SEARCH · Engineering Papers

Results for “numerical integration”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,009 records · Page 56

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Fast growing high-yield wheat and canola for efficient nutrient recycling systems

Wheat and canola are two major rotation crops in the U.S. each offering advantageous traits for the agricultural value chain. Canola, a dicot rotation crop, generally offers high seed oil content. Wheat, a monocot rotation crop, offers more cellulose and other nutritious carbohydrates. As rotation crops, traits such as rapid growth rates, increased harvest yields, and high quality (digestibility, deconstructability) are desirable for food, biorefinery, and also nutrient recycling for crop rotation. Improvement of such traits has been the goal of numerous biotechnology efforts. However, alternative biotechnology techniques are typically constitutive and when applied to commercial crops have resulted in net negative consequences. For example, efforts to improve quality by lowering lignin biosynthesis have resulted in plants with poor structural integrity and diminished mass at maturity. With supports by SBIR programs from DOE and USDA, JBEI/LBNL and AFINGEN previously demonstrated engineered healthy switchgrass and alfalfa which grew with 20-30% more fermentable sugar release, 25% less lignin, faster growth, and more biomass yields than control plants. In this CRADA project supported by NASA STTR program, AFINGEN again collaborated with JBEI/LBNL and transferred the simple tissue-targeting technology from the demonstrated switchgrass and alfalfa to the two major rotation crops wheat and canola for efficient nutrient recycling systems.

09 BIOMASS FUELS↗

DOE OSTI2021

Root Influences on Mobilization and Export of Mineral-bound Soil Organic Matter

Biogeochemical cycles within mountainous watersheds are key regulators of ecosystem carbon storage and downstream nutrient loadings, and they have shown to be particularly vulnerable to climate change impacts. Increasing temperature and persistent droughts have already dramatically changed vegetation cover across the mountainous western US, with unknown consequences for soil carbon and nutrient cycles belowground. What remains elusive is to what extent associated changes in root-soil interactions may mobilize the vast pool of organic matter (OM) that has been stabilized by associations with minerals for centuries or millennia. Although plant root-driven OM mobilization from minerals may be a central control on carbon loss and nutrient export, such mechanisms are currently missing from conceptual and numerical models. The overall objective of this Exploratory Project is to identify the biogeochemical mechanisms by which roots destabilize mineral-associated organic matter (MAOM) and the cumulative impact on carbon and nutrient fate. To accomplish this goal, we integrated well-controlled laboratory experiments with in-field measurements and a scalable modeling approach. First, we conducted model system experiments to assess the vulnerability of MAOM to exudate-mediated mechanisms. Our results show that common root exudates effectively destabilize MAOM not only through direct, ligand-driven mobilization mechanisms, but also indirect, microbially-mediated mechanisms relying on secondary metabolites and enzymes. We further found that OM bound to poorly crystalline Fe and Al (hydr)oxides is more vulnerable to exudate-induced destabilization than OM bound to more crystalline phases, particularly in response to direct, ligand-promoted mechanisms. These findings demonstrate that the stability of MAOM is not just a function of their inherent properties, but also will depend in large parts on the ability of plant roots and microbes to produce exudates capable of triggering suitable mobilization mechanisms. We further employed a well-controlled rhizobox approach, combining advanced microsensor and mass spectrometry techniques, to resolve spatiotemporal variations in the composition and availability of exudates along single growing roots of grasses. Our results show that the composition of functionally relevant exudate compounds varies at extremely short time scales, seemingly shifting from ligands such as aromatic acids around root tips to less reactive metabolites such as amino acids around mature root segments. These results suggest a prevalence of direct MAOM mobilization mechanisms around the root tip, while indirect MAOM mobilization strategies may dominate around more mature root segments. Additionally, we utilized microsensor measurements in rhizoboxes to parameterize a rhizosphere (hydro)biogeochemistry reactive transport model (eSTOMP-ROOTS). The resulting model was used to assess how root exudations affects the stability of MAOM. Model simulations show that diel pulses of root exudation are strong enough to cause oscillations in biogeochemical conditions—particularly in pH, oxygen concentrations, and microbial activity— that repeatedly disrupt MAOM. Finally, we assessed field-scale impacts of root-driven MAOM destabilization over short and long time scales. A combination of in-field incubations and field-based characterizations showed that MAOM may not only be vulnerable to seasonal variations in root activity, but also to root-driven weathering over pedogenic time scales. In sum, results from our Exploratory Award highlight the strong control plant roots exert on MAOM mobilization and, thus, on the potential for carbon and nutrient export from watersheds.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Building a FAIR data ecosystem for incorporating single-cell transcriptomics data into agricultural genome to phenome research

Introduction The agriculture genomics community has numerous data submission standards available, but the standards for describing and storing single-cell (SC, e.g., scRNA- seq) data are comparatively underdeveloped. Methods To bridge this gap, we leveraged recent advancements in human genomics infrastructure, such as the integration of the Human Cell Atlas Data Portal with Terra, a secure, scalable, open-source platform for biomedical researchers to access data, run analysis tools, and collaborate. In parallel, the Single Cell Expression Atlas at EMBL-EBI offers a comprehensive data ingestion portal for high-throughput sequencing datasets, including plants, protists, and animals (including humans). Developing data tools connecting these resources would offer significant advantages to the agricultural genomics community. The FAANG data portal at EMBL-EBI emphasizes delivering rich metadata and highly accurate and reliable annotation of farmed animals but is not computationally linked to either of these resources. Results Herein, we describe a pilot-scale project that determines whether the current FAANG metadata standards for livestock can be used to ingest scRNA-seq datasets into Terra in a manner consistent with HCA Data Portal standards. Importantly, rich scRNA-seq metadata can now be brokered through the FAANG data portal using a semi-automated process, thereby avoiding the need for substantial expert curation. We have further extended the functionality of this tool so that validated and ingested SC files within the HCA Data Portal are transferred to Terra for further analysis. In addition, we verified data ingestion into Terra, hosted on Azure, and demonstrated the use of a workflow to analyze the first ingested porcine scRNA-seq dataset. Additionally, we have also developed prototype tools to visualize the output of scRNA-seq analyses on genome browsers to compare gene expression patterns across tissues and cell populations. This JBrowse tool now features distinct tracks, showcasing PBMC scRNA-seq alongside two bulk RNA-seq experiments. Discussion We intend to further build upon these existing tools to construct a scientist-friendly data resource and analytical ecosystem based on Findable, Accessible, Interoperable, and Reusable (FAIR) SC principles to facilitate SC-level genomic analysis through data ingestion, storage, retrieval, re-use, visualization, and comparative annotation across agricultural species.

Genetics & Heredity↗

DOE OSTI2022

Numerical algorithms for water waves with background flow over obstacles and topography

Abstract We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply connected fluid domain that includes stationary obstacles and variable bottom topography. One approach is formulated in terms of the surface velocity potential while the other evolves the vortex sheet strength. Both methods employ layer potentials in the form of periodized Cauchy integrals to compute the normal velocity of the free surface, are compatible with arbitrary parameterizations of the free surface and boundaries, and allow for circulation around each obstacle, which leads to multiple-valued velocity potentials but single-valued stream functions. We prove that the resulting second-kind Fredholm integral equations are invertible, possibly after a physically motivated finite-rank correction. In an angle-arclength setting, we show how to avoid curve reconstruction errors that are incompatible with spatial periodicity. We use the proposed methods to study gravity-capillary waves generated by flow around several elliptical obstacles above a flat or variable bottom boundary. In each case, the free surface eventually self-intersects in a splash singularity or collides with a boundary. We also show how to evaluate the velocity and pressure with spectral accuracy throughout the fluid, including near the free surface and solid boundaries. To assess the accuracy of the time evolution, we monitor energy conservation and the decay of Fourier modes and compare the numerical results of the two methods to each other. We implement several solvers for the discretized linear systems and compare their performance. The fastest approach employs a graphics processing unit (GPU) to construct the matrices and carry out iterations of the generalized minimal residual method (GMRES).

Ambrose, David M.↗

DOE OSTI2020

Dynamic Behavior of Natural Seep Vents: Analysis of Field and Laboratory Observations and Modeling (Final Scientific/Technical Report)

In this project, we have analyzed data collected by the U.S. Department of Energy (DOE), National Energy Technology Laboratory (NETL) in a high pressure water tunnel (HPWT) and data from two research cruises to natural seeps in the Gulf of Mexico to adapt and validate a numerical model to predict the dynamics of natural seeps in the deep oceans. The HPWT data include video observations of the shrinkage rate of individual methane and natural gas bubbles under simulated deep-water conditions. Field data were collected during two cruises by the Gulf Integrated Spill Research (GISR) Consortium led by Texas A&M University and funded by the Gulf of Mexico Research Initiative (GoMRI). These data included in situ observations from a remotely operated vehicle (ROV) of gas bubbles at two natural seep sites in the Gulf and acoustic observations of the natural seep bubble flares in the ocean water column. The acoustic data were from multibeam echosounders, one mounted in a forward-looking orientation on the ROV and another mounted down-looking in the haul of the ship. All of these laboratory and field data were focused on the dynamics of natural gas bubbles at temperatures and pressures favorable for clathrate hydrate formation between the gas and water. Our analyses of this data focused on understanding the mechanisms responsible for gas bubble dissolution within the hydrate stability zone (HSZ) of the oceans. Ice-like hydrate shells may form on the bubble-water interface under these conditions, and it was unknown how this might affect the mass transfer of gas into the ocean. We were able to extract bubble shrinkage rates from the HPWT datasets. Using this data we determined that mass transfer coefficients with and without a hydrate shell match empirical values for bubbles in contaminated systems (so-called dirty bubbles contaminated by naturally occurring surfactants). We also showed that free gas, and not gas hydrate, is the dominant dissolving phase when the hydrate sub-cooling is below 11 degree Celsius (temperature difference between hydrate the hydrate formation temperature and ambient temperator) or the pressure is reducing as bubbles rise through the ocean water column. Using this mass transfer model, our numerical model of bubble dissolution matched the over 200 HPWT experiments with an average error of 10% for predicting the bubble size at the end of an experiment. From field data in the literature, we also observed that gas bubbles dissolve faster when they are initially released, following mass transfer coefficients for so-called clean-bubbles (those not yet contaminated by surfactants). Shortly after release within the HSZ, a hydrate shell forms on the bubble-water interface, and the mass transfer reduces to rates matching those of dirty bubbles. We correlated this transition time from clean to dirty bubble behavior with the initial bubble surface area and the hydrate sub-cooling. With this model for hydrate formation time and using the mass transfer coefficients deduced from the HPWT data, we validated our numerical model for predicting the rise heights of natural seep flares in the oceans. Flare heights are commonly observed in haul-mounted acoustic multibeam data. The numerical model predicts bubbles to rise high in the ocean water column owing to the slower mass transfer rates for dirty bubbles that accompany the majority of their rise time. We found that the numerical model predictions matched the observed flare heights within 5% to 10% accuracy when we compared the rise heights of the largest bubbles released from the seafloor with the bubbles acoustically visible in the multibeam data. Bubbles become acoustically transparent as they shrink to sizes of order 1 mm in diameter for the multibeam frequencies used in the field. The forward-looking multibeam on the ROV also provided data on the lateral spreading of bubbles in natural seep flares. Our analysis of this data showed that spreading follows a diffusion process, with the effective diffusivity correlating with the wobbling length scale of these ellipsoidal bubbles. When we apply this diffusivity in a random displacement model of bubble spreading, our numerical simulations match closely the lateral spread observed by the M3 in the ocean water column. Finally, we compared the seep model predictions for the acoustic properties of these natural seep plumes with that observed by the acoustic instruments in the field. The M3 and EM 302 observations were converted to relative values of target strength using a calibration we obtained in the laboratory for the M3 and using an algorithm from the manufacturer for the EM 302. Comparing the numerical seep model to these data, we obtain good agreement over the whole height of rise of these bubble flares. This further validates the numerical model. Overall, our validated seep model captures the key dynamics of gas bubbles released from natural seeps in the oceans and helps to predict the fate of methane in the water column.

03 NATURAL GAS↗

DOE OSTI2021

A Butterfly-Accelerated Volume Integral Equation Solver for Broad Permittivity and Large-Scale Electromagnetic Analysis

In this work, a butterfly-accelerated volume integral equation (VIE) solver is proposed for fast and accurate electromagnetic (EM) analysis of scattering from heterogeneous objects. The proposed solver leverages the hierarchical off-diagonal butterfly (HOD-BF) scheme to construct the system matrix and obtain its approximate inverse, used as a preconditioner. Complexity analysis and numerical experiments validate the O(N log 2 N) construction cost of the HOD-BF-compressed system matrix and O(N log 1.5 N) inversion cost for the preconditioner, where N is the number of unknowns in the high-frequency EM scattering problem. For many practical scenarios, the proposed VIE solver requires less memory and computational time to construct the system matrix and obtain its approximate inverse compared to a H matrix-accelerated VIE solver. The accuracy and efficiency of the proposed solver have been demonstrated via its application to the EM analysis of large-scale canonical and real-world structures comprising of broad permittivity values and involving millions of unknowns.

42 ENGINEERING↗

DOE OSTI2025

Addressing Critical Challenges of Coal Mines for Underground Pumped Storage Hydropower Using Numerical Calculations

Using existing coal mines to build underground pumped storage hydropower (UPSH) power plants could help reduce the costs associated with starting a new PSH operation. This innovative approach can leverage the existing infrastructure of coal mine facilities available in many regions of the United States. However, technical challenges associated with water quality, mineral chemistry and integrity of subsurface topologies have thus far prevented any of these facilities from going online. Rye Development is investigating the feasibility of UPSH at existing coal mine facilities. In this project, Rye Development received the technical assistance from Oak Ridge National Laboratory to investigate the impacts of minerals, metal particles, and chemical substances in water flow on hydraulic equipment and assess the overall structural integrity of hydraulic equipment in former coal mines.

13 HYDRO ENERGY↗

DOE OSTI2021

Constructing tensor network influence functionals for general quantum dynamics

Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗

DOE OSTI2022

An extrapolation method to remove spurious stress concentration in micromechanical analyses of composites using pixel-based meshes

It is easier to generate a finite element mesh of complicated geometries with voxel-based meshes compared to conformal meshes. However, the local stresses in voxel-based meshes are higher owing to artificial stress concentration caused due to jagged lines that approximate a curve. Here, we propose a method that accounts for this anomaly which would lead to accurate prediction of maximum von Mises stress in voxel-based meshes. The method is based on the variation of reciprocal of stresses and associated numerical gradient. The prediction of the proposed method is compared against the results of a conformal mesh by considering four two-dimensional example problems. The accuracy of the proposed method is verified using different mesh densities, material properties, and integration schemes. The proposed method was also implemented on a conformal mesh to verify that it filters out just the spurious stress concentration and not the realistic stress concentration.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Statistical description of coalescing magnetic islands via magnetic reconnection

The physical picture of interacting magnetic islands provides a useful paradigm for certain plasma dynamics in a variety of physical environments, such as the solar corona, the heliosheath and the Earth's magnetosphere. In this work, we derive an island kinetic equation to describe the evolution of the island distribution function (in area and in flux of islands) subject to a collisional integral designed to account for the role of magnetic reconnection during island mergers. This equation is used to study the inverse transfer of magnetic energy through the coalescence of magnetic islands in two dimensions. We solve our island kinetic equation numerically for three different types of initial distribution: Dirac delta, Gaussian and power-law distributions. The time evolution of several key quantities is found to agree well with our analytical predictions: magnetic energy decays as $\tilde {t}^{-1}$ , the number of islands decreases as $\tilde {t}^{-1}$ and the averaged area of islands grows as $\tilde {t}$ , where $\tilde {t}$ is the time normalised to the characteristic reconnection time scale of islands. General properties of the distribution function and the magnetic energy spectrum are also studied. Finally, we discuss the underlying connection of our island-merger models to the (self-similar) decay of magnetohydrodynamic turbulence.

Physics↗

DOE OSTI2020

An Adaptive Framework for Extreme Deformation and Failure in Solids

Recent developments at Sandia in meshfree methods have delivered improved robustness in solid mechanics problems that prove difficult for traditional Lagrangian, mesh-based finite elements. Nevertheless, there remains a limitation in accurately predicting very large material deformations. It seems robust meshfree discretizations and integration schemes are necessary, but not sufficient, to close this capability gap. This state of affairs directly impacts current and future LEPs, whose simulation needs are not well met for extremely large deformation problems. We propose to use a new numerical framework, the Optimal Transportation Meshfree (OTM) method enhanced by meshfree adaptivity, as we believe that a combination of both will provide a novel way to close this capability gap.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Progress Report on Model Development for the Transport of Aerosol through Microchannels

This report summarizes the current progress in the development of a phenomenological model of aerosol transport, deposition, and plugging through microchannels. The purpose is to introduce a generic, reliable numerical model for the prediction of aerosol transport, deposition, and plugging in leak paths while accounting for potential plugging formation, to a user community involving researchers, regulators, and industry. In that regard, a Graphical User Interface (GUI) was generated by integrating the individual MATLAB scripts that make up the model and adding additional features to aid the general understanding of the problem to a user. This report focuses on the model development and features included. Further, predictions from the GUI are compared with experimental data for validation. The strength of the GUI is the ability of a user to plug in basic parameters such as the initial pressure conditions and canister model specifications in order to obtain a first principal approximation of vital information such as the blowdown pressure differential, aerosol penetration, and deposition as a function of time. The user can obtain this without the know-how of the underlying MATLAB scripts and thus enables the model to be readily applied by regulators, industry, and shareholders to reduce the uncertainty in the off-site radiological consequences. The report also lists future tasks under this work scope. This includes ongoing efforts to include additional crack geometries (divergent and divergent-convergent slots) to the model; GUI development and improvement based on feedback from users, and integration of aerosol source term data from Sibling Pin tests into the model as we approach realistic canister stress corrosion cracking–induced aerosol release scenarios.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

NOW-23: The 2023 National Offshore Wind Data Set

17 WIND ENERGY↗

DOE OSTI2023

NOW-23: the 2023 National Offshore Wind Data Set

In this report, we present the latest wind resource data specifically tailored for offshore regions in the United States. The data set, known as the 2023 National Offshore Wind data set (NOW-23), has been developed by the National Renewable Energy Laboratory (NREL) and its partners, and surpasses the previous resource data set, the Wind Integration National Dataset (WIND) Toolkit, which was released approximately ten years ago, in its offshore component. The WIND Toolkit has been widely utilized by stakeholders involved in wind resource assessments across the continental United States. However, with significant advancements in numerical weather prediction modeling over the past decade, the NOW-23 data set incorporates the latest research and development progress to provide stakeholders with an updated and cutting-edge resource for offshore wind analysis. The NOW-23 data set is created using the Weather Research and Forecasting (WRF) model and its output is available, as for its predecessor, at 5-minute time resolution and 2-kilometer horizontal spatial resolution. However, the NOW-23 data set improves upon the WIND Toolkit through: 1. A modeling period of at least 20 years (and as long as 23 years in selected regions), starting in 2000 (compared to the 7-year 2007–2013 modeling period in the WIND Toolkit). 2. For several offshore regions, a region-specific sensitivity analysis, driven by an ensemble of WRF simulations, to assess the most adequate region-specific WRF setup. 3. An updated WRF model, from Version 3.4 used in the WIND Toolkit to Version 4.2.1 used for the NOW-23 data set, which incorporates significant research advancements. 4. The use of the state-of-the-art reanalysis product ERA5 (which supersedes the older ERA-Interim used in the WIND Toolkit) to provide atmospheric forcing at the WRF domain boundaries. Figure 1 shows the NOW-23 mean wind speed at 160 m above sea level (asl), which we use as proxy for hub-height of a commercial offshore wind turbine in this report across all regions.

17 WIND ENERGY↗

DOE OSTI2021

Investigations into Balancing Peak-to-Average Power Ratio and Mean Power Extraction for a Two-Body Point-Absorber Wave Energy Converter

The power harnessed by wave energy converters (WECs) in oceans is highly variable and, therefore, has a high peak-to-average power (PTAP) ratio. To minimize the cost of a WEC power take off (PTO) system, it is desirable to reduce the PTAP ratio while maximizing the mean power extracted by WECs. The important issue of how PTAP ratio reduction measures (such as adding an inertia element) can affect the mean power extracted in a reference model has not been thoroughly addressed in the literature. To investigate this correlation, this study focuses on the integration of the U.S. Department of Energy’s Reference Model 3, a two-body point absorber, with a slider-crank WEC for linear-to-rotational conversion. In the first phase of this study, a full-scale numerical model was developed that predicts how PTO system parameters, along with an advanced control algorithm, can potentially affect the proposed WEC’s PTAP ratio as well as the mean power extracted. In the second phase, an appropriate scaled-down model was developed, and extracted power results were successfully validated against the full-scale model. Finally, numerical and hardware-in-the-loop (HIL) simulations based on the scaled-down model were designed and conducted to optimize or make trade-offs between the operational performance and PTAP ratio. The initial results with numerical and HIL simulations reveal that gear ratio, crank radius, and generator parameters substantially impact the PTAP ratio and mean power extracted.

16 TIDAL AND WAVE POWER↗

DOE OSTI2021

"Hybrid fracture/matrix modeling for well completion options evaluation"

Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Here we present the development of a methodology to rapidly and efficiently numerically simulate mixed fracture-matrix flow systems for evaluation of well design and completion options. The methodology is based on a loose coupling framework, allowing the fracture and matrix systems to be meshed separately. The fracture system includes the integration of fracture growth and aperture data from well stimulation simulations of stochastically generated fracture networks. Automatic mesh refinement is used in the matrix simulation to resolve heat transfer near the fracture network. This simulation framework is used to efficiently determine optimal production and injection well placement using adaptive sampling.

15 GEOTHERMAL ENERGY↗

DOE OSTI2023

Hierarchical Flexibility Offering Strategy for Integrated Hybrid Resources in Real-time Energy Markets

This paper proposes a hierarchical model for determining the energy flexibility offering strategy of integrated hybrid resources (IHRs) in power distribution systems to participate in real-time energy markets. The proposed model utilizes the scalability, fast response time, and uncertainty observation of deep reinforcement learning (DRL) to overcome the scalability issue of operating numerous flexible resources and deliverability of energy flexibility to the real-time markets in the presence of the network constraints. To that end, the power distribution system is divided into multiple IHRs, where different types of flexible loads, energy storage systems, and solar plants with controllable inverters are operated through local IHR controllers, trained by deep deterministic policy gradient (DDPG) algorithm. Active power request and reactive power capacity of IHRs are then transmitted to a central flexibility controller, where a quadratic optimization model ensures the deliverability of the energy flexibility to the real-time energy market by satisfying the distribution network constraints. The proposed model is implemented on the 123-bus test power distribution system, demonstrating the capability of DRL-based hierarchical model for scalable operation of IHRs in order to offer deliverable energy flexibility to the real-time energy market.

Majidi, Majid↗