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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

Effective Li-Ion Transport Quantification in Composite Cathodes for All-Solid-State Batteries via Multiscale Modeling and Experiments

The tortuosity factor of composite cathodes significantly affects the rate performance of all-solid-state batteries (ASSBs) and has significant differences from systems with liquid electrolytes. Here, in this work, we report a simulation-experiment combined approach that quantifies the effective Li-ion transport in an ASSB composite cathode, which links tortuosity factor on ∼ μm scale to terminal voltage during cycling at the cell level (on ∼ cm scale). Two independent approaches of tortuosity factor quantification are considered: fitting electrochemical cycling data and verifying at different cycling rates and calculating from segmented tomography images, with the tortuosity factor quantified from both methods reaching self-consistency. The simulated terminal voltage using the quantified tortuosity factor has a small relative error of <3% compared to the experimental measurements. We find a significantly reduced value of the Bruggeman exponent of the catholyte phase (1.75), and using shape analysis, we show that rod-shaped catholyte particles play an important role in lowering the tortuosity factor.

Yao, Archie Mingze [Univ. of Michigan, Ann Arbor, ↗
DOE OSTI2021

An in-depth field validation of “DUSST”: A novel low-maintenance soiling measurement device

This study presents indoor and field validation results for two versions of the “DUSST” optical soiling sensor, intended to be a low-cost and low-maintenance device for measuring photovoltaic soiling losses. Indoor testing covers irradiance calibration and temperature dependencies, which are necessary to achieve high accuracy, low uncertainty field measurements. Field testing includes an array of different environments including Saudi Arabia, California, Utah, and Colorado. DUSST versions include a configuration with a 530-nm light emitting diode (LED) (discussed in previous work) and a unit with seven white LEDs and a polycarbonate collimating optic. The new design increases light intensity fivefold and demonstrates a single linear calibration coefficient is effective to measure soiling losses as high as 75%. Field data from Utah and California demonstrate that daily soiling loss measurements and soiling rate calculations closely match both reference cell and full-size module measurements of soiling losses and soiling rates. Corrective methods employed on the Utah DUSST sensor suggest that it is possible to achieve measurement errors as low as ±0.1% at two standard deviations. Field data from both Colorado and Saudi Arabia demonstrate that LED lens soiling can occur and that further design optimizations are needed. The lesson learned from all the field deployment locations suggests directions for future design improvements.

14 SOLAR ENERGY↗
DOE OSTI2023

Machine learning interatomic potential for silicon-nitride (Si 3 N 4 ) by active learning

Silicon nitride (Si 3 N 4 ) is an extensively used material in the automotive, aerospace, and semiconductor industries. However, its widespread use is in contrast to the scarce availability of reliable interatomic potentials that can be employed to study various aspects of this material on an atomistic scale, particularly its amorphous phase. In this work, we developed a machine learning interatomic potential, using an efficient active learning technique, combined with the Gaussian approximation potential (GAP) method. Our strategy is based on using an inexpensive empirical potential to generate an initial dataset of atomic configurations, for which energies and forces were recalculated with density functional theory (DFT); thereafter, a GAP was trained on these data and an iterative re-training algorithm was used to improve it by learning on-the-fly. When compared to DFT, our potential yielded a mean absolute error of 8 meV/atom in energy calculations for a variety of liquid and amorphous structures and a speed-up of molecular dynamics simulations by 3–4 orders of magnitude, while achieving a first-rate agreement with experimental results. Our potential is publicly available in an open-access repository.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Deterministic High-Fidelity Neutronics Simulation of Pebble Bed Reactors Using Pebble Tracking Transport

The pebble tracking transport (PTT) algorithm offers a high-fidelity deterministic approach for neutron transport for pebble bed reactors (PBRs). This approach requires the mesh for the active-core region to consist exclusively of tetrahedral elements, where each node in the pebble-packing region represents a pebble centroid. This paper investigates the application of PTT for full-scale PBRs, considering both the isothermal and the temperature-dependent core conditions. Macroscopic cross sections are generated using Serpent 2 full-core eigenvalue simulations where pebbles are grouped into disjoint subsets using machine learning. To minimize the need for individual cross-section sets for each pebble in the core, K-means clustering is used to group pebbles by temperature and neutronic environment parameters. Here, we compare the multiplication factor and power rate distributions between PTT simulations using the Griffin reactor physics software and reference solutions from Serpent 2. Our analysis shows that a full-core, high-fidelity PTT calculation produces accurate results with minimal local (pebblewise) errors. Additionally, timing results indicate that PTT simulations converge rapidly on modern supercomputing platforms.

Griffin↗
DOE OSTI2023

Neural networks for large eddy simulations of wall-bounded turbulence: numerical experiments and challenges

Here, we examine the application of neural network-based methods to improve the accuracy of large eddy simulations of incompressible turbulent flows. The networks are trained to learn a mapping between flow features and the subgrid scales, and applied locally and instantaneously—in the same way as traditional physics-based subgrid closures. Models that use only the local resolved strain rate are poorly correlated with the actual subgrid forces obtained from filtering direct numerical simulation data. We see that highly accurate models in a priori testing are inaccurate in forward calculations, owing to the preponderance of numerical errors in implicitly filtered large eddy simulations. A network that accounts for the discretization errors is trained and found to be unstable in a posteriori testing. We identify a number of challenges that the approach faces, including a distribution shift that affects networks that fail to account for numerical errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations

The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Generalized Lapse Rate Formulas for Use in Entraining CAPE Calculations

Abstract Common assumptions in temperature lapse rate formulas for lifted air parcels include neglecting mixing, hydrostatic balance, the removal of all condensate once it forms (pseudoadiabatic), and/or the retention of all condensate within the parcel (adiabatic). These formulas are commonly derived from the conservation of entropy, which leads to errors when nonequilibrium mixed-phase condensate is present. To evaluate these assumptions, a new general lapse rate formula is derived from an expression for energy conservation, rather than entropy conservation. This new formula incorporates mixing of the parcel with its surroundings, relaxes the hydrostatic assumption, allows for nonequilibrium mixed-phase condensate, and can be formulated for pseudoadiabatic or adiabatic ascent. The new formula is shown to exactly conserve entropy for reversible ascent. Predictions by the new formula are compared to that of older and less general formulas. The errors in previous formulas arise from the assumption of hydrostatic balance, which results in considerable warm biases due to the neglect of the energy sink from buoyancy. Predictions of ascent with entrainment using the new formula are then compared to parcel properties along trajectories in large eddy simulations. Simulated parcel properties are better predicted by the formula using a diluted analogy to adiabatic ascent, wherein condensate is diluted at the same rate as other parcel properties, than by the diluted analogy to pseudoadiabatic ascent, wherein all condensate is removed. These results suggest that CAPE should be computed with adiabatic, rather than pseudoadiabatic, parcel ascent.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

An Assessment of Global Positioning System Velocity Uncertainty in California

We analyze data from 580 continuous global positioning system (GPS) stations in California to quantify differences in published velocity estimates from five analysis centers. Horizontal and vertical rates for individual stations can differ up to 5 mm/yr, with systematic differences in some areas comparable to deformation rates. Published velocity uncertainties vary between analysis centers and are systematically underreported in the horizontal relative to empirical uncertainties calculated from the scatter of analysis center velocities. In the vertical, published velocity uncertainties are both over and underreported and vary more widely between centers. An interpolated ensemble vertical velocity field shows high-subsidence regions in the Central Valley and Salton Trough have the largest empirical uncertainties, while station density has a modest impact on uncertainties. Applications that rely on subcentimeter GPS accuracy should consider the possibility that formal errors published with velocity rate estimates understate true velocity uncertainties in both the horizontal and vertical.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Automated Reaction Kinetics of Gas-Phase Organic Species over Multiwell Potential Energy Surfaces

Automation of rate-coefficient calculations for gas-phase organic species became possible in recent years and has transformed how we explore these complicated systems computationally. Kinetics workflow tools bring rigor and speed and eliminate a large fraction of manual labor and related error sources. In this paper we give an overview of this quickly evolving field and illustrate, through five detailed examples, the capabilities of our own automated tool, KinBot. Here we bring examples from combustion and atmospheric chemistry of C-, H-, O-, and N-atom-containing species that are relevant to molecular weight growth and autoxidation processes. The examples shed light on the capabilities of automation and also highlight particular challenges associated with the various chemical systems that need to be addressed in future work.

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

On the computational solution of vector-density based continuum dislocation dynamics models: A comparison of two plastic distortion and stress update algorithms

Continuum dislocation dynamics models of mesoscale plasticity consist of dislocation transport-reaction equations coupled with crystal mechanics equations. The coupling between these two sets of equations is such that dislocation transport gives rise to the evolution of plastic distortion (strain), while the evolution of the latter fixes the stress from which the dislocation velocity field is found via a mobility law. Earlier solutions of these equations employed a staggered solution scheme for the two sets of equations in which the plastic distortion was updated via time integration of its rate, as found from Orowan's law. In this work, we show that such a direct time integration scheme can suffer from accumulation of numerical errors. We introduce an alternative scheme based on field dislocation mechanics that ensures consistency between the plastic distortion and the dislocation content in the crystal. The new scheme is based on calculating the compatible and incompatible parts of the plastic distortion separately, and the incompatible part is calculated from the current dislocation density field. Stress field and dislocation transport calculations were implemented within a finite element based discretization of the governing equations, with the crystal mechanics part solved by a conventional Galerkin method and the dislocation transport equations by the least squares method. A simple test was first performed to show the accuracy of the two schemes for updating the plastic distortion, which shows that the solution method based on field dislocation mechanics is more accurate. This method then was used to simulate an austenitic steel crystal under uniaxial loading and multiple slip conditions. By considering dislocation interactions caused by junctions, a hardening rate similar to discrete dislocation dynamics simulation results was obtained. Finally, the simulations show that dislocations exhibit some self-organized structures as the strain is increased.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Verification and Validation Tests of Gamma Library of MC2-3 for Coupled Neutron and Gamma Heating Calculation

For the accurate assessment of the heat generation rate in fast reactors, the gamma library of MC2 -3 and the MC2 -3 + GAMSOR procedure employing the coupled neutron and gamma heating calculation has been thoroughly verified against Monte Carlo results and validated using the ZPPR-15D gamma dose measurement data. NJOY outputs are post-processed in a consistent way with the NJOY procedure to avoid any missing data or double counting of data. Prompt heating for 379 out of 391 isotopes in the gamma library was verified against MCNP6.2 to within 1% relative error in total heating for most isotopes. For both a simple one-dimensional slab problem representing a sodium cooled fast reactor and the Experimental Breeder Reactor II (EBR-II) benchmark problem, the root-mean-square values of assembly power error were less than 0.5% for fuel assemblies, ~1% in blankets and ~1 to ~3% in reflectors compared to MCNP6.2 results. The most plausible cause for the 3% error in a reflector assembly is believed to be the error in the multigroup neutron cross sections for the reflector assembly. For validation, gamma doses measured with thermoluminiscent dosimeters (TLDs) in the ZPPR-15D experiment were calculated using GAMSOR. Due to the uncertainty in the TLD measurement with regards to the energy deposition of photons and neutrons, the validation data leads to a 12.7% uncertainty on the experimental measurement. With this uncertainty bound, the calculated doses all fell within one standard deviation of the measured value. Combined with the accurate calculation of reaction rate distributions and neutron spectrum measurements, these results indicate good agreement for the neutron and gamma heating calculations that were performed.

coupled neutron and gamma heating↗
DOE OSTI2024

Implementation of new mixture rules has a substantial impact on combustion predictions for H 2 and NH 3

Complex-forming reactions comprise a substantial fraction of all important combustion reactions and are central to combustion behavior. Despite being often called “pressure-dependent” reactions, their rate constants depend on not only the pressure but also the composition. While modern combustion codes allow arbitrarily high accuracy in treating pressure dependence, recent work has consistently demonstrated dramatic failures of essentially all available treatments of mixture dependence. In situations where mixture dependence is treated at all, it is inevitably treated through specification of pressure-dependent rate constants for a set of pure bath gases, which are then combined to estimate the rate constant in a mixture via a “mixture rule.” While there had been a generally unquestioning confidence in these mixture rules, they had, in reality, been scarcely tested until the last decade, when comparisons against master equation calculations revealed order-of-magnitude errors for important pressure-dependent reactions. New mixture rules, based on the reduced pressure, have recently been proposed and shown to reproduce master equation calculations for broad classes of complex-forming reactions very accurately. Here, in this work, we present an implementation of one such new mixture rule (“LMR-R”) in Cantera and then use it to enable simulations that use new high-accuracy ab initio data for individual bath gases (for the first time, since codes previously could not accommodate the complex bath gas dependence). Demonstrations focus on combustion of H 2 and NH 3 , where (1) high-accuracy ab initio data are available and (2) the impact is expected to be large due to the high fractions of efficient colliders (e.g., H 2 O and NH 3 ) in the burned and unburned gases. Indeed, we find the impact of this treatment to be substantial and may explain previous modeling difficulties for these important carbon-free fuels, particularly for NH 3 , whose extraordinarily high third-body efficiency (~20) is often omitted from kinetic models.

Ammonia↗
DOE OSTI2023

Characterizing the Variation and Covariation of Cloud Microphysical Properties and Implications for Simulation of Subgrid-scale Warm-Rain Processes in Earth System Models (Final DOE-ASR Report)

Warm marine boundary layer (MBL) clouds constitute an important component in the global climate system, and precipitation plays a central role in controlling the water budget, radiative effects, and lifetime of these MBL clouds. Unfortunately, because of the relatively coarse effective grid resolution of the current generation of Earth system models (ESMs), the variety of cloud microphysical processes occurring inside an ESM grid cell are often oversimplified or unconstrained by observations. For example, the warm rain processes (e.g., autoconversion and accretion) are usually parameterized as nonlinear functions of grid-mean cloud properties. Because of the nonlinear nature of these functions, neglecting variability within the ESM grid volume can lead to substantial biases in precipitation production, cloud cover, and surface radiative fluxes. In state-of-the art ESMs, the influence of subgrid-scale variability is represented as an enhancement factor (EF) coefficient to the autoconversion, and accretion rates calculated from the model variables. However, EF is typically taken to be a constant or even used as a knob to tune model cloud properties to match observations, an ad hoc approach that may yield a desired cloud outcome yet introduce compensating errors. In this project, we used the combination of in situ cloud microphysics measurements from the ACE-ENA field campaign and large-eddy simulations (LES) to characterize and understand subgrid-scale variations and co-variations of cloud microphysical properties and use the results to evaluate and improve the representation of subgrid warm-rain processes in ESMs, in particular the EF used to tune the autoconversion and accretion processes. In this final report, we summarize our research activities and main findings in Section 2, provide a list of publications (Section 3) and presentations (Section 4) resulted from our research, and briefly discuss the student activities supported by this project.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Accurate Identification of Deamidation and Citrullination from Global Shotgun Proteomics Data Using a Dual-Search Delta Score Strategy

While proteins with deamidated/citrullinated amino acids play critical roles in the pathogenesis of many human diseases, identifying these modifications in complex biological samples has been an ongoing challenge. Herein we present a method to accurately identify these modifications from shotgun proteomics data from a deep proteome profiling study of human pancreatic islets obtained by laser capture microdissection. All MS/MS spectra were searched against database by MSGF+ twice with or without a +0.9840 Da mass shift on amino acids asparagine, glutamine, and arginine (NQR) as a dynamic modification. Consequently, for each spectrum the resulting two peptide-to-spectrum matches (PSM) with their respective MSGF+ scores were used for Delta Score calculation. It was observed that all PSMs with positive Delta Score values were clustered with mass errors around 0 ppm, while PSMs with negative Delta Score values were distributed nearly equally within the defined mass error range (20 ppm) for database searching. To estimate false discovery rate (FDR), a “pseudo-decoy” approach was applied whether datasets were searched against a database with a “real modification” mass shift (+0.9840 Da) and a “mock modification” mass shift (+1.0227 Da). FDR was controlled to ~2% with a Delta Score filter greater than zero. Manual inspection of spectra showed that PSMs with positive Delta Score value contained deamidated/citrullinated fragments in their MS/MS spectra. Finally, the results demonstrated that in-situ deamidated/citrullinated peptides can be accurately identified from shotgun tissue proteomics data by the Dual-search Delta Score Strategy.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Mass measurement of 27 P to constrain type-I x-ray burst models and validate the isobaric multiplet mass equation for the $A = 27, T = \frac{3}{2}$ isospin quartet

Background: Light curves are the primary observable of type-I x-ray bursts. Computational x-ray burst models must match simulations to observed light curves. Most of the error in simulated curves comes from uncertainties in rp process reaction rates, which can be reduced via precision mass measurements of neutron-deficient isotopes in the rp process path. Purpose: Perform a precise atomic mass measurement of 27 P. Use this new measurement to calculate rp process reaction rates and input these rates into an x-ray burst model to reduce simulated light curve uncertainty. Use the mass measurement of 27 P to validate the isobaric multiplet mass equation (IMME) for the A = 27 T = 3/2 isospin quartet which 27 P belongs to. Method: High-precision Penning trap mass spectrometry utilizing the time-of-flight ion cyclotron resonance technique was used to determine the atomic mass of 27 P. The MESA code (Modules for Experiments in Stellar Astrophysics) was then used to simulate x-ray bursts using a one-dimensional multizone model to produce updated light curves. Results: The mass excess of 27 P was measured to be –670.7(6) keV, a 14-fold precision increase over the mass reported in the 2020 Atomic Mass Evaluation (AME2020). The 26 Si(p, $γ$) 27 P– 27 P($γ$, p) 26 Si rate equilibrium has been determined to a higher precision based on the precision mass measurement of 27 P. x-ray burst light curves were produced with the MESA code using the new reaction rates. Changes in the mass of 27 P seem to have minimal effect on light curves, even in burster systems tailored to maximize impact. Conclusion: The mass of 27 P does not play a significant role in x-ray burst light curves. It is important to understand that more advanced models do not just provide more precise results, but often qualitatively different ones. This result brings us a step closer to being able to extract stellar parameters from individual x-ray burst observations. In addition, the IMME has been validated for the A = 27, T = 3/2 quartet. The normal quadratic form of the IMME using the latest data yields a reduced $χ$ 2 of 2.9. Finally, the cubic term required to generate an exact fit to the latest data matches theoretical attempts to predict this term.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Experiences Detecting Defective Hardware in Exascale Supercomputers

In May 2022, the newest supercomputer to top the TOP 500 list was Frontier at Oak Ridge National Laboratory, demonstrating the capability of computing more than 1.1 quintillion (1018) floating-point calculations every second. Driving this ground-breaking rate of computing is Frontier’s more than 37,000 graphics processing units (GPUs) and 9,408 central processing units (CPUs). In total, Frontier contains more than 60 million parts. At this scale, the smallest margin of error may generate hundreds of hardware errors across the system. These errors are capable of directly hindering world-class science performed on Frontier if not found. In this work, we describe and evaluate two strategies for finding hardware-level faults in Frontier’s 9,408 compute nodes. There are two strategies developed: the first uses the Slurm scheduler to scavenge available compute time to run the node screen, the second builds upon the lessons learned in the first strategy and enforces a weekly screen of each node. Using June 2023 as a case study, we find that the first scheduling strategy consumed more than ten times the resources as the second scheduling strategy, but successfully detected five hardware defects in Frontier. We summarize the lessons learned while developing and running a node screen on the world’s first exascale supercomputer.

Hagerty, Nick↗
DOE OSTI2023

Anomaly Detection in Liquid Sodium Cold Trap Operation with Multisensory Data Fusion Using Long Short-Term Memory Autoencoder

Sodium-cooled fast reactors (SFR), which use high temperature fluid near ambient pressure as coolant, are one of the most promising types of GEN IV reactors. One of the unique challenges of SFR operation is purification of high temperature liquid sodium with a cold trap to prevent corrosion and obstructing small orifices. We have developed a deep learning long short-term memory (LSTM) autoencoder for continuous monitoring of a cold trap and detection of operational anomaly. Transient data were obtained from the Mechanisms Engineering Test Loop (METL) liquid sodium facility at Argonne National Laboratory. The cold trap purification at METL is monitored with 31 variables, which are sensors measuring fluid temperatures, pressures and flow rates, and controller signals. Loss-of-coolant type anomaly in the cold trap operation was generated by temporarily choking one of the blowers, which resulted in temperature and flow rate spikes. The input layer of the autoencoder consisted of all the variables involved in monitoring the cold trap. The LSTM autoencoder was trained on the data corresponding to cold trap startup and normal operation regime, with the loss function calculated as the mean absolute error (MAE). The loss during training was determined to follow log-normal density distribution. During monitoring, we investigated a performance of the LSTM autoencoder for different loss threshold values, set at a progressively increasing number of standard deviations from the mean. The anomaly signal in the data was gradually attenuated, while preserving the noise of the original time series, so that the signal-to-noise ratio (SNR) averaged across all sensors decreased below unity. Results demonstrate detection of anomalies with sensor-averaged SNR < 1.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2026

Stochastic Microgrid Scheduling With Chance‐Constrained Resilience Consideration

Traditionally, it is assumed that microgrids transition seamlessly from grid‐connected operation to islanded mode in the event of sudden main grid outages. In reality, the islanding process, especially unintentional islanding, is rarely seamless. Instead, it is subject to voltage and frequency fluctuations caused by the instantaneous disconnection of the point of common coupling (PCC) switch, variations in loads and renewable generation output and even the protection tripping of distributed energy resources (DERs). To mitigate these fluctuations and facilitate a smooth islanding process, we propose a stochastic microgrid scheduling model that incorporates chance‐constrained resilience measures. Specifically, the resilience measure is defined as the probability of successful islanding (PSI), that is, the probability that a microgrid can mitigate the generation‐demand imbalance caused by the disconnection of the PCC switch, variations in load and renewable generation and DER tripping. This measure is modelled using chance constraints. Unlike existing reliability and resilience indices, which typically neglect the possibility of microgrid/DER failure under extreme events and assume their survival while primarily focussing on reducing impact duration or magnitude, the proposed PSI‐based framework explicitly addresses microgrid and DER survival during the islanding transition. The formulated nonlinear chance constraints are approximated using a multiinterval approach and equivalently represented as a mixed‐integer linear programming (MILP) formulation. Case study results validate the proposed method, showing that the PSI estimation error is reduced to less than 8%, compared to approximately 28% with existing methods. Various sensitivity analyses on the DER tripping rate and PSI settings were performed to validate the robustness of the proposed method. In particular, the necessity of accounting for DER tripping in the PSI calculation was demonstrated.

chance constrained optimization↗