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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 OSTI2020

Scalable Knowledge Graph Analytics at 136 Petaflop/s

We are motivated by newly proposed methods for data mining large-scale corpora of scholarly publications, such as the full biomedical literature, which may consist of tens of millions of papers spanning decades of research. In this setting, analysts seek to discover how concepts relate to one another. They construct graph representations from annotated text databases and then formulate the relationship-mining problem as one of computing all-pairs shortest paths (APSP), which becomes a significant bottleneck. In this context, we present a new high-performance algorithm and implementation of the Floyd-Warshall algorithm for distributed-memory parallel computers accelerated by GPUs, which we call DSNAPSHOT (Distributed Accelerated Semiring All-Pairs Shortest Path). For our largest experiments, we ran DSNAPSHOT on a connected input graph with millions of vertices using 4, 096nodes (24,576GPUs) of the Oak Ridge National Laboratory's Summit supercomputer system. We find DSNAPSHOT achieves a sustained performance of 136×1015 floating-point operations per second (136petaflop/s) at a parallel efficiency of 90% under weak scaling and, in absolute speed, 70% of the best possible performance given our computation (in the single-precision tropical semiring or “min-plus” algebra). Looking forward, we believe this novel capability will enable the mining of scholarly knowledge corpora when embedded and integrated into artificial intelligence-driven natural language processing workflows at scale.

Kannan, Ramakrishnan {ramki}↗
DOE OSTI2024

LENS: Learning Enabled Network Synthesis

RTRC and UMD have developed novel machine learning based methods under the ARPA-E DIFFERENTIATE program for rapid acceleration of hypothesis generation in complex architecture design spaces involving both discrete choices of component inclusion and interconnection and continuous parametric decisions. The project named Learning Enabled Network Synthesis (LENS) further demonstrated the developed methods on challenging electrical power converter design problems by identifying the most suitable circuit topologies and simultaneously selecting the most appropriate components to achieve optimized design of power converter with improved performances. We demonstrated that LENS could enable exploration of very large design space of circuit topologies and components by addressing the limitations of conventional design process in non-linear, high switching speed, multi-dimensional power converter design and optimization. The key innovation developed in LENS is the seamless integration of statistical learning and logical reasoning techniques and building on the individual strengths of these techniques for rapid hypothesis discovery. The main component of LENS comprises of: 1) Graph Reasoning Engine (GRE) to enforce composition rules that rapidly reject all discrete architectures that are composed incorrectly and generates an adaptive database of feasible designs which can be used by ML modules, 2) Graph Generative Learning module which is a deep neural network based generative model for graph architectures which can enable design space exploration beyond the dataset generated by the GRE, 3) Graph Reduced Order Model (ROM) for graph domains for accelerating computation of output metrics, and 4) Active learning and Rule Discovery module for sample efficient learning and extracting logical rules from the learned ML models which will be integrated in the GRE to enhance the filtering effectiveness. LENS approach can be applied to any design domains where designs can be represented as multi-attribute graphs. The LENS team integrated the various technical innovations listed above into an optimization pipeline and exercised the optimization pipeline on the converter design problem. The LENS project demonstrated that the developed AI/ML technologies can be used to generate novel converter circuits >45x faster than experts on chosen use-cases. This can enable faster design space exploration and identification of new designs which are not considered by experts due to the increasing design space complexity. This has significant potential impact on the public and energy needs of the country. It is currently estimated that 30% of all electrical powers generated passes through power converters. The future estimate is that 80% of all power generated would be passing through converters. LENS fills a critical gap in this space since by accelerating the design process the designers would be able to generate more efficient converters which can lead to significant energy savings for the country.

42 ENGINEERING↗
DOE OSTI2025

General field evaluation in high-order meshes on GPUs

Robust and scalable function evaluation at any arbitrary point in the finite/spectral element mesh is required for querying the partial differential equation solution at points of interest, comparison of solution between different meshes, and Lagrangian particle tracking. This is a challenging problem, particularly for high-order unstructured meshes partitioned in parallel with MPI, as it requires identifying the element that overlaps a given point and computing the corresponding reference space coordinates. Here, we present a robust and efficient technique for general field evaluation in large-scale high-order meshes with quadrilaterals and hexahedra. In the proposed method, a combination of globally partitioned and processor-local maps are used to first determine a list of candidate MPI ranks, and then locally candidate elements that could contain a given point. Next, element-wise bounding boxes further reduce the list of candidate elements. Finally, Newton’s method with trust region is used to determine the overlapping element and corresponding reference space coordinates. Since GPU-based architectures have become popular for accelerating computational analyses using meshes with tensor-product elements, specialized kernels have been developed to utilize the proposed methodology on GPUs. The method is also extended to enable general field evaluation on surface meshes. The paper concludes by demonstrating the use of the proposed method in various applications ranging from mesh-to-mesh transfer during r-adaptivity to Lagrangian particle tracking.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Evaluating Performance Portability with the CMS Heterogeneous Pixel Reconstruction code

In the past years the landscape of tools for expressing parallel algorithms in a portable way across various compute accelerators has continued to evolve significantly. There are many technologies on the market that provide portability between CPU, GPUs from several vendors, and in some cases even FPGAs. These technologies include C++ libraries such as Alpaka and Kokkos, compiler directives such as OpenMP, the SYCL open specification that can be implemented as a library or in a compiler, and standard C++ where the compiler is solely responsible for the offloading. Given this developing landscape, users have to choose the technology that best fits their applications and constraints. For example, in the CMS experiment the experience so far in heterogeneous reconstruction algorithms suggests that the full application contains a large number of relatively short computational kernels and memory transfer operations. In this work we use a stand-alone version of the CMS heterogeneous pixel reconstruction code as a realistic use case of HEP reconstruction software that is capable of leveraging GPUs effectively. We summarize the experience of porting this code base from CUDA to Alpaka, Kokkos, SYCL, std::par, and OpenMP offloading. We compare the event processing throughput achieved by each version on NVIDIA and AMD GPUs as well as on a CPU, and compare those to what a native version of the code achieves on each platform.

Andriotis, Nikolaos↗
DOE OSTI2025

Accelerating GNNs on GPU Sparse Tensor Cores through N:M Sparsity-Oriented Graph Reordering

Recent advancements in GPU hardware support have introduced the capability to leverage N:M sparse patterns for substantial performance gains. Graphs in Graph Neural Networks (GNNs) are typically sparse, but the sparsity is often irregular, not conforming to such sparse patterns. In this paper, we propose a novel graph reordering algorithm, the first of its kind, to reshape irregular graph data into the N:M structured sparse pattern at the tile level, allowing linear-algebra-based graph operations in GNNs to benefit from the N:M sparse hardware. The optimization is lossless, maintaining the accuracy of GNN. It can remove 98-100\% violations of the N:M sparse patterns at the vector level, and increase the proportion of conforming graphs in SuiteSparse collection from 5-9\% to 88.7-93.5\%. On A100 GPUs, the optimization accelerates Sparse Matrix Matrix (SpMM) by up to 43X (2.3X -- 7.5X on average) and speeds up the key graph operations in GNNs on real graphs by as much as 8.6X (3.5X on average).

artificial intelligence, graph neural networks↗
DOE OSTI2020

The Kokkos Ecosystem [Brief]

In 2016/2017, the field of High-Performance Computing (HPC) entered a new era driven by fundamental physics challenges to produce ever more energy and cost-efficient processors. Since the convergence on the Message-Passing Interface (MPI) standard in the mid-1990s, application developers enjoyed a seemingly static view of the underlying machine — that of a distributed collection of homogeneous nodes executing in collaboration. However, after almost two decades of dominance, the sole use of MPI to derive parallelism acted as a limiter to improved future performance. While MPI is widely expected to continue to function as the basic mechanism for communication between compute nodes for the immediate future, additional parallelism is required on the computing node itself if high performance and efficiency goals are to be realized. When reviewing the architectures of the top HPC systems today, the change in paradigm is clear: the compute nodes of the leading machines in the world are either powered by many-core chips with a few dozen cores each, or use heterogeneous designs, where traditional CPUs marshal work to massively parallel compute accelerators which has as many as 200,000 processing threads in flight simultaneously. Complicating matters further for application developers, each processor vendor has its own preferred way of writing code for their architecture.The Kokkos EcoSystem was released by Sandia in 2017 to address this new era in HPC system design by providing a vendor independent performance portable programming system for scientific, engineering, and mathematical software applications written in the C++ programming language. Using Kokkos, application developers can be more productive because they will not have to create and maintain separate versions of their software for each architecture, nor will they have to be experts in each architecture's peculiar requirements. Instead, they will have a single method of programming for the diverse set of modern HPC architectures. While Kokkos started in 2011 as a programming model only, it soon became clear that complex applications needed more. It is also critical to have a portable mathematical functions and developers need tools to debug their applications, gain insight into the performance characteristics of their codes and tune algorithm performance parameters through automated processes. The Kokkos EcoSystem addresses those needs through its three main components: the Kokkos Core programming model, the Kokkos Kernels math library, and the Kokkos Tools project.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

kynema-fmb [SWR-23-07]

Kynema-FMB (FKA: Kynema) is an open-source performance portable flexible multibody (FMB) dynamics solver designed for time-domain simulations. While originally tailored for wind turbine structural dynamics, the formulation and implementation are those of a general flexible-multidbody dynamics solver that can readily be applied to a wide range of systems. Kynema was designed with a narrow focus, namely to provide a lightweight, fast, accurate FMD solver for coupling to computational-fluid-dynamics (CFD) codes, especially the CFD codes in the Kynema suite, for fluid-structure-interaction (FSI) simulations. Kynema-FMB is equipped to model systems that can be represented as a collection of beams and rigid bodies that are connected through constraints. Degrees of freedom are defined in the inertial/global frame of reference and include displacements and rotations (formally as rotation matrices, but stored as quaternions). The underlying formulation is built on a Lie-group time integrator designed for index-3 differential-algebraic equations, which is second-order accurate in time (Bruls et al., 2012). Beam models are based on geometrically exact beam theory and are discretized as high-order spectral finite elements similar to those in BeamDyn (Wang et al., 2017). The governing equations for a FMD system like a wind turbine constitute a highly nonlinear system of constrained partial-differential equations. Kynema-FMB uses analytical Jacobians in the nonlinear-system solves in each time step. Linear systems use sparse storage and several third-party sparse-linear-system solvers are enabled. Ill conditioning of linear systems is mitigated with preconditioning described in Bottasso et al, 2008. Kynema-FMB is integrated with a simple open-source controller (ROSCO). There is an application programming interface (API) for coupling to geometry-resolved CFD (like that in Sharma et al., 2023) and actuator-force CFD (like that in Kuhn et al., 2025). In the latter, for actuator-line models, Kynema-FMB includes an internal blade-element solver that depends on user-provided lookup tables for coefficients of lift and drag, i.e., aerodynamic polars. Kynema-FMB is written in C++ and leverages Kokkos and Kokkos-Kernels (KokkosEcosystem) as its performance portability layer enabling simulations on both CPU and GPU systems. The repository is equipped with extensive automated testing at the unit and regression/system levels. The following describes the high-level development objectives conceived for Kynema: *Kynema will follow modern software development best practices, including test-driven development (TDD), version control, hierarchical automated testing, and continuous integration (CI) for a robust development environment. *The core data structures are memory efficient and enable vectorization and parallelization at multiple levels. *Data structures are data-oriented to exploit methods for accelerated computing including high utilization of chip resources (e.g., single instruction multiple data (SIMD) instruction sets) and parallelization using GP-GPUs. *The computational algorithms incorporate robust open-source libraries for mathematical operations, resource allocation, and data management. *The API design considers multiple stakeholder needs and ensure integration with existing and future ecosystems for data science, machine learning, and AI. *Kynema-FMB is written in modern C++ and leverages Kokkos as its performance-portability library with inspiration from the kynema stack.

Sprague, MichaelA.↗
DOE OSTI2020

Electronic Bottleneck Suppression in Next‐Generation Networks with Integrated Photonic Digital‐to‐Analog Converters

Digital‐to‐analog converters (DAC) are indispensable functional units in signal processing instrumentation and wide‐band telecommunication links for both civil and military applications. As photonic systems are capable of high data throughput and low latency, an increasingly found system limitation stems from the required domain crossing such as digital to analog and electronic to optical. A photonic DAC implementation, in contrast, enables a seamless signal conversion with respect to both energy efficiency and short signal delay, often requiring bulky discrete optical components and electric–optic transformation, hence introducing inefficiencies. Herein, a novel coherent parallel photonic DAC concept along with a 4‐bit experimental prototype capable of performing this DAC without optic–electric–optic domain crossing is introduced. This new paradigm guarantees a linear intensity weighting among bits when operating at high sampling rates (50 GHz), featuring an exceptional sampling efficiency (> 100 GS ) and small footprint (≈1 mm 2 ) in an 8‐bit implementation. Importantly, this photonic DAC enables seamless interfaces of next‐generation data processing hardware with high relevance in data centers, task‐specific compute accelerators such as neuromorphic engines, and network edge processing applications.

Meng, Jiawei↗
DOE OSTI2026

Graph Identification of Proteins in Tomograms (GRIP-Tomo) 2.0: Topologically aware classification for proteins

Cryo-electron tomography (cryo-ET) enables structural characterization of biomolecules under near-native conditions. Existing approaches for interpreting the resulting three-dimensional volumes are computationally expensive and have difficulty interpreting density associated with small proteins/complexes. To explore alternate approaches for identifying proteins in cryo-ET data we pursued a Graph Network and topologically invariant approach. Here, we report on a fast algorithm that classifies particles by searching for nuances of evolutionarily conversed motifs and the geometrical characteristics of protein structure. GRIP-Tomo 2.0 is a machine-learning pipeline that extracts interpretable topological features of protein structures within noisy experimental backgrounds. Compared to version 1.0, the new pipeline includes three upgrades that significantly improve performance including synthetic tomogram generation simulating realistic noise, graph-based persistent feature extraction as protein fingerprints, and high-performance computing acceleration. GRIP-Tomo 2.0 achieves over 90% accuracy in classifying between proteins and noise using both real and synthetic datasets which represents a foundational step toward advancing cryo-ET workflows and empowering automated visual proteomics.

Li, Chengxuan↗
DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗
DOE OSTI2022

Large-scale scenarios of electric vehicle charging with a data-driven model of control

Transportation electrification is forecast to bring millions of new electric vehicles to roads worldwide this decade. Planning to support those vehicles depends on detailed scenarios of their electricity demand in both uncontrolled and controlled or smart charging scenarios. In this work, we present a novel modeling approach to enable rapid generation of demand estimates that represent the impact of controlled charging for large-scale scenarios with millions of individual drivers. To model the effect of load modulation control on aggregate charging profiles, we propose a novel machine learning approach that replaces traditional optimization approaches. We demonstrate its performance modeling workplace charging control under a range of electricity rate schedules, achieving small errors (2.5%–4.5%) while accelerating computations by more than 4000 times. To generate the uncontrolled charging demand for scenarios with residential, workplace, and public charging we use statistical representations of a large data set of real charging sessions. We demonstrate the methodology by generating diverse sets of scenarios for California's charging demand in 2030 which consider multiple charging segments and controls, each run locally in under 50 s. We further demonstrate support for rate design by modeling the large-scale impact of a new, custom rate schedule for workplace charging.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Insights into Supported Subnanometer Catalysts Exposed to CO via Machine-Learning-Enabled Multiscale Modeling

Subnanometer catalysts offer high noble metal utilization and superior performance for several reactions. However, understanding their structures and properties on an atomic scale under working conditions is challenging due to the large configurational space. Here, we introduce an efficient multiscale framework to predict their stability exposed to an adsorbate. The framework integrates a comprehensive toolset including density functional theory (DFT) calculations, cluster expansion, machine learning, and structure optimization. The end-to-end machine-learning workflow guides DFT data generation and enables significant computational acceleration. We demonstrate the approach for CO-adsorbed Pdn (n = 1–55) clusters on CeO 2 (111). Simulation results reveal that CO can facilitate restructuring by stabilizing smaller planar structures and bilayer structures of specific intermediate sizes, consistent with experimental reports. Metal–support interactions, preferential CO adsorption, and metal nuclearity and structure control catalyst stability. As a result, the framework allows automatic discovery of stable catalyst structures and a systematic strategy to exploit properties in the subnanometer scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Ligand removal energetics control CO 2 electroreduction selectivity on atomically precise, ligated alloy nanoclusters

Atomically precise, thiolate-protected gold nanoclusters (TPNCs) exhibit remarkable catalytic performance for the electrochemical reduction of carbon dioxide (CO 2 R) to CO. The origin of their high CO 2 R activity and selectivity has been attributed to partial ligand removal from the thiolate-covered surfaces of TPNCs to expose catalytically active sulfur atoms. Recently, heterometal doped (alloy) TPNCs have been shown to exhibit enhanced CO 2 R activity and selectivity compared to their monometallic counterparts. However, systematic studies on the effect of doping (metal type and location on TPNC) on active site exposure and CO 2 R activity are missing in literature. Herein, we apply Density Functional Theory calculations to investigate the effect of heterometal (Pt, Pd, Hg and Cd) doping of Au 25 (SR) 18 TPNC on the active site exposure and CO 2 R activity and selectivity. In this study, we reveal that doping significantly modifies relevant TPNC electronic properties, such as electron affinity, while also altering partial ligand removal and carboxyl (*COOH) intermediate formation energies. Furthermore, we demonstrate that changing the dopant (e.g. Hg) position can change the selectivity of the TPNC towards CO (g) or H 2(g) formation, highlighting the importance of dopant locations in TPNC-based CO 2 R. Most notably, we report a universal (i.e. capturing different dopant types and positions) linear trend between the ligand removal energy and i) the *COOH formation energy, as well as, ii) the hydrogen (*H) formation energy on the different alloy TPNCs. Thus, utilizing the ligand removal energy as a descriptor for CO 2 RR activity and selectivity, our work opens new avenues for accelerated computational screening of different alloy TPNCs for electrocatalytic CO 2 R applications.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Electronic descriptors for dislocation deformation behavior and intrinsic ductility in bcc high-entropy alloys

Controlling the balance between strength and damage tolerance in high-entropy alloys (HEAs) is central to their application as structural materials. Materials discovery efforts for HEAs are therefore impeded by an incomplete understanding of the chemical factors governing this balance. Through first-principles calculations, this study explores factors governing intrinsic ductility of a crucial subset of HEAs—those with a body-centered cubic (bcc) crystal structure. Analyses of three sets of bcc HEAs comprising nine different compositions reveal that alloy chemistry profoundly influences screw dislocation core structure, dislocation vibrational properties, and intrinsic ductility parameters derived from unstable stacking fault and surface energies. Key features in the electronic structure are identified that correlate with these properties: the fraction of occupied bonding states and bimodality of the d-orbital density of states. The findings enhance the fundamental understanding of the origins of intrinsic ductility and establish an electronic structure–based framework for computationally accelerated materials discovery and design.

36 MATERIALS SCIENCE↗
DOE OSTI2025

OpenARC

OpenARC is an open-sourced, very High-Level Intermediate Representation (HLIR)-based, extensible compiler framework, where various performance optimizations, traceability mechanisms, fault tolerance techniques, etc., can be built for better debuggability/performance/resilience on the complex accelerator computing. OpenARC is the first OpenACC compiler supporting Altera FPGAs, in addition to NVIDIA GPUs, AMD GPUs, and Intel Xeon Phis.

Lee, Seyong [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2025

Seismic DAS Observations of a large underground chemical explosion in dry tuff

On 18 October 2023 a 16.3-ton TNT equivalent chemical explosion was detonated underground at the Nevada National Security Site, generating a seismic event (Meyers et al., 2024). The associated seismic wavefield was measured on a Distributed Acoustic Sensing (DAS) array with slant range distances from 27 m – 1123 m. The first arriving phase traveled at an apparent velocity of about 2640 m s -1 from 27 m to 420 m slant range and about 2470 m s -1 from 505 m to 1123 m slant range according to the first arrival moveouts on the DAS data. The first arrival from the explosion temporarily saturated the cable from a slant range of 27 m – 186 m and 0.009 s to 0.084 s post detonation. From 186 m slant range to 420 m slant range, peak strain rates of 5.6 x 10 6 nm m -1 s -1 were observed for the first arrival phase. For the first arrival from 505 m slant range to 1123 m slant range, peak strain rates reduced to 8.0 x 10 4 nm m -1 s -1 . A comparison of the scaled accelerations computed from DAS, the geophone pairs, and the measurements of co-located accelerometer pairs show common agreement at the scaled ranges of the single point sensors. This study adds to the body of work reporting near-source DAS observations of the seismic wavefields generated by underground chemical explosions. These results indicate that near-source DAS observations can refine interpretations of phase identification from single-point sensor observations. Phase identification could be one mechanism that contributes scatter to single point seismic measurements which would confound the performance of empirical relationships for small explosions. Removing that mechanism may therefore reduce interstation variability and increase empirical relationship performance for small explosions.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2025

Seismic DAS observations of a large underground chemical explosion in dry tuff

On 18 October 2023 a 16.3-ton TNT equivalent chemical explosion was detonated underground at the Nevada National Security Site, generating a seismic event with a magnitude of 1.7 (Meyers et al., 2024). The associated seismic wavefield was measured on a Distributed Acoustic Sensing (DAS) array with slant range distances from 27 m – 1123 m. The first arriving phase traveled at an apparent velocity of about 2640 m s -1 from 27 m to 420 m slant range and about 2470 m s -1 from 505 m to 1123 m slant range according to the first arrival moveouts on the DAS data. The first arrival from the explosion temporarily saturated the cable from a slant range of 27 m – 186 m and 0.009 s to 0.084 s post detonation. From 186 m slant range to 420 m slant range, peak strain rates of 5.6 x 10 6 nm m -1 s -1 were observed for the first arrival phase. For the first arrival from 505 m slant range to 1123 m slant range, peak strain rates reduced to 8.0 x 104 nm m -1 s -1 . A comparison of the scaled accelerations computed from DAS, the geophone pairs, and the measurements of co-located accelerometer pairs show common agreement at the scaled ranges of the single point sensors. This study adds to the body of work reporting near-source DAS observations of the seismic wavefields generated by underground chemical explosions. These results indicate that near-source DAS observations can refine interpretations of phase identification from single-point sensor observations. Phase identification could be one mechanism that contributes scatter to single point seismic measurements which would confound the performance of empirical relationships for small explosions. Removing that mechanism may therefore reduce interstation variability and increase empirical relationship performance for small explosions.

58 GEOSCIENCES↗
DOE OSTI2022

Hierarchical Optimal Power Flow with Improved Gradient Evaluation

Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which rested on primal-dual gradients evaluated in a linearized distribution power flow model. Specifically, we identify a risk of voltage violation arising from the model linearization, and propose a more accurate gradient evaluation method to eliminate that risk. We further develop a hierarchical primal-dual algorithm to solve OPF based on the proposed gradient evaluation method. Numerical results on IEEE networks show that our algorithm can enhance voltage safety with satisfactory computational efficiency.

distributed algorithm↗