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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 289 records · Page 16

New approach to determining radiative capture reaction rates at astrophysical energies

Radiative capture reactions play a crucial role in stellar nucleosynthesis but have proved challenging to determine experimentally. In particular, the large uncertainty (≈100%) in the measured rate of the 12 C(α,γ) 16 O reaction is the largest source of uncertainty in any stellar evolution model. With development of high-current energy-recovery linear accelerators (ERLs) and high-density gas targets, measurement of the 16 O(e,e'α) 12 C reaction close to threshold using detailed balance allows a new approach to determine the 12 C(α,γ) 16 O reaction rate with significantly increased precision (<20%). We present the formalism to relate photo- and electrodisintegration reactions and consider the design of an optimal experiment to deliver increased precision. Furthermore, once the new ERLs come online, an experiment to validate the approach we propose should be carried out. This approach has broad applicability to radiative capture reactions in astrophysics.

6 ≤ A ≤ 19↗

ISPyB for BioSAXS, the gateway to user autonomy in solution scattering experiments

The ISPyB information-management system for crystallography has been adapted to include data from small-angle X-ray scattering of macromolecules in solution experiments. Logging experiments with the laboratory-information management system ISPyB (Information System for Protein crystallography Beamlines) enhances the automation of small-angle X-ray scattering of biological macromolecules in solution (BioSAXS) experiments. The ISPyB interface provides immediate user-oriented online feedback and enables data cross-checking and downstream analysis. To optimize data quality and completeness, ISPyBB (ISPyB for BioSAXS) makes it simple for users to compare the results from new measurements with previous acquisitions from the same day or earlier experiments in order to maximize the ability to collect all data required in a single synchrotron visit. The graphical user interface (GUI) of ISPyBB has been designed to guide users in the preparation of an experiment. The input of sample information and the ability to outline the experimental aims in advance provides feedback on the number of measurements required, calculation of expected sample volumes and time needed to collect the data: all of this information aids the users to better prepare for their trip to the synchrotron. A prototype version of the ISPyBB database is now available at the European Synchrotron Radiation Facility (ESRF) beamline BM29 and is already greatly appreciated by academic users and industrial clients. It will soon be available at the PETRA III beamline P12 and the Diamond Light Source beamlines I22 and B21.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Monitoring Sulfuric Acid and Temperature Using Raman Spectroscopy and Multivariate Chemometrics

Multivariate regression models were optimized for the quantification of sulfuric acid (H 2 SO 4 ) [0–8 M] and temperature (20 °C–80 °C) in the presence of ammonium sulfate ((NH 4 ) 2 SO 4 [0–0.6 M]) using Raman spectroscopy. Optical vibrational spectroscopy is a useful nondestructive technique for the in situ analysis of complex chemical systems notoriously difficult to monitor in situ and in real-time. Multivariate analysis, a chemometrics method, can be paired with these nondestructive optical methods for determining analyte concentration and speciation in complex solutions, such as dissociated species in polyprotic acids, e.g., H 2 SO 4 . The effect of temperature is often overlooked although it can have a major influence on speciation and the corresponding Raman spectra. Here, in this study, partial least squares regression models were optimized for the quantification of H 2 SO 4 and its two deprotonated forms as a function of temperature. Measuring bisulfate as a function of temperature is particularly challenging owing to changes in the second dissociation constant. A designed training set effectively minimized the sample set size and trained a robust predictive model with percent root mean square error of <3% for H 2 SO 4 . The practical strategy employed here was demonstrated to be effective for building chemometric models that directly account for dynamic temperatures with static samples and is shown to be amenable to flow cell analysis applications with a simple calibration transfer for process monitoring applications.

D-optimal design↗

Optimizing the Accelerated Recursive Doubling Algorithm for Block Tridiagonal Systems of Equations

The need to solve block tridiagonal systems with hundreds or thousands of right-hand sides for the same block tridiagonal matrix is common in a variety of disciplines. To meet this need, the Accelerated Recursive Doubling Algorithm was developed. After a right-hand side independent phase, the algorithm allows for the quick, online calculation of solutions for different right-hand sides. In this work, we present methods to optimize the Accelerated Recursive Doubling Algorithm in memory usage and computation time in a hybrid parallelization model. The right-hand side independent phase of the naïve implementation takes ≥ 11/3 the amount of memory required to store the tridiagonal matrix, while our implementation reduces the fraction to ≈ 5/3 . The right-hand side dependent phase of the naïve implementation takes ≥ 6 times the amount of memory required to store the right-hand side, while our implementation reduces the fraction to ≈ 3. The computation time for the independent phase is reduced to ≈ 2/3 times that of the naïve implementation, while the computation time for the dependent phase is reduced to ≈ 5/9 . With increasing numbers of shared-memory threads q on every distributed processing element, we have O(q) theoretical speedup.

97 MATHEMATICS AND COMPUTING↗

Constrained Deep Reinforcement Learning for Energy Sustainable Multi-UAV Based Random Access IoT Networks With NOMA

In this paper, we apply the Non-Orthogonal Multiple Access (NOMA) technique to improve the massive channel access of a wireless IoT network where solar-powered Unmanned Aerial Vehicles (UAVs) relay data from IoT devices to remote servers. Specifically, IoT devices contend for accessing the shared wireless channel using an adaptive p-persistent slotted Aloha protocol; and the solar-powered UAVs adopt Successive Interference Cancellation (SIC) to decode multiple received data from IoT devices to improve access efficiency. To enable an energy-sustainable capacity-optimal network, we study the joint problem of dynamic multi-UAV altitude control and multi-cell wireless channel access management of IoT devices as a stochastic control problem with multiple energy constraints. We first formulate this problem as a Constrained Markov Decision Process (CMDP), and propose an online model-free Constrained Deep Reinforcement Learning (CDRL) algorithm based on Lagrangian primal-dual policy optimization to solve the CMDP. Extensive simulations demonstrate that our proposed algorithm learns a cooperative policy in which the altitude of UAVs and channel access probability of IoT devices are dynamically controlled to attain the maximal long-term network capacity while ensuring energy sustainability of UAVs, outperforming baseline schemes. The proposed CDRL agent can be trained on a small network, yet the learned policy can efficiently manage networks with a massive number of IoT devices and varying initial states, which can amortize the cost of training the CDRL agent.

42 ENGINEERING↗

SU-F-BRB-07: A Plan Comparison Tool to Ensure Robustness and Deliverability in Online-Adaptive Radiotherapy

Purpose: To develop a plan comparison tool that will ensure robustness and deliverability through analysis of baseline and online-adaptive radiotherapy plans using similarity metrics. Methods: The ViewRay MRIdian treatment planning system allows export of a plan file that contains plan and delivery information. A software tool was developed to read and compare two plans, providing information and metrics to assess their similarity. In addition to performing direct comparisons (e.g. demographics, ROI volumes, number of segments, total beam-on time), the tool computes and presents histograms of derived metrics (e.g. step-and-shoot segment field sizes, segment average leaf gaps). Such metrics were investigated for their ability to predict that an online-adapted plan reasonably similar to a baseline plan where deliverability has already been established. Results: In the realm of online-adaptive planning, comparing ROI volumes offers a sanity check to verify observations found during contouring. Beyond ROI analysis, it has been found that simply editing contours and re-optimizing to adapt treatment can produce a delivery that is substantially different than the baseline plan (e.g. number of segments increased by 31%), with no changes in optimization parameters and only minor changes in anatomy. Currently the tool can quickly identify large omissions or deviations from baseline expectations. As our online-adaptive patient population increases, we will continue to develop and refine quantitative acceptance criteria for adapted plans and relate them historical delivery QA measurements. Conclusion: The plan comparison tool is in clinical use and reports a wide range of comparison metrics, illustrating key differences between two plans. This independent check is accomplished in seconds and can be performed in parallel to other tasks in the online-adaptive workflow. Current use prevents large planning or delivery errors from occurring, and ongoing refinements will lead to increased assurance of plan quality.

60 APPLIED LIFE SCIENCES↗

SU-F-J-105: Towards a Novel Treatment Planning Pipeline Delivering Pareto- Optimal Plans While Enabling Inter- and Intrafraction Plan Adaptation

Purpose: To develop a new IMRT treatment planning methodology suitable for the new generation of MR-linear accelerator machines. The pipeline is able to deliver Pareto-optimal plans and can be utilized for conventional treatments as well as for inter- and intrafraction plan adaptation based on real-time MR-data. Methods: A Pareto-optimal plan is generated using the automated multicriterial optimization approach Erasmus-iCycle. The resulting dose distribution is used as input to the second part of the pipeline, an iterative process which generates deliverable segments that target the latest anatomical state and gradually converges to the prescribed dose. This process continues until a certain percentage of the dose has been delivered. Under a conventional treatment, a Segment Weight Optimization (SWO) is then performed to ensure convergence to the prescribed dose. In the case of inter- and intrafraction adaptation, post-processing steps like SWO cannot be employed due to the changing anatomy. This is instead addressed by transferring the missing/excess dose to the input of the subsequent fraction. In this work, the resulting plans were delivered on a Delta4 phantom as a final Quality Assurance test. Results: A conventional static SWO IMRT plan was generated for two prostate cases. The sequencer faithfully reproduced the input dose for all volumes of interest. For the two cases the mean relative dose difference of the PTV between the ideal input and sequenced dose was 0.1% and −0.02% respectively. Both plans were delivered on a Delta4 phantom and passed the clinical Quality Assurance procedures by achieving 100% pass rate at a 3%/3mm gamma analysis. Conclusion: We have developed a new sequencing methodology capable of online plan adaptation. In this work, we extended the pipeline to support Pareto-optimal input and clinically validated that it can accurately achieve these ideal distributions, while its flexible design enables inter- and intrafraction plan adaptation. This research is financially supported by Elekta AB, Stockholm, Sweden.

60 APPLIED LIFE SCIENCES↗

Data association algorithm for large-scale multi-object tracking with complex interactions

We present an online multi-object tracking algorithm to track multiple objects across a large number of image frames. Our work is motivated by the need to study evolution of nanoscale objects by transmission electron microscopy. The proposed approach is based on the existing multi-way data association tracking algorithm that is capable of tracking interacting objects with complex behaviors (i.e., merge, split, overlap, and appearance or disappearance). The multi-way data association is an offline algorithm to associate objects across all image frames at one step with a global optimization, which does not scale very well for large number of image frames. The proposed online tracking algorithm processes image frames as they arrive by detecting all objects in the newly arrived image frame and making the associations of the objects to those detected from the previous frame by the multi-way data association. This frameby-frame association scheme can cause fragmented traces of the objects that are occasionally misdetected for some image frames. We overcome this issue by allowing previously unassociated objects to be associated when the objects reappear within a fixed number of future image frames, namely the frame-delayed association. We combine the multi-way data association with the frame-delayed association to be able to track interacting objects with accurate handling of object disappearance events. The proposed method is validated through applications to simulated multi-object tracking problem and a real multi-object tracking problem. Here, the outcome of the proposed method is compared with four state-of-the-art algorithms.

36 MATERIALS SCIENCE↗

Optimization with Neural Network Feasibility Surrogates: Formulations and Application to Security-Constrained Optimal Power Flow

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data assimilation and for Bayesian estimation. They also open a perspective for optimal experimental design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Distribution System State Estimation With High Penetration of Demand Response Enabled Loads

Demand-side operations incentivize utility customers to take part in various grid services. A demand response enabled load (DREL) is a flexible grid asset that schedules electricity consumption in response to a time-of-use (TOU) energy price. Consequently, its energy profile differs from that of a conventional load that is insensitive to price. This difference may cause new challenges for distribution system state estimation (DSSE). It is well known that DSSE often needs to use pseudo-measurements based on historic load profiles to increase system observability. However, historic profiles of conventional loads are not representative of DREL behaviors. Additionally, the inaccuracy impacts DSSE results and other DSSE-dependent operations. In this paper, we propose an online pseudo-measurement generation approach for DSSE with DRELs. We formulate an optimization model to represent DRELs self-adjusting actions. Sampling-based stochastic optimization techniques are proposed to account for uncertainties in DRELs. A set of representative DREL behavior data corresponding to the samples are used to characterize DREL pseudo-measurements. Case studies with modified IEEE 123-bus test system verify the validity of the proposed work.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Online Model-Free DER Dispatch Via Adaptive Voltage Sensitivity Estimation and Chance Constrained Programming

This paper proposes an online data-driven distributed energy resource management system (DERMS) for distribution system optimal DER dispatch as well as voltage regulation. Here, the key innovation is to leverage the Local Sensitivity Factor (LSF) for transforming the DER control into a computationally efficient linear programming (LP) problem. By taking real-time measurements, the estimation of LSF eliminates the need for an accurate distribution system model as well as full nodal load information, which is difficult to achieve in practice. A robust recursive least squares method is also developed to ensure the robust estimation of LSF, which is initialized using reasonable values from model-derived LSFs. This allows the system to adapt to changing operational conditions effectively. A scenario-based, chance-constrained framework is further employed to ensure voltage remains within acceptable limits in the presence of measurement and estimation uncertainties. Test results on a real-world, 759-node distribution network located in western Colorado, U.S., validate the effectiveness and robustness of the proposed control approach and demonstrate its superior performance as compared to alternative methods.

24 POWER TRANSMISSION AND DISTRIBUTION↗

US Department of Energy, Office of Science High Performance Computing Facility Operational Assessment 2021: Oak Ridge Leadership Computing Facility

Oak Ridge National Laboratory’s (ORNL’s) Leadership Computing Facility (OLCF) continues to surpass its operational target goals of supporting users; delivering fast, reliable computational ecosystems; creating innovative solutions for high-performance computing (HPC) needs; contributing to the community to build the next generation HPC workforce, and managing risks, safety, and security associated with operating some of the most powerful computers in the world. The results can be seen in the cutting-edge science conducted by users and the praise from the research community. Calendar year (CY) 2021 saw continued excellence in research supported by the OLCF’s leadership-class computing resources, including Summit (the nation’s most powerful supercomputer), the global scratch file system Alpine, the Scalable Protected Infrastructure (SPI), the Exploratory Visualization Environment for Research in Science and Technology (EVEREST), and the archival mass-storage resource High-Performance Storage System (HPSS). While maintaining access and exceptional user support for Summit, the OLCF continued to make progress on the installation and deployment of Frontier, which will be the nation’s first exascale system when it comes online at the start of CY 2023. Users have already begun running and optimizing scientific codes on Crusher, the OLCF test and development system equipped with Frontier’s architecture. Throughout the year, the OLCF maintained a strong culture of operational excellence, including risk management, workplace safety, and cybersecurity. The OLCF’s rigorous risk management strategy anticipated and mitigated risks, and at this time there are no high-priority operational risks. Similarly, ORNL and the OLCF were committed to operating under the US Department of Energy’s (DOE’s) safety regulations that ensure a safe workplace. Technical staff tracked and monitored existing threats and vulnerabilities within the OLCF while continually developing tools and practices to enhance operations without increasing the facility’s risk. CY 2021 was filled with outstanding results and accomplishments, including a very high rating from users on overall satisfaction for the eighth consecutive year; a tremendous number of node hours delivered to 1,671 researchers on Summit; and the successful delivery of the allocation split of roughly 60%, 20%, and 20% of core-hours offered for the Innovative and Novel Computational Impact on Theory and Experiment (INCITE), Advanced Scientific Computing Research Leadership Computing Challenge (ALCC), and Director’s Discretionary (DD) programs, respectively (Section 2). COVID-19 research remained a focus in 2021, and the ALCC and DD programs allocated over 1 million Summit hours to the COVID-19 High Performance Computing Consortium. These accomplishments, coupled with the high utilization rates (i.e., overall and capability usage), represent the fulfillment of the promise of leadership class machines: efficient facilitation of leadership-class computational applications.

97 MATHEMATICS AND COMPUTING↗

An Online Generalized Multiscale Discontinuous Galerkin Method (GMsDGM) for Flows in Heterogeneous Media

Abstract Offline computation is an essential component in most multiscale model reduction techniques. However, there are multiscale problems in which offline procedure is insufficient to give accurate representations of solutions, due to the fact that offline computations are typically performed locally and global information is missing in these offline information. To tackle this difficulty, we develop an online local adaptivity technique for local multiscale model reduction problems. We design new online basis functions within Discontinuous Galerkin method based on local residuals and some optimally estimates. The resulting basis functions are able to capture the solution efficiently and accurately, and are added to the approximation iteratively. Moreover, we show that the iterative procedure is convergent with a rate independent of physical scales if the initial space is chosen carefully. Our analysis also gives a guideline on how to choose the initial space. We present some numerical examples to show the performance of the proposed method.

Physics↗

New Technology-Large-Area Three- Dimensional Surface Profiling Using Only Focused Air-Coupled Ultrasound-Given 1999 R&D 100 Award

Surface topography, which significantly affects the performance of many industrial components, is normally measured with diamond-tip profilometry over small areas or with optical scattering methods over larger areas. To develop air-coupled surface profilometry, the NASA Glenn Research Center at Lewis Field initiated a Space Act Agreement with Sonix, Inc., through two Glenn programs, the Advanced High Temperature Engine Materials Program (HITEMP) and COMMTECH. The work resulted in quantitative surface topography profiles obtained using only high-frequency, focused ultrasonic pulses in air. The method is nondestructive, noninvasive, and noncontact, and it does not require light-reflective surfaces. Air surface profiling may be desirable when diamond-tip or laserbased methods are impractical, such as over large areas, when a significant depth range is required, or for curved surfaces. When the configuration is optimized, the method is reasonably rapid and all the quantitative analysis facilities are online, including two- and three-dimensional visualization, extreme value filtering (for faulty data), and leveling.

Roth, Don J.↗

Data reduction through optimized scalar quantization for more compact neural networks

Raw data generation for several existing and planned large physics experiments now exceeds TB/s rates, generating untenable data sets in very little time. Those data often demonstrate high dimensionality while containing limited information. Meanwhile, Machine Learning algorithms are now becoming an essential part of data processing and data analysis. Those algorithms can be used offline for post processing and post data analysis, or they can be used online for real time processing providing ultra low latency experiment monitoring. Both use cases would benefit from data throughput reduction while preserving relevant information: one by reducing the offline storage requirements by several orders of magnitude and the other by allowing ultra fast online inferencing with low complexity Machine Learning models. Moreover, reducing the data source throughput also reduces material cost, power and data management requirements. In this work we demonstrate optimized nonuniform scalar quantization for data source reduction. This data reduction allows lower dimensional representations while preserving the relevant information of the data, thus enabling high accuracy Tiny Machine Learning classifier models for online fast inferences. We demonstrate this approach with an initial proof of concept targeting the CookieBox, an array of electron spectrometers used for angular streaking, that was developed for LCLS-II as an online beam diagnostic tool. We used the Lloyd-Max algorithm with the CookieBox dataset to design an optimized nonuniform scalar quantizer. Optimized quantization lets us reduce input data volume by 69% with no significant impact on inference accuracy. When we tolerate a 2% loss on inference accuracy, we achieved 81% of input data reduction. Finally, the change from a 7-bit to a 3-bit input data quantization reduces our neural network size by 38%.

97 MATHEMATICS AND COMPUTING↗

Optimization of greenhouse gas emissions in second-hand consumer product recovery through reuse platforms

Highlights: • Effects of waste diversion on flow of products to reuse processes. • Framework for solid waste management that focuses on reuse processes for waste diversion. • Application of framework on the material flow and GHG emissions from clothing reuse. - Abstract: Product reuse in the solid waste management sector is promoted as one of the key strategies for waste prevention. This practice is considered to have favorable impact on the environment, but its benefits have yet to be established. Existing research describes the perspective of “avoided production” only, but has failed to examine the interdependent nature of reuse practices within an entire solid waste management system. This study proposes a new framework that uses optimization to minimize the greenhouse gas emissions of an integrated solid waste management system that includes reuse strategies and practices such as reuse enterprises, online platforms, and materials exchanges along with traditional solid waste management practices such as recycling, landfilling, and incineration. The proposed framework uses material flow analysis in combination with an optimization model to provide the best outcome in terms of GHG emissions by redistributing product flows in the integrated solid waste management system to the least impacting routes and processes. The optimization results provide a basis for understanding the contributions of reuse to the environmental benefits of the integrated solid waste management system and the exploration of the effects of reuse activities on waste prevention. A case study involving second-hand clothing is presented to illustrate the implementation of the proposed framework as applied to the material flow. Results of the case study showed the considerable impact of reuse on GHG emissions even for small replacement rates, and helped illustrate the interdependency of the reuse sector with other waste management practices. One major contribution of this study is the development of a framework centered on product reuse that can be applied to identify the best management strategies to reduce the environmental impact of product disposal and to increase recovery of reusable products.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Attention Enabled Multi-Agent DRL for Decentralized Volt-VAR Control of Active Distribution System Using PV Inverters and SVCs

This paper proposes attention enabled multi-agent deep reinforcement learning (MADRL) framework for active distribution network decentralized Volt-VAR control. Using the unsupervised clustering, the whole distribution system can be decomposed into several sub-networks according to the voltage and reactive power sensitivity relationships. Then, the distributed control problem of each sub-network is modeled as Markov games and solved by the improved MADRL algorithm, where each sub-network is modeled as an adaptive agent. An attention mechanism is developed to help each agent focus on specific information that is mostly related to the reward. All agents are centrally trained offline to learn the optimal coordinated Volt-VAR control strategy and executed in a decentralized manner to make online decisions with only local information. Compared with other distributed control approaches, the proposed method can effectively deal with uncertainties, achieve fast decision makings, and significantly reduce the communication requirements. Comparison results with model-based and other data-driven methods on IEEE 33-bus and 123-bus systems demonstrate the benefits of the proposed approach.

distribution network↗