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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 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Analysis of styrene maleic acid alternating copolymer supramolecular assemblies in solution by small angle X-ray scattering

Over the past decade, Styrene Maleic Acid alternating copolymers (SMA) have gained interest as an alternative to detergent solubilization for the isolation of integral membrane proteins. The formation of SMA lipid particles (SMALPs) presents a novel opportunity to isolate the proximal membrane environment, encompassing and throughout membrane proteins in vitro. Neither the organization or structure of SMAs in an aqueous buffer nor the mechanism by which SMA transforms the membrane bilayer into a SMALP is known. This study investigates the shape and size of diverse SMA polymer complexes/aggregates in solution at various pH, ionic strength, SMA concentration and temperature, analyzed by small angle X-ray scattering. It is clear that SMAs of differing physicochemical properties (styrene to maleic acid ratio, length of copolymer fragments and functionalization) display highly variable sizes/shapes in solution over a range of environmental conditions. The SMA supramolecular aggregates exhibit similar prolate ellipsoidal geometry of varying size, dependent on the degree of hydrophobicity of the SMA copolymer. At elevated temperature, particles composed of SMAs enriched in styrene increase in both radius of gyration and maximum particle diameter. Interestingly, we observe a correlation between the SMALP dimensions and that of native membranes. Future work will investigate if there may be a complimentary relationship between SMA aggregate dimensions and bilayer thickness (and/or protein transmembrane domain thickness), similar to what has been observed for tandem facial amphiphiles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Roadmap and Benchmarking: Privacy in Federated Load Forecasting

Data-driven techniques for energy demand forecasting continue to emerge with promising impacts on distribution grid planning. However, the development of robust and generalizable machine learning models requires that representative high quality training data are available. Distributed energy resources have begun to embed intelligence, gathering large amounts of data on customer demand, behavior, and household devices that are connected to the grid. Though utilities aggregate meter-level demand data for load shaping, demand response, outage management, reliability planning, and billing applications, there lies an inherent privacy concern in sharing consumption data that may identify individual consumer behavioral patterns. Hence, while sharing the data is crucial, the private sensitive customer data must be safeguarded from being exposed or manipulated. In this study, we propose a roadmap for implementing a based privacy preserving framework to support the advancement of data-driven analytics in data-sensitive distributed energy resources environments. The roadmap incorporates federated learning–a distributed training framework, differential privacy–a statistical framework that provides guarantees to safeguard the leakage of sensitive data, secure multiparty computation and homomorphic encryption– techniques for encrypting model gradients and applying secure aggregation on the server. Moreover, we perform baseline experiments on the federated short-term load forecasting (STLF) task using open-source residential load profile datasets, offering insights into the challenges of integrating differential privacy into federated learning.

Abebe, Waqwoya [Oak Ridge National Laboratory (ORN↗
DOE OSTI2022

Tri-level hybrid interval-stochastic optimal scheduling for flexible residential loads under GAN-assisted multiple uncertainties

Various building loads, such as heating, ventilation, and air conditioners (HVACs), electric water heaters (EWHs), and electric vehicles (EVs), can introduce opportunities for improving the flexibility of electricity consumption while satisfying the needs of building owners as well as benefiting the resilience of distribution system. To utilize such flexibility, a tri-level distribution market framework is established, including residential consumers, load aggregators (LAs), and the distribution system operator (DSO). In this work, the uncertainties from all three levels are considered. The random consumption behavior at the consumer level is modeled as a Gaussian noise that is also aggregated and transmitted to the LA level. The weather temperature in the LA level is forecasted as an interval, and the photovoltaic (PV) power in the market-clearing level is modeled by a set of power scenarios generated by Generative Adversarial Networks (GANs). Then, a hybrid interval-stochastic programming is proposed to transform the uncertain problems in the first two levels into deterministic ones. For real-time implementations, a rolling horizon optimization (RHO) scheme is employed to continuously optimize the power consumption based on the latest operating information. Finally, case studies on a modified IEEE 69-bus system validate the effectiveness of the proposed uncertainty modeling strategies and the RHO scheme.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Conservation management decreases surface runoff and soil erosion

Conservation management practices – including agroforestry, cover cropping, no-till, reduced tillage, and residue return – have been applied for decades to control surface runoff and soil erosion, yet results have not been integrated and evaluated across cropping systems. In this study we collected data comparing agricultural production with and without conservation management strategies. We used a bootstrap resampling analysis to explore interactions between practice type, soil texture, surface runoff, and soil erosion. We then used a correlation analysis to relate changes in surface runoff and soil erosion to 13 other soil health and agronomic indicators, including soil organic carbon, soil aggregation, infiltration, porosity, subsurface leaching, and cash crop yield. Across all conservation management practices, surface runoff and erosion had respective mean decreases of 67% and 80% compared with controls. Use of cover cropping provided the largest decreases in erosion and surface runoff, thus emphasizing the importance of maintaining continuous vegetative cover on soils. Coarse- and medium-textured soils had greater decreases in both erosion and runoff than fine-textured soils. Changes in surface runoff and soil erosion under conservation management were highly correlated with soil organic carbon, aggregation, porosity, infiltration, leaching, and yield, showing that conservation practices help drive important interactions between these different facets of soil health. This study offers the first large-scale comparison of how different conservation agriculture practices reduce surface runoff and soil erosion, and at the same time provides new insight into how these interactions influence the improvement or loss of soil health.

58 GEOSCIENCES↗
DOE OSTI2024

Expression, purification, and characterization of diacylated Lipo-YcjN from Escherichia coli

YcjN is a putative substrate binding protein expressed from a cluster of genes involved in carbohydrate import and metabolism in Escherichia coli. Here, we determine the crystal structure of YcjN to a resolution of 1.95 Å, revealing that its three-dimensional structure is similar to substrate binding proteins in subcluster D-I, which includes the well-characterized maltose binding protein. Furthermore, we found that recombinant overexpression of YcjN results in the formation of a lipidated form of YcjN that is posttranslationally diacylated at cysteine 21. Comparisons of size-exclusion chromatography profiles and dynamic light scattering measurements of lipidated and nonlipidated YcjN proteins suggest that lipidated YcjN aggregates in solution via its lipid moiety. Additionally, bioinformatic analysis indicates that YcjN-like proteins may exist in both Bacteria and Archaea, potentially in both lipidated and nonlipidated forms. Together, our results provide a better understanding of the aggregation properties of recombinantly expressed bacterial lipoproteins in solution and establish a foundation for future studies that aim to elucidate the role of these proteins in bacterial physiology.

Escherichia coli↗
DOE OSTI2020

Connecting particle interactions to agglomerate morphology and rheology of boehmite nanocrystal suspensions

Rheology imposes significant challenges on processing of complex suspensions such as nuclear waste slurries at the Hanford and Savannah River sites. Understanding rheology connecting to microstructures and underlying particle interactions in complex slurries is therefore important for both fundamental knowledge and practical applications. Here, we use suspensions of aluminum oxyhydroxide minerals in the form of boehmite as an analog of the radioactive waste slurry to gain physical insights on the correlation between particle interactions, microstructures, and slurry rheology. Specifically, we use a combination of Couette rheometry and small-angle scattering techniques (independently and simultaneously) to understand how the slurry microstructure changes under flow and how these structural changes manifest themselves in the bulk rheology of the suspensions. Our experiments show that the boehmite slurries are thixotropic, with the rheology and structure of the suspensions changing with increasing exposure to flow. In the slurries, particle aggregates begin as loose, system-spanning clusters, but exposure to moderate shear rates causes the aggregates to irreversibly consolidate into denser clusters of finite size. The microstructural changes directly influence the rheological properties of the slurries such as viscosity and viscoelasticity. More importantly, our study shows that solution pH affects the amount of structural rearrangement and the kinetics of the rearrangement process, with an increase in pH leading to faster and more dramatic changes in the bulk rheology. Such dynamic microstructural changes and resultant rheology are understood via correlations between particle interactions and strength of particle network, coupled with surface chemistry and anisotropic nature of particle interactions. Nearly identical structural changes are also observed in Poiseuille flow geometries, implying that the observed changes are relevant in the pipe flow conditions present during waste processing.

Weston, Javen S.↗
DOE OSTI2023

Understanding the trade-offs of national municipal solid waste estimation methods for circular economy policy

Policies embracing circular economy concepts have taken hold in national legislation around the world. As the number of governments and organizations adopting circular economy policies increases, so does the need for accurate and timely measurement of material resource flows. Since many countries do not have access to centrally reported municipal solid waste (MSW) data, estimation and modeling are critical in evaluating circular economy policy effectiveness. The purpose of this paper is to examine three modeling approaches estimating national MSW data in the United States, including industry-based material flow analysis, waste-extended input-output modeling, and aggregated regional waste reporting. We establish five criteria to guide the analysis through the context of policy monitoring (data quality, flow totality, update frequency, sensitivity to disruption, and product granularity) and use these criteria to analyze and score each model. We then use a literature search to identify five, internationally-implemented options for circular economy policy and determine the data and modeling components that are most helpful in evaluating policy effectiveness. Finally, we provide a crosswalk of the model scores and policy needs to inform the suitability of model selection by policy type. We found that data quality and update frequency are identified as critical components for evaluating circular economy policies within the models evaluated, and can both be fulfilled by aggregated regional waste reporting. Flow totality, sensitivity to disruption, and product granularity requirements vary by both model and policy types. While none of the evaluated models satisfy the combination of requirements for any of the five policies, industry-based material flow analysis offers flow totality for extended producer responsibility, landfill bans, and recycling rate target policies that typically require it. Here, the waste-extended input-output model can provide disruption sensitivity and product granularity as needed for policies like minimum recycled content and market restrictions. Policy developers in areas where strong centralized data collection is not an option should design policy action(s) with modeling tradeoffs in mind, including the potential hybridization of modeling approaches that may provide the most accurate national MSW estimates.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Sintering effects on NpO 2 grain size and morphology: The role of precursor Np phase

Neptunium dioxide (NpO 2 ) is a key phase in nuclear material processing as a target material for the production of plutonium-238 ( 238 Pu) and has been historically synthesized via the calcination of a Np oxalate precursor. Alternative synthesis methods for NpO 2 are now more prevalent, necessitating their study and comparison with the more common oxalate route. The purpose of this work was to investigate the microstructural properties of NpO 2 synthesized from a nitrate-based Np precursor phase via the assessment of NpO 2 particle size and morphology as a function of calcination temperature and time. Scanning electron microscopy (SEM) was used to probe the primary grain size and morphology of NpO 2 after calcination at temperatures ranging from 700 to 1100 °C and hold times ranging from 1 to 10 h. Post-image analysis using ImageJ software enabled the quantification of mean particle diameter. This analysis indicated that particle diameter increases with both increasing calcination temperature and hold time. Primary particles were shown to be clumped in irregular patterns into the overall rough, blocky aggregates, but this macroscopic morphology was not affected by calcination time or temperature. Although trends in primary grain size of NpO 2 were consistent with available literature from other Np precursor phases, the macroscopic morphology of the NpO 2 aggregates was quite different than reported for other precursors. Through comparison with historical literature on Np oxalate, this work emphasizes the importance of Np precursor on the physical properties of NpO 2 .

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2020

A highly stable Cu(OH) 2 -Poly(vinyl alcohol) nanocomposite membrane for dramatically enhanced direct borohydride fuel cell performance

Nano-additive aggregation, limited performance, and unclear modification mechanisms are the main obstacles in developing nanocomposite anion exchange membranes (AEMs). In this work, for the first time, an effective and highly stable Poly(vinyl alcohol) (PVA)-based AEMs with dispersive Cu(OH)$_2$ nanoclusters (Cu-AEMs) are prepared by a simple and eco-friendly three-step method: ‘CuCl$_2$ doping-casting-KOH immersing’. The doped Cu$^{2+}$ ions chemically combine with OH- ions to form anionic conductive Cu(OH)2 nanoclusters intermediated by attaching resins. The PVA skeletons wrap around Cu(OH)$_2$ while the hydroxyl groups expose to bulk water, forming Cu(OH)$_2$-PVA complex, which avoids nano-additive aggregation, increases anionic channels, and strengthens additive-matrix connection. A direct borohydride fuel cell using Cu-AEM with 0.56 wt % CuCl$_2$ possess the highest power density of 403.3 mW cm$^{-2}$ at 60 °C and a life span of over 200 h. The high-performance and durability come from the unique structure of Cu(OH)$_2$ nanoclusters-PVA complex. ‘Vehicle’ theory is considered to be the dominant mechanism for enhancing such nanocomposite Cu-AEMs. This work demonstrates a new concept for preparing the stable AEMs toward high-performance fuel cells. The synthetic chemistry involved can be broadly extended for fabricating versatile AEMs.

25 ENERGY STORAGE↗
DOE OSTI2020

Tailoring electrode microstructure via ink content to enable improved rated power performance for platinum cobalt/high surface area carbon based polymer electrolyte fuel cells

Improvements in polymer electrolyte fuel cell (PEFC) electrode performance have primarily focused on catalyst and ionomer developments, marginalizing the importance of catalyst ink formulation. In this study, the effect of ink formulation is examined across a series of cathodes comprised of PtCo supported on high surface area carbon (PtCo/ HSC ) and Nafion ionomer using an array of in situ electrochemical and ex situ characterization techniques. In contrast to prior work on Pt/Vu systems, ink water content had little effect on the electrochemically determined ionomer coverage for the PtCo/HSC electrocatalyst examined here. Characterization using nano-scale resolution X-ray computed tomography (nano-CT) demonstrated that water-rich ink formulations lead to a reduction in aggregate size (ionomer + PtCo/HSC), improving local O 2 transport. This understanding, combined with the use of a commercially-available electrocatalyst was used to produced state-of-the-art membrane electrode assemblies with Pt loadings of 0.03/0.08 mg Pt /cm 2 on the anode and cathode respectively, having; i) > 1 A/mg Pt (0.9 V iR-free , 150 kPa, 80 °C, 100% RH, H 2 /O 2 ), ii) 320 mA/cm 2 at 0.8 V, 150 kPa, 80 ° C, 100% RH, H 2 /Air), and iii) > 1 W/cm 2 elec at rated power (0.67 V, 250 kPa, 94 °C, 65% RH, H 2 /Air) or < 0.11 g Pt /kW rated .

25 ENERGY STORAGE↗
DOE OSTI2025

Microstructure and CPO evolution of dynamically recrystallized olivine during complex deformation conditions: a full-field numerical modeling approach

The rheological properties of mantle rocks are strongly dependent on their crystallographic preferred orientation (CPO). Olivine CPO, defined by the orientation of seismically fast [100] axes parallel to flow direction, is also thought to be a dominant contributor to seismic anisotropy in the Earth's upper mantle. However, the amount of deformation needed to overprint a new CPO on a pre-existing fabric and the impact of the inherited CPOs on the transient microstructure evolution, remain unknown. This study employs a full-field numerical approach (VPFFT-ELLE) to explore the dynamic recrystallization and microstructural evolution of olivine polycrystalline aggregates under complex deformation conditions. We test four combinations of successive pure shear and simple shear boundary conditions. Findings indicate that inherited CPOs influence subsequent deformation in a manner dependent on the kinematic relationship between successive stages. In all cases, a minor strain increment (ε ∼0.3–0.6) is sufficient to erase the previous microstructure and CPO. However, when deformation conditions change dramatically (e.g., stretching direction changes orthogonally), the intensity of the new CPO developed is significantly lower and strain distribution are specially altered. During a transient strain stage, pre-existing microstructures undergo extensive reworking, especially when deformation conditions are changed dramatically, such as switching from simple shear to a pure shear condition with a parallel shortening direction relative to the stretching direction. We estimate the significance of these results in interpreting observations of seismic velocity anisotropy, concluding that P-wave seismic anisotropy is significantly and positively correlated with the evolution of olivine CPO with deformation history. This research underscores the transient nature of microstructural rearrangement in olivine aggregates and the necessity for caution in interpreting seismic anisotropy in regions with complex deformation histories, as inherited CPOs can influence current fabric development and induce deviation to the present deformation conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2018

The effects of Cr particles addition on the aging behavior and mechanical properties of SiCp/7075Al composites

Highlights: • The novel investigated the effects of Cr particles on the aging behavior and mechanical properties of SiC{sub p}/7075Al composites. • The addition of Cr particles didn't change precipitation sequence, but significantly degraded precipitation kinetics of composites. • Cr particles had a significant effect on the tensile properties of the peak-aged composite because of Mg aggregation. - Abstract: The effects of Cr particles addition on the aging behavior and mechanical properties of SiC{sub p}/7075Al composites were systematically investigated. The results show that the precipitation sequence of (5 vol% Cr + 50 vol% SiC)/7075Al composites (C-7075Al) is still: GP zone → η′ → η (MgZn{sub 2}), but Cr particles degrade the precipitation kinetics of the C-7075Al composite in comparison to (5 vol% SiC{sub p} + 50 vol% SiC{sub p})/7075Al (B-7075Al) because of reduced dislocation density present in the matrix and higher thermal activation energy of the η′ phase. Besides, the addition of Cr particles has a significant effect on the mechanical properties of the C-7075Al composite during the aging process. In contrast to the as-cast state, the ultimate tensile strength of the C-7075Al composite obtains an increase of 120 MPa at the peak-aged period, significantly lower than those of 7075Al alloy (207 MPa) and the B-7075Al composite (151 MPa), which is attributable to the severe aggregation of elemental Mg at the interface between Cr particles and the Al matrix.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Bismuth borate zinc glass braze for bonding sapphire in air

Highlights: • Sapphire was brazed with a novel 50Bi{sub 2}O{sub 3}–40B{sub 2}O{sub 3}–10ZnO (mol.%) glass at temperatures of 600–700 °C for 20 min in air. • Bi{sub 4}B{sub 2}O{sub 9} and Bi{sub 24}B{sub 2}O{sub 39} were formed in the joints brazed at 600 and 625 °C, respectively. • ZnAl{sub 2}O{sub 4} particles were formed in the joints when the brazing temperature was 635 °C. • The maximum shear strength of 85 MPa was obtained for the joints brazed at 650 °C for 20 min. - Abstract: Reliable brazing of sapphire was successfully achieved by using a novel 50Bi{sub 2}O{sub 3}–40B{sub 2}O{sub 3}–10ZnO (mol%) glass braze and joining cycles that peak at temperatures of 600 − 700 °C for 20 min in air. The effect of the brazing temperature on microstructure evolution as well as mechanical properties of the sapphire/sapphire joints was investigated. The results showed that Bi{sub 4}B{sub 2}O{sub 9} and Bi{sub 24}B{sub 2}O{sub 39} were formed in the joints brazed at 600 and 625 °C, respectively. ZnAl{sub 2}O{sub 4} particles were formed in the joints when the brazing temperature was 635 °C due to a reaction between the glass and the sapphire substrate. With the brazing temperature increasing, ZnAl{sub 2}O{sub 4} particles exhibited steady growth, from ~ 160 nm at 635 °C to ~ 455 nm at 700 °C. Besides, ZnAl{sub 2}O{sub 4} particles began to aggregate when the temperature was 675 °C. The strength increased sharply when the brazing temperature increased to 635 °C, which was mainly attributed to the formation of ZnAl{sub 2}O{sub 4} particles in the joint domain. The maximum shear strength of 85 MPa was obtained for the joints brazed at 650 °C for 20 min. The joint shear strength decreased due to the aggregation of ZnAl{sub 2}O{sub 4} particles in the joint.

36 MATERIALS SCIENCE↗
DOE OSTI2018

The GdF3 phosphors with enhanced multicolor luminescence via multi-channel excitation and energy migration procedure

Highlights: • Core-shell structured GdF{sub 3} phosphors were synthesized by hydrothermal method. • SiO{sub 2} coating layers prevent aggregation and sintering during thermal annealing. • The annealed CSS nanophosphors were highly dispersible. • The inserted PMA significantly enhances multicolor luminescence. • The annealed CSS phosphors exhibit enhanced multicolor luminescence properties. - Abstract: A collection of GdF{sub 3} core-shell structured (CSS) phosphors were synthesized by hydrothermal method. The as-prepared (AP) phosphors were coated with SiO{sub 2} layers to avoid aggregation and sintering during thermal annealing at 800 °C, after which the SiO{sub 2} layers were etched off and the annealed phosphors became highly dispersible. The annealed CSS phosphor aGdF{sub 3}:Eu{sup 3+}@GdF{sub 3}:Ce{sup 3+},Dy{sup 3+} shows excellent multicolor luminescence performance with the aid of dual-channel excitation and energy migration (EM) procedure of Gd{sup 3+} ions. By inserting pyromellitic acid (PMA) organic ligands into the interfaces between annealed core and AP shell layer regions, the so-called antenna effect of organic ligands of PMA forms a new excitation channel, which makes the CSS phosphor aGdF{sub 3}:Eu{sup 3+}@PMA@GdF{sub 3}:Ce{sup 3+},Dy{sup 3+} exhibit significantly enhanced multicolor luminescence via multi-channel excitation and EM process. The prepared CSS phosphors in this work are excellent candidates for applications in solid-state lighting.

36 MATERIALS SCIENCE↗
DOE OSTI2020

New self-consistent homogenization for thermo-elastic polycrystals with imperfect interfaces

Here we present a new thermo-elastic self-consistent formulation to calculate the thermo-mechanical response of polycrystalline aggregates with imperfect interfaces. The new model is based on an improved treatment of the effect of imperfect interfaces on the micromechanical response of the grains compared to pre-existing models. New expressions/algorithms are derived for the effective elastic and thermal properties, localization relations, and calculation of intragranular field fluctuations. In addition, derivation of a novel integral equation for the strain field in a heterogeneous elastic medium subjected to arbitrary thermal strain field and displacement jumps is presented. The new model is applied to study the effective thermo-elastic properties and average field fluctuations as a function of the interface properties for imperfectly-bonded triaminotrinitrobenzene (TATB) polycrystalline granular aggregates. The proposed formulation is general in the sense that it can be extended to other material systems and deformation regimes that require a proper consideration of the effect of imperfect interface properties on the material's thermo-mechanical response.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Linking water quality, fouling layer composition, and performance of reverse osmosis membranes

Fouling of polyamide membranes during reverse osmosis (RO) is a major challenge for adopting membrane technologies to treat highly contaminated waters, especially those containing organic foulants (e.g., natural organic matter (NOM), polysaccharides) and dominant cations (e.g., sodium, magnesium, calcium). Here, this work combines bench-scale membrane fouling experiments with detailed characterization of feedwater chemistry and fouling layer composition/morphology to reveal fundamental mechanisms of (in)organic fouling during RO. Divalent cations are shown to promote fouling by hydrophobic NOM containing aromatic and carboxyl groups, while NOM fouling in the presence of a monovalent cation, sodium, occurs by smaller fulvic acids containing larger fractions of carboxyl groups and other oxygen-rich moieties. Calcium-carboxyl bridging occurs in solution and near the membrane surface to induce NOM aggregation on nanometer length scales. In complex waters containing foulant mixtures, co-fouling by calcium-carboxyl bridging and CaCO 3 precipitation influence membrane performance at longer timeframes. However, the flux decline observed for the co-fouling mechanism was less significant than the sum of its parts, suggesting both synergistic and antagonistic fouling mechanisms should be considered in membrane design/operation. These results encourage the design of pretreatment processes to reduce concentrations of multivalent ions and hydrophobic NOM in RO feedwaters, and of membrane materials to limit attachment/deposition of aggregates to/on polyamide surfaces.

42 ENGINEERING↗
DOE OSTI2026

Omega-Limit Sets and Input-To-State Stability in Power Grids with Switching Equilibria

This paper studies a power transmission system with both conventional generators (CGs) and distributed energy assets (DEAs) providing frequency control. We consider an operating condition with demand aggregating two dynamic components: one that switches between different values on a finite set, and one that varies smoothly over time. Such dynamic operating conditions may result from protection scheme activations, external cyber-attacks, or due to the integration of dynamic loads, such as data centers. Mathematically, the dynamics of the resulting system are captured by a system that switches between a finite number of vector fields - or modes -, with each mode having a distinct equilibrium point induced by the demand aggregation. To analyze the stability properties of the resulting switching system, we leverage tools from hybrid dynamic inclusions and the concept of ..omega.. -limit sets from sets. Specifically, we characterize a compact set that is semi-globally practically asymptotically stable under the assumption that the switching frequency and load variation rate are sufficiently slow. For arbitrarily fast variations of the load, we use a level-set argument with multiple Lyapunov functions to establish input-to-state stability of a larger set and with respect to the rate of change of the loads. The theoretical results are illustrated via numerical simulations on the IEEE 39-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗