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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Robust Distribution State Estimation for Reliable Locational Marginal Pricing under Cyber-Attacks

Here this paper examines the impact of false data injection (FDI) cyber-attacks on distribution system state estimation (DSSE) and the resulting distribution locational marginal price (DLMP) in power markets. Two robust high-breakdown regression estimators, namely S- and MM- estimators, are implemented to provide resistance against FDI attacks targeting measurements and grid topology, creating leverage points. The introduced estimators are compared to the weighted least squares (WLS) with a bad data detection and rejection module (BDD) and the robust Huber M-estimator. The proposed estimators are shown to be effective and compare favorably to both existing Huber M- and the WLS with BDD in the presence of topology FDI attacks. Both the S- and MM-estimators provide good performance in the case of clean and corrupted measurements. Their performance is comparable in this case to the Huber M- and the WLS, followed by a BDD module. The simulation considered a modified distribution IEEE 13 and 34-bus systems where the impact of FDI attack scenarios is shown on the state and the DLMP pricing in the presence of distributed Generation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The impact of sampling scale: A comparison of methods for estimating external contaminant exposure in free-ranging wildlife

The impacts of contaminants on wildlife are dose dependent, and thus being able to track or predict exposure following contamination events is important for monitoring ecosystem health. However, the ability to track exposure in free-ranging wildlife is often severely limited. Consequently, researchers have predominantly relied on simple methods for estimating contaminant exposures in wildlife with little regard for spatial contaminant heterogeneity or an animal’s use of diverse habitats. We evaluated the influence sampling scale (i.e., how finely contaminant distribution and organism’s spatial use of the landscape is mapped) has on (1) realism and (2) conservativeness of exposure estimates. To do this, we monitored the actual exposure of wild boar (Sus scrofa) in Fukushima, Japan to radioactive contamination using GPS27 coupled contaminant monitors placed on individual animals. We compared empirical exposures to estimates generated by combining varying amounts of information about an individual boar’s location and/or movement, with the distribution of contamination on the landscape. Here we found that the most realistic exposure estimates were produced when finer-scale contaminant distribution surveys (e.g., airborne surveys) were combined with more accurate estimates of an individual’s space use (e.g., home ranges or core areas). Importantly, estimates of exposure based on single point surveys at a trap site (a simple method commonly used in the literature), did not correlate with actual exposure rates, suggesting dose-effects studies using this method may result in spurious conclusions. These results suggest that researchers seeking realistic estimates of exposure, such as in dose-effect studies, should ensure they have adequately accounted for fine-scale contaminant distribution patterns and areas of higher use by study organisms. However, conservative estimates of exposure i.e., intentionally over-predicting exposure as is done in initial tiers of ecological risk analyses) were not as scale sensitive and could be achieved with a single known location and coarse contaminant distribution maps.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2024

A road map to cosmological parameter analysis with third-order shear statistics: III. Efficient estimation of third-order shear correlation functions and an application to the KiDS-1000 data

Context. Third-order lensing statistics contain a wealth of cosmological information that is not captured by second-order statistics. However, the computational effort it takes to estimate such statistics in forthcoming stage IV surveys is prohibitively expensive. Aims. We derive and validate an efficient estimation procedure for the three-point correlation function (3PCF) of polar fields such as weak lensing shear. We then use our approach to measure the shear 3PCF and the third-order aperture mass statistics on the KiDS-1000 survey. Methods We constructed an efficient estimator for third-order shear statistics that builds on the multipole decomposition of the 3PCF. We then validated our estimator on mock ellipticity catalogs obtained from N -body simulations. Finally, we applied our estimator to the KiDS-1000 data and presented a measurement of the third-order aperture statistics in a tomographic setup. Results. Our estimator provides a speedup of a factor of ∼100–1000 compared to the state-of-the-art estimation procedures. It is also able to provide accurate measurements for squeezed and folded triangle configurations without additional computational effort. We report a significant detection of tomographic third-order aperture mass statistics in the KiDS-1000 data (S/N = 6.69). Conclusions. Our estimator will make it computationally feasible to measure third-order shear statistics in forthcoming stage IV surveys. Furthermore, it can be used to construct empirical covariance matrices for such statistics.

Astronomy & Astrophysics↗
DOE OSTI2024

Probing Signal-Based Inertia and Frequency Response Estimation for Power Systems With High Levels of Inverter-Based Resources

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

frequency response↗
DOE OSTI2022

Rain Drop Size Distributions Estimated from NOAA Snow-Level Radar Data

Using NOAA’s S-band High-Power Snow-Level Radar (HPSLR), a technique for estimating the rain drop size distribution (DSD) above the radar is presented. This technique assumes the DSD can be described by a four parameter, generalized gamma distribution (GGD). Using the radar’s measured average Doppler velocity spectrum and a value (assumed, measured, or estimated) of the vertical air motion w, an estimate of the GGD is obtained. Four different methods can be used to obtain w. One method that estimates a mean mass-weighted raindrop diameter D m from the measured reflectivity Z produces realistic DSDs compared to prior literature examples. These estimated DSDs provide evidence that the radar can retrieve the smaller drop sizes constituting the “drizzle” mode part of the DSD. Here, this estimation technique was applied to 19 h of observations from Hankins, North Carolina. Results support the concept that DSDs can be modeled using GGDs with a limited range of parameters. Further work is needed to validate the described technique for estimating DSDs in more varied precipitation types and to verify the vertical air motion estimates.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

High Order Implicit Residual-Based Spatial Discretization Error Estimation for S N Neutron Transport

This work demonstrates our novel residual source spatial discretization error estimator (LeR/TEAD) for a DGFEM-1 discretization and assesses it along with two contemporary estimators, Ragusa and Wang's h -refinement estimator (RW) and Duo, Azmy, and Zikatanov's explicit residual-based estimator (DAZ), on a suite of Method of Manufactured Solutions (MMS) 2D problems and three realistic problem geometries. LeR/TE-AD is attractive because it directly estimates the local error in the angular flux, as opposed to a mere indicator of the error's behavior, on the same mesh and method order as the original numerical solution, thus typically being less computationally intensive than a refinement-based method. On the MMS suite, LeR/TE-AD consistently displayed a reduced performance versus its DGFEM-0 results in terms of accuracy and precision metrics, though it was not typically grossly inaccurate. This is attributed to the irregularities in the true solution across singular characteristics limiting the local accuracy of the numerical flux solution, leading to poor derivative approximations used in the residual approximations. The error transport problem then spreads the error in the residual to nearby cells, causing a greater degree of imprecision that did not afflict DAZ or RW. In testing the estimators on realistic problem geometries, however, LeR/TE-AD fared better. In practice, the true error is much larger in non-idealized geometries like in MMS, and a superlinear true solution means that RW and DAZ are not beneficially biased for DGFEM-1 error estimation. LeR/TE-AD was typically first or second in accuracy, primarily competing with RW, but the latter usually consumed 2-4 times the computational time as LeR/TE-AD, and requires a solution with four times as many unknowns. Furthermore, RW and LeR/TE-AD can be used to compute direct estimates of the error in any quantity of interest that is based on the angular ux solution, such as the fission rate density in a fuel pin, whereas DAZ requires a heuristic extension due to its norm-based nature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Application of Point Precipitation Frequency Estimates to Watersheds

This report documents work sponsored by the U.S. Nuclear Regulatory Commission (NRC) at the Oak Ridge National Laboratory (ORNL) as part of the RES project, “Application of Point Precipitation Frequency Estimates to Watersheds.” This project was implemented as part of the Probabilistic Flood Hazard Assessment (PFHA) Research Program. The objective of the PFHA Research Program is to develop tools and guidance on the use of PFHA methods to risk-inform NRC’s licensing of new facilities as well as licensing and oversight of currently operating facilities as they relate to flooding hazards. Many nuclear power plants (NPPs) are located on or near rivers so riverine flooding hazards need to be considered in their design and operation. Probabilistic riverine flood models are important tools for realistic assessment of flooding risks. However, these models require areal estimates of the depth, duration, and frequency of rainfall distributed over the watershed, which are not often available. Point precipitation frequency estimates are more widely available. For example, the National Oceanic and Atmospheric Administration (NOAA) has published NOAA Atlas 14, which provides point precipitation frequency estimates for 5-minute through 60-day durations at average recurrence intervals of 1-year through 1,000-year. The research documented in this report addresses areal reduction factors (ARFs), which can be used to convert the widely available point precipitation frequency estimates, to estimates of areal precipitation frequency over a watershed. The most widely used ARF source is Technical Paper 29 (TP-29) published by the then U.S. Weather Bureau in 1958. However, both the methods and the underlying precipitation data used to produce TP-29 are seriously out of date. For example, due to the small gauge network available at the time of TP-29’s compilation, ARF estimates developed are only for watersheds smaller than about 400 square miles. Due to the relatively short record lengths of precipitation data available, frequency considerations could not be accurately determined. Other factors such as regional climate and seasonality were not addressed. Several newer methods have been published since TP-29 was developed and both the type and quantity of precipitation data have increased significantly, along with computational resources and analytical tools such as geographic information systems. This report reviewed and assessed the available precipitation products and methods for conducting ARF analysis. The work applied up-to-date precipitation data products and analysis methods with a novel watershed-based approach to investigate how ARF estimates vary across different methods, data sources, geographical locations, return periods, and seasons. The overall findings reported here regarding basic ARF trends are in line with other recent studies showing that ARFs decrease with increasing area, increase with increasing duration, and decrease with increasing return period. This study found significant differences among the available ARF methods. This work also found a strong geographical variability across different US hydrologic regions, suggesting that the ARF are specific to regional climate patterns and geographical characteristics and should not be applied arbitrarily to other locations. The results also reveal the importance of data record length, especially for high return level ARFs. The work reported in NUREG/CR-7271 will assist NRC staff in assessing different classes of ARF methods in conjunction with available rainfall data sets. It will also support the development of guidance for application of point precipitation data in PFHAs. It should be noted that the ARF values presented in this report for any location or region were developed for the purposes of comparing methods and investigating the factors that influence ARFs. They should not be considered official and should not be used in leu of a site-specific analysis.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Improved Muon Energy Estimation Using a Detailed Model of Multiple Coulomb Scattering in the MicroBooNE LArTPC

We present an improved technique for estimating a muon's energy by measuring the deflections along its path inside the MicroBooNE detector from multiple Coulomb scattering (MCS). This approach implements several innovations that better capture detector non-idealizations compared to previous MCS-based muon energy estimators. As a result, it achieves improved resolution, reduced bias, and better data-model agreement. Using model simulation, for fully contained events the estimated bias is within 1\% and the estimated resolution narrows from 10\% to 4.3\% as muon energy increases from 0.1\,GeV to 2\,GeV. For events with particles exiting the detector volume, at least a meter of reconstructed muon track, and a muon energy below 2\,GeV, the estimated bias is less than 2\% and the estimated resolution varies from 7\% to 17\% over muon energy. These demonstrate significant improvements over the performance of previous work using an MCS-based energy estimator at MicroBooNE~\cite{mcs_2017}, which exhibited approximately twice worse resolution and a bias of 20\% over the same energy region. Data-model goodness-of-fit studies are used to validate the estimator's performance on data, showing good agreement within model uncertainties.

Cooper-Troendle, London [U. Pittsburgh (main); Fer↗
DOE OSTI2021

Examining the Characteristics of the Cropland Data Layer in the Context of Estimating Land Cover Change

The United States Department of Agriculture (USDA) Cropland Data Layer (CDL) provides spatially explicit information about crop production area and has served as a prevalent data source for characterizing cropland change in the U.S. in the last decade. Understanding the accuracy of the CDL is paramount because of the reliance on it for management and policy making. This study examined the characteristics of the CDL from 2007 to 2017 using comparisons to other USDA datasets. The results showed when examining the cropland area for the same year, the CDL produced comparable trends with other datasets (R 2 > 0.95), but absolute area differed. The estimated area of cropland changes from 2007 to 2012, 2008 to 2012 and 2012 to 2017 varied from weak to moderate correlation between the CDL and the tabular data (R 2 = 0.005~0.63). Differences in area of cropland change varied widely between data sources with the CDL estimating much larger change area. A series of image processing techniques designed to improve the confidence in cropland change estimated using the CDL reduced the area of estimated cropland change. The techniques also, unexpectedly, lowered the correlation in change estimated between the CDL and the tabular datasets. Estimated land cover change area varied widely based on analyses applied and could reverse from increasing to declining area in cropland. Further analyses showed unlikely change scenarios when comparing different year combinations. The authors recommend the CDL only be used for land cover change analysis if the error can be estimated and is within change estimates.

58 GEOSCIENCES↗
DOE OSTI2023

Harmonising the land-use flux estimates of global models and national inventories for 2000–2020

As the focus of climate policy shifts from pledges to implementation, there is a growing need to track progress on climate change mitigation at the country level, particularly for the land-use sector. Despite new tools and models providing unprecedented monitoring opportunities, striking differences remain in estimations of anthropogenic land-use CO 2 fluxes between, on the one hand, the national greenhouse gas inventories (NGHGIs) used to assess compliance with national climate targets under the Paris Agreement and, on the other hand, the Global Carbon Budget and Intergovernmental Panel on Climate Change (IPCC) assessment reports, both based on global bookkeeping models (BMs). Recent studies have shown that these differences are mainly due to inconsistent definitions of anthropogenic CO 2 fluxes in managed forests. Countries assume larger areas of forest to be managed than BMs do, due to a broader definition of managed land in NGHGIs. Additionally, the fraction of the land sink caused by indirect effects of human-induced environmental change (e.g. fertilisation effect on vegetation growth due to increased atmospheric CO 2 concentration) on managed lands is treated as non-anthropogenic by BMs but as anthropogenic in most NGHGIs. We implement an approach that adds the CO 2 sink caused by environmental change in countries' managed forests (estimated by 16 dynamic global vegetation models, DGVMs) to the land-use fluxes from three BMs. This sum is conceptually more comparable to NGHGIs and is thus expected to be quantitatively more similar. Our analysis uses updated and more comprehensive data from NGHGIs than previous studies and provides model results at a greater level of disaggregation in terms of regions, countries and land categories (i.e. forest land, deforestation, organic soils, other land uses). Our results confirm a large difference (6.7 GtCO 2 yr —1 ) in global land-use CO 2 fluxes between the ensemble mean of the BMs, which estimate a source of 4.8 GtCO 2 yr —1 for the period 2000–2020, and NGHGIs, which estimate a sink of —1.9 GtCO 2 yr —1 in the same period. Most of the gap is found on forest land (3.5 GtCO 2 yr —1 ), with differences also for deforestation (2.4 GtCO 2 yr —1 ), for fluxes from other land uses (1.0 GtCO 2 yr —1 ) and to a lesser extent for fluxes from organic soils (0.2 GtCO 2 yr —1 ). By adding the DGVM ensemble mean sink arising from environmental change in managed forests (—6.4 GtCO 2 yr —1 ) to BM estimates, the gap between BMs and NGHGIs becomes substantially smaller both globally (residual gap: 0.3 GtCO 2 yr —1 ) and in most regions and countries. However, some discrepancies remain and deserve further investigation. For example, the BMs generally provide higher emissions from deforestation than NGHGIs and, when adjusted with the sink in managed forests estimated by DGVMs, yield a sink that is often greater than NGHGIs. In summary, this study provides a blueprint for harmonising the estimations of anthropogenic land-use fluxes, allowing for detailed comparisons between global models and national inventories at global, regional and country levels. This is crucial to increase confidence in land-use emissions estimates, support investments in land-based mitigation strategies and assess the countries' collective progress under the Global Stocktake of the Paris Agreement.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Novel estimation of aerosol processes with particle size distribution measurements: a case study with the TOMAS algorithm v1.0.0

Atmospheric aerosol microphysical processes are a significant source of uncertainty in predicting climate change. Specifically, aerosol nucleation, emissions, and growth rates, which are simulated in chemical transport models to predict the particle size distribution, are not understood well. However, long-term size distribution measurements made at several ground-based sites across Europe implicitly contain information about the processes that created those size distributions. This work aims to extract that information by developing and applying an inverse technique to constrain aerosol emissions as well as nucleation and growth rates based on hourly size distribution measurements. We developed an inverse method based upon process control theory into an online estimation technique to scale aerosol nucleation, emissions, and growth so that the model–measurement bias in three measured aerosol properties exponentially decays. The properties, which are calculated from the measured and predicted size distributions, used to constrain aerosol nucleation, emission, and growth rates are the number of particles with a diameter between 3 and 6 nm, the number with a diameter greater than 10 nm, and the total dry volume of aerosol ( N 3–6 , N 10 , V dry ), respectively. In this paper, we focus on developing and applying the estimation methodology in a zero-dimensional “box” model as a proof of concept before applying it to a three-dimensional simulation in subsequent work. The methodology is first tested on a dataset of synthetic and perfect measurements that span diverse environments in which the true particle emissions, growth, and nucleation rates are known. The inverse technique accurately estimates the aerosol microphysical process rates with an average and maximum error of 2 % and 13 %, respectively. Next, we investigate the effect that measurement noise has on the estimated rates. The method is robust to typical instrument noise in the aerosol properties as there is a negligible increase in the bias of the estimated process rates. Finally, the methodology is applied to long-term datasets of in situ size distribution measurements in western Europe from May 2006 through June 2007. At Melpitz, Germany, and Hyytiälä, Finland, the average diurnal profiles of estimated 3 nm particle formation rates are reasonable, having peaks near noon local time with average peak values of 1 and 0.15 cm –3 s –1 , respectively. The normalized absolute error in estimated N 3–6 , N 10 , and V dry at three European measurement sites is less than 15 %, showing that the estimation framework developed here has potential to decrease model–measurement bias while constraining uncertain aerosol microphysical processes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Expedited Walkdowns and Preparation of Cost Estimates for Decontamination and Demolition of Excess Facilities - 20335

Lawrence Livermore National Security, LLC (LLNS) is the prime contractor responsible for managing and operating Lawrence Livermore National Laboratory (LLNL). The mission of the LLNL is to strengthen security of the United States through development and application of world-class science and technology to enhance the nation's defense, reduce the global threat from terrorism and weapons of mass destruction, and respond with vision, quality, integrity, and technical excellence to scientific issues of national importance. To accomplish its mission, LLNL must plan and manage its campus space and facilities to optimize use of its relatively small one-square-mile footprint. LLNL currently has numerous excess facilities that require decontamination and demolition (D and D). The LLNL Legacy Facility Program is responsible for stewardship and risk reduction programs to effectively manage these excess assets at LLNL. The Legacy Facility Program identified 10 excess facilities at LLNL that were candidates for demolition based on risks from further degradation of the facilities, potential exposure to hazardous materials, or need for removal to make way for new program facilities. The buildings range from a structure built in 1943 to serve as a US Navy drill hall during World War II, to a facility that provided neutrons to study material properties for the fusion energy program. The National Nuclear Security Administration (NNSA) appropriated FY19 funding for the development of Class 3 estimates for these 10 excess facilities that would be used to develop a Program Management Plan for funding consideration. Class 3 estimates are not conceptual, nor overly detailed, but adequate to be used for budget and appropriation purposes. Using existing strategic sourcing agreements, LLNL was able to organize a team of senior subject matter experts (SMEs) with diverse technical backgrounds across the Department of Energy (DOE) Complex to complete extensive process knowledge (PK) reviews and walk-downs of each excess facility and to deliver accurate and complete estimates under an expedited schedule (i.e., within eight weeks). To facilitate the expedited schedule, LLNL was fully prepared for the arrival of the JGMS team, which consisted of the following companies: J.G. Management Systems, Inc. (JGMS); Strata-G, LLC; and Michael Baker International. LLNL provided background and PK information on the excess facilities, pictures, supporting historical documentation, and radiological survey history as well as escorted access to the facilities. The JGMS team has previous experience supporting Program Management Plans for excess facilities at the Y-12 National Security Complex. The team mobilized to LLNL and performed the facility walk-downs from January 22-25, 2019. Using a methodical evaluation process, expertise, and experience, the team was able to deliver walk-down draft reports and estimates to LLNL before their February 8, 2019 deadline. LLNL then in turn reviewed, completed the estimates by adding waste management costs and other LLNL costs, and delivered the estimates to NNSA by February 15, 2019. The completed final reports, including draft D and D estimates, were delivered to LLNL before their March 6, 2019 deadline. The work was successfully completed ahead of the expedited schedule required by LLNL, resulting in a commendation from the client. This paper describes how the partnership and collaboration as a fully integrated team comprised of the prime contractor, LLNS, and the JGMS team successfully met the needs of the US government, resulting in the performance of expedited site walk-downs, the development of summary evaluation reports, and the preparation of draft Class 3 estimates and preliminary schedules for the D and D of 10 excess facilities at LLNL. The efforts of the team will enable the D and D of the first excess facility in the 2020-2021 time frame. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

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

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

frequency response↗
DOE OSTI2021

Decentralized Data-Driven Estimation of Generator Rotor Speed and Inertia Constant Based on Adaptive Unscented Kalman Filter

This paper proposes an online decentralized and data-driven method for synchronous generator rotor speed and inertia estimation. First, an analytical relationship between the generator terminal voltage/current phasors and its internal rotor speed is derived using the Thevenin equivalent. The parameters of the latter are obtained via a recursive estimator, which allows us to estimate the generator's internal rotor speed from voltage/current phasors without the need for any generator information. Second, we reformulate the equivalent swing equation into the Kalman filter form, which enables us to use a priori-estimated internal rotor speed along with measured real and reactive power injections to obtain an estimate of the inertia for each online synchronous generator. This is achieved through an adaptive unscented Kalman filter. We demonstrate that the use of terminal bus frequency to approximate the rotor speed for inertia estimation by existing methods leads to large estimation biases/errors. Numerical simulations carried out on the IEEE 39-bus and Texas 2000-bus systems reveal that our proposed method is consistently more accurate than existing methods. Moreover, our proposed method is insensitive to both the type and location of system disturbances, and it is robust to different levels of measurement noise.

bus frequency↗
DOE OSTI2020

Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems

Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This paper proposes a blocktensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Herein, feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems and a 100- node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

Herein, this article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Inertia estimation for power grids: A review of methods, challenges, and future prospects

The electric power grid is undergoing a significant transformation, shifting from traditional synchronous generators to inverter-based resources (IBRs) such as solar photovoltaics, wind turbines, and energy storage systems. This evolution leads to a reduction in system inertia, a critical attribute for maintaining frequency stability in response to disturbances. Consequently, the ability to monitor and estimate system inertia has become increasingly essential. This paper provides a comprehensive review of existing inertia estimation methodologies, analyzing them from multiple perspectives, including the types of data utilized, underlying estimation principles, operational modes, and system-wide applicability. A comparative summary table is included to distill commonalities and key characteristics across various studies. In addition, the paper examines practical implementations of inertia estimation across several major power systems worldwide, including the U.S. interconnections, the Nordic power system, and the U.K. grid. Key challenges are identified, particularly in estimating contributions from virtual inertia sources and load-induced inertia in increasingly converter-dominated networks. To address these emerging challenges, the paper proposes an integrated framework for real-time inertia estimation and monitoring. This framework encompasses critical components such as data acquisition, inertia estimation from both synchronous and non-synchronous sources, load-induced effects, optimization techniques, forecasting, and virtual inertia scheduling. Collectively, these elements enable dynamic, system-wide monitoring and adaptive control of grid inertia.

Inertia estimation↗