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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

Evaluation of nonlinear control performance of air handling units under variable operation conditions using root distribution approach

The control systems at Air handling units (AHUs) have nonlinear nature, resulting potentially in sluggish, aggressive, or oscillatory responses under variable operation conditions. This paper is to develop an approach for evaluating the nonlinear control performance of AHUs under variable operation conditions and for identifying the impact of varying multiple operation parameters which guides controller design. To do so, an operation parameter-based root distribution technique, intended to sketch the paths traced by closed-loop poles as multiple operation parameters are varied, is first introduced. The technique—which may be viewed as an extension of conventional, single-variable root locus—is then applied to a fan speed control system that includes a motor with a variable frequency drive and a supply fan with an air duct under variable fan speed and duct static pressure. Using the technique, the system’s stability region is graphically identified. The system is also found to be aggressive and gradually lose its stability as the fan speed decreases and the duct static pressure increases, which is validated by the field tests. Here, the root distribution approach is an effective tool to evaluate the performance of any nonlinear control systems at AHUs with multiple variable operation parameters without requiring time-domain simulations.

42 ENGINEERING↗

Comprehensive Analysis of Model Parameter Uncertainty Influence on Evaluation of HVAC Operation to Mitigate Indoor Virus: A Case Study for an Office Building in a Cold and Dry Climate

Simulation-based studies of HVAC operation to mitigate indoor virus have been conducted to understand tradeoffs between indoor air quality (IAQ) and energy consumption. However, the influence of model parameter uncertainty in these studies has not been systematically quantified, which is critical when providing guidance to building operators. To address this gap, we identify 20 model parameters for a typical medium office building system in a cold and dry climate that can influence IAQ and energy consumption for indoor virus scenarios. Next, the distributions of the parameter values are estimated from literature and a set of simulation samples for three representative days is generated that simultaneously sample all of the parameters from their distributions. Two HVAC virus mitigation strategies are studied: increased filtration using MERV 13 filters and increased ventilation, via supply of 100% outdoor air into buildings. The model parameter uncertainty leads to significant variability in the results, particularly for the IAQ because of the highly uncertain virus generation rate. Use of 100% outdoor air can be beneficial for some uncertain scenarios on the hot day, but shows less IAQ improvement and/or significant energy increases on the other days. The virus removal efficiency and pressure drop of the HVAC filter, fan efficiency, and internal heat gain are the most important parameters to determining the tradeoffs of the two strategies. Our results demonstrate how this model parameter uncertainty analysis methodology can provide practical guidance to building operators.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Intermetallic particle heterogeneity controls shear localization in high-strength nanostructured Al alloys

The mechanical behavior of two nanocrystalline Al alloys, Al-Mg-Y and Al-Fe-Y, is investigated with in-situ micropillar compression testing. Both alloys were strengthened by a hierarchical microstructure including grain boundary segregation, nanometer-thick amorphous complexions, carbide nanorod precipitates with sizes of a few nanometers, and submicron-scale intermetallic particles. The maximum yield strength of the Al-Mg-Y system is measured to be 950 MPa, exceeding that of the Al-Fe-Y system (680 MPa), primarily due to a combination of more carbide nanorods and more amorphous complexions. Both alloys exhibited yield strengths much higher than those of commercial Al alloys, and therefore have great potential for structural applications. However, some micropillar specimens were observed to plastically soften through shear banding. Post-mortem investigation revealed that intermetallic-free deformation pathways of a few micrometers in length were responsible for this failure. Further characterization showed significant grain growth within the shear band. The coarsened grains maintained the same orientation with each other, pointing to grain boundary mechanisms for plastic flow, specifically grain rotation and/or grain boundary migration. Here, the presence of intermetallic particles makes it difficult for both matrix and intermetallic grains to rotate into the same orientation due to the different lattice parameters and slip systems. Therefore, we are able to conclude that a uniform distribution of intermetallic particles with an average spacing less than the percolation length of shear localization can effectively prevent the maturation of shear bands, offering a design strategy for high-strength nanocrystalline Al alloys with both high strength and stable plastic flow.

36 MATERIALS SCIENCE↗

A review of technical and regulatory limits for hydrogen blending in natural gas pipelines

We report there is rising interest globally in the use of hydrogen for the provision of electricity or heat to industry, transport, and other applications in low-carbon energy systems. While there is attention to build out dedicated hydrogen infrastructure in the long-term, blending hydrogen into the existing natural gas pipeline network is also thought to be a promising strategy for incorporating hydrogen in the near-term. However, hydrogen injection into the existing gas grid poses additional challenges and considerations related to the ability of current gas infrastructure to operate with blended hydrogen levels. This review paper focuses on analyzing the current understanding of how much hydrogen can be integrated into the gas grid from an operational perspective and identifies areas where more research is needed. The review discusses the technical limits in hydrogen blending for both transmission and distribution networks; facilities in both systems are analyzed with respect to critical operational parameters, such as decrease in energy density, increased flow speed and pressure losses. Safety related challenges such as, embrittlement, leakage and combustion are also discussed. The review also summarizes current regulatory limits to hydrogen blending in different countries, including ongoing or proposed pilot hydrogen blending projects.

08 HYDROGEN↗

Accelerating Embedding Potential Optimization by Reconstructing the Pseudo-Valence Electron Density

Density functional embedding theory (DFET) enables use of electronic structure methods with higher accuracy than density functional theory in a local region, with applications thus far ranging from (photo/electro)catalysis to reactions in solution. DFET partitions a large collection of atoms into smaller groups that interact via a shared embedding (interaction) potential V emb , determined via functional optimization. The optimized effective potential (OEP) process used to optimize V emb is time-consuming and becomes a computational bottleneck due to sharp, oscillating features of V emb near nuclei. Here, similar to pseudopotential theory, by reconstructing electron densities used in the OEP process from smoother pseudo-valence-only (PVO) electron densities as proxies for total densities of the full system and subsystems, we can retain accuracy in the embedded electronic structure calculations while potentially reducing the overhead of V emb construction, within the projector augmented-wave (PAW) formalism. We explore three different chemical reactions as exemplars to test PVO–DFET, namely, H 2 dissociative adsorption on a Cu(111) surface, H 2 O adsorption on a Pt(111) surface, and aqueous [Ca 2+ –SO 4 2– ] ion-pair formation. The PVO approximation works well for all three systems with minimal loss of accuracy (∼10–70 meV error relative to the original exact-derivative (ED) approach) while accelerating V emb generation for the Cu and Pt systems respectively by 20× and 5×. Given proper numerical convergence parameters, the spatial distributions of differences between PVO- and ED-based V emb outside the core regions are small, explaining the exceptional agreement between the two approaches. Finally, we anticipate that this more efficient PVO–DFET approximation will be useful whenever computation of V emb is much more expensive than subsequent embedded high-level electron correlation calculations.

approximation↗

Visualization of phase-space orbit topological boundary using imaging neutral particle analyzer

A newly-developed imaging neutral particle analyzer (INPA) in the DIII-D tokamak interrogates phase space occupied by fast ions on multiple different orbit topologies, including passing, stagnation, trapped and potato orbits. Depending on plasma parameters and beam injection geometries, this new INPA system is capable of visualizing distributions of fast ions on the selected orbit topology and its associated orbit topology boundaries. More importantly, the system is able to directly visualize the pitch angle scattering process in phase space by measuring fast ions that are scattered across the trapped-passing orbit topology boundaries. It also enables visualization of fast ion confined-loss boundaries, which are determined by particle energy, plasma current and magnetic field.The key goal of this new INPA system is to directly measure pitch angle scattering across phase space induced by drift waves and its interaction with Alfv'en eigenmodes, i.e., a key issue towards \redit{a} future fusion power plant.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adaptive machine learning for time-varying systems: low dimensional latent space tuning

Machine learning (ML) tools such as encoder-decoder convolutional neural networks (CNN) can represent incredibly complex nonlinear functions which map between combinations of images and scalars. For example, CNNs can be used to map combinations of accelerator parameters and images which are 2D projections of the 6D phase space distributions of charged particle beams as they are transported between various particle accelerator locations. Despite their strengths, applying ML to time-varying systems, or systems with shifting distributions, is an open problem, especially for large systems for which collecting new data for re-training is impractical or interrupts operations. Particle accelerators are one example of large time-varying systems for which collecting detailed training data requires lengthy dedicated beam measurements which may no longer be available during regular operations. We present a novel method of adaptive ML for time-varying systems. Our approach is to map very high (N ≈ 100k) dimensional inputs (a combination of scalar parameters and images) into the low dimensional (N ≈ 2) latent space at the output of the encoder section of an encoder-decoder CNN. We then actively tune the low dimensional latent space-based representation of complex system dynamics by the addition of an adaptively tuned feedback vector directly before the decoder sections builds back up to our image-based high-dimensional phase space density representations. This method allows us to learn correlations within and to quickly tune the characteristics of incredibly large parameter space systems and to track their evolution in real time based on feedback without massive new data sets for re-training. We demonstrate that our method can accurately predict and track the phase space of charged particle beams at various locations in a particle accelerator by adaptively adjusting in real-time while the unknown input beam distribution of the accelerator is changing in shape, charge, and offset and while the RF system of the accelerator itself is also changing in an unpredictable way. For FACET-II we demonstrate that such an approach has the potential to use transverse deflecting cavity and energy spread spectrum beam measurements to accurately predict 2D projections of the 6D phase space of the electron beam at the plasma wakefield acceleration interaction point where such diagnostics are unavailable.

47 OTHER INSTRUMENTATION↗

Deep Reinforcement Learning Enabled Physical-Model-Free Two-Timescale Voltage Control Method for Active Distribution Systems

Active distribution networks are being challenged by frequent and rapid voltage violations due to renewable energy integration. Conventional model-based voltage control methods rely on accurate parameters of the distribution networks, which are difficult to achieve in practice. This paper proposes a novel physical-model-free two-timescale voltage control framework for active distribution systems. To achieve fast control of PV inverters, the whole network is first partitioned into several subnetworks using voltage-reactive power sensitivity. Then, the scheduling of PV inverters in the multiple sub-networks is formulated as Markov games and solved by a multi-agent soft actor-critic (MASAC) algorithm, where each subnetwork is modeled as an intelligent agent. All agents are trained in a centralized manner to learn a coordinated strategy while being executed based on only local information for fast response. For the slower time-scale control, OLTCs and switched capacitors are coordinated by a single agent-based SAC algorithm using the global information with considering control behaviors of the inverters. Particularly, the two-level agents are trained concurrently with information exchange according to the reward signal calculated from the data-driven surrogate model. Comparative tests with different benchmark methods on IEEE 33-and 123-bus systems and 342-node low voltage distribution system demonstrate that the proposed method can effectively mitigate the fast voltage violations and achieve systematical coordination of different voltage regulation assets without the knowledge of accurate system model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Measurement-informed Dynamic Aggregation of Distribution Systems

This paper proposes a measurement-informed dynamic aggregation methodology in order to create equivalent representations of distribution systems that are compatible with large-scale transmission analysis. By optimizing an equivalent feeder parameters using time-series measurements of active power, reactive power, and voltage at the Point of Interconnection (POI), the approach yields simplified yet dynamically accurate equivalents. Implemented in PSCAD with models of photovoltaic–battery systems, three-phase motors, and static loads, the method employs hybrid differential evolution and bounded least-squares optimization laying the foundation for for real-time state estimation and optimized sensor placement in distribution networks.

Ahmed, Kazi Ishrak [University of Tennessee, Knoxv↗

Fully Distributed Acoustic and Magnetic Field Monitoring Via a Single Fiber Line for Optimized Production of Unconventional Resource Plays

This is the final technical report for the Virginia Tech Center for Photonics Technology (VT-CPT) research project entitled “Fully Distributed Acoustic and Magnetic Field Monitoring Via a Single Fiber Line for Optimized Production of Unconventional Resource Plays”. In the the four-year effort, VT-CPT collaborated with the Departments of Mathmatics at VT and Sentek Instrument, LLC (Sentek) to develop a fiber-optic sensing system capable of real-time simultaneous distributed measurement of multiple subsurface, drilling, and production parameters. The ultra-sensitive fiber optic distributed acoustic sensing technology, picoDAS, developed by Sentek was integrated with a novel multi-material optical sensing fiber fabricated by CPT-VT to obtain distributed acoustic and magnetic field measurements with ultrahigh sensitivity and high spatial resolution. The sensing technology successfully developed and demonstrated under this research program is truly unique has application beyond subsurface imaging to include carbon storage and electrical grid monitoring, as well as healthcare and nuclear fusion. The project, sponsored by the Advanced Technology Program, began in 2019 and had the original goal of developing the next generation of harsh environment sensing systems. Exhaustive theoretical modeling was performed to optimize the multi-material optical fiber design. VT developed the processing techniques employed to successfully fabricate single mode fibers with metal cladding wires. Sensing fibers with nickel and Metglas cladding wires were fully characterized, inscribed with sensors, and fully integrated with the picoDAS system. Laboratory scale testing was performed to demonstrate performance upon exposure to lateral and transverse magnetic fields. Preliminary field trials were performed for prototype magnetic and acoustic sensing systems upon near surface deployment at VT. The distributed acoustic and magnetic field sensing system was advanced from a (Technology Readiness Level) TRL=2 to a TRL=5 via laboratory scale system validation in relevant environments. The truly one-of-its kind distributed magnetic and acoustic sensing system is expected to find immediate applications that require subsurface monitoring, to include carbon storage site monitoring, and has the potential to be a distributive technology in healthcare and electric grid markets. The technologies developed by Virginia Tech’s Center for Photonics Technology will support the mission of the National Energy Technology Laboratory (NETL) to drive innovation and deliver solutions for an environmentally sustainable and prosperous energy future by ensuring affordable, abundant, and reliable energy that drives a robust economy and national security. Technical accomplishments during the program are summarized briefly here and described in detail in the remainder of the report.

02 PETROLEUM↗

Cathodic Protection Modeling for Hanford Underground Double-Shell Tank Farms

Hanford stores millions of gallons of radioactive and chemically hazardous waste from the production of weapon materials in tank farms consisting of underground carbon-steel storage tanks surrounded by reinforced concrete. Six of these Hanford tank farms use double-shell storage tanks (DSTs). The DST farms were constructed from 1968 to 1986 with a planned 40–50 year design life, so some are already operating beyond their initial life expectancy. Ultrasonic testing (UT) has indicated significant thinning on the bottom of the secondary (outer) liner of these tanks, believed to arise from groundwater intrusion driving concrete side corrosion. There is no direct access to the steel/concrete interface between the tank and the concrete pad, making it difficult to apply a chemical-based mitigation strategy or to conduct repairs, but cathodic protection (CP) is a possible method to inhibit further concrete-side corrosion. Hanford already uses CP to protect below grade steel piping within the tank farms and connected to the tanks, but this system was not designed to protect the tank bottoms. CP design must account for the structures surrounding the DSTs, including the steel reinforcing bars (rebar) within the concrete pad and vault, various process lines, and the existing CP system. In this study, finite element analysis (FEA) modeling was carried out to simulate CP protection of 1) a single tank and CP anode to develop options for modeling the rebar and to compare to a simpler circuit model and 2) the entire Hanford AN tank farm as a representative example consisting of seven tanks, associated piping, and both existing and new CP anodes. Both circuit and FEA models predict that significant protective current could be delivered to the bottoms of the tanks with the addition of tank-protection anodes below the depth of the tanks. Simulations with only the existing pipe-protection anodes active confirmed that only a very small current to the tank bottoms is predicted under present conditions. Multiple simplified representations of the dome and wall rebar were tested to reduce the computational complexity of the tank-farm simulations, resulting in modeling the rebar as edge elements with a prescribed effective circumference that matches the real rebar surface area. The geometry of the rebar is also simplified into horizontal hoops around the tank walls and radial rebar over the dome with increased effective circumference to retain the target surface area. This simplification was found to greatly reduce the complexity and solution time of the models without large changes in current distributions, especially to the tank bottom. A range of values were tested for model parameters such as soil and concrete resistivities and polarization resistance to investigate their impact on the current and electric potential distributions. Depending on the parameters used, FEA simulations predict some risk of overprotection, particularly on the piping system; since overprotection can also lead to surface damage associated with hydrogen gas generation at the interface (e.g. hydrogen embrittlement or damage to coatings), this needs to be considered when refining the design of the new CP system. Comparison between the FEA models and the circuit model representation demonstrated that the circuit model could not match the predicted FEA current distribution, even when using the exact same surface areas. This discrepancy appeared to be at least partly attributable to the impact of the relative positions of the tank components and anodes to each other and to the ground surface. The FEA model accounts for the relative positions since it solves the governing equations in three dimensions, but the circuit model cannot account for the positioning. In particular, the circuit model underpredicts the current to the tank bottom and overpredicts the current to the dome compared to FEA for the baseline geometry. The FEA models omitted the electrically isolated rebar in the bottom concrete slab. However, a circuit based stray current model estimated that only 2.1% of the total current through the slab would stray into the rebar, corresponding to ~0.21 A for a target current density of 2 mA/ft2 to the tank bottom. The estimated corrosion driven by this amount of stray current is predicted to yield a lifetime of >400 years for the minimum rebar diameter, assuming an acceptable cross-section area loss of 10%.

d'Entremont, Anna [Savannah River National Laborat↗

Role of local atomic short-range order distribution in alloys: Why it matters in Si-Ge-Sn alloys

Short-range order (SRO) in alloys refers to deviations from a perfectly random distribution of atoms in lattice sites within a short distance. Conventionally, the degree of the deviations has been quantified using an average SRO parameter, but such a coarse-grained description does not reflect how the deviations occur at a finer level. Here we show the distribution of the local atomic SRO parameter, which describes the occurring frequency of a local structural motif, carries the crucial information for both structures and properties in Si-Ge-Sn alloy system. Here this is demonstrated through the fact that distinct SRO structures can exhibit the same average SRO parameter but very different distributions and disparate electronic structures. By deliberately creating special structures that explicitly match the structural information at different levels, we show the distribution of local atomic SRO parameters contain critical structural features that are missing in the average SRO parameter but can substantially contribute to material’s properties. Our finding thus calls for the need for considering the finer structural details to effectively describe alloys’ structures and properties.

36 MATERIALS SCIENCE↗

Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

Science & Technology - Other Topics↗

Accurate data-driven surrogates of dynamical systems for forward propagation of uncertainty

Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. Here, this work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.

42 ENGINEERING↗

Capture Cavities For The Cw Polarized Positron Source Ce + baf

The initial design of the capture cavities for the continuous wave (CW) polarized positron beams at Jefferson Lab (Ce + BAF) is presented. A chain of standing wave multi-cell copper cavities inside a solenoid tunnel are selected to improve the positron capture efficiency. The cavity design strategy is presented to accommodate constrains from the large phase distribution of the incident beams, RF power and RF heating. A matrix of design parameters’ range are given for future system optimization when the capture cavities are considered together with other sub-systems and beam dynamics. The contents will also be useful for other CW cavity design for beams with large phase space distribution.

43 PARTICLE ACCELERATORS↗

Origin of spin–orbit misalignments: the microblazar V4641 Sgr

ABSTRACT Of the known microquasars, V4641 Sgr boasts the most severe lower limit (>52°) on the misalignment angle between the relativistic jet axis and the binary orbital angular momentum. Assuming the jet and black hole spin axes coincide, we attempt to explain the origin of this extreme spin–orbit misalignment with a natal kick model, whereby an aligned binary system becomes misaligned by a supernova kick imparted to the newborn black hole. The model inputs are the kick velocity distribution, which we measure customized to V4641 Sgr, and the immediate pre/post-supernova binary system parameters. Using a grid of binary stellar evolution models, we determine post-supernova configurations that evolve to become consistent with V4641 Sgr today and obtain the corresponding pre-supernova configurations by using standard prescriptions for common envelope evolution. Using each of these potential progenitor system parameter sets as inputs, we find that a natal kick struggles to explain the origin of the V4641 Sgr spin–orbit misalignment. Consequently, we conclude that evolutionary pathways involving a standard common envelope phase followed by a supernova kick are highly unlikely for V4641 Sgr. An alternative interpretation is that the jet axis does not reliably trace the black hole spin axis. Our results raise concerns about compact object merger statistics gleaned from binary population synthesis models, which rely on unverified prescriptions for common envelope evolution and natal kicks. We also challenge the spin–orbit alignment assumption routinely invoked to measure black hole spin magnitudes.

79 ASTRONOMY AND ASTROPHYSICS↗

An Assessment of Receiver Algorithms for Distributed Massive MIMO Systems: Investigating Design Solutions and Performance

This study investigates receiver design solutions for distributed Massive Multiple Input Multiple Output (D-m MIMO) systems, taking into account parameters such as number of access points as well as concerns related to channel estimates that use single-carrier frequency-domain equalization (SC-FDE). A significant contribution of this research is the integration of Low-Density Parity-Check (LDPC) codes to simplify coding complexity and enhance communication efficiency. The research examines different receiver designs, such as spatial antenna correlation and sophisticated channel estimation methods. The authors propose integrating LDPC codes into the receiver architecture to simplify computations and enhance error correction and decoding. Moreover, the paper examines performance evaluation measures and approaches, highlighting the trade-offs among complexity, spectral efficiency, and error performance. The comparative analysis indicates the benefits, in terms of performance, of incorporating LDPC codes and improving system throughput and dependability. We examine four distinct receiver algorithms: zero-forcing (ZF), minimum mean square error (MMSE), maximum ratio combining (MRC), and equal gain combining (EGC). The study shows that MRC and EGC receivers work well in D-m MIMO because they make the receiver system less computationally demanding.

Gashtasbi, Ali↗

Multisource Data Fusion Outage Location in Distribution Systems via Probabilistic Graphical Models

Efficient outage location is critical to enhancing the resilience of power distribution systems. However, accurate outage location requires combining massive evidence received from diverse data sources, including smart meter (SM) last gasp signals, customer trouble calls, social media messages, weather data, vegetation information, and physical parameters of the network. This is a computationally complex task due to the high dimensionality of data in distribution grids. In this paper, we propose a multi-source data fusion approach to locate outage events in partially observable distribution systems using Bayesian networks (BNs). A novel aspect of the proposed approach is that it takes multi-source evidence and the complex structure of distribution systems into account using a probabilistic graphical method. Our method can radically reduce the computational complexity of outage location inference in high-dimensional spaces. The graphical structure of the proposed BN is established based on the network’s topology and the causal relationship between random variables, such as the states of branches/customers and evidence. Utilizing this graphical model, accurate outage locations are obtained by leveraging a Gibbs sampling (GS) method, to infer the probabilities of de-energization for all branches. Compared with commonly-used exact inference methods that have exponential complexity in the size of the BN, GS quantifies the target conditional probability distributions in a timely manner. As a result, a case study of several real-world distribution systems is presented to validate the proposed method.

24 POWER TRANSMISSION AND DISTRIBUTION↗