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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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Modeling of a Generic Pebble Bed High-temperature Gas-cooled Reactor (PB-HTGR) with SAM

This report presents the modeling of the core of a generic pebble-bed reactor (PBR) at the system level using the System Analysis Module (SAM) code. This work is an extension of a previous work by the authors (Ooi et al. (2021)) that used the so-called 2-D ring model approach to model the PBMR-400. With the new approach, the pebble bed of the reactor is modeled with multiple PBCoreChannel components with spherical heat structures which allows the code to calculate thermal fluid parameters with built-in closure relations. The new core-channel approach is an improvement to the 2-D ring model approach as it does not introduce geometric distortions to the model and thus reduces the uncertainties of the predictions. In addition to thermal fluid simulations, point kinetics (PKE) are included to the model. Simulations are performed under a steady-state normal operation condition and a load-following transient scenario. This particular transient scenario is chosen as it tests both the thermal fluid and neutronics aspects of the model. The predicted results from both the steady-state and transient scenarios are compared with the results by Stew- art et al. (2021) who performed similar simulations with a Griffin-Pronghorn coupled tool. Despite the differences between the codes, with SAM being a system-analysis code and Pronghorn being a porous-medium code, both sets of results compare favorably. The over- all profiles and trends of the predicted temperatures and reactivities from the SAM and Griffin/Pronghorn simulations are similar, with some differences in their predicted values. The first part of the report covers the significance of a relatively fast-running approach that is capable of modeling the pebble bed reactor at the system-level while simultaneously capturing the radial thermal behavior of the core. Then, the modeling approach used in this work is discussed in details. Lastly, the results and comparisons with the Griffin/Pronghorn simulation are presented.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2024

Validation of Exploding Wire Tests Using Alegra-NG

Exploding wire tests are used to characterize materials undergoing high voltage loading and to validate computational models in a simple configuration. In this report, the materials emphasized are gold, aluminum, copper and nickel wires. Model validation is presented using the nominal model (no uncertainty) in the form of heat maps (per material) that show model bias across scalar quantities and initial voltage. Mesh convergence and uncertainty quantification is also presented.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Uncertainty Quantification for Capacity Expansion Planning

This report quantifies the uncertainty in output decisions from a Capacity Expansion Planning (CEP) model. The need to understand how uncertainties within CEP models and modeling assumptions affect Quantities of Interest (QoIs) such as expansion and operating costs, as well as expansion decisions remains an ongoing challenge in scientific research and industrial operations. This area of research is particularly important for models which seek to capture how large networks will evolve and operate under increased sources of variable generation, i.e., higher penetration of renewable technologies such as solar and wind generators. Uncertainty quantification (UQ) of CEP models which estimate expansion costs and decisions, and production cost models which estimate operating costs and dispatch decisions, is a key focus of research at NREL. The Regional Energy Deployment System (ReEDS) represents a state-of-the-art CEP model and considers a range of possible grid evolutions in an attempt to identify key drivers, ramifications, and decisions which contribute to better informed investment and policy decisions. However, research to quantify how uncertainties and model assumptions, such as unit commitment (UC), within ReEDS may be affecting its outputs remains challenging due to to size and complexity of the model

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Constraining the impact of chlorine as a neutron absorber in next-gen fast reactor designs

The role of chlorine as a neutron poison and as a seed for producing radioactive waste in nuclear systems has driven a renewed interest to improve its nuclear data uncertainties. Additionally, basic and applied science programs that use CLYC (Cs 2 LiYCl 6 :Ce) detectors for neutron spectroscopy and monitoring are also very sensitive to any change in chlorine nuclear data for simulations of the detector response. In this work, sensitivities relevant for these different applications are addressed through simulations of the efficiency of CLYC detectors in a fast fission spectrum when applying new chlorine nuclear data as input. These simulations are validated by an experimental measurement using CLYC detectors coupled to an ionization chamber loaded with a 252 Cf spontaneous fission source. The results are then used to obtain the first reliable direct measurement of the 35 Cl(n,p 0 ) and summed Cl(n,p+n,α) fission spectrum average cross sections, found to be 54.7(32) and 105.0(98) mb, respectively. The results are within uncertainty of calculated fission spectrum averaged cross sections based on recently re-evaluated chlorine nuclear data, which confirm recent impact studies performed for the Molten Chloride Reactor Experiment. Meanwhile, there currently exists only one published criticality benchmark experiment that is sufficiently sensitive to chlorine nuclear data. Discrepancies are found with this set of criticality safety benchmarks, which are more sensitive to thermal and epithermal neutron energies than the energies, above 100 keV, tested in this current work. Hence, there is still a need to re-evaluate the chlorine nuclear data at lower energies to assess these discrepancies. Interpretation of the data from future “faster” criticality benchmarks, which are needed for next-gen fast reactor designs, benefit from the improved constraints on the chlorine nuclear data validated in this work.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Measuring Saturn's Electron Beam Energy Spectrum using Webb's Wedges

It is very difficult to measure the voltage of the load on the Saturn accelerator. Time-resolved measurements such as vacuum voltmeters and V-dot monitors are impractical at best and completely change the pulsed power behavior at the load at worst. We would like to know the load voltage of the machine so that we could correctly model the radiation transport and tune our x-ray unfold methodology and circuit simulations of the accelerator. Step wedges have been used for decades as a tool to measure the end - point energies of high energy particle beams. Typically, the technique is used for multi-megavolt accelerators, but we have adapted it to Saturn's modest <2 MV end-point energy and modified the standard bremsstrahlung x-ray source to extract the electron beam without changing the physics of the load region. We found clear evidence of high energy electrons >2 MV. We also attempted to unfold an electron energy spectrum using a machine learning algorithm and while these results come with large uncertainties, they qualitatively agree with PIC simulation results.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Evaluation of 1/100-Scale Mooring Systems for Wave Energy Converters

This study evaluates the feasibility, accuracy, and limitations of using 1/100th scale physical mooring systems to represent full-scale mooring behavior for wave energy converters (WECs) during small-scale tank testing. The work focuses on an RM3-style point absorber deployed in conditions representative of the PacWave South test site and examines whether small-scale physical testing can reliably inform numerical modeling, design decisions, and future prototype development. Overall, this study concludes that small-scale (1/100th) physical mooring models can provide valuable qualitative insights, including relative comparisons between mooring types and trends in device behavior, but cannot reliably replicate full-scale mooring loads or dynamic response without significant scaling distortion. Physical tests at this scale are most appropriate for motion characterization and model validation within known limitations, not for deriving absolute mooring loads or final engineering design values. Key lessons learned emphasize the importance of improved instrumentation strategies, iterative wave tank tuning, more precisely manufactured scaled mooring components, and enhanced anchoring systems to reduce experimental uncertainty.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Multifidelity Monte Carlo estimation for efficient uncertainty quantification in climate-related modeling

Abstract. Uncertainties in an output of interest that depends on the solution of a complex system (e.g., of partial differential equations with random inputs) are often, if not nearly ubiquitously, determined in practice using Monte Carlo (MC) estimation. While simple to implement, MC estimation fails to provide reliable information about statistical quantities (such as the expected value of the output of interest) in application settings such as climate modeling, for which obtaining a single realization of the output of interest is a costly endeavor. Specifically, the dilemma encountered is that many samples of the output of interest have to be collected in order to obtain an MC estimator that has sufficient accuracy – so many, in fact, that the available computational budget is not large enough to effect the number of samples needed. To circumvent this dilemma, we consider using multifidelity Monte Carlo (MFMC) estimation which leverages the use of less costly and less accurate surrogate models (such as coarser grids, reduced-order models, simplified physics, and/or interpolants) to achieve, for the same computational budget, higher accuracy compared to that obtained by an MC estimator – or, looking at it another way, an MFMC estimator obtains the same accuracy as the MC estimator at lower computational cost. The key to the efficacy of MFMC estimation is the fact that most of the required computational budget is loaded onto the less costly surrogate models so that very few samples are taken of the more expensive model of interest. We first provide a more detailed discussion about the need to consider an alternative to MC estimation for uncertainty quantification. Subsequently, we present a review, in an abstract setting, of the MFMC approach along with its application to three climate-related benchmark problems as a proof-of-concept exercise.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Demonstration of Super-X divertor exhaust control for transient heat load management in compact fusion reactors

Nuclear fusion could offer clean, abundant energy. However, managing the power exhausted from the core fusion plasma towards the reactor wall remains a major challenge. This is compounded in emerging compact reactor designs promising more cost-effective pathways towards commercial fusion energy. Alternative Divertor Configurations (ADCs) are a potential solution. In this work, we demonstrate exhaust control in ADCs, employing a novel method to diagnose the neutral gas buffer, which shields the target. Our work on the Mega Ampere Spherical Tokamak Upgrade shows that ADCs tackle key risks and uncertainties for fusion energy. Their highly reduced sensitivity to perturbations enables active exhaust control in otherwise unfeasible situations and facilitates an increased passive absorption of transients, which would otherwise damage the divertor. We observe a strong decoupling of each divertor from other reactor regions, enabling near-independent control of the divertors and core plasma. Our work showcases the real-world benefits of ADCs for effective heat load management in fusion power reactors.

Imaging techniques↗
DOE OSTI2022

Review of Experimental Data for Validating Computer Codes Used in Shielding Calculations for Spent Fuel Storage and Transportation Systems

This report presents a review of available radiochemical assay data and shielding benchmarks applicable to spent nuclear fuel (SNF) shielding calculations. The relevant information reviewed herein includes the Spent Fuel Composition (SFCOMPO) database, the Shielding Integral Benchmark Archive and Database (SINBAD), the International Handbook of Evaluated Criticality Safety Benchmark Experiments, and published measurements of external dose rates of casks loaded with SNF. The relevant experimental data identified in this report may be used to support verification and validation of computer codes used in SNF cask/transport shielding applications, as well as development of calculation uncertainties. It should be noted that a relatively small subset of the identified experimental data (e.g., criticality alarm experiments) is available in a standard format established by the international community participating in experimental isotopic and shielding data evaluations. An effort of the SFCOMPO Technical Review Group (TRG) is underway to publish first isotopic evaluations of individual assay data using a standard data evaluation format. The SINBAD TRG has recently initiated benchmark evaluations and modernization of the database. Therefore, more relevant information is expected in the future that will enable users to select quality experimental data in depletion code and shielding code validations for SNF applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Neural correspondence to spectrum of environmental uncertainty in multiple-cue probability judgment system with time delay

Despite state-of-the-art technologies like artificial intelligence, human judgment is critically essential in cooperative systems, such as the multi-agent system (MAS), which collect information among agents based on multiple-cue judgment. Human agents can prevent impaired situational awareness of automated agents by confirming situations under environmental uncertainty. System error caused by uncertainty can result in an unreliable system environment, and this environment affects the human agent, resulting in non-optimal decision-making in MAS. Thus, it is necessary to know how human behavior is changed to capture system reliability under uncertainty. Another issue affecting MAS is time delay, which can delay agent information transfer, resulting in low performance and instability. However, it is difficult to find studies on the influence of time delay on human agents. This study is about understanding the human decision-making process under a specific system reliability environment by uncertainty with time delay. We used concepts of expected and unexpected uncertainty to implement reliability of the system usage environment with three types of time delay conditions: no time delay, regular time delay, and irregular time delay conditions. We used electroencephalogram (EEG) for human cognitive neural mechanisms in multiple-cue judgment systems to understand human decision-making. In the reliability of system usage environment, the unreliable system environment significantly creates less memory load by less utilization of system rules for decision-making. In terms of time delay, delayed information delivery does not significantly affect memory load for decision-making.

cognitive process↗
DOE OSTI2024

Pelletization with Spark Plasma Sintering and Characterization of Metal Iodides: An Assessment of Long-Term Radioiodine Immobilization Options

Four promising iodine “getter” materials (Ag, Cu, Bi, and Sn) for radioiodine capture were assessed in their pure metal-iodide (MI x ) pelletized forms to compare relative chemical durabilities. To study chemical durability, commercial MI x compounds of AgI, BiI 3 , BiOI, CuI, and SnI 4 were converted to dense monolithic pellets using spark plasma sintering. Semidynamic leach testing in the form of modified ASTM C1308 tests was then performed on the pellets in two different forms including unmounted (as-pressed) specimens (i.e., “U”) and epoxy-mounted specimens (i.e., “M”) with polished surfaces. The chemical durability results and sample characterizations showed that three of the five MI x compounds tested (i.e., AgI, CuI, and BiOI) displayed moderate to high leach resistances. Further, the remaining two MI x compounds (i.e., BiI 3 and SnI 4 ), which are both desirable iodine waste forms due to their high iodine loading capacities, readily decomposed during leach testing, indicated by crystallographic changes in the specimens as well as large amounts of iodine detected in the leachate solutions. The instabilities of BiI 3 and SnI 4 raise uncertainties for using the base metals/cations (i.e., Bi 0 /Bi 3+ and Sn 0 /Sn 4+ , respectively) as viable getters for radioiodine capture due to likely poor waste form chemical durabilities after capture and consolidation into waste forms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Distribution Grid Impacts of Community Solar [Slides]

Community solar (CS) projects often face uncertain interconnection costs and fees associated with distribution grid infrastructure upgrades required to connect the project. These costs can determine the economic viability of a CS project, but they are difficult to assess. Cost uncertainty can discourage new projects and prevent communities from accessing the benefits of community solar projects. At the same time, CS deployment strategies hold potential to defer or avoid some distribution costs due to new loads. To mitigate CS interconnection costs, it is important to find least-cost combinations of distribution system infrastructure solutions (transformer upgrades, reconductoring, voltage regulators, storage), and to understand how location of CS projects within a feeder impact distribution grid upgrade costs. This study aims to quantify CS impacts on the distribution grid and provide policy and regulatory insights and CS deployment strategies to address them. It is the first analysis that has systematically studied the technical impacts of community solar projects on a wide range of distribution feeders using state-of-the-art optimization and power flow tools. The analysis employs Berkeley Lab’s novel Least-cost Optimal Distribution Grid Expansion (LODGE) model, a deterministic version of the REPAIR model, that optimally upgrades hundreds or even thousands of distribution circuits or feeders. This is the first application of the LODGE model. LODGE finds the least-cost portfolio of traditional distribution system upgrades to integrate CS in combination with alternative solutions, such as utility-owned storage and downsizing CS capacity. Working with a set of least-cost solutions per feeder allows us to benchmark, compare and find techno-economic trends in CS interconnection.

14 SOLAR ENERGY↗
DOE OSTI2024

A Framework for Identifying Building Energy Models of Localized Utility Service Areas Using Smart Meter Data

Bottom-up load modeling of buildings offers a versatile approach to simulating baseline demand and scenarios of future technology evolution and adoption at the individual building level. This capability is essential to understanding how future load shapes may change with the adoption of electric equipment and vehicles, particularly as it relates to grid planning and infrastructure investments. Traditionally, grid planning techniques have used historical load data to predict future load and infrastructure needs. However, with the anticipated rise in adoption of electrification technologies such as heat pumps and electric vehicles, historical data become less reliable predictors of the future. By employing ResStock, a high-fidelity building stock modeling tool, we can fine-tune electrification scenarios and aggregate models to represent varying geographic resolutions of the grid system, while considering the underlying features of homes. This may enable a more accurate and responsive approach to anticipate and plan for the evolving landscape of energy demands. We present a new framework that leverages building stock energy modeling to identify building models that align with the load shapes and housing attributes of buildings with AMI data. This approach applies two model layers: (1) a classification step that identifies the presence of air conditioning, electric heating, and electric water heating, and (2) an optimization routine that identifies building energy models aligning with load profile data from advanced metering infrastructure meters. This report demonstrates one approach to deploying this framework, and presents results for three test cases that use both modeled and AMI data to assess performance. For a test case using AMI data in Fort Collins, Colorado, we observed a median monthly electricity load CV-RMSE of 16.6%, and a top ten daily heating and cooling median absolute percent error of 7.7% and 8.3%, respectively. For each AMI meter, we identify a set of potential energy models so that downstream use-cases can account for uncertainty driven by variability of baseline technologies and occupant behavior, which impact the response to electrification and energy efficiency scenarios. Our results indicate that ResStock has potential as a scalable solution for modeling residential energy demand at local grid resolutions. Its performance depends on location-specific factors, underlying building characteristics, and the level of aggregation, offering a path towards more precise and adaptive distribution grid planning for the evolving energy landscape.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

OC6 Phase II: Integration and verification of a new soil–structure interaction model for offshore wind design

Abstract This paper provides a summary of the work done within the OC6 Phase II project, which was focused on the implementation and verification of an advanced soil–structure interaction model for offshore wind system design and analysis. The soil–structure interaction model comes from the REDWIN project and uses an elastoplastic, macroelement model with kinematic hardening, which captures the stiffness and damping characteristics of offshore wind foundations more accurately than more traditional and simplified soil–structure interaction modeling approaches. Participants in the OC6 project integrated this macroelement capability to coupled aero‐hydro‐servo‐elastic offshore wind turbine modeling tools and verified the implementation by comparing simulation results across the modeling tools for an example monopile design. The simulation results were also compared to more traditional soil–structure interaction modeling approaches like apparent fixity, coupled springs, and distributed springs models. The macroelement approach resulted in smaller overall loading in the system due to both shifts in the system frequencies and increased energy dissipation. No validation work was performed, but the macroelement approach has shown increased accuracy within the REDWIN project, resulting in decreased uncertainty in the design. For the monopile design investigated here, that implies a less conservative and thus more cost‐effective offshore wind design.

17 WIND ENERGY↗
DOE OSTI2024

Security Constrained Distributed Transaction Model for Multiple Prosumers

Massive access of renewable energy has prompted demand-side distributed resources to participate in regulation and improve flexibility of power systems. With large-scale access of massive, decentralized, and diverse distributed resources, demand-side market members have transformed from traditional “consumers” to “prosumers”. To explore the distributed transaction model of prosumers, in this paper, a multi-prosumer distributed transaction model is proposed, and the Conditional Value-at-Risk (CVaR) theory is applied to quantify potential risks caused by the stochastic characteristics inherited from renewable energy. First, a prosumer model under constraints of the distribution network including photovoltaic units, fuel cells, energy storage system, central air conditioning and flexible loads is established, and a multi-prosumer distributed transaction strategy is proposed to achieve power sharing among multiple prosumers. Second, a prosumer transaction model based on CVaR is constructed to measure risks inherited from the uncertainty of PV output within the prosumer and ensure safety of system operation in extreme PV output scenarios. Then, the alternating direction multiplier method (ADMM) is utilized to solve the constructed model efficiently. Finally, distributed transaction costs of prosumers are distributed fairly based on the generalized Nash equilibrium to maximize social benefits. Simulation results show the multi-prosumer distributed transaction mechanism established under the proposed generalized Nash equilibrium method can encourage power sharing among prosumers, increasing their own income and social benefits. Also, the CVaR can assist decision making of prosumers in weighting the risks and benefits, improving system resilience through energy management of prosumers.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

ANNIE: the Accelerator Neutrino Neutron Interaction Experiment

The Accelerator Neutrino Neutron Interaction Experiment (ANNIE) is a Gadolinium-loaded water Cherenkov detector placed in the Booster Neutrino Beam (BNB) at the Fermi National Accelerator Laboratory, USA. The primary physics goal of ANNIE is to perform neutrino cross-section measurements that will constrain systematic uncertainties in the next generation of long-baseline neutrino experiments. The first measurement will be the multiplicity of final-state neutrons from neutrino-nucleus interactions in water. Alongside these measurements, ANNIE has achieved the first ever deployments of two novel detector technologies in a neutrino beam: Large Area Picosecond Photodetectors (LAPPDs) and Water-based Liquid Scintillator (WbLS). LAPPDs are micro-channel-plate-based devices that provide timing resolution of ~100 picoseconds and sub-centimeter spatial resolution. WbLS combines the low attenuation and Cherenkov production of pure water with the high light-yield and low detection threshold of liquid scintillator. This talk will discuss the status of ANNIE's physics and R&D measurements.

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Demonstration of the On-the-Fly Shielding Analysis Method: Spent Fuel and Waste Disposition

This report documents work performed supporting the US Department of Energy (DOE) Office of Nuclear Energy (NE) Spent Fuel and Waste Disposition (SFWD) Integrated Waste Management activities under work breakdown structure element 1.08.02.04.01, “Data and Tools Development, Validation, and Maintenance.” In particular, this report fulfills milestone M3SF-21OR020401016, “Implement on-the-fly dose analysis methodology in UNF-ST&DARDS” within work package SF-21OR02040101, “Commercial SNF Characterization - ORNL.” The Used Nuclear Fuel - Storage, Transportation & Disposal Analysis Resource and Data System (UNFST& DARDS) enables automated dose rate calculations for spent nuclear fuel (SNF) transportation packages and storage casks using a Monte Carlo radiation transport code. The explicit method uses a detailed model of the SNF system and its contents. Therefore, a dose rate calculation is required for each as-loaded transportation package or storage cask because the SNF assemblies within a canister typically have unique irradiation characteristics. An alternate method, referred to as the “on-the-fly” shielding analysis method, has been proposed that requires only a set of Monte Carlo dose rate calculations for each transportation packaging/storage cask design. The results of the Monte Carlo dose rate calculations are independent of the SNF assembly irradiation and decay characteristics. The dose rate values may then be combined with the radiation source strength of the SNF assemblies associated with a particular transportation packaging/storage cask design to determine actual dose rates. This report presents on-the-fly dose rate calculations for a representative SNF storage cask and verification of the on-the-fly dose rate calculation results by comparison with reference dose rate calculations using the explicit Monte Carlo dose rate calculation. The on-the-fly shielding analysis method was implemented in UNF-ST&DARDS. A Python program was developed to process the MAVRIC dose rate results obtained by source particle type, energy group, and fuel geometry region. A Python processor created binary files, which were saved as a special UNF-ST&DARDS library for on-the- fly shielding analyses. UNF-ST&DARDS uses the precalculated on-the-fly binary libraries generated by the Python data processor and directly executes the Python code for on-the-fly dose analysis. This Python code unzips the pre-generated binary files mentioned above, reads the data, and combines them with user-specified sources for dose and uncertainty calculations. The Python programs were verified using Excel calculations and by comparison with the values obtained with the MAVRIC post-processing utilities applied to the 3dmap files. This method can currently be used to determine dose rates for as-loaded HI-STORM FW storage casks. The UNF-ST&DARDS analysis wizard for on-the-fly shielding analysis is described in this report.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

AlphaBuilding ResCommunity: A multi-agent virtual testbed for community-level load coordination

Training and validating algorithms in a simulation testbed can accelerate research and applications of optimal control of residential loads to improve energy flexibility and grid resilience. We developed an open-source simulation environment, AlphaBuilding ResCommunity, that can be used to train and validate algorithms to control a single thermostatically controlled load (TCL) or coordinate a group of TCLs. We used reduced-order models to simulate the thermodynamics of TCLs, and the parameter values were determined from the connected smart thermostat data of real households. The environment was built upon the standardized OpenAI Gym interface. Ancillary functions, such as retrieving the parameters and weather forecasts, are provided to facilitate control strategies that require predictive information. Compared with existing efforts, AlphaBuilding ResCommunity has three advantages: (1) more realistic model settings because the parameter values are identified from actual household operating data, and modelling and measurement uncertainty are considered; (2) passive thermal storage control; and (3) ease of use due to a simple software dependency and standardized interface. We demonstrated the applications of the environment by implementing a Kalman Filter and Model Predictive Control on a single TCL and a Priority-Stack-Based Control and Alternating Direction Method of Multipliers to coordinate multiple TCLs for load tracking.

Wang, Z↗