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At least 235 records · Page 13

Magnetic energy storage and conversion in the solar atmosphere

According to the approach employed in this investigation, particularly important simple configurations of magnetic field and plasma are identified, and it is attempted to achieve an understanding of the large-scale dynamic processes and transformations which these systems can undergo. Fundamental concepts are discussed, taking into account aspects of magnetic energy generation, ideal MHD theory, non-MHD properties, the concept of 'anomalous' resistivity, and global electrodynamic coupling. Questions of magnetically controlled energy conversion are examined, giving attention to magnetic modifications of plasma transport, the transition region structure and flows, channeling and acceleration of plasma, channeling and dissipation of MHD waves, and anomalous dissipation of field-aligned currents. A description of the characteristics of magnetohydrodynamic energy conversion is also provided, and outstanding questions are discussed.

Spicer, D. S.↗

Dynamics of streamflow permanence in a headwater network: Insights from catchment-scale model simulations

The hillslope and channel dynamics that govern streamflow permanence in headwater systems have important implications for ecosystem functioning and downstream water quality. Recent advancements in process-based, semi-distributed hydrologic models that build upon empirical studies of streamflow permanence in well-monitored headwater catchments show promise for characterizing the dynamics of streamflow permanence in headwater systems. However, few process-based models consider the continuum of hillslope-stream network connectivity as a control on streamflow permanence in headwater systems. The objective of this study was to expand a process-based, catchment-scale hydrologic model to better understand the spatiotemporal dynamics of headwater streamflow permanence and to identify controls of streamflow expansion and contraction in a headwater network. Further, we aimed to develop an approach that enhanced the fidelity of model simulations, yet required little additional data, with the intent that the model might be later transferred to catchments with limited long-term and spatially explicit measurements. This approach facilitated network-scale estimates of the controls of streamflow expansion and contraction, albeit with higher degrees of uncertainty in individual reaches due to data constraints. Our model simulated that streamflow permanence was highly dynamic in first-order reaches with steep slopes and variable contributing areas. The simulated stream network length ranged from nearly 98±2% of the geomorphic channel extent during wet periods to nearly 50±10% during dry periods. The model identified a discharge threshold of approximately 1 mm d –1 , above which the rate of streamflow expansion decreases by nearly an order of magnitude, indicating a lack of sensitivity of streamflow expansion to hydrologic forcing during high-flow periods. Overall, we demonstrate that process-based, catchment-scale models offer important insights on the controls of streamflow permanence, despite uncertainties and limitations of the model. We encourage researchers to increase data collection efforts and develop benchmarks to better evaluate such models.

54 ENVIRONMENTAL SCIENCES↗

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗

Characterizing Turbulence at a Forest Edge: Comparing Sub-Filter Scale Turbulence Models in Simulations of Flow over a Canopy

In wildfires, atmospheric turbulence plays a major role in the transfer of turbulent kinetic energy. Understanding how turbulence feeds back into a dynamical system is important, down to the varying small scales of fuel structures (i.e. pine needles, grass). Large eddy simulations (LES) are a common way of numerically representing turbulence. The Smagorinsky model (1963) serves as one of the most studied sub-grid scale representations in LES. In this investigation, the Smagorinsky model was implemented in HIGRAD/FIRETEC, LANL’s coupled fire-atmosphere model. This study was motivated by the need to quantitatively investigate the vorticity budget equation in HIGRAD/FIRETEC. The Smagorinsky turbulent kinetic energy (TKE) was compared to FIRETEC’s 1.5-order TKE eddy-viscosity subgrid-scale model, known as the Linn turbulence model. This was done in simulations of flow over flat terrain with a homogeneous, cuboidal canopy in the center of the domain. Examinations of the modeled vertical TKE profile and turbulent statistics at the leading edge, and throughout the canopy, show that the Smagorinsky model provides comparable results to that of the original closure model posed in FIRETEC.

58 GEOSCIENCES↗

Deviations from uniform power law scaling in nonstationary time series

A classic problem in physics is the analysis of highly nonstationary time series that typically exhibit long-range correlations. Here we test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate. We develop techniques based on the Fano factor and Allan factor functions, as well as on detrended fluctuation analysis, for quantifying deviations from uniform power-law scaling in nonstationary time series. By analyzing extremely long data sets of up to N = 10(5) beats for 11 healthy subjects, we find that the fluctuations in the heart rate scale approximately uniformly over several temporal orders of magnitude. By contrast, we find that in data sets of comparable length for 14 subjects with heart disease, the fluctuations grow erratically, indicating a loss of scaling stability.

Non-NASA Center↗

IM3 Phase 2 Official Simulations: GCAM-Demeter-SELECT Annualized Land Use and Land Cover, Wood Harvest and Fertilization Data with Dynamic Urbanization Harmonized to CLM Land Definitions at 0.125 Degrees

Annualized land use land cover data, including wood harvest and fertilizer use data from the Global Change Analysis Model (GCAM) downscaled to 0.125 degrees for couping with the Community Land Model (CLM). GCAM here refers to GCAM-USA v5.3.im3 which has an enhanced electricity sector and an updated data system needed to represent regional to local scale dynamics. Data is also harmonized with future urbanization projections from the Spatially-Explicit, Long-term, Empirical City developmenT (SELECT) model. Projections/Data are generated using the demeter land use and land cover downscaling model. Original projections were generated at 0.05 degrees before being aggregared to 0.125 degrees. Projections are available for 8 alternative scenarios. Two versions of final data are included- one with managed forests or harvested forest area per pixel broken out and one with the same aggregated into total forests. Following folders are included: demeter_78_PFT_output:This is the final output of dynamic land use land cover change for 78 PFTs as required by CLM raw_outputs_incl_managed_forest: This is the final output but with managed forests broken out as a different PFT. Essentially a 79th PFT is added. wood_harvest_outputs: Wood harvest output per pixel in gC/m2 fertilization_outputs: Fertilizer use per pixel in gN/m2 Each NetCDF file in each folder represents a projection for a separate year, scenario. Land use outputs are organized as PFT level data saved as subdata. Link to GCAM version used- https://data.msdlive.org/records/yb23g-44274 Link to SELECT documentation -https://www.sciencedirect.com/science/article/pii/S1364815219301707 Link to CLM documentation- - https://www.cesm.ucar.edu/models/clm In case of questions contact- kanishka.narayan@pnnl.gov

GCAM-USA↗

Revolutionizing Energy Storage: AI, Automation, and Advanced Modeling as Catalysts for Next-Generation Breakthroughs

The Presidential Symposium (PRES) at the 2025 Fall Meeting, hosted by the President’s Office and Energy and Fuels Division, American Chemical Society (ACS) in Washington, DC, brought together a diverse group of chemists, engineers, and materials scientists working in battery materials & systems, automation and artificial intelligence from academia, industry, and national laboratories. The accelerating demand for high-performance, scalable, and sustainable energy storage has catalyzed a paradigm shift in how materials are dis-covered, devices are engineered, and systems are optimized. This Presidential Symposium, entitled “Revolutionizing Energy Storage: AI, Automation, and Advanced Modeling Driving Next-Gen Breakthroughs”, brings together global leaders to unveil transformative strategies anchored in the AAA framework: Artificial Intelligence, Automation, and Advanced Modeling. Artificial Intelligence is redefining the frontiers of energy storage by enabling predictive design, real-time optimization, and intelligent control across diverse chemistries and architectures. Automation is streamlining the synthesis, characterization, and testing of battery materials, dramatically accelerating innovation cycles and unlocking scalable solutions for grid and mobility applications. Advanced Modeling, spanning atomic to system-level scales, provides unprecedented insight into electrochemical dynamics, degradation pathways, and thermal behavior, particularly when coupled with physics-informed machine learning and digital twin technologies. Digital twins, in turn, leverage the AAA framework by integrating real-time data, physics-based models, and AI predictions into dynamic virtual replicas, enabling proactive diagnostics, optimization, and system resilience. Together, these synergistic pillars are not only re-shaping the scientific landscape but also forging a new era of reproducible, data-driven, and resilient energy storage innovation. In conclusion, this symposium marks a pivotal moment in the convergence of computational intelligence and experimental rigor, charting the course for next-generation breakthroughs in lithium-ion, solid-state, and flow battery technologies.

Artificial Intelligence (AI)↗

MLMOD: Machine Learning Methods for Data-Driven Modeling in LAMMPS

MLMOD is a software package for incorporating machine learning approaches and models into simulations of microscale mechanics and molecular dynamics in LAMMPS. Recent machine learning approaches provide promising data-driven approaches for learning representations for system behaviors from experimental data and high fidelity simulations. The package facilitates learning and using data-driven models for (i) dynamics of the system at larger spatial-temporal scales (ii) interactions between system components, (iii) features yielding coarser degrees of freedom, and (iv) features for new quantities of interest characterizing system behaviors. MLMOD provides hooks in LAMMPS for (i) modeling dynamics and time-step integration, (ii) modeling interactions, and (iii) computing quantities of interest characterizing system states. The package allows for use of machine learning methods with general model classes including Neural Networks, Gaussian Process Regression, Kernel Models, and other approaches. Here we discuss our prototype C++/Python package, aims, and example usage. For related papers, examples, updates, and additional information see https://github.com/atzberg/mlmod and http://atzberger.org/.

97 MATHEMATICS AND COMPUTING↗

Nonlinear dynamics of global atmospheric and earth system processes

During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

Zhang, Taiping↗

Application of a Distributed Element Roughness Model to Additively Manufactured Internal Cooling Channels

Abstract Design for cooling effectiveness in turbine blades relies on accurate models for dynamic losses and heat transfer of internal cooling passages. Metal additive manufacturing (AM) has expanded the design space for these configurations, but can give rise to large-scale roughness features. The range of roughness length scales in these systems makes morphology resolved computational fluid dynamics (CFD) impractical. However, volumetric roughness models can be leveraged, as they have computational costs orders of magnitude lower. In this work, a discrete element roughness model (DERM), based on the double-averaged Navier–Stokes equations, is presented and applied to additively manufactured rough channels, representative of gas turbine blade cooling passages. Unique to this formulation of DERM is a generalized sheltering-based treatment of drag, a two-layer model for spatially averaged Reynolds stresses, and explicit treatment of dispersion. Six different AM rough surface channel configurations are studied, with roughness trough to peak sizes ranging from 15% to 60% nominal channel passage half-width, and the roughness Reynolds number ranges from Rek = 60 to 300. DERM predictions for spatially and temporally averaged mean flow quantities are compared to previously reported direct numerical simulation results. Good agreement in the mean velocity profiles, stress balances, and drag partitions are observed. While DERM models are typically calibrated to specific deterministic roughness morphologies at comparatively small roughness Reynolds numbers, the present more generalized DERM formulation has wider applicability. Here, it is demonstrated that the model can accommodate random roughness of large scale, typical of AM.

Engineering↗

GCAM-USA: IM3 Phase 2 Official Simulations

Overview GCAM-USA simulates 21st century energy-water-land interactions in global regions with sub-national detail in the United States (US). The IM3 project is focused on US multisector dynamics and has created eight GCAM-USA simulations by combining two Shared Socioeconomic Pathways (SSP3 and SSP5) with four high-resolution climate projections specific to the United States (see https://tgw-data.msdlive.org/). These climate projections include "hotter" and "cooler" variants for two Representative Concentration Pathways (RCP4.5 and RCP8.5). The resulting eight GCAM-USA simulations are named: rcp45cooler_ssp3 rcp45cooler_ssp5 rcp45hotter_ssp3 rcp45hotter_ssp5 rcp85cooler_ssp3 rcp85cooler_ssp5 rcp85hotter_ssp3 rcp85hotter_ssp5 Detailed Assumptions The SSPs describe alternative socioeconomic futures and their implications for both the US and global environmental challenges. As implemented in GCAM-USA, the primary difference between SSP3 and SSP5 in the US is their population growth projections, with SSP3 foreseeing lower growth and SSP5 projecting higher growth. The four climate projections explore moderate (RCP4.5) and high (RCP8.5) greenhouse gas emission (GHG) trajectories, each with a hotter and cooler climate variation based on the range of global climate model simulations in CMIP6s. These four climate projections are used in precursor models to develop climate impacts on building heating and cooling degree-hours, water availability, and agricultural yields that are provided as inputs to GCAM-USA. GCAM-USA reproduces the RCP4.5 and RCP8.5 GHG emissions trajectories consistent with each climate projection, using dynamic carbon prices to achieve RCP4.5. When the four climate projections are combined with the two SSP projections, the resulting eight scenarios allow GCAM-USA to explore how a wide, yet plausible, range of climate and socioeconomic impacts affects the interconnected energy, water, and land systems across the contiguous United States. Technical Details IM3 uses a version of GCAM-USA v5.3 that has an enhanced electricity sector and an updated data system needed to represent regional to local scale dynamics.

IM3↗

Multipartite entanglement in the one-dimensional spin- 1 2 Heisenberg antiferromagnet

Multipartite entanglement refers to the simultaneous entanglement between multiple subsystems of a many-body quantum system. While multipartite entanglement can be difficult to quantify analytically, it is known that it can be witnessed through the quantum Fisher information (QFI), a quantity that can also be related to dynamical Kubo response functions. In this work, we first show that the finite temperature QFI can generally be expressed in terms of a static structure factor of the system, plus a correction that vanishes as T→0. This implies that the static structure factor witnesses multipartite entanglement near quantum critical points at temperatures below a characteristic energy scale of the system. Therefore, in systems with a known static structure factor, we can deduce finite temperature scaling of multipartite entanglement and low temperature entanglement depth without knowledge of the full dynamical response function of the system. This is particularly useful to study 1D quantum critical systems in which sub-power-law divergences can dominate entanglement growth, where the conventional scaling theory of the QFI breaks down. Furthermore, the 1D spin- 1 2 antiferromagnetic Heisenberg model is an important example of such a system, and we show that multipartite entanglement in the Heisenberg chain diverges nontrivially as ~ln(1/T) 3/2 . We verify these predictions with calculations of the QFI using conformal field theory and matrix product state simulations. Finally, we discuss the implications of our results for experiments to probe entanglement in quantum materials, comparing to neutron scattering data in KCuF 3 , a material well described by the Heisenberg chain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Bipartite mutual information in classical many-body dynamics

Information theoretic measures have helped to sharpen our understanding of many-body quantum states. As perhaps the most well-known example, the entanglement entropy (or more generally, the bipartite mutual information) has become a powerful tool for characterizing the dynamical growth of quantum correlations. By contrast, although computable, the bipartite mutual information (MI) is almost never explored in classical many particle systems; this owes in part to the fact that computing the MI requires keeping track of the evolution of the full probability distribution, a feat which is rarely done (or thought to be needed) in classical many-body simulations. Here, we utilize the MI to analyze the spreading of information in 1D elementary cellular automata (CA). Broadly speaking, we find that the behavior of the MI in these dynamical systems exhibits a few different types of scaling that roughly correspond to known CA universality classes. Of particular note is that we observe a set of automata for which the MI converges parametrically slowly to its thermodynamic value. We develop a microscopic understanding of this behavior by analyzing a two-species model of annihilating particles moving in opposite directions. Furthermore, our work suggests the possibility that information theoretic tools such as the MI might enable a more fine-grained characterization of classical many-body states and dynamics.

Cellular automata↗

Derivation of A Representative Elementary Volume (REV) for Upscaled Two-Phase Flow in Porous Media

Relative permeability plays an important role in the upscaling of multiphase flow in porous media from the pore scale to the Darcy scale. The entire concept of relative permeability is contingent on the existence of a representative elementary volume (REV). As we move to smaller samples to measure relative permeability, such as with digital core analysis, the concept of a classical REV has become increasingly unlikely when using the conventional approach to defining a representative volume. The “‘conventional”’ understanding of an REV is that a large enough volume must be considered such that spatial variability averages out. In digital rock methods, such as pore-scale simulations based on micro-computed tomography (CT) images, the domain size is typically 2 to 4 mm. This is approximately the length scale of a single-phase flow REV using the classic REV approach. However, the single-phase perspective does not consider the complex dynamics and fluctuations often observed in multiphase flow systems, even at centimeter-scale experiments and/or simulations. A fundamental question is, therefore, whether the domain size commonly used in digital rock simulations can provide a consistent energy budget such that the concept of relative permeability exists. Based on first principles, relative permeability accounts for the rate of energy dissipated in a stationary process. If the dynamics are fluctuating, the energy dissipated can vary but will average out over a long enough timescale. The key to determining the validity of the relative permeability is the timescale of the measurement, not the spatial scale. The conventional REV theory assumes that spatial, temporal, and ensemble averages are equivalent in an ergodic system, but it does not provide a way to test this assumption. We provide a formal way to identify the timescale where the relative permeability accurately captures energy dissipation as a way to validate relative permeability measurements and quantitatively assess their accuracy. This result will be tested for a practical SCAL test, determining how long a flow experiment needs to be run to accurately characterize the rate of energy dissipation by the flow. The outcome will be a best practice guide for the determination of relative permeability from core-scale experiments and/or digital core simulations that ensure the energy budget is fully accounted for in the relative permeability coefficient.

Mcclure, James [Virginia Tech, Blacksburg]↗

Some Aeronautical Communications Experiments

Classically there has existed an asymmetry between the computing and communicating sides of aerospace systems. Over the past few decades, this asymmetry has shifted to favoring communication link technologies, meaning that advancements in available central processing units (CPUs), storage devices, and internal data buses have stagnated. Indeed, the increased emphasis placed on refining subsystem performance such as with antenna bandwidth in phased arrays, amplifier power efficiency, software defined radio (SDR) flexibility and encoding for data compression and error correction has given rise to successful debuts of multi-gigabit-per-second data return from long space-link distances. These accomplishments are easily quantifiable through link budgets and illustrate what is possible, but also reveal the deficiencies in overall communications capabilities. In particular, the ever-accelerating presence of aerospace vehicles gives rise to newer and larger classes of challenges to address the needs of 21st century systems. Furthermore remote sensing and imaging capabilities have far outpaced our ability to transmit their products to the ground, so we are increasingly dependent on pre-processing and downselection to contend with the communications bottleneck. No longer may we depend upon the constrained logistics in delivering end-to-end data delivery through manual reconfigurations, static event scheduling and execution on a per-vehicle basis, for these methods do not scale and therefore must give way to dynamic, networked approaches with an overall systems view in mind. Emerging mission requirements exhibit a trend toward multiple smaller-scale vehicles working together to perform dissimilar observations. Such operations necessitate sensor fusion across a constellation, and where data processing may be distributed throughout a fairly disconnected network whose topology changes over time in non-deterministic manners. Individual communications link performance is still very relevant to deploying an effective communications system, but now must be embedded within a greater architecture of capability to optimally utilize the bandwidth available from each link to generate an ultimate end-to-end quality of service. The deleterious effects of timing uncertainty across the arrangement presents a challenge to measurement synchronization and delivery, so a successful deployed system needs to be tolerant to the delays inherent in time-of-light between elements and digital processing latencies existing at each node. In this presentation we share the flight test results from a high performance Gbps laser communications terminal evaluated with a suite of store and forward capabilities called High-rate Delay Tolerant Networking (HDTN). The communications payload is operated over Lake Erie across a range of configurations including several convergence layers, and is evaluated to determine recovery time after link disruptions, information loss, efficiency and speed. The effectiveness of utilizing a flying laboratory to increase the Technology Readiness Level (TRL) of an integrated system in relevant environments is discussed, as well as the value of conducting aeronautics experiments to retire risk for technology infusion into space missions. Upcoming flight campaigns will be presented, including opportunities to demonstrate secure command and control, data intensive hyperspectral imaging, quantum link characterization, 4k High Definition (HD) video streaming and internetworked space-ground-aero relay operations. These experiments will pave the way for future missions which will depend upon interoperability across disparate government and privately owned networks, involve contention with uncertain and dynamic timing, and require agility to autonomously configure optimal parameters across networks of ever-increasing size and complexity to ensure data delivery. https://www1.grc.nasa.gov/space/scan/acs/tech-studies/dtn/

Daniel Raible↗

The Effect of the Density Ratio on the Nonlinear Dynamics of the Unstable Fluid Interface

Here we report multiple harmonic theoretical solutions for a complete system of conservation laws, which describe the large-scale coherent dynamics in RTI and RMI for fluids with a finite density ratio in the general three-dimensional case. The analysis yields new properties of the bubble front dynamics. In either RTI or RMI, the obtained dependencies of the bubble velocity and curvature on the density ratio differ qualitatively and quantitatively from those suggested by the models of Sharp (1984), Oron et al. (2001), and Goncharov (2002). We show explicitly that these models violate the conservation laws. For the first time, our theory reveals an important qualitative distinction between the dynamics of the RT and RM bubbles.

Abarzhi, S. I.↗

Dynamic voltage and frequency scaling based on memory channel slack

A processing system scales power to memory and memory channels based on identifying causes of stalls of threads of a wavefront. If the cause is other than an outstanding memory request, the processing system throttles power to the memory to save power. If the stall is due to memory stalls for a subset of the memory channels servicing memory access requests for threads of a wavefront, the processing system adjusts power of the memory channels servicing memory access request for the wavefront based on the subset. By boosting power to the subset of channels, the processing system enables the wavefront to complete processing more quickly, resulting in increased processing speed. Conversely, by throttling power to the remainder of channels, the processing system saves power without affecting processing speed.

Das, Shomit N.↗

Coherency-Aware Learning Control of Inverter-Dominated Grids: A Distributed Risk-Constrained Approach

Here, this letter investigates the importance of integrating the coherency knowledge for designing controllers to dampen sustained oscillations in wide-area power networks with significant penetration of inverter-interfaced resources. Coherency is a fundamental property of power systems, where time-scale separation in frequency dynamics leads to clustered behavior among generators of different groups. Large-scale penetration of inverter-driven low inertia resources replacing conventional synchronous generators (SGs) can lead to perturbation in the coherent partitioning; hence, integrating such information is of utmost importance for oscillation control designs. We present the coherency-aware design of a distributed output feedback-based reinforcement learning method that additionally incorporates risk constraints to capture the uncertainties related to net-load fluctuations. The use of domain-aware coherency information has produced improved training and oscillation performance than the coherency-agnostic control design, hence proving to be effective in controller design. Finally, we validated the proposed method with numerical experiments on the benchmark IEEE 68-bus test system.

24 POWER TRANSMISSION AND DISTRIBUTION↗