Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “coordinated energy system”

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.

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

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Approximate Dynamic Programming With Enhanced Off-Policy Learning for Coordinating Distributed Energy Resources

Herein this paper proposes an innovative approximate dynamic programming (ADP) method for distributed energy resource coordination with the loss of life of battery energy storage system (BESS) explicitly modeled. The dispatch policy is designed to account for both calendrical and cyclical aging effects on BESS, explicitly modeling the impacts of ambient temperature on BESS lifespan. The proposed ADP employs an adaptive critic method and enhanced off-policy deterministic policy gradient (DPG) strategy, addressing the limitations of the on-policy gradient-based ADP approaches, including inadequate exploration, low data usage, and computational complexity. In particular, a customized policy is proposed to guide the algorithm to explore some promising decisions and thereby improve exploration capability and learning efficiency compared to conventional DPG-based learning approaches, which may struggle to find a global optimum due to random noisy action-based exploration or require expert demonstration with extra effort. The proposed method is illustrated using the IEEE 123-node system and compared with the existing ADP methods to prove solution accuracy and demonstrate the effects of incorporating degradation models into control design. Case studies showed that the proposed ADP effectively coordinates DERs with a 10 times smaller optimization gap compared to existing methods, and the incorporation of the BESS life loss model ensures the expected lifespan and results in significant cost savings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Packages of Distributed Energy Technologies Demonstrating Demand Flexibility at Community Scale

The combination of increased electric load growth across all sectors, deferred electrical infrastructure investment, and other factors resulting in variable electric power supply, has created technical challenges to maintaining a resilient and reliable grid. Many federal, regional, and local efforts are in play to modernize the electric grid, including advancing building technologies and distributed energy resources (DERs) that are utilizing smarter controls to become responsive to both occupant and grid needs. This report reviews ten pilot projects demonstrating how groups of buildings combined with behind-the-meter (BTM) DERs such as electric vehicle (EV) charging, battery storage, flexible HVAC and domestic hot water systems, and photovoltaic systems can reliably and cost effectively provide grid services. Each of the ten pilot projects aim to deliver both energy efficiency and demand flexibility (DF) while supporting load growth. The ten demonstration teams are piloting flexible DER packages across diverse communities of residential and commercial buildings to address a variety of regional grid needs. The outcomes of these pilot projects will be used to inform future scaling through utility program development. This paper characterizes the ten teams, showcasing the decision-making process used by each group to develop their packages (Section 2), the grid services they plan to deliver (Section 3), the types of DER packages selected for deployment within building sectors (Section 4) and trends between building sector, DER types, and grid services In order to achieve community scale benefits, the pilot projects must utilize aggregated control mechanisms for coordinating buildings and DERs together. Several types of coordinated control architectures have evolved amongst the teams, influenced by use type, existing market conditions, and integration type. Three coordinated controls architectures have been characterized, highlighting their use cases, benefits, challenges, and tradeoffs in their design. These insights can aid utilities, control vendors, and developers in scaling community-level energy systems (Paul, 2024). Ultimately, the technology packages selected by the ten teams will be coordinated to provide power system services, also known as grid services. Insights from these demonstrations will be useful for grid operators, regulators, aggregators and other stakeholders as they look to deploy demand flexible resources as grid services in the future. The grid services that each team is targeting for demonstration are described in Section 3 and Section 4. Methods for evaluating the grid services have been described in the paper Metrics for Evaluating Grid Service Provision from Communities of Grid-interactive and Efficient Buildings and other DER (MacDonald, 2023). To identify technology packages for demonstration, Section 2 shows that project teams used a range of analysis approaches, including building energy modeling, AMI data analysis, cost-benefit frameworks, and utility pilot data. Some teams emphasized technical modeling to quantify grid impacts and demand reduction potential, while others prioritized economic evaluations, stakeholder input, or exploratory pilots to inform deployment decisions. This diversity reflects the need to tailor selection methods to project goals, available data, and organizational context. Section 5 discusses trends between the DER technologies deployed and the grid service provisions from each team. Residential buildings (multifamily and single family) lean towards technologies that enhance energy efficiency (e.g. weatherization upgrades, smart thermostats) and onsite power generation integration (e.g. solar PV). Commercial building demonstrations prioritize technologies that ensure operational reliability (e.g. battery storage) and centralized energy management systems and optimization solutions. Teams that are deploying controllable storage-based technologies are more likely to provide grid services that require a near real-time response. Teams incorporating load shifting technologies like smart thermostats with HEMs are likely to include energy markets participation and customer bill management offerings. Campus demonstrations are adopting diverse sets of DERs to emphasize renewable generation, paired with centralized control. This section also describes technologies that were considered during project planning but ultimately excluded from final deployment. These demonstrations reveal that effective DER package design should be tailored to building type, customer segment, and construction vintage. Multifamily buildings benefit from centralized HVAC upgrades and supervisory controls, while single-family homes are well-suited for individualized technologies like solar, storage, and smart home energy monitors. Commercial and campus settings prioritize EMIS integration and load optimization. New construction enables cost-effective integration of DER-ready infrastructure, whereas retrofits require deployments aligned with owner and tenant value streams. For utility program planners, early coordination with developers and building owners, paired with segmented and modular program offerings, can improve adoption, scalability, and grid impact.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

QM Investigation of Rare Earth Ion Interactions with First Hydration Shell Waters and Protein-Based Coordination Models

Here, conventional methods for extracting rare earth metals (REMs) from mined mineral ores are inefficient, expensive, and environmentally damaging. Recent discovery of lanmodulin (LanM), a protein that coordinates REMs with high-affinity and selectivity over competing ions, provides inspiration for new REM refinement methods. Here, we used quantum mechanical (QM) methods to investigate trivalent lanthanide cation (Ln 3+ ) interactions with coordination systems representing bulk solvent water and protein binding sites. Energy decomposition analysis (EDA) showed differences in the energetic components of Ln 3+ interaction with representatives of solvent (water, H 2 O) and protein binding sites (acetate, CH 3 COO – ), highlighting the importance of accurate description of electrostatics and polarization in computational modeling of REM interactions with biological and bioinspired molecules. Relative binding free energies were obtained for Ln 3+ with coordination complexes originating from binding sites in PDB structures of a lanthanum binding peptide (PDB entry 7CCO) and LanM, with explicit consideration of the first hydration shell waters, according to quasi-chemical theory (QCT). Beyond the first shell, the bulk solvent environment was represented with an implicit continuum model. Ln 3+ interactions with (H 2 O) 9 and both binding site models became more favorable, moving down the periodic series. This trend was more pronounced with the protein binding site models than with water, resulting in affinity increasing with periodic number, except for the last REM, Lu 3+ , which bound less favorably than the preceding element, Yb 3+ . Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. Conversely, the previously reported experimental data for LanM show a preference for the earlier lanthanides; this is likely due to longer-range interactions and cooperative effects, which are not represented by the reduced models. Using the truncated 7CCO binding site model, the magnitude and trend of the experimental Ln 3+ relative binding free energies for the whole 7CCO peptide were reproduced. In contrast to the previously reported experimental data for LanM, the peptide preferentially binds the earlier lanthanides. This difference likely arises due to longer-range interactions and cooperative effects not represented by the peptide. Further investigation of Ln 3+ interactions with whole proteins using polarizable molecular mechanics models with explicit solvent is warranted to understand the influence of longer-ranged interactions, cooperativity, and bulk solvent. Nevertheless, the present work provides new insights into Ln 3+ interactions with biomolecules and presents an effective computational platform for designing specific single-site REM binding peptides more efficiently.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Transmission and Distribution Coordination

This webinar explores planning the future grid and interconnected energy system while examining balancing generation (G), transmission (T), distribution (D), & customer (C) resources all while also increasingly capturing engineering details in planning.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1952

Axisymmetric supersonic flow in rotating impellers

General equations are developed for isentropic, frictionless, axisymmetric flow in rotating impellers with blade thickness taken into account and with blade forces eliminated in favor of the blade-surface function. It is shown that the total energy of the gas relative to the rotating coordinate system is dependent on the stream function only, and that if the flow upstream of the impeller is vortex-free, a velocity potential exists which is a function of only the radial and axial distances in the impeller. The characteristic equations for supersonic flow are developed and used to investigate flows in several configurations in order to ascertain the effect of variations of the boundary conditions on the internal flow and the work input. Conditions varied are prerotation of the gas, blade turning rate, gas velocity at the blade tips, blade thickness, and sweep of the leading edge.

Goldstein, Arthur W↗
DOE OSTI2024

An Innovative Energy Management System for Microgrids with Multiple Grid-Forming Inverters

As increasingly more grid-forming (GFM) inverter-based resources replace traditional fossil-fueled synchronous generators as the GFM sources in microgrids, the existing microgrid energy management systems (EMS) need to be updated to control and coordinate multiple GFM inverters that consider system control objectives under different microgrid connection states.For each state, we formulate an optimization problem and apply a real-time feedback-based control algorithm; altogether, the control algorithms seamlessly connect the states into a generic microgrid EMS that controls the nodal voltages and frequencies, becomes a virtual power plant (VPP) when connected to the main grid, and coordinates power sharing responsibility among GFM sources when islanded. We showcase the EMS on a real-world simulation of a microgrid under the different states to demonstrate its operational effectiveness.

energy management system↗
DOE OSTI2024

An Innovative Energy Management System for Microgrids with Multiple Grid-Forming Inverters

As increasingly more grid-forming (GFM) inverter-based resources replace traditional fossil-fueled synchronous generators as the GFM sources in microgrids, the existing microgrid energy management systems (EMS) need to be updated to control and coordinate multiple GFM inverters that consider system control objectives under different microgrid connection states. For each state, we formulate an optimization problem and apply a real-time feedback-based control algorithm; altogether, the control algorithms seamlessly connect the states into a generic microgrid EMS that controls the nodal voltages and frequencies, becomes a virtual power plant (VPP) when connected to the main grid, and coordinates power sharing responsibility among GFM sources when islanded. We showcase the EMS on a real-world simulation of a microgrid under the different states to demonstrate its operational effectiveness.

energy management systems↗
DOE OSTI2024

Active learning of ternary alloy structures and energies

Abstract Machine learning models with uncertainty quantification have recently emerged as attractive tools to accelerate the navigation of catalyst design spaces in a data-efficient manner. Here, we combine active learning with a dropout graph convolutional network (dGCN) as a surrogate model to explore the complex materials space of high-entropy alloys (HEAs). We train the dGCN on the formation energies of disordered binary alloy structures in the Pd-Pt-Sn ternary alloy system and improve predictions on ternary structures by performing reduced optimization of the formation free energy, the target property that determines HEA stability, over ensembles of ternary structures constructed based on two coordinate systems: (a) a physics-informed ternary composition space, and (b) data-driven coordinates discovered by the Diffusion Maps manifold learning scheme. Both reduced optimization techniques improve predictions of the formation free energy in the ternary alloy space with a significantly reduced number of DFT calculations compared to a high-fidelity model. The physics-based scheme converges to the target property in a manner akin to a depth-first strategy, whereas the data-driven scheme appears more akin to a breadth-first approach. Both sampling schemes, coupled with our acquisition function, successfully exploit a database of DFT-calculated binary alloy structures and energies, augmented with a relatively small number of ternary alloy calculations, to identify stable ternary HEA compositions and structures. This generalized framework can be extended to incorporate more complex bulk and surface structural motifs, and the results demonstrate that significant dimensionality reduction is possible in thermodynamic sampling problems when suitable active learning schemes are employed.

Chemistry↗
DOE OSTI2022

DSO+T: Transactive Energy Coordination Framework (DSO+T Study: Volume 3)

This report describes a transactive energy coordination scheme designed to integrate into existing day-ahead and real-time wholesale energy markets. This scheme was evaluated in the Distribution System Operator with Transactive (DSO+T) study to assess the engineering and economic performance of the transactive energy coordination of a large-scale deployment of distributed energy resources (DER). Transactive agents were developed for a range of DERs (heating, ventilation, and air conditioning units, water heaters, batteries, and electric vehicles) that optimize flexibility over a 48-hour horizon and adjust their strategy in response to changes in real-time prices. A transactive energy coordination scheme, executed by a DSO retail market operator, aggregates these DER bids from participating customers and clears them against a DSO supply curve using a double auction market mechanism. The process of constructing the price-quantity DSO supply curve includes distribution-level transportation constraints (for example, substation congestion limits) and forecast locational marginal price of the DSO’s connected transmission node. The resulting day-ahead and real-time quantities are then bid into a competitive wholesale market operated by an independent system operator. This report also details additional capabilities for proper marketplace simulation such as wholesale price, weather, and load forecasting. The report concludes with a discussion of lessons learned and key design features required to ensure successful operation.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2025

Impacts and emerging research opportunities in Vehicle-Grid Integration for transportation: A review

This review provides a comprehensive examination of Vehicle-Grid Integration (VGI) technologies and their impacts on transportation systems, with a particular emphasis on the transportation-energy nexus. It systematically explores how VGI affects key transportation applications such as charging infrastructure planning, electric vehicle (EV) routing, smart charging coordination, shared mobility, and dynamic pricing. By synthesizing recent literature from both transportation and energy systems perspectives, this study highlights how advanced methodologies, such as reinforcement learning, game theory, and optimization techniques, are used to model the complex interactions between EVs, mobility patterns, and distributed energy systems. Furthermore, the review also identifies critical challenges, including behavioral factors, data limitations, and system scalability. Drawing on these insights, the paper outlines emerging research opportunities to support the design of integrated, resilient, and user-centric VGI solutions that advance sustainable mobility and energy system efficiency.

Charging coordination↗
DOE OSTI2022

Distributed Energy Resource Cybersecurity Framework and Cyber Range Integration

Distributed energy resource (DER) systems feature complex, data-driven communications networks that require careful system coordination and constant vigilance to ensure that grid assets are secure. Because DERs are an important component of the decarbonization strategy, agencies need to secure energy data that could implicate issues of national security if compromised. To help federal energy managers assess, monitor, and manage cybersecurity while achieving decarbonization, the National Renewable Energy Laboratory's (NREL's) Distributed Energy Resource Cybersecurity Framework (DER-CF) offers a comprehensive, web-based assessment tool focusing on cyber governance or policies, technical management, and physical security. The DER-CF currently presents users with a series of pertinent cybersecurity questions that are used to generate a site-specific report and recommendations. This paper outlines a plan to integrate the DER-CF with another key asset-NREL's cyber range-to visualize cybersecurity resilience and compliance and to enhance the usability and accessibility of the DER-CF for federal facility energy managers and planners. This integration will result in a visualization environment to interpret and interact with compliance data. Its development will include regular conversations with stakeholders to assess the effectiveness of these efforts, refine the visualization capability, and ensure its value to our partners.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS2013

On the Use of Quartic Force Fields in Variational Calculations

The use of quartic force fields (QFFs) has been shown to be one of the most effective ways to efficiently compute vibrational frequencies for small molecules. In this paper we outline and discuss how the simple-internal or bond-length bond-angle (BLBA) coordinates can be transformed into Morse-cosine(-sine) coordinates which produce potential energy surfaces from QFFs that possess proper limiting behavior and can effectively describe the vibrational (or rovibrational) energy levels of an arbitrary molecular system. We investigate parameter scaling in the Morse coordinate, symmetry considerations, and examples of transformed QFFs making use of the MULTIMODE, TROVE, and VTET variational vibrational methods. Cases are referenced where variational computations coupled with transformed QFFs produce accuracies compared to experiment for fundamental frequencies on the order of 5 cm(exp −1) and often as good as 1 cm(exp −1).

quartic force field↗
DOE OSTI2024

Position Papers for the 2024 ASCR Workshop on Energy-Efficient Computing for Science

On behalf of the Advanced Scientific Computing Research (ASCR) program in the US Department of Energy (DOE) Office of Science, we are organizing a Workshop on Energy-Efficient Computing for Science (EECS). Energy efficiency involves coordination across all the interoperating components of a computing system—in particular, applications, algorithms, system software, programming models, data management, and the hardware on which they run. Looking 10-15 years into the future, the goal is to dramatically lower the energy costs of the computational platforms (from the data center to the edge) serving DOE science while expanding the capabilities of these systems, broadening their applicability to science challenges of interest to DOE and the nation.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Modeling and Rapid Prototyping of Integrated Transmission-Distribution OPF Formulations with PowerModelsITD.jl

Conventional electric power systems are composed of different unidirectional power flow stages of generation, transmission, and distribution, managed independently by transmission system and distribution system operators. However, as distribution systems increase in complexity due to the integration of distributed energy resources, coordination between transmission and distribution networks will be imperative for the optimal operation of the power grid. However, coupling models and formulations between transmission and distribution is non-trivial, in particular due to the common practice of modeling transmission systems as single-phase, and distribution systems as multi-conductor phase-unbalanced. To enable the rapid prototyping of power flow formulations, in particular in the modeling of the boundary conditions between these two seemingly incompatible data models, we introduce PowerModelsITD.jl, a free, open-source toolkit written in Julia for integrated transmission-distribution (ITD) optimization that leverages mature optimization libraries from the InfrastructureModels.jl-ecosystem. The primary objective of the proposed framework is to provide baseline implementations of steady-state ITD optimization problems, while providing a common platform for the evaluation of emerging formulations and optimization problems. In this work, we introduce the nonlinear formulations currently supported in PowerModelsITD.jl, which include AC-polar, AC-rectangular, current-voltage, and a linear network transportation model. Results are validated using combinations of IEEE transmission and distribution networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Quantifying Energetic and Entropic Pathways in Molecular Systems

When examining dynamics occurring at nonzero temperatures, both energy and entropy must be taken into account to describe activated barrier crossing events. Furthermore, good reaction coordinates need to be constructed to describe different metastable states and the transition mechanisms between them. Here we use a physics-based machine learning method called state predictive information bottleneck (SPIB) to find nonlinear reaction coordinates for three systems of varying complexity. SPIB is able to correctly predict an entropic bottleneck for an analytical flat-energy double-well system and identify the entropy- and energy-dominated pathways for an analytical four-well system. Lastly, for a simulation of benzoic acid permeation through a lipid bilayer, SPIB is able to discover the entropic and energetic barriers to the permeation process. Given these results, we thus establish that SPIB is a reasonable and robust method for finding the important entropy, energy, and enthalpy barriers in physical systems, which can then be used to enhance the understanding and sampling of different activated mechanisms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

AURORA - AUtonomous and Resilient Operation of energy systems with RenewAbles

This presentation provides an overview of the AURORA project. The objective of AURORA is to develop and validate novel functions for Energy Management Systems (EMS) containing Security Situational Awareness (SSA), Distributed Microgrid Coordination (DMC), Autonomous Microgrid Restoration (AMR).

14 SOLAR ENERGY↗
DOE OSTI2024

Reducing uncertainty of polar to midlatitude linkages using DOE’s E3SM in a coordinated model-experiment setting

This project brought DOE’s climate modeling effort with the Energy Exascale Earth System Model into the Polar Amplification Model Intercomparison Project (PAMIP), which is part of the sixth and latest Coupled Model Intercomparison Project, CMIP6. PAMIP examines the causes and consequences of polar amplification, when external forcing results in a larger temperature increase in high latitudes than the global average, in a coordinated set of model experiments with a common modeling protocol. Our teams from UC Irvine and the University of Toronto have designed, carried out, analyzed, and disseminated PAMIP output from the Energy Exascale Earth System Model (E3SM) and the Community Earth System Model (CESM). PAMIP’s ongoing stream of significant new results have advanced progress in the community’s understanding and led to new outstanding research questions that have motivated further work. PAMIP has led to improved consensus on the atmospheric response to sea ice loss. The important finding is that for a similar sea ice anomaly forcing, the simulated atmospheric response in the troposphere is remarkably consistent among the 16 models’ runs analyzed. The zonal-mean tropospheric response consists of a very robust equatorward shift of the westerly flow in mid-latitudes. However, while the multi-model mean response is robust, it has a weak amplitude relative to internal variability. We identified a weakness in the models (including E3SM) in terms of their response to sea-ice forcing that is related to eddy forcing (or nonlinear dynamical effects) at mid- to high latitudes. In fact, E3SM is an outlier in terms of the models participating, and in that sense, it turned out to be a vital participant model. We found that reductions in energy transport due sea-ice loss and involving dry air only are compensated by increases in moist energy transport from warmer sea surface temperature in midlatitudes. This leads to a large spread in energy transport into the Arctic and is a potential source of spread in Arctic amplification. We identified an important role that climate modes, including tropical modes of variability (El Nino and the Southern Oscillation (ENSO); the Quasi-biennial Oscillation (QBO)) play in the response to sea-ice anomalies, including in ocean coupled experiments. Similarly, we identified and quantified the contribution of sea-ice thickness to the atmospheric response compared to the response to sea-ice extent only. We found that it is important to run large ensembles and even with an ensemble size of 100 simulations the response is largely influenced by internal variability. We demonstrated convincingly that Ural blocking, not sea-ice loss, provides the weakening of the stratospheric polar vortex in fall/early winter and a negative phase of the North Atlantic Oscillation that can last for up to two months. However, sea-ice anomalies can influence the background flow so that the response to Ural blocking is more persistent under low sea-ice conditions in the Barents/Kara Sea than high sea ice Atmospheric model hierarchies that progressively add individual processes have a long history in providing dynamical insight for modeling the atmosphere. Similarly, coupled model hierarchies that progressively add individual ocean processes can provide insights into the workings of the coupled climate system, however such hierarchies have not been available except for a non-dynamical slab ocean model. Because of the missing processes, surface flux corrections must be added to produce a target climate. In this project, we managed to overcome this problem and develop a globally coupled ocean model hierarchy in CESM that can turn on and off the processes of mixed-layer entrainment and Ekman flow. We used the hierarchy to study the impact of Arctic sea-ice loss on the climate system. We find that the effect of mixed-layer entrainment on ocean heat uptake influences the atmospheric circulation by shifting the latitudinal positions of the mid-latitude westerly jet and the Intertropical Convergence Zone (ITCZ). In quadrupled CO 2 experiments, we studied how air-sea coupling affects the response of tropical rainfall under global warming. In order to identify the importance of individual ocean processes, we used the hierarchy of ocean models to separate the effects of seasonal mixed-layer entrainment, wind-driven Ekman flows, and frictional flows. We showed that including Ekman and frictional flows allows our simulation to produce the Pacific Ocean's enhanced equatorial warming pattern and equatorward ITCZ contraction noted in previous climate simulations. We also showed that the frictional flow, which has yet to receive much attention, is as important as the Ekman flow in generating equatorial heat convergence.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Interplay of effects of neutron skins in coordinate space and proton skins in momentum space on emission of hard photons in heavy-ion collisions near the Fermi energy

Within an isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck transport model, we investigate the hard photons emission from neutron-proton bremsstrahlung in the reaction system of 208 Pb + 208 Pb around Fermi energy. Effects of neutron skins in coordinate (r) space and proton skins in momentum (k) space on the time evolution, the angular distribution, and the transverse momentum spectra of hard photons with different energies are studied. It is shown that the emission of direct hard photons is sensitive to the neutron skin, which has larger effects for more energetic hard photons. Meanwhile, we find that the proton skins have an important influence on the emission of direct hard photons, and its effect is actually even larger than that of neutron skins. Furthermore, it needs to take the effect of proton skins into account when we determine the size of neutron skins by comparing transport mode predictions of hard photons with the corresponding experimental measurements.

190 ≤ A ≤ 219↗