stepping procedure to simulate the rotational Brownian motion of arbitrary shaped aerosol particles by solving Euler’s equation of rotation. A Langevin formulation of the rotation equations is used, wherein Brownian motion due to thermal collisions between a particle and background gas molecules is represented using a stochastic fluctuating torque and fluid resistance is included as a drag torque. To avoid singularities associated with describing the orientation of a shape with Euler angles, we employ a quaternion formulation that leads to first-order stochastic differential equations to describe the evolution of the angular position and angular velocity of a rigid body. We perform all the rotational dynamics calculations in the body-fixed frame of reference attached to the rotating shape whose basis vectors are the normalized eigenvectors of the inertia tensor of the particle. Numerical solutions to rotation under torque-free conditions, damped rotation without Brownian motion, and stochastic rotation for arbitrary shapes are presented and discussed. The presented method enables time-resolved simulation of Brownian rotation for direct comparison with experimentally measured trajectories or statistical measures. The second order accuracy of the used time-stepping procedure places a severe restriction on the timestep that can be used for obtaining accurate results. Animations of presented simulations are included for visualizing rotational motion at various gas pressures. To aid implementation, MATLAB ® codes are also provided. Extension to include translation Brownian motion is straightforward.

Roy, Mrittika↗
DOE OSTI2024

A general mechanistic framework for cross-scale understanding of hot spots and hot moments in carbon and water fluxes

Semi-arid ecosystems, like those in the American Southwest, exert a massive impact on the interannual variability of carbon and water cycling. Unfortunately, these carbon and water fluxes are notoriously difficult to predict due to their high spatial and temporal variability, which is poorly captured by the current generation of vegetation models. Indeed, this region is exemplified by the ‘hot spots and hot moments’ concept, which states that small areas in space (‘hot spots’) and transient moments in time (‘hot moments’) exert an outsized influence on biogeochemical cycling. However, the factors that regulate these pulses in biogeochemical activity are unknown, as is their variability across space and time. These uncertainties severely limit efforts to better represent hot spots and hot moments in models. Here, we seek to develop a generalized method for detecting and quantifying the importance of hot spots and hot moments from individual plant to regional scales. Underpinning this method is our recently developed statistical approach for identifying hot spots and hot moments. By applying this method to semi-continuous measurements of plant water status, a depth profile of soil water potential, and ecosystem fluxes via eddy covariance, we will track the fate of water through the soil-plant-atmosphere continuum and identify the mechanistic drivers of these transient pulses in biogeochemical activity. Then, we will expand this approach across a broad network of Ameriflux towers, and apply a machine learning approach that will allow us to upscale measurements of hot spots and hot moments across the American Southwest and quantify their impact on carbon and water cycles. These products will allow us to identify hot spots and hot moments across spatio-temporal scales and will serve as crucial data sources for validating a new generation of models that can better capture highly dynamic carbon and water fluxes. The proposed method will be easily transferable across biomes and will serve as a framework for future research on hot spots and hot moments across the plant ecophysiology, biometeorology, and vegetation modeling communities.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Applications of emulation and Bayesian methods in heavy-ion physics

Abstract Heavy-ion collisions provide a window into the properties of many-body systems of deconfined quarks and gluons. Understanding the collective properties of quarks and gluons is possible by comparing models of heavy-ion collisions to measurements of the distribution of particles produced at the end of the collisions. These model-to-data comparisons are extremely challenging, however, because of the complexity of the models, the large amount of experimental data, and their uncertainties. Bayesian inference provides a rigorous statistical framework to constrain the properties of nuclear matter by systematically comparing models and measurements. This review covers model emulation and Bayesian methods as applied to model-to-data comparisons in heavy-ion collisions. Replacing the model outputs (observables) with Gaussian process emulators is key to the Bayesian approach currently used in the field, and both current uses of emulators and related recent developments are reviewed. The general principles of Bayesian inference are then discussed along with other Bayesian methods, followed by a systematic comparison of seven recent Bayesian analyses that studied quark-gluon plasma properties, such as the shear and bulk viscosities. The latter comparison is used to illustrate sources of differences in analyses, and what it can teach us for future studies.

Paquet, Jean-François (ORCID:0000000187368171)↗
DOE OSTI2023

Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems

We consider a high-dimensional nonlinear computational model of a dynamical system, parameterized by a vector-valued control parameter, in the presence of uncertainties represented by an uncontrolled parameter modeled by a vector-valued random variable, and possibly with stochastic excitation. The objective is to construct a statistical surrogate model where the input is any deterministic value of the control parameter, and the output is a vector-valued observation of the computational model, which is a random vector whose probability measure is updated using a target dataset. To construct this statistical surrogate model, the stochastic response of the computational model must be built, which is a vector-valued time-discretized stochastic process in high dimension, depending on the control parameter. It is assumed that the computational cost of a single evaluation of the deterministic model is high. For the probabilistic updating, we consider a subset of the components of the observation of the computational model, defined as the “identification observation” of the computational model, for which a small target dataset is available. Therefore, the target dataset is associated with partial observability, corresponding to an incomplete data case. Given a prior probability model of the random control and uncontrolled parameters, a training dataset is constructed, consisting of realizations of the random triplet composed of the stochastic response, the random identification observation, and the random control parameter. Since the computational cost of a single evaluation of the deterministic model is assumed to be large, the training dataset is also of small size. The main challenges in this problem are the high dimensionality, partial observability leading to incomplete data in the target dataset for the identification observation of the computational model (which is not sufficient to identify the computational stochastic responses), and the availability of a small training dataset. To address these challenges, we propose a methodology based on statistical methods for constructing necessary reduced representations, direct probabilistic learning under constraints using probabilistic learning on manifolds (PLoM) constrained by the target dataset, and the use of a weak formulation of the Fourier transform of probability measures. Statistical conditioning is also employed to explore the learned dataset. The constructed predictive statistical surrogate model can be implemented in the context of online computation. Here, we apply this approach to a problem of nonlinear stochastic dynamics in high dimensions within the framework of deformable solids mechanics.

Engineering↗
DOE OSTI2021

The utility of Bayesian data reconciliation for separations

Data reconciliation methods for separation processes typically rely on classical statistical approaches to generate estimates of true mass flow rates from measurements. Knowledge regarding the uncertainty of these estimates has value in decision making, but is often not acquired. Bayesian approaches intrinsically quantify uncertainty; however, literature for Bayesian data reconciliation of separation processes is scarce. This publication outlines two Bayesian data reconciliation models and provides details for how the models were implemented for the BayesMassBal (V 1.0.0) software package written in R. To demonstrate the advantages of this approach for data reconciliation, the models were first applied to simulated data and then compared to a classical model through a Monte Carlo experiment. In this example, the Bayesian models were found to provide more accurate estimates of the simulated data, while also providing quantitative information on the estimate uncertainty. To demonstrate the use of the technique in a practical problem, the models were also applied to real data collected from a pilot-scale rare earth solvent extraction process. Here, this publication provides a small window into how Bayesian methods can be used for data reconciliation, but findings suggest Bayesian data reconciliation models for separation processes have distinct advantages over classical alternatives.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2022

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗