Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Injection data analysis”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

CO2 Storage Economic Analysis: CarbonSAFE Use Case

Poster on “CO2 Storage Economic Analysis: CarbonSAFE Use Case” for the CCUS 2025 conference held in Houston, Texas March 3-5, 2025. The cost of designing, permitting, constructing, operating, and closing a CO2 storage project is of vital importance to project developers. The National Energy Technology Laboratory has developed the NRAP/SMART Technoeconomic and Liability Evaluation for Storage (TALES) Model to provide quantitative cost-based insights to support developers planning CO2 injection and storage projects. This study presents a collaborative economic analysis applying TALES with data from the San Juan Basin CarbonSAFE Phase III project led by the New Mexico Institute of Mining and Technology to estimate potential costs incurred during the implementation of a real-world commercial-scale carbon storage project. Scenario analysis was implemented in which different operational and cost attributes were varied and the associated cost implications observed. Key results data and project cost summary metrics, first-year breakeven price of CO2 ($/tonne) and net present value (NPV), are presented for base and alternative cases. Output provides a unique perspective for project stakeholders towards evaluating the influence of different operational strategies and financing approaches on overall project cost and financial viability.

carbon storage↗
NASA NTRS2004

Perspectives on African Ozone from Sondes, Dobson and Aircraft Measurements

We have been studying variability in ozone over Africa using data from ozonesondes (vertical profiles from surface to stratosphere), aircraft (the MOZAIC dataset with cruise altitude and landing/takeoff profiles) and the ground (Dobson spectrophotometer total ozone column measurement). The following may give context for ozone investigations during AMMA: 1. Total ozone measurements since 1989 show considerable variability in mean value among the African stations in Algeria, Kenya, Egypt, South Africa, as well as in seasonal cycles and year-to-year. Trends are not evident. 2. The impacts of convection, stratospheric injection, biomass burning and lightning appear in ozone sounding profile data. Time-series analysis and case studies point to periodic influences of long-range interactions with the Atlantic ("ozone paradox," wave-one") and Indian Oceans. 3. Tropospheric ozone variations, observed in tropospheric profiles and integrated column amount, follow general seasonal patterns but short- term variability is so strong that simple averages are inadequate for describing "climatology" and statistical classification approaches may be required.

Thompson, A. M.↗
DOE OSTI2021

Subsurface Characterization and Machine Learning Predictions at Brady Hot Springs: Preprint

Subsurface data analysis, reservoir modeling, and machine learning (ML) techniques have been applied to the Brady Hot Springs (BHS) geothermal field in Nevada, USA to further characterize the subsurface and assist with optimizing reservoir management. Hundreds of reservoir simulations have been conducted in TETRAD-G and CMG STARS to explore different injection and production fluid flow rates and allocations and to develop a training data set for ML. This process included simulating the historical injection and production since 1979 and prediction of future performance through 2040. ML networks were created and trained using TensorFlow based on multilayer perceptron (MLP), long short-term memory (LSTM), and convolutional neural network (CNN) architectures. These networks took as input selected flow rates, injection temperatures, and historical field operation data and produced estimates of future production temperatures. This approach was first successfully tested on a simplified single fracture doublet system, followed by the application to the BHS reservoir. Using an initial BHS dataset with 37 simulated scenarios, the trained and validated network predicted the production temperature for 6 production wells with the mean absolute percentage error of less than 8%. In a complementary analysis effort, the principal component analysis applied to 13 BHS geological parameters revealed that vertical fracture permeability shows the strongest correlation with fault density and fault intersection density. A new BHS reservoir model was developed considering the fault intersection density as proxy for permeability. This new reservoir model helps to explore under-exploited zones in the reservoir. A data gathering plan to obtain additional subsurface data was developed; it includes temperature surveying for three idle injection wells, at which the reservoir simulations indicate high bottom-hole temperatures. The collected data assist with calibrating the reservoir model and may lead to converting these wells to producers to access under-exploited zones in the reservoir. Data gathering activities are planned for the first quarter of 2021.

40 EE - Geothermal Technologies Office (EE-4G)↗
NASA NTRS1976

Teledyne Continental Motors emissions data and analysis and flight test results

Five different engine models were tested covering combinations of all engine categories in current production in the range from 100 to 435 brake horsepower. Engines were divided into five major types: carbureted, fuel injected, direct drive, geared, and turbocharged. Emissions data were categorized by three separate fuel system schedules: baseline, case 1, and case 2. Baseline was defined as the average fuel flow rate established by the fuel system's production tolerance band when operated with the mixture control at the full-rich position. Case 1 was defined as the minimum allowable fuel flow rate established by the engine certification. Case 2 was defined as the fuel rate corresponding to the leanest fuel-air ratio obtainable before a safety limit occurred with the engine operating on a propeller test stand. Safety limits that developed during testing were cylinder-head overheating or inadequate acceleration from a given mode of operation.

Rezy, B. J.↗
DOE OSTI2020

Distributed Temperature Sensing (DTS) to Monitor CO 2 Migration in an Enhanced Oil Recovery Field in Northern Michigan

The Midwest Regional Carbon Sequestration Partnership (MRCSP) was founded in 2003 as part of the U.S. Department of Energy’s (DOE’s) Regional Carbon Sequestration Partnership initiative. Since its founding, MRCSP has made significant strides toward making CCUS a viable option for states in the region. The public/private consortium, funded through the DOE Regional Carbon Sequestration Initiative, brings together nearly 40 industry partners and 10 states. Battelle, as the project lead, oversees research, development and operations and coordinates activities among the partners. The incremental, phased approach has built a valuable knowledge base for the industry and paved the way for commercial-scale adoption of CCUS technologies. From 2008 to 2020, MRCSP Phase III focused on the development of large-scale injection projects. This report is part of a series of reports prepared under the Midwestern Regional Carbon Sequestration Partnership (MRCSP) Phase III (Development Phase). These reports summarize and detail the findings of the work conducted under the Phase III project. MRCSP conducted analysis of CO 2 flow patterns using distributed temperature sensing (DTS) data acquired from the Chester 16 pinnacle reef located in Otsego County, Michigan. The reef has one injection well Chester 6-16 and one monitoring well Chester 8-16 where DTS is installed. DTS provides a means to track temperature within the wellbores in real time and characterize the migration patterns of CO 2 in the subsurface when DTS data is combined with other operational data such as the injection rates, bottomhole pressures and temperature. The primary objective of this study was to determine the distribution of CO 2 inflow zones in the A1 Carbonate and Brown Niagaran formations.

01 COAL, LIGNITE, AND PEAT↗
NASA NTRSDate not supplied

SAGE III/ISS Rapid Data Analysis Through Dashboarding with Jupyter Notebooks

Spaceborne remote sensing observations of Earth’s atmosphere produce significant quantities of data over the life of each mission. In the case of the Stratospheric Aerosol and Gas Experiment III on the International Space Station (SAGE III/ISS) nearly four years of vertical profiles of atmospheric ozone, water vapor, and nitrogen dioxide concentrations as well as aerosol extinction coefficients have been released. The dichotomy of the desire for both long-term trends in the atmospheric state alongside the assessment of short-term impacts of major disruptive events such as volcanic eruptions and pyrocumulus injections requires agile tools to handle these cases in near real-time as new data are produced. The analysis landscape is further complicated by the desire to compare results between the numerous contemporary observations available for a given dataset. The SAGE III/ISS team has developed a suite of tools leveraging modern web-based frameworks allowing members to interact with a dashboard-style interface to load the data record, assess new profiles as they are generated and in ensemble, compare between species, and additionally add in measurements observed by other platforms as necessary. Leveraging a commonly packaged data format of NetCDF alongside the Python Jupyter Notebook framework, the data can be served to interested parties from an analysis server while still runnable on personal systems if required. This presentation illustrates the ecosystem developed by the SAGE III/ISS team, the applicability to measurements made by any limb-observing platform, and the benefit to transforming routine analyses into readily accessible dynamic plots. Frameworks currently exist at larger scales with projects such as GIOVANNI, and this illustration seeks to show that similar frameworks are accessible and possible within the local research environment while simultaneously unloading human processing cycles for more specialized analysis tasks.

Dashboarding↗
DOE OSTI2020

H-mode pedestal improvements with neon injection in DIII-D

Improvements in the H-mode pedestal pressure and global energy confinement were determined on DIII-D with both 3 and 6 MW of neutral beam (NBI) heating with neon injection. The pedestal pressure increased, primarily associated with a significant increase in the pedestal density with a relatively smaller decrease in the pedestal temperature. At the same neon injection rate, a rapid decrease in edge localized mode (ELM) frequency and ~35% increase in plasma stored energy were observed in the 3 MW discharge, while in the 6 MW discharge, the ELM frequency was gradually decreased and the plasma stored energy gradually increased by up to 20%. The measured pedestal widths from both 3 and 6 MW discharges matched the EPED1.0 width scaling, ${\Delta _{{\psi _N}}} = 0.089\beta _{p,ped}^{1/2}$ ,data-, within 20% deviations before and after neon injection. The peeling-ballooning mode (PBM) stability analysis showed that after neon injection, the ballooning stability boundary was increased, while the peeling stability boundary only dropped once the neon level was relatively high. The ballooning stability boundary increase with neon injection is consistent with increase of the ion diamagnetic stabilization (i.e. including the contribution from carbon, neon as well as deuterium ions) which is used in the criterion to determine when the calculated linear growth rates of PBM are unstable. Consequently, the new ELITE computed PBM boundaries were more consistent with the operating points than when only deuterium was included. This in turn suggests that the impurity may help to improve pedestal pressure through affecting ion diamagnetic frequency in the pedestal region, which could positively lead to the ballooning stability boundary extension.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Global Sensitivity Analysis of Large Distribution System with PVs using Deep Gaussian Process

Global sensitivity analysis (GSA) of the voltage to uncertain power injection variations plays an important role for appropriate Volt-VAR optimization. This paper proposes a data-driven GSA method for large-scale distribution systems with a large number of uncertain sources. Specifically, the deep Gaussian process is used to identify the mapping relationship between uncertain power injections and voltages. This allows us to resort to the analysis of variance framework to calculate the Sobol indices for GSA. Unlike the existing polynomial chaos expansion and Gaussian process-based approaches, our proposed method has much better scalability. Test results on the EPRI 1747-node K1 circuit with a different number and different probability distributions of uncertain sources demonstrate that the proposed method can achieve accurate GSA under various conditions.

14 SOLAR ENERGY↗
DOE OSTI2022

Findings on Subtask 3.1 - Bakken Rich Gas Enhanced Oil Recovery Project

Total in-place oil for the Bakken petroleum system (BPS) (which includes the Bakken and Three Forks Formations) has been estimated to be 600 billion barrels (bbl). However, BPS wells have decline rates as high as 85% over the first 3 years of their lives, and primary recovery factors typically range from 3% to 10% of original oil in place. Given the low initial recovery rates, even small incremental productivity improvements could dramatically increase technically recoverable oil in the BPS. One potential solution is enhanced oil recovery (EOR) using gas injection, such as carbon dioxide (CO2) or hydrocarbon (HC) gases. While commonly used in conventional reservoirs, CO2 EOR in unconventional tight oil reservoirs has been limited to pilot tests. EOR using rich gas (mixture of methane, ethane, and propane) has also been employed in numerous pilots in several unconventional plays and has recently been successfully applied in the Eagle Ford play. If successful, large-scale gas-based EOR in the BPS could dramatically increase oil productivity and recovery factors and extend the life of the play for decades. While CO2 may be a technically suitable working fluid for EOR in the BPS, supplies are limited and costs for using CO2 in EOR pilots are prohibitively high. Meanwhile, produced gas flaring has presented challenges for BPS operators in North Dakota. Analysis conducted by the North Dakota Pipeline Authority indicates that the current gas-gathering infrastructure in North Dakota is insufficient to accommodate all of the associated gas that is produced from the BPS. The geographically isolated location of North Dakota relative to large natural gas markets, combined with suppressed natural gas prices, has made it economically challenging for industry to invest capital in expanding gas-gathering infrastructure in the state. These circumstances led to a research program conducted by the Energy & Environmental Research Center (EERC) in partnership with Liberty Resources Management Company LLC (LR) to examine the potential to use rich gas injection for EOR and mitigate flaring. A rich gas EOR pilot test was designed and executed by LR at its Stomping Horse development area in Williams County, North Dakota. From July 2018 through May 2019, a total of 160 million standard cubic feet (MMscf) of rich produced gas was injected into the BPS using five different wells in a sequential injection strategy. LR’s Leon–Gohrick drill spacing unit (DSU) was used as the test site. Regulatory oversight was provided by the North Dakota Industrial Commission (NDIC). Technical support was provided by the EERC through a series of laboratory, modeling, and field-based activities, and additional post-pilot research activities incorporated learnings from the test, developed new laboratory data, improved fracture modeling methods, and developed machine learning and big data analytics. The results from the Stomping Horse rich gas EOR pilot activities indicate that developing an effective, economical EOR approach for the BPS will require more field tests. Another key lesson learned from the Stomping Horse tests is that detailed pre- and posttest data on reservoir conditions and fluids production are essential. Robust reservoir characterization provides information that is crucial to creating realistic geomodels and conducting valid dynamic simulations of potential EOR scenarios. A detailed understanding of the completions and production history of offset wells is also necessary for valid test result interpretations. This knowledge is essential to designing the operational parameters of injectivity tests and interpreting the results. A conformance control strategy is also essential to success. Laboratory-based examinations of rich gas interactions with reservoir fluids and rocks were conducted, with an emphasis on determining the ability to mobilize oil in the tight reservoir rocks and shales of the BPS. Injection fluid composition was shown to have a positive impact on reducing reservoir oil minimum miscibility pressure (MMP), reducing interfacial tension (IFT), and altering wettability. IFT and contact angle measurements demonstrated that wettability can be altered in the presence of rich gas, suggesting the potential to improve oil recovery. Iterative modeling of surface infrastructure and reservoir performance using data generated by the various project activities was conducted. A geologic model of the Stomping Horse area was built; history-matched oil, gas, and water production was used in simulations of various EOR scenarios. Early programmatic modeling results were used to support LR’s design and operation of the EOR pilot and to provide insight regarding optimization of future commercial-scale BPS EOR design and operations. Post-pilot modeling focused on alternative methods of understanding complex fracture networks and accelerating simulation time. These led to improved simulation run times and provide excellent history-matching results. Several of these iterative models were used as the bases for developing algorithms into machine learning and big data analytics. History matching in reservoir simulation is time-consuming and computer processing-intensive. Machine learning algorithms were created, and an automated history-matching tool was developed. A large set of synthetic reservoir simulations were created to generate well responses (oil, gas, and water production, well bottomhole pressure [BHP], and tracer or propane breakthrough) for a set of EOR operating parameters that included offset well status (open or closed), injectate (rich gas or propane), injection rate, and injection well BHP. A user interface was developed to provide real-time visualization. Machine learning-based models were developed to provide rapid forecasting of well performance given a set of user-defined EOR operating parameters. These predictive models allow the user to modify the offset well status, injection rate, and injection well BHP and rapidly forecast future production performance. The combination of real-time visualization tools with real-time forecasting tools provides a framework for real-time control—operational changes that the EOR site operator can enact (e.g., changing gas injection rates) to affect the observed performance and potentially improve the EOR outcome. There is great reason to be optimistic about the future of EOR in the Bakken. The results of the laboratory studies suggest significant potential for high rates of oil mobilization using produced field gas injection under the right conditions. The results of the lab studies, combined with rigorous statistical analysis of well production data and associated modeling efforts, confirm the notion that fluid mobility within the reservoir is controlled by fractures. As more knowledge is gained about the nature and distribution of fracture networks in the Bakken, the industry will be in a better position to predict and, ultimately, influence fluid mobility. New field tests are necessary to develop a more complete understanding of those conditions. Thoughtful and creatively engineered field tests within a well-characterized geologic setting will yield the fundamental knowledge needed to take Bakken oil production to the next level. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission’s Oil and Gas Research Program and Computer Modelling Group.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2022

Experimental Investigation of Low-Frequency Distributed Acoustic Strain-Rate Responses to Propagating Fractures

Summary Low-frequency distributed acoustic sensing (LF-DAS) responds to strain changes due to far-field fracture propagation. To better understand the LF-DAS response to fracture propagation, we performed laboratory-scale hydraulic fracture experiments with embedded optical strain sensors. The objectives of this research are to generate hydraulic fractures of known geometry, measure the strain response along the embedded fiber-optic cable comparable to LF-DAS measurements, and use the results to inform the interpretation of field-derived LF-DAS data. The experiments were conducted in unconfined transparent cubic blocks with a dimension of 8 in. on each side. The block was made of transparent epoxy to visualize the fracture propagation. Fiber-optic sensing cables were embedded in the block at different distances to the source of injection. We injected dyed water through an injection tubing to generate a transverse, radial fracture along an initial flaw. An optical interrogator recorded the response of offset fiber Bragg grating (FBG) strain sensors normal to the plane of the fracture. The strain data were visualized on a waterfall plot, akin to visualizations of field-derived LF-DAS data. Dimensional analysis was used to scale the laboratory results to field conditions. We compared the evolution of the strain response at the fiber-optic cable, injection pressure, and rate with known fracture geometry. The measured strains were compared with Sneddon’s (1946) linear elastic solution for a penny-shaped crack and found to follow this behavior. The generated radial fractures in transparent media can be modeled with Sneddon’s linear elastic radial fracture model and a Mode I critical stress intensity factor. The LF-DAS characteristic response of a narrowing region of extension surrounded by compression was exhibited as a fracture that approached and intersected the fiber-optic cable. The experimentally derived strain and strain-rate waterfall plots with known fracture geometry, injection rate, and pressure response provide insight in understanding LF-DAS responses in the field. Furthermore, we developed a method to estimate fracture geometry evolution from the fiber-optic strain data and validated the method against the experimental data.

Engineering↗
NASA NTRS1988

Observations related to the acceleration, injection, and interplanetary propagation of energetic protons during the solar cosmic ray event on February 16, 1984

This paper presents an analysis of data collected by the worldwide network of neutron monitors and from IMP-8 cosmic-ray telescopes, as well as by particle detectors on the GOES 5 and 6 and ICE satellites, on the solar cosmic ray event that took place on February 16, 1984. Using these data, the intensity-time (IT) profiles, the anisotropy-time profiles, the energy spectra, and the pitch angle distributions of the solar protons near earth were deduced. It was found that the solar protons propagated essentially scatter-free from the sun to the earth. The solar protons had easy access to the IMF lines to earth; the time from the onset to maximum intensity and the shape of the IT profiles at earth as a function of energy could be explained by the diffusion of the flare protons near the acceleration region. The energy spectrum of the solar flare protons injected into the undisturbed IMF at the sun was changing with time in both amplitude and shape. The observations suggest a shock acceleration process.

Debrunner, H.↗
DOE OSTI2021

Chemically Enabled CO 2 -Enhanced Oil Recovery in Multi-Porosity, Hydrothermally Altered Carbonates in the Southern Michigan Basin - Task 2 Topical Report

This attachment A is a detailed Topical Report for Task 2 (Advanced Field Characterization and Machine Learning Based Data Integration) under the project "Chemically Enabled CO 2 -Enhanced Oil Recovery in Multi-Porosity, Hydrothermally Altered Carbonates in the Southern Michigan Basin." The overall project activity and finding, including the field pilot testing of CO 2 injection are summarized in the companion Final Technical Report The Advanced Field Characterization and Machine Learning Based Data Integration task (Task 2) involved a systematic geologic characterization of the Trenton-Black River (TBR) play in the SMB which included the development of comprehensive datasets, advanced data analytics, risk assessment, and piggyback field characterization. These activities aimed to address the complex carbonate systems by evaluating the extent of fractures, dolomitization, facies, and reservoir properties with the primary objective of informing the static and dynamic modeling, field injection test, and providing input into the development strategy plan. The task was divided into four subtasks: • Subtask 2.1 – Data compilation, review, and analysis • Subtask 2.2 – Risk Assessment • Subtask 2.3 – Advanced Field Characterization • Subtask 2.4 – Integrated Physics-Based Machine Learning and Advanced Data Analytics

02 PETROLEUM↗
NASA NTRS1975

Thrust vector control by liquid injection for solid propellant rockets

In liquid injection thrust vector control, a rocket jet is deflected for steering purposed by injecting a liquid into the nozzle exit cone. The liquid is preferably both dense and reactive so that it adds mass and energy and generates shocks in the supersonic exhaust. This behavior increases thrust in the affected part of the jet producing not only a side force for steering but an addition to axial thrust. This paper presents a summary of current liquid injection thrust vector control technology, including procedures for design, development, analysis, testing and evaluation, together with supporting data and references.

Zeamer, R. J.↗
NASA NTRS1976

Research of Magnetospheric Physics Phenomena Using Sounding Rockets

A bibliography of approximately 25 papers is presented on the Electron Echo Experiments. The data analysis included an extensive study of the electron accelerator beam, detector data correlations with the electron beam injections, and the study of about 30 onboard detected echoes.

Steffen, J. E.↗
NASA NTRS1993

Experimental evaluation of the certification-trail method

Certification trails are a recently introduced and promising approach to fault-detection and fault-tolerance. A comprehensive attempt to assess experimentally the performance and overall value of the method is reported. The method is applied to algorithms for the following problems: huffman tree, shortest path, minimum spanning tree, sorting, and convex hull. Our results reveal many cases in which an approach using certification-trails allows for significantly faster overall program execution time than a basic time redundancy-approach. Algorithms for the answer-validation problem for abstract data types were also examined. This kind of problem provides a basis for applying the certification-trail method to wide classes of algorithms. Answer-validation solutions for two types of priority queues were implemented and analyzed. In both cases, the algorithm which performs answer-validation is substantially faster than the original algorithm for computing the answer. Next, a probabilistic model and analysis which enables comparison between the certification-trail method and the time-redundancy approach were presented. The analysis reveals some substantial and sometimes surprising advantages for ther certification-trail method. Finally, the work our group performed on the design and implementation of fault injection testbeds for experimental analysis of the certification trail technique is discussed. This work employs two distinct methodologies, software fault injection (modification of instruction, data, and stack segments of programs on a Sun Sparcstation ELC and on an IBM 386 PC) and hardware fault injection (control, address, and data lines of a Motorola MC68000-based target system pulsed at logical zero/one values). Our results indicate the viability of the certification trail technique. It is also believed that the tools developed provide a solid base for additional exploration.

Sullivan, Gregory F.↗
DOE OSTI2023

New scaling law for turbulent boundary layers with high surface mass transfer

A fundamental understanding of the phenomena occurring in the turbulent boundary layer in the presence of surface blowing is limited, and considerable disagreements persist even in describing primary quantities, such as the boundary layer profile. The theories based on the linear boundary layer equations show that the thickness of the sublayer increases in the presence of surface blowing; therefore, the viscous sublayer and law of the wall modify. In this study, direct numerical simulations (DNS) of turbulent boundary layers with uniform surface mass transfers are carried out in order to scale the velocity profile. Emphasis is placed on moderate to high mass transfer rates, which are relevant to the most common hybrid rockets configuration. DNS data are used to establish a functional law of the wall and a law of wake by means of the relation between the wall shear stress and surface mass transfer. Analysis of the mean kinetic energy budget shows that the magnitude of turbulent kinetic energy increases by surface mass transfer, and the production rate extends significantly in the inner layer as the injection rate increases. DNS data of various surface blowing are used to complete the closure of turbulence kinetic energy equation and develop an eddy viscosity model. The predicted turbulent kinetic energy and eddy viscosity agree with DNS data for moderate to high blowing rates.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

A Data-Driven Global Sensitivity Analysis Framework for Three-Phase Distribution System with PVs

Global sensitivity analysis (GSA) of distribution systems with respect to stochastic PV and load variations plays an important role in designing optimal voltage control schemes. This paper proposes a data-driven framework for GSA of distribution systems. In particular, two representative surrogate modeling-based approaches are developed, including the traditional Gaussian process-based and the analysis of variance (ANOVA) kernel ones. The key idea is to develop a surrogate model that captures the hidden global relationship between voltage and real and reactive power injections from the historical data. With the surrogate model, the Sobol indices can be conveniently calculated through either the sampling-based method or the analytical method to assess the global sensitivity of voltage to variations of PV and load power injections. The sampling-based method approximates the Sobol indices using Monte Carlo simulations while the analytical method calculates them by resorting to the ANOVA expansion framework. Comparison results with other model-based GSA methods on the unbalanced three-phase IEEE 37-bus and 123-bus distribution systems show that the proposed framework can achieve much higher computational efficiency with negligible loss of accuracy. The results on a real 240-node distribution system using actual smart meter data further validate the feasibility and scalability of the proposed framework.

14 SOLAR ENERGY↗