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At least 361 records · Page 20

Performance Analysis and Simulaion of the Hydraulic Scram System in TREAT Reactor

The Transient Reactor Test Facility (TREAT) at Idaho National Laboratory (INL) serves a vital role in nuclear fuel safety research, enabling transient experiments that simulate reactivity excursions and accident scenarios. Central to these operations is the transient control rod drive system (TCRDS), which drives rapid motion of the transient control rods such that TREAT can simulate rapid power changes typical of reactor accidents. The reliability and performance of this system are critical for protecting both fuel specimens and reactor infrastructure. This study presents the initial phase of a two-year investigation into the dynamics and reliability of the TREAT hydraulic TCRDS. Conducted in collaboration with INL, the research employs a combined computational and experimental approach to analyze the system's response time, pressure transients, and potential failure modes. Emphasis is placed on understanding how fluid characteristics influence the TCRDS’s ability to achieve both rapid power changes and mechanical stability. The TRDS and the skid that powers it will be analyzed throughout this investigation. Computational modeling using computational fluid dynamics (CFD) will simulate the hydraulic response under varying conditions. In parallel, experimental testing planned at INL will validate these models and capture key performance metrics. This paper outlines the system design, analytical framework, and modeling strategies that form the foundation for later testing. Ultimately, this work aims to support improvements to the TCRDS’s design and reliability, contributing to the broader goal of enhancing nuclear fuel safety and sustaining TREAT’s mission as a premier nuclear fuel test facility.

21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗

LLNS Request for Variance From 10 CFR 851 for Construction of LLNL Emergency Operations Center

Lawrence Livermore National Security, LLC (LLNS) is submitting the following variance application requesting the use of the State of California’s Occupational Safety and Health Administration (Cal/OSHA) Regulations in lieu of Title 10 Code of Federal Regulations Part 851 (10 CFR 851, the Rule), Worker Safety and Health Program, Subpart B (Program Requirements), Subpart C (Specific Program Requirements), and Appendix A (Worker Safety and Health Functional Areas), solely with respect to the construction of the new Lawrence Livermore National Laboratory (LLNL) Emergency Operations Center (EOC) facility. The request is in support of the National Nuclear Security Administration (NNSA) “pilot” to streamline the delivery of commercial-like line item construction projects under $50 million. This pilot is aligned with the approved NA-50 safety approach for the projects in the pilot. This pilot is to test and demonstrate innovation leading to a reduced cost of construction for building commercial type structures at Department of Energy (DOE)/NNSA facilities. The variance proposes to permit local/regional construction businesses contracted to Management & Operation contractor operated facilities to bid, operate, execute, and comply with safety and health standards they utilize in their business outside of the DOE Complex. This will permit compliance to standards that are as safe and healthful as those in 10 CFR 851 without confusion, additional cost, and inefficiencies associated with the burden of compliance to an unfamiliar regulatory spectrum.

99 GENERAL AND MISCELLANEOUS↗

Development and experimental qualification of novel disruption prevention techniques on DIII-D

Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I N < 0.3 before terminating, scaling to the 3 MA ITER requirement. This is in contrast to diverted shutdowns, the majority of which disrupt at I N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Development and experimental qualification of novel disruption prevention techniques on DIII-D

Novel disruption prevention solutions spanning a range of control regimes are being developed and tested on DIII-D to enable ITER success. First, a new real-time control algorithm has been developed and tested for regulating nearness to stability limits and maintaining safety-margins. Its first application has been for reliable prevention of vertical displacement events (VDEs) by adjusting plasma elongation (κ) and the inner-gap between the plasma and inner-wall in response to real- time open-loop VDE growth rate (γ) estimators. VDEs were robustly prevented up to average open-loop growth rates of 800 rad/s with initial tunings, with only applying shape modification when near safety limits. Second, the disruption risk during fast, emergency shutdown after large tearing and locked modes can be significantly improved by transitioning to a limited topology during shutdown. More than 50% of emergency limited shutdowns after locked modes reach a final normalized current I_N < 0.3 before terminating, scaling to the 3 MA ITER requirement. Furthermore, this is in contrast to diverted shutdowns, the majority of which disrupt at I_N > 0.8. Despite improvements, these results highlight the critical importance of early prevention. Third, a novel emergency shut down method has been developed which excites instabilities to form a warm, helical core post-thermal quench. The current quench extends to ~100ms and avoids VDEs and runaway electron generation. Novel real-time machine learning disruption prediction has been integrated with the DIII-D proximity controller, and a real- time compatible multi-mode MHD spectroscopy technique has been developed. Results presented here were enabled by a focused effort, the Disruption Free Protocol, in DIII-D’s 2019-20 campaign to complement disruption prevention experiments with a large piggy-back program. In addition to testing novel techniques, it is estimated to have helped avoid 32 potential disruptions in piggyback operations with rapid, early shutdowns after large rotating n=1 or locked modes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Assessing the viability of a new subsize tensile specimen geometry for evaluation of structural nuclear and additively manufactured materials

The use of subsize specimens in nuclear materials testing has been a subject of ongoing interest due to radiation safety concerns and resource conservation needs. It is also of interest in additive manufacturing (AM), also known as 3D-printing, as subsize specimens can more accurately represent the behavior of the small, intricate geometries often produced using AM. A novel, extremely small geometry, called the Subsize Teeny (SST) was recently developed and is of interest for implementation. Given its extraordinarily small size and the complexities associated with subsize specimen testing, adequate vetting of this geometry is necessary to ensure data quality. Here, a variety of unirradiated nuclear structural materials were tested in the SST geometry and compared against the well-established SSJ3 geometry. In addition, two case studies implementing the SST as a screening geometry for AM materials were also conducted. The question of SST viability was found to be highly nuanced and will often be dependent on the context or application in question. It was determined, however, that the SST is a largely invalid geometry for exceptionally coarse-grained materials or in cases where the physical defect volume equals or exceeds 0.1 % or where the specimen machining parameters result in significant surface alterations. On the other hand, it was determined that the SST may be employed with confidence if the test material is nearly or totally free of physical defects, isotropic, demonstrates homogeneous plastic deformation, and possesses a fine-grained, nearly or totally homogeneous microstructure with at least twelve slip systems.

Additive manufacturing↗

Improved Verification and Validation Testing and Tools [Slides]

All MCNP team supported V&V test suites are now developed in a separate repository from the MCNP source code within a Python-based framework. This entire framework will be distributed with the upcoming MCNP6.3 release. Most V&V test suites distributed with MCNP6.2 will be distributed in new framework. New V&V test suites are done or being worked on for the MCNP6.3 release.

97 MATHEMATICS AND COMPUTING↗

EV SALaD 2023 Demonstration: Best Practices and Mitigations for Protecting EVSE Infrastructure

The Electric Vehicle Secure Architecture Laboratory Demonstration (EV SALaD) program is a demonstration of cybersecurity best practices for high-power electric vehicle (EV) charging infrastructure led by Idaho National Laboratory (INL), in collaboration with other DOE National Laboratories participating in the EVs at Scale Consortium.a Sandia National Laboratories (SNL) and Pacific Northwest National Laboratory (PNNL) participated in the first 2-year (FY22-23) demonstration cycle for EV SALaD. This report documents the FY23 demonstration, the second in a series of demonstrations and collaborations in deploying and operating cybersecure EV charging infrastructure. It includes a summary of improvements from the FY22 demonstration, technical analysis of the FY23 demonstration, how the research demonstrates cyber-physical and cybersecurity best practices for high-power EV charging infrastructure, and related impacts to national and energy security. For EV SALaD, the FY22 demonstration focused on the detection, ranking, and prioritization of anomalous events for high-power EV charging. The FY23 demonstration additionally included the demonstration of cybersecurity best practices, which included protection and mitigation solutions to prevent, respond, and recover from anomalous events. During the demonstrations, the multi-lab EV SALaD team conducted a Test Effect Payload (TEP)b evaluation on extreme fast charger (XFC) hardware equipped with Cerberus, a detection and response solution, to demonstrate anomaly detection and mitigation cybersecurity best practices against cyber-enabled events.

33 ADVANCED PROPULSION SYSTEMS↗

Lessons Learned: Summary of Insights From the HERO WEC and Waves to Water Deployments Between 2022 and 2024

In 2020, a team from the National Renewable Energy Laboratory (NREL) partnered with the East Carolina University Coastal Studies Institute to develop a small, modular, wave-powered point absorber desalination prototype. That prototype, known as the hydraulic and electric reverse osmosis wave energy converter (HERO WEC), was intended to de-risk the installation activities planned for the Waves to Water Prize sponsored by the Water Power Technologies Office. The NREL team was given approximately 18 months to design, build, bench test, and deploy the HERO WEC prototype. Since the initial HERO WEC development, it has been used for two in-lab test programs and three ocean deployments. The first in-lab test program focused on ensuring that the overall operation of the device occurred as expected and on validating the operation of safety systems such as pressure relief valves or electrical breakers for load mitigation. The second in-lab test program was the first time the NREL team leveraged NREL’s large-amplitude motion platform to characterize the performance of the HERO WEC. Of the three in-water deployments, the first deployment was effectively an installation and recovery practice with no meaningful wave activity during the time that it was installed. The second deployment was a 2-week effort that enabled both the electric and hydraulic configurations of the device to be in the water for approximately 5 days each. This deployment was also the first time that the team had the opportunity to perform a drivetrain swap on the Coastal Studies Institute research vessel. The third deployment had to be split into two separate installations due to minor damage incurred from the WEC spinning during the initial installation. This report summarizes the deployments, the challenges encountered with each deployment, and the lessons learned for future work.

16 TIDAL AND WAVE POWER↗

Burst characteristics of advanced accident-tolerant FeCrAl cladding under temperature transient testing

Here assessment of burst characteristics of accident-tolerant fuel (ATF) claddings is essential to evaluate the safety margins of nuclear reactors, and better understanding can enable accelerated licensing for reactor concepts that include the new materials. Therefore, this study investigated the burst behavior of an ATF candidate of C26M, which is an iron–chromium–aluminum alloy (FeCrAl) under transient testing like the simulated loss-of-coolant accident (LOCA) conditions, except the water-quenching phase, in light-water reactors (LWRs). The effect of LOCA specimen length was assessed in terms of post-burst tube parameters. No critical length effect was determined on the burst pressure, burst location, and burst size measurements. Burst temperature showed larger variation likely due to its measurement approach used in this study. The post-test diametral strain was identified as the critical parameter to reduce the specimen length as compared to tube burst length or width. Postmortem optical metrology and digital image correlation were employed to determine the local strain-state during the simulated LOCA, which showed the loading path was close to equibiaxial conditions in regions away from the burst location, rather than internally pressurized conditions (or “plane-strain” tension). Pst-test microstructural characterizations of the FeCrAl revealed that ductile damage was present at the edge of the outer radial surface while the rest of the material was ruptured via cleavage at LOCA burst temperatures. Furthermore, internal grain boundary cracks were observed at locations away from the tube burst region. This behavior was considered to occur during the cooling down period of the simulated LOCA test. Overall, this study aimed to provide essential data for fuel performance code development by considering micromechanics of the deformation and failure.

36 MATERIALS SCIENCE↗

IER 516 - Zirconium Test Assembly (ZTA) Preliminary Experimental Design [Slides]

Zirconium present in large quantities in criticality safety applications such as fuel manufacturing and processing facilities, and in commercial thermal nuclear reactors. ICSBEP lacks benchmarks optimized for zirconium sensitivity to validate zirconium evaluations. Evaluators lack isotopic differential nuclear data in regions of high importance to fission systems.

K-PSO 2.0↗

Securing Grid-interactive Efficient Buildings (GEB) through Cyber Defense and Resilient System (CYDRES)

The DOE CYDRES project is driven by the urgent need to address critical research gaps in the domain of cyber-physical security of smart buildings, including Grid-interactive Efficient Buildings (GEBs). CYDRES, a real-time advanced building resilient platform, aims to enhance the cyber-attack-immune capabilities of buildings through multi-layered prevention, detection, and adaptation mechanisms. CYDRES consists of five key modules: a multi-layer network analyzer, an Automatic Fault Detection, Diagnosis, and Prognosis (AFDDP) framework, an intelligent mode selector, a cyber-resilient control framework, and a situation awareness platform. The Network Analyzer employs a data-driven framework that includes a protocol state learning tool and a CRF (Conditional Random Field) command validator. In Hardware-In-the-Loop (HIL) testbeds, it achieved 100% detection accuracy with a false alarm rate of 3%, validating its efficacy in identifying selected cyber-attacks. The AFDDP framework leverages pattern matching, PCA (Principal Component Analysis)-based strategies, and a DBN (Dynamic Bayesian Network)-based fault diagnosis approach to pinpoint the causes of physical system abnormalities using Building Automation System (BAS) data. In HIL experiments, the AFDDP module attained a detection accuracy of over 95% with a false alarm rate below 7%. Additionally, the fault detector utilized machine learning (Random Forest) and deep learning (Multi-Layer Perceptron) methods with acoustic sensor data to achieve a 100% fault detection accuracy in Heating, Ventilation, and Air-Conditioning (HVAC) equipment. The Mode Selector offered real-time impact analysis, allowing immediate actions to protect BASs in the face of emerging threats. The cyber-resilient control framework included an adaptive Model Predictive Control (MPC) and a measurement compensator, reducing temperature violations by up to 94% and improving the total demand flexibility by up to 70% in HIL experiments. Such HIL experiments covered a cyber-attack case and a physical fault case, showcasing CYDRES’ efficiency in maintaining operational continuity during threats. The situation awareness platform in Grafana enhanced real-time threat detection and response visualization, augmenting the operational awareness for building operators. CYDRES demonstrated high technical effectiveness in various test scenarios, particularly in HIL environments. The project's phased development approach ensured efficient use of resources, highlighting its practical feasibility and readiness for commercialization. By enhancing the security and resilience of building operations, CYDRES represents a significant advance in mitigating risks associated with cyber-physical systems, thereby enhancing public confidence in the safety of modern building infrastructure. Future directions for the project include expanding testing protocols, refining AFDDP methodologies, exploring more comprehensive resilient control strategies, and testing in real commercial buildings.

42 ENGINEERING↗

Distributed Coaxial Cable Sensors for In-Situ Condition Based Monitoring of Coal-Fired Boiler Tubes

The increasing contributions of renewable energy sources present new challenges to the operation and maintenance of the existing coal-fired power plants. One of the major operational risks is the unexpected failure of superheater boiler tubes, leading to the most unplanned power plant outrages. The boiler tube failure is difficult to predict due to the harsh operating environments. Therefore, condition-based monitoring (CBM) with a reliable high temperature sensor becomes necessary to produce a meaningful assessment of the health condition of boiler tubes and their remaining lifetime. In this work, the stainless-steel and quartz coaxial cable sensor (SSQ-CCS) is proposed for in-situ distributed monitoring of the boiler tube temperatures in existing coal-fired power plants. Comprehensive tests have been conducted with an in-house testing facility at Clemson University to study and evaluate the sensors’ performance in the temperature range of 100℃ to 600℃. The results indicated that the measurement resolution of the SSQ-CCS sensor is better than 1℃, and the drift is less than 2% over long-period testing. Meanwhile, multi-physics finite element analysis has been conducted to optimize the design and evaluate the safety of the SSQ-CCS temperature sensor under various operational conditions. Based on the performance obtained in the laboratory-scale testing, a field test has been implemented at a power plant. Four SSQ-CCS temperature sensors were installed for in-situ monitoring of the temperatures of a power plant’s superheat tube assembles. The data acquisition system has been successfully set up and collected sensing signals for more than three months. The sensing signals have been post-processed, and the monitored temperature history through the SSQ-CCS temperature sensor has been validated and compared with the conventional high temperature thermal couple data.

Jiao, Xinyu↗

Structural Health Monitoring: Using an Autoencoder to Identify Damage in a Bolted Joint [Capstone Project]

Los Alamos National Laboratory (LANL) is an important fixture in the United States Department of Energy’s (DOE) National Nuclear Security Agency (NNSA) complex. LANL is one of the largest national laboratories in the country, and the laboratory’s primary mission is to support the nation’s nuclear stockpile. The lab functions as a design agencies for the NNSA and performs extensive testing on weapons as part of that mission. The shock and vibration test team at LANL utilizes electrodynamic shaker systems for important qualification testing in support of the laboratory’s mission. Modern engineering relies heavily on bolted joints to connect two objects. During these shaker tests, engineers depend on bolted joints to secure the test article to a fixture and the fixture to the table. The test article may be hazardous and contain high explosives which could create a safety issue if a bolted joint failed. A loss of preload in a bolt will affect the way energy is input to the system and may introduce nonlinearities as the joint opens and closes. The loss of preload can create challenges controlling the test and make acquired signals useless. Being able to monitor preload within bolted joints during testing can improve the quality of the data and keep workers safe.

42 ENGINEERING↗

Research and Test Reactor Fuels

PRO-RR is the research reactor focused program element of the broader Proliferation Resistance Optimization program (PRO-X) under the National Nuclear Safety Administration (NNSA) in the U.S. Department of Energy (DOE). PRO-X provides a framework for integrating proliferation resistance in nuclear system designs to minimize weapons usable nuclear materials (WUNM) production and diversion pathways while optimizing systems performance for peaceful use missions. PRO-RR applies the PRO-X mission objectives to research reactor system design. This document serves as one of the foundational documents for the PRO-RR-Fuel System Design technical team by documenting current research reactor fuels usage. The PRO-RR-Fuel System Design technical team consists of subject matter experts from Argonne National Laboratory (Argonne) and Savannah River National Laboratory (SRNL). In order to determine the preferred fuel of use in upcoming research and test reactors to optimize proliferation resistance, performance, and safety, it is useful to assess the fuels that have been used in the past, or are currently in use. This report reviews the historical and current fuels used in research and test reactors to inform future fuel selection. Chapter 2 discusses the low-enriched uranium (LEU) fuels currently in use in terms of thermal power level and utilization of the reactor. Chapter 3 summarizes the fabrication processes for common fuel types. Chapter 4 discusses in detail the fuel types in use in research and test reactors. A review of the cladding types in use is presented in Chapter 5, and a historical review of research and test reactor fuel fabricators is presented in Chapter 6. The data collection strategy used the International Atomic Energy Agency (IAEA) research reactor database [1] as a starting point. Information on the fuel used was gathered on research reactors (other than critical assemblies) that were listed as operational, planned, or in temporary shutdown in the IAEA database. Data on the fuel type, geometry, enrichment, uranium loading, cladding type, and fabricator were collected for each of the reactors available in the public domain. Sources of data included conference papers, journal articles, and facility and fabricator websites. Data on research reactors operating on LEU fuels are presented in Appendix A, while Appendix B presents data collected on all reactors at the time of publication of this report. Appendix C presents data collected on reactors that were part of the M3 research and test reactor conversion program.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Mid–height seismic isolation of equipment in nuclear power plants

An innovative seismic isolation solution for designers of safety-class equipment in advanced nuclear power plants is introduced. The test specimen was a tall, slender, carbon steel vessel that could represent a reactor vessel, steam generator, or a heat exchanger in a nuclear power plant: 240 inches tall, outer diameter of 60 inches, and wall thickness of 1 inch. The vessel was supported by three radial mounts at its mid-height, near its center of gravity, on a steel frame. The vessel was subjected to three-component ground motions using a 6DOF earthquake simulator. The specimen was filled with water for testing to indirectly account for the fluid and internal equipment present inside a prototype vessel. Three configurations were tested: non-isolated, isolated using single Friction Pendulum (SFP) bearings, and isolated using triple Friction Pendulum (TFP) bearings. The test results demonstrate that mid-height seismic isolation is practical and enables a significant reduction in horizontal spectral accelerations. Furthermore, these outcomes are not specific to the spherical sliding bearings used in the experiments but are broadly applicable to mid-height, seismically isolated equipment.

42 ENGINEERING↗

Guarded Hot Cylinder Apparatus for Characterization of Thermal Insulation Systems and Materials at Liquid Hydrogen Temperatures

As interest in liquid hydrogen (LH2) continues to grow within the energy and mobility sectors, so does the demand for testing capabilities at deep cryogenics temperatures. However, cost-, complexity-, and safety-related challenges associated with handling LH2 effectively limit the landscape of possible options. As an alternative, LH2 temperatures can be accessed via a helium-based cryogenic refrigerator, or “cryocooler”. Recently, NASA and its partners CB&I and Shell began the development of a cryocooler-based calorimeter to characterize the thermal performance of insulations and other materials down to 20 K. Deemed the Guarded Hot Cylinder (GHC), the apparatus utilizes a small vacuum chamber in conjunction with a GM cryocooler and trim heater to control the cold boundary temperature. A sealed, cylindrical copper cup bolts to the cryocooler and houses the material specimen, with an internal, cylindrical test heater assembly to maintain the warm boundary. The steady-state heat load, traveling radially through the specimen, is measured via the electrical input power to the test heater and then used to evaluate the material’s absolute thermal performance. Initial checkout and validation of the GHC using a common bulk-fill insulation material showed close agreement with published data from standardized LN2 boiloff calorimetry testing. The instrument is now considered a lab standard, with the goal of incorporating it into the ASTM C1774 standard in the future, and it is in continuous use, examining insulation materials for next-generation LH2 applications.

Swanger, Adam (ORCID:000000021487592X)↗

Methodology for Generating Covariance Data of Thermal Neutron Scattering Cross Sections

This paper details and implements a framework for evaluating thermal neutron scattering cross sections that provide S(α,β) data and covariance data for hydrogen in light water. This methodology involves perturbing model parameters of molecular dynamics potentials and fitting the simulation results to experimental data. The framework is general and can be applied to any material or simulation method. The fit is made using the Unified Monte Carlo method to experimentally measure double-differential scattering cross sections of light water at the Spallation Neutron Source at Oak Ridge National Laboratory. Mean values and covariance data were generated for model parameters, phonon density of states, double-differential cross sections, and total scattering cross sections. These posterior parameter values were very similar to their prior values with a maximum relative error of 0.54%. This falls within in the Unified Monte Carlo–calculated uncertainties on the order of 2.7%. Additionally, posterior double-differential cross sections agree favorably with ENDF/B-VIII.0 cross sections. The new thermal scattering law was tested by comparing it against benchmarks from the International Criticality Safety Benchmark Evaluation Project Handbook, which showed a slight improvement over the ENDF/B-VIII.0 library. Additionally, the covariance matrix of the phonon density of states was validated to confirm that the spread of k eff from the density of states used to generate the covariance matrix was similar to the spread of k eff from the density of states of the sampled covariance matrix.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

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↗