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DOE OSTI2018

Uncertainty quantification for incident helium flux in plasma-exposed tungsten

In this work, the surface response of a tungsten plasma-facing component was simulated by a cluster-dynamics code, Xolotl, with a focus on quantifying the impact of uncertainty in one of the input parameters to Xolotl, namely, the incident helium flux. The simulated conditions involve a tungsten surface exposed to 100 eV helium ion implantations with a flux of either 4 × 10 22 or 4 × 10 25 He m -2 s -1 . Furthermore, two sources were used to describe the implanted helium depth distribution in tungsten, either molecular dynamics (MD) or a binary collision approximation code, the stopping and range of ions in matter (SRIM). The aim of this work is to evaluate and examine uncertain predictions on the helium retention based on these two different modeling methodologies that either neglect electronic energy loss or the crystalline structure of the solid, respectively. An embedded model-form error approach was pursued here in order to arrive at predictions that account for variability due to the two different data sources, and the impact of this model-form uncertainty in incident helium flux on Xolotl output was presented for the two implantation fluxes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

MS25: Materials Science-Focused Benchmark Data Set for Machine Learning Interatomic Potentials

Here, we present MS25, a benchmark data set for evaluating machine learning interatomic potentials (MLIPs) across diverse materials-relevant systems including MgO surfaces, liquid water, zeolites, a catalytic Pt surface reaction, high-entropy alloys (HEAs), and disordered Zr-oxides. Five MLIP architectures (MACE, NequIP, Allegro, MTP, and Torch-ANI) are trained and tested, focusing not only on traditional metrics (energies, forces, and stresses) but also explicitly validating derived physical observables such as lattice constants, volumes, and reaction barriers. We find that most models reach comparable accuracy on standard error metrics across the simple systems, although equivariant MLIPs offer 1.5–2× improvements over nonequivariant MLIPs in energy and force error for structurally complex or compositionally disordered environments such as HEAs and Zr–O systems. Our analysis highlights that low errors in energy and force predictions do not guarantee reliable observables, emphasizing the necessity of explicit validation. We demonstrate limitations in cross-framework transferability, as models trained on one zeolite framework (CHA) fail to reliably generalize to predictions of structurally distinct frameworks (e.g., MFI). Size-extensive tests show some dependence on system size for MgO, resulting from forced periodicity. The HEA and Zr–O data sets are identified as challenging tests for future benchmarks and MLIP model architecture developments as they show significant differentiation in error between MLIP architectures and are still relatively difficult at 1000 training images. Moving forward, we recommend that benchmarking efforts shift their focus from marginal accuracy improvements in energy and force errors toward identifying and understanding model failure modes, rigorously assessing transferability, and evaluating how their errors affect observable predictions. For researchers looking to choose an MLIP architecture, we suggest selecting equivariant MLIP architectures if the complexity of the system is a challenge. For simple materials problems, auxiliary features such as integration with molecular dynamics engines, trade-offs between computational data set generation cost vs MLIP inference speed, and framework integration may play a more important decision factor than small differences in error metrics that are unlikely to matter for production-level research.

chemical structure↗

DOE OSTI2021

AtomSets as a hierarchical transfer learning framework for small and large materials datasets

Abstract Predicting properties from a material’s composition or structure is of great interest for materials design. Deep learning has recently garnered considerable interest in materials predictive tasks with low model errors when dealing with large materials data. However, deep learning models suffer in the small data regime that is common in materials science. Here we develop the AtomSets framework, which utilizes universal compositional and structural descriptors extracted from pre-trained graph network deep learning models with standard multi-layer perceptrons to achieve consistently high model accuracy for both small compositional data (<400) and large structural data (>130,000). The AtomSets models show lower errors than the graph network models at small data limits and other non-deep-learning models at large data limits. They also transfer better in a simulated materials discovery process where the targeted materials have property values out of the training data limits. The models require minimal domain knowledge inputs and are free from feature engineering. The presented AtomSets model framework can potentially accelerate machine learning-assisted materials design and discovery with less data restriction.

Chen, Chi (ORCID:0000000180087043)↗

DOE OSTI2022

Signal-Compensation-Based Adaptive PID Control for Fused Magnesia Smelting Processes

For fused magnesia smelting processes, the proportional-integral-derivative (PID) controller is difficult to regulate the smelting currents within desired ranges due to unexpected variations of the dynamics caused by material feeding operations. To solve this problem, we first proposed its dynamic model composed of a linear model and an uncertain nonlinear dynamic system that describes the unknown time-varying dynamics of nonlinearity and strong couplings among controlled variables. Then, using the accurately calculated value of the uncertain part at the previous sampling time instant and the tracking error that reflects the influence of its change rate, we developed a feedforward and a one-step optimal control to obtain two signal compensators to eliminate the impact of frequent variations of the uncertainties. For the compensators, we proposed a weight selection method to minimize the sum of the squared tracking error with ensured closed-loop stability. Based on the abovementioned modeling and control structure, we finally developed a novel adaptive PID controller augmented with signal compensators to control the whole process. Industrial applications have shown that the proposed method can always keep the tracking error and the control input within their targeted ranges, leading to a significantly reduced energy consumption per ton and increased fused magnesia production.

Wang, Weizhou↗

DOE OSTI2024

Impact of Systematic Modeling Uncertainties on Kilonova Property Estimation

The precise atomic structure and therefore the wavelength-dependent opacities of lanthanides are highly uncertain. This uncertainty introduces systematic errors in modeling transients like kilonovae and estimating key properties such as mass, characteristic velocity, and heavy metal content. Here, we quantify how atomic data from across the literature as well as choices of thermalization efficiency of r-process radioactive decay heating impact the light curve and spectra of kilonovae. Specifically, we analyze the spectra of a grid of models produced by the radiative transfer code Sedona that span the expected range of kilonova properties to identify regions with the highest systematic uncertainty. Our findings indicate that differences in atomic data have a substantial impact on estimates of lanthanide mass fraction, spanning approximately 1 order of magnitude for lanthanide-rich ejecta, and demonstrate the difficulty in precisely measuring the lanthanide fraction in lanthanide-poor ejecta. Mass estimates vary typically by 25%–40% for differing atomic data. Similarly, the choice of thermalization efficiency can affect mass estimates by 20%–50%. Observational properties such as color and decay rate are highly model dependent. Velocity estimation, when fitting solely based on the light curve, can have a typical error of ∼100%. Atomic data of light r-process elements can strongly affect blue emission. Even for well-observed events like GW170817, the total lanthanide production estimated using different atomic data sets can vary by a factor of ∼6.

Gravitational wave sources↗

DOE OSTI2015

Fault tolerance in an inner-outer solver: A GVR-enabled case study

Resilience is a major challenge for large-scale systems. It is particularly important for iterative linear solvers, since they take much of the time of many scientific applications. We show that single bit flip errors in the Flexible GMRES iterative linear solver can lead to high computational overhead or even failure to converge to the right answer. Informed by these results, we design and evaluate several strategies for fault tolerance in both inner and outer solvers appropriate across a range of error rates. We implement them, extending Trilinos’ solver library with the Global View Resilience (GVR) programming model, which provides multi-stream snapshots, multi-version data structures with portable and rich error checking/recovery. Lastly, experimental results validate correct execution with low performance overhead under varied error conditions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

The electric vehicles-solar photovoltaics Nexus: Driving cross-sectoral adoption of sustainable technologies

Residential and transportation energy consumption account for more than one-half of the overall energy consumption in the United States. Adoption of electric vehicles (EVs) can play a key role in decarbonizing the transportation sector, while the adoption of renewable energy sources (e.g., solar photovoltaics [PVs]) could bring similar benefits to the residential energy sector and in turn support transport electrification. Although the market shares for both EVs and PVs continue to grow, both of these emerging technologies are deployed rather disjointly, without considering the existence of potential similarities among users who own (or aspire to own) these technologies. This might be due to lack of understanding of the behavioral interdependence in consumer preferences toward these technologies. To fill this gap in knowledge, this study utilizes data from the 2018 WholeTraveler Transportation Behavior Study to develop an integrated model system that explores interactive EV and PV adoption behaviors. A structural equation model is employed that incorporates direct effects as well as error correlations among the adoption behaviors for EVs and PVs. Model results indicate that the adoption behavior for both these technologies is indeed interconnected and significantly influenced by attitudes, values, and personality traits. Findings from this research suggest that incentives (e.g., subsidies) that drive bundled adoption of EV-PV systems could accelerate the adoption of both of these sustainable technologies. In conclusion, this study highlights the need to consider transport and building energy-efficient technology adoption behavior in a single integrated structure.

14 SOLAR ENERGY↗

DOE OSTI2022

Anomalous structural recovery in the near glass transition range in a polymer glass: Data revisited in light of temperature variability in vacuum oven‐based experiments*

Abstract There is considerable interest in data reported by Cangialosi et al. [Cangialosi, D., Boucher, V. M., Alegría, A., & Colmenero, J. (2013). Physical Review Letters , 111 (9), 095701] that purportedly showed unusual irregular responses in the isothermal structural recovery behavior of glasses because the observation challenges the general view of the dynamics being smooth functions of time as observed in extensive dilatometric experiments by Kovacs [Kovacs, A. J. (1964). In Fortschritte der Hochpolymeren‐Forschung , 3 , 394–507. Springer, Berlin, Heidelberg.] in the 1960s. The reported data show an apparent two mechanism structural (enthalpy) recovery at aging temperatures ranging from 6 to 17 K below which is also controversial as it could not be reproduced in work from Koh and Simon [Koh, Y. P., & Simon, S. L. (2013). Macromolecules , 46(14), 5815–5821.] where a second plateau observed in the enthalpy loss curve was not reproduced in nearly 1‐year‐long experiments at 15 K below . Therefore, it is important to determine what might be possible reasons for the apparent non‐smooth relaxations. Here, we examine the possibility that the poor temperature control of a typical vacuum oven could explain the anomalous results. We used the Tool–Narayanaswamy–Moynihan (TNM) model of structural recovery to calculate the effect of typical vacuum oven temperature variation on the structural recovery of polystyrene and find that we can reproduce the reported experimental results. The issue of temperature control using a vacuum oven is discussed, and data from thermocouple measurements of temperature at various locations inside a vacuum oven are shown.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Data-driven estimation of energy consumption for electric bus under real-world driving conditions

Reliable and accurate estimation of an electric bus’s instantaneous energy consumption is critical in evaluating energy impacts of planning and control of electric bus operations. In this study, we developed machine learning-based long short-term memory (LSTM) and artificial neural network (ANN) models to estimate 1 Hz energy consumption of electric buses based on continuous monitoring data of electric buses in Chattanooga, Tennessee, in 2019 and 2020. We propose a data-partitioning algorithm to separate energy charging and discharging modes before applying data-driven estimation models. Here, a K-fold cross-validation-based model selection process was conducted to identify the optimal model structure and input variables in terms of prediction accuracy. The estimation results show the predicted mean absolute percentage error rates of LSTM and ANN models were 3% and 5%, respectively. We compared the proposed models with existing models in the literature based on the same testing data to demonstrate the predictability of our models.

Artificial neural network↗

DOE OSTI2019

Effects of Inflow Spatiotemporal Discretization on Wake Meandering and Turbine Structural Response using FAST.Farm

FAST.Farm is a newly developed multiphysics, midfidelity engineering tool that can be used to predict turbine power and structural loads of wind turbines in a wind farm with minimal computational expense. Previous studies have shown similarities and differences in wind turbine performance between FAST.Farm and high-fidelity large-eddy simulations (LES) using both LES precursor-generated inflow and TurbSim-generated synthetic inflow. While conservative resolutions have been used to date, no formal spatial or temporal discretization study has been performed for the FAST.Farm model wind domains. This work aims to study the effects of varying the spatial and temporal discretization of the wind domains on wake meandering (low-resolution domain) and turbine structural response (high-resolution domains) and resulting wake and load calculations. The purpose of this study is to establish convergence criteria and recommendations for discretization values in terms of rotor diameter (D, expressed in meters) that will maximize computational efficiency. To ensure a percent error of ≤ 1% in standard deviation of wake center position relative to the finest included resolution, a low-resolution time step of 0.024D s, 0.016D s, and 0.0079D s and a low-resolution spatial discretization of 0.079D m, 0.16D m, and 0.24D m is recommended for 8 m/s, 12 m/s, and 18 m/s mean ambient wind speed at hub height, respectively. These guidelines are likely applicable to other implementations of the dynamic wake meandering model. To ensure a percent error of ≤ 1% in standard deviation of all considered structural response outputs, a high-resolution time step that captures the highest influential excitation and natural frequencies in the system and a high-resolution spatial discretization comparable to the maximum airfoil cord length is recommended. Lastly, these guidelines are likely applicable to any aeroelastic analysis.

17 WIND ENERGY↗

DOE OSTI2023

Analysis of picosecond coherent anti-Stokes Raman spectra for gas-phase diagnostics

We present a hybrid frequency- and time-domain solution, applicable to the case of picosecond coherent anti-Stokes Raman scattering (CARS), for gas-phase diagnostics. A solution has been derived based on both physical arguments and four-wave mixing equations for picosecond CARS, with pulse durations that are comparable to the dephasing time scale for gas-phase Raman coherence—a regime where commonly employed solutions for impulsive (femtosecond) or cw (nanosecond) pump/Stokes forcing are not strictly valid. We present the ps-CARS spectrum in the form of incoherent sums of CARS intensity spectra, calculated from the fundamental solution for impulsive pump/Stokes Raman preparation. The solution was examined for temperatures from 1000–3000 K, for four plausible experimental configurations, with laser pulse durations of 50–150 ps, and probe pulse delays from −20 to 240 ps. Approximations based on cw and impulsive pump/Stokes preparation to fit picosecond CARS spectra at atmospheric pressure were examined and the relative thermometric accuracy and computational cost of these approximations were quantified for the case of a zero nonresonant CARS contribution, and a nonresonant susceptibility equal to 10% of the Raman-resonant value at the N 2 bandhead. The nanosecond CARS approximation can result in large fitting errors when the probe pulse time delay is less than the probe pulse duration. Errors as large as 10–20% are observed in the fit temperatures for a zero picosecond probe pulse delay, when the nonresonant background is neglected, largely due to an inability of the time-independent cw model to capture transient frequency spread dephasing effects at the Q -branch bandhead. The inclusion of a nonresonant background results in 40–60% thermometry errors with a nanosecond model at a zero-probe delay. Time-dependent impulsive calculations used for femtosecond CARS better approximate the structure of the N 2 bandhead, reducing temperature fitting errors to 5–10% at a short probe pulse delay. The impulsive approximation results in errors up to 10% at intermediate probe pulse delays, where the coherence of the pump and probe pulses leads to multiple terms in the picosecond CARS solution. Both approximations improve as the probe pulse delay exceeds the probe duration. The nanosecond approximation results in a 2–3% error, while the impulsive model results in differences of less than 1% in some cases. Fits to experimental data obtained using short, ∼60ps pulses at a zero probe time delay and longer 100 ps pulses at a substantial 200 ps delay are presented with accuracies of 1–3% in the fit temperature.

Kearney, Sean P.↗

DOE OSTI2022

Is the Adoption of Electric Vehicles (EVs) and Solar Photovoltaics (PVs) Interdependent or Independent? An Integrated EVs-PVs Modeling Framework

Transportation and residential energy consumption account for more than one-half of the overall energy consumption in the United States. Adoption of electric vehicles (EVs) can play a key role in decarbonizing the transportation sector, while the adoption of renewable energy sources (e.g., solar photovoltaics or PVs) could bring similar benefits to the residential energy sector and in turn support transport electrification. Although the market share for both EVs and PVs continue to grow, both these emerging technologies are deployed rather disjoint without considering the existence of potential similarities among users who own (or aspire to own) EVs and PVs. This might be due to lack of understanding of the behavioral interdependence in consumer preferences towards these technologies. To fill this gap in knowledge, this study utilizes data from the 2018 WholeTraveler Transportation Behavior Study to develop an integrated model system that explores EV and PV adoption behaviors. A structural equations model (SEM) is employed that incorporates direct effects as well as error correlations among the adoption behaviors for EVs and PVs. Model results indicate that the adoption behavior for both these technologies is indeed interconnected and significantly influenced by attitudes, values and personality traits. Findings from this research suggest that incentives (e.g., subsidies) that drive 'bundled' adoption of EVs and PVs could accelerate the adoption of both these sustainable technologies. The results highlights the need to consider transport and building energy efficient technology adoption behavior in a single integrated structure.

ADVANCED PROPULSION SYSTEMS,ENERGY PLANNING, POLIC↗

DOE OSTI2015

A revised partiality model and post-refinement algorithm for X-ray free-electron laser data

An updated partiality model and post-refinement algorithm for XFEL snapshot diffraction data is presented and confirmed by observing anomalous density for S atoms at an X-ray wavelength of 1.3 Å. Research towards using X-ray free-electron laser (XFEL) data to solve structures using experimental phasing methods such as sulfur single-wavelength anomalous dispersion (SAD) has been hampered by shortcomings in the diffraction models for X-ray diffraction from FELs. Owing to errors in the orientation matrix and overly simple partiality models, researchers have required large numbers of images to converge to reliable estimates for the structure-factor amplitudes, which may not be feasible for all biological systems. Here, data for cytoplasmic polyhedrosis virus type 17 (CPV17) collected at 1.3 Å wavelength at the Linac Coherent Light Source (LCLS) are revisited. A previously published definition of a partiality model for reflections illuminated by self-amplified spontaneous emission (SASE) pulses is built upon, which defines a fraction between 0 and 1 based on the intersection of a reflection with a spread of Ewald spheres modelled by a super-Gaussian wavelength distribution in the X-ray beam. A method of post-refinement to refine the parameters of this model is suggested. This has generated a merged data set with an overall discrepancy (by calculating the R{sub split} value) of 3.15% to 1.46 Å resolution from a 7225-image data set. The atomic numbers of C, N and O atoms in the structure are distinguishable in the electron-density map. There are 13 S atoms within the 237 residues of CPV17, excluding the initial disordered methionine. These only possess 0.42 anomalous scattering electrons each at 1.3 Å wavelength, but the 12 that have single predominant positions are easily detectable in the anomalous difference Fourier map. It is hoped that these improvements will lead towards XFEL experimental phase determination and structure determination by sulfur SAD and will generally increase the utility of the method for difficult cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Investigation of 3D printed lightweight hybrid composites via theoretical modeling and machine learning

Hybrid composites combine two or more different fillers to achieve multifunctional or advanced material properties, such as lightweight and enhanced mechanical properties. The properties of the composites significantly depend on their microstructures, which can be tailored via advanced 3D printing processes. Understanding the process-structure-property relationships is critical to enable the design and engineering of novel hybrid composites for applications in aerospace, automotive, and protective coatings. Here, for this work, we develop 3D printable and lightweight hybrid composites and leverage the conventional design of experiments, a theoretical hybrid model, and an image-driven machine learning (ML) method to investigate their mechanical behaviors. The hybrid composites are formulated with elastomer matrix, microfillers, and thin-shell particles, enabling a significant degree of design freedom of microstructures with densities and mechanical properties varying up to 70% and 91%, respectively. Our statistical analysis indicates that the 3D printing path direction and the microfibers fraction are dominating process parameters with contribution percentages of 45.3% and 57.7% on the specific stiffness and strength, respectively. A hybrid mechanics model is developed based on a simple Weibull distribution function and classical single-filler models to effectively capture the variations in mechanical properties, however, it overestimates the values due to its statistical constraints and idealization of experimental uncertainty. The image-driven ML model leverages the microscale images directly without losing the structural details, shows more accurate predictions with experimental data, and has 48.6% lower root mean square error than the theoretical model.

3D printing↗

DOE OSTI2018

Spatiotemporal video-domain high-fidelity simulation and realistic visualization of full-field dynamic responses of structures by a combination of high-spatial-resolution modal model and video motion manipulations

Structures with complex geometries, material properties, and boundary conditions exhibit spatially local dynamic behaviors. A high-spatial-resolution model of the structure is thus required for high-fidelity analysis, assessment, and prediction of the dynamic phenomena of the structure. The traditional approach is to build a highly refined finite element computer model for simulating and analyzing the structural dynamic phenomena based on detailed knowledge and explicit modeling of the structural physics such as geometries, materials properties, and boundary conditions. These physics information of the structure may not be available or accurately modeled in many cases, however. In addition, the simulation on the high-spatial-resolution structural model, with a massive number of degrees of freedom and system parameters, is computationally demanding. Here this study, on a proof-of-principle basis, proposes a novel alternative approach for spatiotemporal video-domain high-fidelity simulation and realistic visualization of full-field structural dynamics by an innovative combination of the fundamentals of structural dynamic modeling and the advanced video motion manipulation techniques. Specifically, a low-modal-dimensional yet high-spatial (pixel)-resolution (as many spatial points as the pixel number on the structure in the video frame) modal model is established in the spatiotemporal video domain with full-field modal parameters first estimated from line-of-sight video measurements of the operating structure. Then in order to simulate new dynamic response of the structure subject to a new force, the force is projected onto each modal domain, and the modal response is computed by solving each individual single-degree-of-freedom system in the modal domain. The simulated modal responses are then synthesized by the full-field mode shapes using modal superposition to obtain the simulated full-field structural dynamic response. Finally, the simulated structural dynamic response is embedded into the original video, replacing the original motion of the video, thus generating a new photo-realistic, physically accurate video that enables a realistic, high-fidelity visualization/animation of the simulated full-field vibration of the structure. Laboratory experiments are conducted to validate the proposed method, and the error sources and limitations in practical implementations are also discussed. Compared with high-fidelity finite element computer model simulations of structural dynamics, the video-based simulation method removes the need to explicitly model the structure's physics. In addition, the photo-realistic, physically accurate simulated video provides a realistic visualization/animation of the full-field structural dynamic response, which was not traditionally available. Lastly, these features of the proposed method should enable a new alternative to the traditional computer-aided finite element model simulation for high-fidelity simulating and realistically visualizing full-field structural dynamics in a relatively efficient and user-friendly manner.

42 ENGINEERING↗

DOE OSTI2018

Statistical Interpolation for Surface Reconstruction of PDV and BLR Data

Data collection is becoming more and more dense in dynamic experiments, requiring a variety of diagnostics. Data are detected through such means as holography, Mie scattering / extinction, assay foils, surface imaging, and high-speed photography. The data are measured by radiography, velocimetry, ranging, Fiber Bragg, and pyrometry. The question is how can we unify information from multiple diagnostics and incorporate uncertainties to tell a coherent story about an experiment in a meaningful way? This presentation provides an overview of statistical interpolation by means of Kriging. Kriging involves three basic steps: (1) compute and model covariance spatial structure; (2) compute weights by minimizing mean squared prediction error; and (3) predict at the desired prediction sites.

dynamic experiments, holography, Mie scattering/ex↗

DOE OSTI2014

The coyote universe extended: Precision emulation of the matter power spectrum

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide predictions that are at least as accurate as the measurements, as well as robust estimates of systematic errors that are inherent to the modeling process. In the nonlinear regime of structure formation, this challenge can only be overcome by developing a large-scale, multi-physics simulation capability covering a range of cosmological models and astrophysical processes. As a first step to achieving this goal, we have recently developed a prediction scheme for the matter power spectrum (a so-called emulator), accurate at the 1% level out to k ∼ 1 Mpc{sup –1} and z = 1 for wCDM cosmologies based on a set of high-accuracy N-body simulations. It is highly desirable to increase the range in both redshift and wavenumber and to extend the reach in cosmological parameter space. To make progress in this direction, while minimizing computational cost, we present a strategy that maximally reuses the original simulations. We demonstrate improvement over the original spatial dynamic range by an order of magnitude, reaching k ∼ 10 h Mpc{sup –1}, a four-fold increase in redshift coverage, to z = 4, and now include the Hubble parameter as a new independent variable. To further the range in k and z, a new set of nested simulations run at modest cost is added to the original set. The extension in h is performed by including perturbation theory results within a multi-scale procedure for building the emulator. This economical methodology still gives excellent error control, ∼5% near the edges of the domain of applicability of the emulator. A public domain code for the new emulator is released as part of the work presented in this paper.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

A Hierarchical OPF Algorithm with Improved Gradient Evaluation in Three-Phase Networks

Linear approximation commonly used in solving alternating-current optimal power flow (AC-OPF) simplifies the system models but incurs accumulated voltage errors in large power networks. Such errors will make the primal-dual type gradient algorithms converge to solutions with voltage violation. In this paper, we improve a recent hierarchical OPF algorithm that rested on primal-dual gradients evaluated with a linearized distribution power flow model. Specifically, we propose a more accurate gradient evaluation method based on an unbalanced three-phase nonlinear distribution power flow model to mitigate the errors arising from linearization. The resultant gradients feature a blocked structure that enables our development of an improved hierarchical primal-dual algorithm to solve the OPF problem. Numerical results on the IEEE 123-bus test feeder and a 4,518-node test feeder show that the proposed method can enhance voltage safety at comparable computational efficiency with the linearized algorithm.

approximation algorithms↗