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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Accelerate M-TIP on GPUs and deploy to Summit and NERSC-9 (against simulated data) WBS 2.2.4.05 ExaFEL, Milestone ADSE13-199

We evaluated the orientation matching step in the M-TIP SPI workflow for potential offloading to accelerators. We ported the code to GPUs, benchmarked it, optimized and down-selected the best versions. The accelerated version of the orientation matching code that was developed at LANL (LANL GPU v3) is 34-55X faster than sequential, 2.4-4.9X faster than the fastest OpenMP open source version we found (FAISS OpenMP) and 1.5-4X faster than the fastest GPU open source version we found (FAISS GPU). Summit single-node GPU versions were somewhat faster than Cori GPU. Image size plays a role; mid-range image sizes take more time. The LANL CUDA multi-node, multi-GPU implementation shows mostly linear strong scaling. I/O also plays a large role; splitting data into parts improves read time and burst buffers dramatically improve read times. This work will be integrated into the M-TIP workflow as part of the next milestone ADSE13-193.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Developing Accelerated Test Protocols and Tuning Microstructures of the Common Materials to Improve Robustness, Reliability, and Endurance of SOFC Cells

This work is built on our prior work where we found that phase transformation in praseodymium nickelates, e.g. Pr 2 NiO 4 (PNO) and (Pr 1-x Nd x ) 2 NiO 4 (PNNO), can be electrochemically driven, and is substantially faster when compared to thermal annealing studies. The first task aims at an attempt to further accelerate the phase transformation in the oxygen electrode by alternating the current input in the cells, which lead to the development of accelerated test protocols (ATPs). ATPs showed up to 60x faster phase transformation and up to 10x faster performance degradation in (Pr 0.50 Nd 0.50 ) 2 NiO 4 electrodes, when compared to long-term operation under constant current density. Furthermore, the phase stable Nd 2 NiO 4 and (La 0.6 Sr 0.4 )(Co 0.8 Fe 0.2 )O 3 (LSCF6482) electrodes were tested in full cells under ATPs, and showed up to 10x faster performance degradation within 1,100 hours in a comparison with long-term thermal annealing studies and electrochemical operation under constant current density. The second task aims at the quantification of the contributions of cell components to the total impedance of a solid oxide fuel cell (SOFC) using electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT). Specifically, the role of gas composition at both anode and cathode was systematically studied, aiming at deconvoluting, identifying and quantifying the contributions of different electrode processes. This was achieved by first tuning the partial pressure of H 2 at the anode and subsequently varying the partial pressure of O 2 at the cathode. The results suggest that, while DRT offers a viable way of deconvoluting different times distributions, additional attention is needed before assigning a peak to a specific electrode process due to the significant overlap of the contributions from the cathode and the anode. Density function theory studies show that both Pr-vacancies and O-defects play a key role on the activity and stability for nickelates towards oxygen reduction reaction. The resident O-interstitials and oxygen ions in the PrO layer form peroxide (O 2 2- ) nearby Pr vacancies. The O 2 2- limits oxygen-ion transport due to the required additional energy to break its O-O bond. We further calculated the formation and segregation energies for different Ln ions (La, Pr, Nd, Pm, Sm, Gd, Tb, Dy, and Ho) in PNO and CeO 2 (111) surfaces. In addition to Nd, Pm and La are suggested as potential dopants in PNO to enhance it stability without decomposition due to their more negative formation energies, lower diffusion energies, and positive separation energies.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Integration of sensors through additive manufacturing leading to increased efficiencies of gas turbines for power generation and propulsion

To realize the full capability of additively manufactured components in complex energy systems, it is imperative to minimize early component failures during development phases and during operation. Traditional field feedback timelines and offline inspection protocols significantly reduce the design-manufacturing iteration times. To address this specific question, the project developed and demonstrated a method for the integration of sensors into complex components through additive manufacturing. The team used gas turbine engines as a platform, which meets the need of both power generation and propulsion and offer opportunities for cost reductions and efficiency increases. The innovation of this intelligent integration of sensors into complex components uniquely customized to address questions of integrity and durability for additively manufactured components. With real-time sensing data from additively manufactured components, turbine manufacturers will realize higher efficiencies, reduced component failures, and a 30-50% acceleration in product deployment of high efficiency gas turbine components due to a faster reduction in component risk assessment under actual operating conditions. This is a transformative shift towards a data-driven design and qualification of additively manufactured gas turbine components. To directly integrate sensors into additively manufactured components with all the complexities of actual hardware, powder bed fusion (direct metal laser sintering) and laser metal deposition technologies was developed. Validation took take place in two university laboratories both of which contain actual engine hardware and closely simulate a gas turbine prior to demonstrating the technology in a turbine development test. Indeed, two major technologies from this research cold impact turbine systems in the near future: (1) higher efficiency materials and designs enabled by additive manufacturing with 50% faster design to manufacturing cycle time, to enable faster time-to-market targets; and (2) integration of sensors into additively manufactured components enabling broad health and condition based prognostics for faster component and engine risk reduction.

33 ADVANCED PROPULSION SYSTEMS↗
NASA NTRS1991

Generalized conjugate-gradient methods for the Navier-Stokes equations

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Ajmani, Kumud↗
NASA NTRS2001

The Impact of Increasing Carbon Dioxide on Ozone Recovery

We have used the GSFC coupled two-dimensional (2D) model to study the impact of increasing carbon dioxide from 1980 to 2050 on the recovery of ozone to its pre-1980 amounts. We find that the changes in temperature and circulation arising from increasing CO2 affect ozone recovery in a manner which varies greatly with latitude, altitude, and time of year. Middle and upper stratospheric ozone recovers faster at all latitudes due to a slowing of the ozone catalytic loss cycles. In the lower stratosphere, the recovery of tropical ozone is delayed due to a decrease in production and a speed up in the overturning circulation. The recovery of high northern latitude lower stratospheric ozone is delayed in spring and summer due to an increase in springtime heterogeneous chemical loss, and is speeded up in fall and winter due to increased downwelling. The net effect on the higher northern latitude column ozone is to slow down the recovery from late March to late July, while making it faster at other times. In the high southern latitudes, the impact of CO2 cooling is negligible. Annual mean column ozone is predicted to recover faster at all latitudes, and globally averaged ozone is predicted to recover approximately ten years faster as a result of increasing CO2.

Rosenfield, Joan E.↗
NASA NTRS1997

Up-down Asymmetries in Speed Perception

We compared speed matches for pairs of stimuli that moved in opposite directions (upward and downward). Stimuli were elliptical patches (2 deg horizontally by 1 deg vertically) of horizontal sinusoidal gratings of spatial. frequency 2 cycles/deg. Two sequential 380 msec reveal presentations were compared. One of each pair of gratings (the standard) moved at 4 Hz (2 deg/sec), the other (the test) moved at a rate determined by a simple up-down staircase. The point of subjectively equal speed was calculated from the average of the last eight reversals. The task was to fixate a central point and to determine which one of the pair appeared to move faster. Eight of 10 observers perceived the upward drifting grating as moving faster than a grating moving downward but otherwise identical. on average (N = 10), when the standard moved downward, it was matched by a test moving upward at 94.7+/-1.7(SE)% of the standard speed, and when the standard moved upward it was matched by a test moving downward at 105.1+/-2.3(SE)% of the standard speed. Extending this paradigm over a range of spatial (1.5 to 13.5 c/d) and temporal (1.5 to 13.5 Hz) frequencies, preliminary results (N = 4) suggest that, under the conditions of our experiment, upward matter is seen as faster than downward for speeds greater than approx.1 deg/sec, but the effect appears to reverse at speeds below approx.1 deg/sec with downward motion perceived as faster. Given that an up-down asymmetry has been observed for the optokinetic response, both perceptual and oculomotor contributions to this phenomenon deserve exploration.

Thompson, Peter↗
NASA NTRS2008

Effects of Different Lifting Cadences on Ground Reaction Forces during the Squat Exercise

The purpose of this investigation was to determine the effect of different cadences on the ground reaction force (GRF(sub R)) during the squat exercise. It is known that squats performed with greater acceleration will produce greater inertial forces; however, it is not well understood how different squat cadences affect GRF(sub R). It was hypothesized that faster squat cadences will result in greater peak GRF(sub R). METHODS: Six male subjects (30.8+/-4.4 y, 179.5+/-8.9 cm, 88.8+/-13.3 kg) with previous squat experience performed three sets of three squats using three different cadences (FC = 1 sec descent/1 sec ascent; MC = 3 sec descent/1 sec ascent; SC = 4 sec descent/2 sec ascent) with barbell mass equal to body mass. Ground reaction force was used to calculate inertial force trajectories of the body plus barbell (FI(sub system)). Forces were normalized to body mass. RESULTS: Peak GRF(sub R) and peak FI(sub system) were significantly higher in FC squats compared to MC (p=0.0002) and SC (p=0.0002). Range of GRF(sub R) and FI(sub system) were also significantly higher in FC compared to MC (p<0.05), and MC were significantly higher than SC (p<0.05). DISCUSSION: Faster squat cadences result in significantly greater peak GRF(sub R) due to the inertia of the system. GRF(sub R) was more dependent upon decent cadence than on ascent cadence. PRACTICAL APPLICATION: This study demonstrates that faster squat cadences produce greater ground reaction forces. Therefore, the use of faster squat cadences might enhance strength and power adaptations to long-term resistance exercise training. Key Words: velocity, weight training, resistive exercise

Bentley, Jason R.↗
DOE OSTI2024

Open‐Source Anaerobic Digestion Modeling Platform, Anaerobic Digestion Model No. 1 Fast (ADM1F)

An open‐source modeling platform, called Anaerobic Digestion Model No. 1 Fast (ADM1F), is introduced to achieve fast and numerically stable simulations of anaerobic digestion processes. ADM1F is compatible with an iPython interface to facilitate model configuration, simulation, data analysis, and visualization. Faster simulations and more stable results are accomplished by implementing an advanced open‐source library of numerical methods called Portable Extensive Toolkit for Scientific Computation (PETSc) to solve the ADM1 system of equations. Leveraging PETSc, ADM1F can consistently complete a steady‐state simulation under 0.2 s, over 99% faster than a benchmark ADM1 model implemented with MATLAB while achieving agreement of model outputs within 1% of those obtained with the benchmark model. For dynamic simulations, however, ADM1F has a computational speed advantage only when the influent characteristics update more frequently than every 4 h. The ability of ADM1F to be useful as a tool to study anaerobic digestion systems is demonstrated through two example implementations of ADM1F: (1) a two‐phase co‐digestion scenario evaluating the impact of the organic loading rate and the substrate composition on reactor performance and stability, and (2) a conventional digester scenario assessing the effectiveness of recovery strategies after disruptions that led to instability. These examples demonstrate how the high simulation speed and the convenience of the iPython interface allow ADM1F to complete complex analyses within minutes, much faster than computational strategies currently reported in the literature.

anaerobic co-digestion↗
DOE OSTI2013

A retrospective planning analysis comparing intensity modulated radiation therapy (IMRT) to volumetric modulated arc therapy (VMAT) using two optimization algorithms for the treatment of early-stage prostate cancer

The primary aim of this study is to compare intensity modulated radiation therapy (IMRT) to volumetric modulated arc therapy (VMAT) for the radical treatment of prostate cancer using version 10.0 (v10.0) of Varian Medical Systems, RapidArc radiation oncology system. Particular focus was placed on plan quality and the implications on departmental resources. The secondary objective was to compare the results in v10.0 to the preceding version 8.6 (v8.6). Twenty prostate cancer cases were retrospectively planned using v10.0 of Varian's Eclipse and RapidArc software. Three planning techniques were performed: a 5-field IMRT, VMAT using one arc (VMAT-1A), and VMAT with two arcs (VMAT-2A). Plan quality was assessed by examining homogeneity, conformity, the number of monitor units (MUs) utilized, and dose to the organs at risk (OAR). Resource implications were assessed by examining planning and treatment times. The results obtained using v10.0 were also compared to those previously reported by our group for v8.6. In v10.0, each technique was able to produce a dose distribution that achieved the departmental planning guidelines. The IMRT plans were produced faster than VMAT plans and displayed improved homogeneity. The VMAT plans provided better conformity to the target volume, improved dose to the OAR, and required fewer MUs. Treatments using VMAT-1A were significantly faster than both IMRT and VMAT-2A. Comparison between versions 8.6 and 10.0 revealed that in the newer version, VMAT planning was significantly faster and the quality of the VMAT dose distributions produced were of a better quality. VMAT (v10.0) using one or two arcs provides an acceptable alternative to IMRT for the treatment of prostate cancer. VMAT-1A has the greatest impact on reducing treatment time.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2017

The Reactivity of the Nitrate Radical ( • NO 3 ) in Aqueous and Organic Solutions

In this study, rate constants for the ( • NO 3 ) radical reaction with alcohols, alkanes, alkenes and several aromatic compounds were measured in aqueous and tert-butanol solution for comparison to aqueous and acetonitrile values from the literature. The measured trends provide insight into the reactions of the • NO 3 radical in various media. The reaction with alcohols primarily consists of hydrogen-atom abstraction from the alpha-hydroxy position, and is faster in solvents of lower polarity where the diffusivity of the radical is greater. Alkenes react faster than alkanes, and their rate constants are also faster in non-polar solution. The situation is reversed for nitrate radical reaction with the aromatic compounds, where the rate constants in tert-butanol are slower. This is attributed to the need to solvate the NO 3 - anion and corresponding tropylium cation produced by the • NO 3 radical electron transfer reaction. Finally, a linear correlation was found between measured rate constants in water and acetonitrile, which can be used to estimate aqueous nitrate radical rate constants for compounds having low water solubility.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Weighted relaxation for multigrid reduction in time

Current trends in computer architectures now mean that faster computation speed must come primarily from increased concurrency, not faster clock speeds, which are stagnating. Thus, this situation creates bottlenecks for serial algorithms, including the well-known bottleneck for sequential time-integration, where each individual time-value (i.e., time-step) is computed sequentially. One approach to alleviate this and achieve parallelism in time is with multigrid. Here, in this work, we consider multigrid-reduction-in-time (MGRIT), a multilevel method applied to the time dimension that computes multiple time-steps in parallel. Like all multigrid methods, MGRIT relies on the complementary relationship between relaxation on a fine-grid and a correction from the coarse grid to solve the problem. All current MGRIT implementations are based on unweighted-Jacobi relaxation; here we introduce the concept of weighted relaxation to MGRIT. We derive new convergence bounds for weighted relaxation, and use this analysis to guide the selection of relaxation weights. Numerical results then demonstrate that by choosing appropriate non-unitary relaxation weights, one can achieve faster convergence rates and lower iteration counts for MGRIT when compared with unweighted relaxation. In most cases, weighted relaxation yields a 10%–20% saving in iterations, which is significant when using large high-performance computers. For A-stable integration schemes, results also illustrate that under-relaxation can restore convergence in some cases where unweighted relaxation is not convergent.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices

Summary In this article, we introduce a fast, memory efficient and robust sparse preconditioner that is based on a direct factorization scheme for sparse matrices arising from the finite‐element discretization of elliptic partial differential equations. We use a fast (but approximate) multifrontal approach as a preconditioner and use an iterative scheme to achieve a desired accuracy. This approach combines the advantages of direct and iterative schemes to arrive at a fast, robust, and accurate preconditioner. We will show that this approach is faster (∼2×) and more memory efficient (∼2–3×) than a conventional direct multifrontal approach. Furthermore, we will demonstrate that this preconditioner is both faster and more effective than other preconditioners such as the incomplete LU preconditioner. Specific speedups depend on the matrix size and improve as the size of the matrix increases. The preconditioner can be applied to both structured and unstructured meshes in a similar manner. We build on our previous work and utilize the fact that dense frontal and update matrices, in the multifrontal algorithm, can be represented as hierarchically off‐diagonal low‐rank matrices. Using this idea, we replace all large dense matrix operations in the multifrontal elimination process with O ( N ) hierarchically off‐diagonal low‐rank operations to arrive at a faster and more memory efficient factorization scheme. We then use this direct factorization method at low accuracies as a preconditioner and apply it to various real‐life engineering test cases. Copyright © 2016 John Wiley & Sons, Ltd.

Aminfar, AmirHossein↗
DOE OSTI2017

Dephosphorization Kinetics between Bloated Metal Droplets and Slag Containing FeO: The Influence of CO Bubbles on the Mass Transfer of Phosphorus in the Metal

Dephosphorization kinetics of bloated metal droplets was investigated in the temperature range from 1813 K to 1913 K (1540 °C to 1640 °C). The experimental results showed that the overall mass transfer coefficient, k{sub o}, decreased with increasing temperature because of decreasing phosphorus partition ratio, L P . It was also found that the mass transfer coefficient for phosphorus in the metal, k m , had the highest value at the lowest temperature [i.e., 1813 K (1540 °C)] because the formation of smaller CO bubbles increased the rate of surface renewal, leading to faster mass transport. Meanwhile, metal droplets without carbon were also employed to study the effect of decarburization on dephosphorization. The results show that although decarburization lowers the driving force significantly, k{sub m} (6.2 × 10 -2 cm/s) for a carbon containing droplet is two orders of magnitude higher than that for carbon free droplets (5.3 × 10 -4 cm/s) because of the stirring effect provided by CO bubbles. This stirring offers a faster surface renewal rate, which surpasses the loss of driving force and then leads to a faster dephosphorization rate.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Using θ' interfaces as templates for planar L1 2 precipitation in AlCuMnZr alloys

Controlled Mn and Zr additions to Al-Cu alloys have allowed for the improved retention of mechanical properties after extended 350°C exposures by stabilizing the main strengthening θ' (Al 2 Cu) phase. Ultimately, θ'/L1 2 (Al 3 Zr) co-precipitate formation stabilizes θ' most effectively; however, Zr diffuses sluggishly and has low solubility in aluminum castings. Increasing the Zr segregation rate would allow for faster and more effective θ'/L1 2 co-precipitation. It is demonstrated that the Zr segregation rate is faster when the Zr matrix content is higher. A much higher Zr matrix content was achieved by rapid cooling during additive manufacturing (AM) that produces θ'/L1 2 co-precipitation faster, which is shown by scanning transmission electron microscopy and atom probe tomography experiments. It was also found that Zr continuously segregates to θ' interfaces up to the most aggressive heat treatment studied such that planar L1 2 precipitates remain after the metastable θ' dissolves. In this manner, we demonstrate that θ' coherent interfaces serve as perfect templates to form stable planar L1 2 precipitates that can provide strength at higher temperatures than traditional θ' strengthened AlCu alloys. This work introduces an alloy design strategy that uses metastable precipitates to quickly nucleate and grow co-precipitates with a desired geometry that contain slow diffusing elements. These ideas can be applied to engineer more heat resistant alloys by taking advantage of high solute matrix contents enabled by rapid cooling during additive manufacturing.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An experimental and detailed kinetic modeling study of the pyrolysis and oxidation of allene and propyne over a wide range of conditions

Allene and propyne are important intermediates in the pyrolysis and oxidation of higher hydrocarbon fuels, and they are also a major source of propargyl radical formation, which can recombine into different C 6 H 6 isomers and finally produce soot. In a prior work (Panigrahy et al., “A comprehensive experimental and improved kinetic modeling study on the pyrolysis and oxidation of propyne”, Proc. Combust. Inst 38 (2021)), the pyrolysis, ignition , and laminar flame speed of propyne were investigated. To understand the kinetic features of initial fuel breakdown and oxidation of the two C 3 H 4 isomers, new measurements for allene pyrolysis and oxidation are conducted in the present paper at the same operating conditions as those studied previously for propyne. Ignition delay times of allene are measured using a high-pressure shock tube and a heated twin-opposed piston rapid compression machine in the temperature range 690– 1450 K at equivalence ratios of 0.5, 1.0 and 2.0 in ‘air’, and at pressures of 10 and 30 bar. Pyrolysis species measurements of allene and propyne are also performed using a gas chromatography integrated singlepulse shock tube in the temperature range 1000–1700 K at pressure of 2 and 5 bar. Furthermore, laminar flame speeds of allene are measured at elevated gas temperatures of 373 K at pressures of 1 and 2 bar for a wide range of equivalence ratios from 0.6 to 1.5. A newly updated kinetic mechanism developed for this study is the first model that can well reproduce all of the experimental results for both allene and propyne. It is observed that in the pyrolysis process, allene dissociates faster than propyne. Both isomers exhibit similar ignition delay times at high temperatures (>1000 K), while, at intermediate temperatures (770–1000 K) propyne is the faster to ignite, and at lower temperatures (< 770 K) allene becomes more reactive. Furthermore, laminar flame speeds for propyne are found to be slightly faster than those for allene under the conditions studied in this work

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

An Efficient Algorithm for Automatic Structure Optimization in X-ray Standing-Wave Experiments

We present that x-ray standing-wave photoemission experiments involving multilayered samples are emerging as unique probes of the buried interfaces that are ubiquitous in current device and materials research. Such data require for their analysis a structure optimization process comparing experiment to theory that is not straightforward. In this work, we present a new computer program for optimizing the analysis of standing-wave data, called SWOPT, that automates this trial-and-error optimization process. The program includes an algorithm that has been developed for computationally expensive problems: so-called black-box simulation optimizations. It also includes a more efficient version of the Yang X-ray Optics Program (YXRO) [Yang, S.-H., Gray, A.X., Kaiser, A.M., Mun, B.S., Sell, B.C., Kortright, J.B., Fadley, C.S., J. Appl. Phys. 113, 1 (2013)] which is about an order of magnitude faster than the original version. Human interaction is not required during optimization. We tested our optimization algorithm on real and hypothetical problems and show that it finds better solutions significantly faster than a random search approach. The total optimization time ranges, depending on the sample structure, from minutes to a few hours on a modern laptop computer, and can be up to 100x faster than a corresponding manual optimization. Finally, these speeds make the SWOPT program a valuable tool for realtime analyses of data during synchrotron experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2021

On Anomaly Detection for Transactive Energy Systems with Competitive Market

Two anomaly-detection criteria are proposed for transactive energy systems with competitive markets. Participants of transactive energy systems seek an optimal power allocation through hybrid economic-control methods to facilitate the integration of various types of distributed energy resources to power distribution systems. In transactive energy systems, every participant is assumed to be a rational entity, and consumers have diminishing marginal utility and suppliers have increasing marginal cost. With the first proposed anomaly-detection criterion, the monotonicity of marginal cost and marginal utility are examined. The impact of line flow constraints is also taken into consideration. Then, the second anomaly-detection criterion is proposed for TESs with marginal cost and marginal utility which change faster than a certain rate. The second criterion is more accurate than the first one for TES with marginal cost and marginal utility which change faster than a certain rate, but it requires the knowledge of that rate. Neither criteria requires more data than those necessary to find the optimal power allocation and the market-clear price in a transactive energy system. Therefore, the proposed criteria do not disclose any more data than necessary. As the monotonicity of marginal cost and marginal utility in a TES with competitive markets results in convex objective functions in an optimization problem and strongly convex ones when marginal cost and marginal utility changes faster than a certain rate, the two detection criteria are also applicable to anomaly detection of general convex optimization problems. Simulations are carried out to show the efficacy of the proposed criteria to detect anomalies caused by cyberattacks.

Wang, Peng↗