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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
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 OSTI2025

JHTDB-wind: a web-accessible large-eddy simulation database of a wind farm with virtual sensor querying

This paper introduces JHTDB-wind (https://turbulence.idies.jhu.edu/datasets/windfarms, last access: 11 November 2025), a publicly accessible database containing large-eddy simulation (LES) data from wind farms. Building on the framework of the Johns Hopkins Turbulence Database (JHTDB), which hosts direct numerical simulation (DNS) and some LES datasets of canonical turbulent flows, JHTDB-wind stores the 4D space–time history of the flow and provides users the ability to access and query the data via a web-based virtual sensor interface. The initial dataset comprises LES results from a large wind farm with 10×6 turbines, modeled using a filtered actuator line method, under conventionally neutral atmospheric conditions. These data comprise 1 h (hour) of flow field data (velocity, pressure, potential temperature deviation, subgrid-scale (SGS) eddy viscosity, and turbine forces, approximately 15 TB (terabytes) and wind turbine data – including both turbine-level operational quantities and blade-level aerodynamic quantities (approximately 1.3 TB) – stored in Zarr and Parquet formats, respectively. Data retrieval is facilitated by the giverny Python package, allowing remote users to query the database in Python or MATLAB (C and Fortran support are available for flow field data). This paper details the simulation setup and demonstrates data access through examples that analyze wind farm flow structures and turbine performance. The framework is extensible to future datasets, including the JHTDB-wind diurnal cycle simulation analyzed in Xiao et al. (2025).

17 WIND ENERGY↗
DOE OSTI2025

The impact of simplified window and exhaust fan assumptions on indoor air quality in multifamily buildings

In residential buildings, the indoor air quality can be significantly affected by ventilation measures initiated by occupants, including the operation of windows and in-unit exhaust fans in kitchens and bathrooms. Many simulations simplify these factors by disregarding window opening behaviors and using fixed schedules for exhaust fan operation across all residential units. To estimate the impact of these simplifications in the U.S. context, this study used coupled CONTAM and EnergyPlus models to simulate airflow and contaminant transport in multifamily buildings. The coupled models parametrically varied climate zone, building airtightness, and mechanical ventilation system types. The study conducted a sensitivity analysis on two key occupant behaviors: (1) operating kitchen and bathroom exhausts on different schedules in individual dwelling units, and (2) scheduling open windows on ground and top floors. The simplified assumptions (i.e. uniform in-unit exhaust fan operation and window operation) had a minimal impact on inter-unit air flow and contaminant transport simulations across a broad range of building air leakage and mechanical ventilation system types. These findings suggest that for buildings with tight construction it is reasonable for most modelling and simulation efforts to ignore the effects of non-uniform exhaust fan operation and window opening.

Occupant behavior↗
DOE OSTI2025

ResStock Technical Reference Documentation (V.3.3.0)

ResStock™ is the best-in-class building stock energy model for simulating and publishing energy use, utility bills, and greenhouse gas emissions from the residential sector of the U.S. ResStock answers two primary questions: (1) How is energy used in the U.S. residential building stock? and (2) What is the timeseries aggregate impact of energy technologies? Specifically, ResStock quantifies energy use across geographical locations, demographic groups, building types, fuels, end uses, and time of day. Additionally, it details the impact of efficiency or electrification measures: total changes in the amount of energy used by measure; where or in what use cases efficiency or electrification upgrade measures save energy; when or at what times of day savings occur; and which building stock or demographic segments have the biggest savings potential. This model, and the datasets it produces, are foundational to identifying pathways to affordable and equitable decarbonization of the U.S. residential buildings sector.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

From Sim to Real: A Pipeline for Training and Deploying Traffic Smoothing Cruise Controllers

Designing and validating controllers for connected and automated vehicles to enhance traffic flow presents significant challenges, from the complexity of replicating real-world stop-and-go traffic dynamics in simulation, to the intricacies involved in transitioning from simulation to actual deployment. In this work, we present a full pipeline from data collection to controller deployment. Specifically, we collect 772 km of driving data from the I-24 in Tennessee, and use it to build a one-lane simulator, placing simulated vehicles behind real-world trajectories. Using policy-gradient methods with an asymmetric critic, we improve fuel efficiency by over 10% when simulating congested scenarios. Our comprehensive approach includes reinforcement learning for controller training, software verification, hardware validation and setup, and navigating various sim-to-real challenges. Furthermore, we analyze the controller's behavior and wave-smoothing properties, and deploy it on four Toyota Rav4’s in a real-world validation experiment on the I-24. Lastly, we release the driving dataset, the simulator and the trained controller, to enable future benchmarking and controller design.

42 ENGINEERING↗
DOE OSTI2024

CDL2PLC translator v0.1.0

The CDL-PLC translator aims at translating control sequences for building energy systems from the CDL CXF format to the PLCopen XML format. The CDL CXF developed at LBL within the OpenBuildingControl project, and now being standardized via ASHRAE Standard 231P, enables expressing control sequences developed in the simulation environment Modelica in a JSON format. The PLCopen XML is an existing exchange format standardized in IEC 61131-10 for Programmable Logic Controllers (PLCs) following the IEC 61131 standard as one target system of CDL among others. The translation from the CDL CXF to the PLCopen XML contributes to a seamless workflow from the model-based development of control sequences in simulation environments, which is not building practice today, and their digital implementation on building controllers, which replaces graphical and textual documents used for this purpose today. The translator is at a prototypical stage and enables, as a proof of concept, the translation of very simple control sequences composed of 4 selected function blocks out of 137 function blocks defined in CDL. The translation includes the connection of inputs and outputs of function blocks and the expression of a control function in CDL to the equivalent code in IEC 61131-3.

Walther, Karl↗
DOE OSTI2024

Large-scale simulation-based parametric analysis of an optimal precooling strategy for demand flexibility in a commercial office building

Achieving success with grid-interactive efficient buildings (GEBs) is closely tied to the utilization of flexible loads. A valuable strategy involves the implementation of precooling techniques before high-demand events, such as peak hours, by adjusting zone air temperature setpoints. This leads to a reduction in thermal loads and peak electricity demand during these times, as the building’s thermal mass stores and subsequently releases thermal energy. However, the effectiveness of the pre-cooling optimization is highly contingent on specific conditions such as building thermal properties, weather conditions, utility rate structure, HVAC equipment sizing, etc. Therefore, investigating the impacts of these condition-specific factors is crucial, especially when considering precooling strategies that utilize thermal mass in commercial buildings. In this paper, we first devised a novel heuristic control approach that incorporates parameterized optimal precooling thermostat schedules to enhance demand flexibility in a commercial office building. Subsequently, we conducted a thorough performance evaluation of this control strategy. Here, the optimal thermostat schedule was parameterized using three optimization variables: the precooling start time, the precooling end time, and the precooling temperature setpoint. Utilizing the DOE medium-sized office building as the virtual testbed, we showed that the parameterized schedule effectively approximates model predictive control and requires drastically reduced computational overhead. In addition, we investigated the impact of different influencing factors on the optimal precooling strategy. These factors include building thermal mass, outdoor air conditions, and energy price profiles. Using high-performance computing, we simulated a total of 225 scenarios, consisting of three levels of thermal mass, five typical outdoor air temperature profiles, and fifteen time-of-use price plans. The results demonstrate that optimal thermostat scheduling could save substantial energy cost in medium-sized office buildings with heavy thermal mass but with some energy penalty. Although the potential for cost savings is lower in buildings with low and medium thermal mass, the energy penalty remains consistent in all three thermal mass scenarios. The study also highlights the need to account for zone diversity and recognize that a one-size-fits-all-zone setpoint schedule may not be suitable for all zones and can lead to unnecessary energy wastage. Furthermore, the results highlight that while outdoor air conditions play a role in cost and energy performance, the cooling load exerts a more immediate and substantial influence on cost savings in precooling strategies. Although cost savings are comparable under certain conditions with the same cooling load, observed deviations in energy penalty indicate potential disparities in the efficiency of the HVAC system during the load-shifting process. In addition, the duration of peak pricing and the ratio between peak and off-peak times exhibit clear correlations with cost savings and energy consumption, aligning with intuitive expectations. These findings offer valuable insights for optimizing precooling strategies in office buildings.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

Machine-learning modeling of magnetization dynamics in quasi-equilibrium and driven metallic spin systems

Here, we present a perspective on recent progress in machine-learning (ML) force-field approaches for large-scale Landau–Lifshitz–Gilbert (LLG) simulations of metallic spin systems. Building on a generalization of the Behler–Parrinello (BP) architecture originally developed for quantum molecular dynamics, we develop scalable and transferable ML models that faithfully capture the complex, environment-dependent electron-mediated exchange fields characteristic of itinerant magnets. A central ingredient of this framework is the implementation of symmetry-aware magnetic descriptors based on group-theoretical bispectrum formalisms. Leveraging these ML force fields, LLG simulations faithfully reproduce hallmark non-collinear magnetic orders—such as the 120° and tetrahedral states—on the triangular lattice, and successfully capture the complex spin textures emerging in the mixed-phase states of a square-lattice double-exchange model under thermal quench. We further discuss a generalized potential theory that extends the BP formalism to incorporate both conservative and nonconservative electronic torques, thereby enabling ML models to learn nonequilibrium exchange fields from computationally demanding microscopic approaches such as nonequilibrium Green’s-function techniques. This extension yields quantitatively accurate predictions of voltage-driven domain-wall motion and establishes a foundation for quantum-accurate, multiscale modeling of nonequilibrium spin dynamics and spintronic functionalities.

Descriptors↗
DOE OSTI2026

Evaluating Energy Savings Measures for Building Retrofits in an Interactive Workshop Environment

As part of the Better Buildings Summit 2025, a workshop was developed to simulate the decision process for implementing a set of energy savings measures on an existing building. As part of the workshop a "game" was created around energy savings strategies, and workshop participants selected renovation cards that provided data around the impacts of that renovation choice. Participants then were able to calculate overall savings and payback from the selected retrofit opportunities. This publication has been produced to package the resources used in the activity in an organized document so that the materials can be distributed and reused more broadly. It provides a comprehensive framework for replicating the workshop, including step-by-step instructions, retrofit "game cards" with data points, and facilitation guidance. By using these materials, readers can conduct their own version of this interactive workshop with stakeholders in their networks, such as building owners, energy managers, or policy makers. The goal is to empower users to simulate the decision-making processes for energy projects, foster collaboration, and drive meaningful discussions around cost-effective retrofit opportunities and goal-oriented outcomes.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2025

Stochastic Ensemble Generation for Improved Characterization of Representing Geologic Variability in a Reservoir: IBDP Case Study for SMART Initiative

This document is a poster covering the findings from activities on training data generation, specifically geologic ensemble generation. The generated geologic realizations captured the range of possible permeability distributions of the subsurface at the Illinois Basin - Decatur Project (IBDP) site, based on available well log variabilities. The percentages of reservoirs and baffles in the injection zone and a truncation of baffle permeability led to more variance in the simulations. This will be used to build forward modeling, history matching, and optimization workflows. The geologic realizations were also ranked according to dynamic measures of hydraulic diffusivity, and simulations confirm a greater contrast between the reservoir and the baffles during injection.

stochastic ensemble generation↗
DOE OSTI2025

The Aerosol Model Benchmarking Repository: A toolkit for model intercomparison

The Aerosol Model Benchmarking Repository and Standards (AMBRS) project was initiated to provide tools and to establish community standards for benchmarking aerosol models. This report describes a set of open-source tools for building, running, and analyzing aerosol box model simulations in a standardized framework. The framework consists of three core components: AMBuilder, a CMake-based build system that compiles supported models consistently; AMBRS, a Python module that defines unified numerical experiments and executes them with aligned inputs; and PyParticle, an aerosol analysis package that standardizes output, computes diagnostics, and visualizes simulation results. Together, these tools enable reproducible intercomparison of aerosol schemes and support process-level evaluation of how model simplifications affect predictions of size distributions, cloud condensation nuclei activity, and other relevant properties relevant for the Earth-Energy system. Beyond its role in benchmarking, AMBRS provides a platform for studying aerosol processes across scales and can be used to generate training data for AI/ML applications in support of a broader hierarchical aerosol modeling strategy.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

New U.S. Data Tools are Playing a Crucial Role in Decarbonizing Buildings at Speed, Scale, and Low Cost

Preparing buildings for retrofits traditionally requires expensive on-site audits or timeintensive simulation models. As a result, the majority of buildings fail to pursue cost-saving retrofits. To address these barriers, the U.S. Department of Energy (DOE) has introduced the Building Efficiency Targeting Tool for Energy Retrofits (BETTER)-a new, free, on-line tool that utilizes a data-driven analytical engine and user-friendly web interface to automatically analyze a building's monthly energy usage in response to weather conditions. The tool benchmarks a building's electric and fossil energy usage against peers; estimates energy, cost, and emissions reductions at the building and portfolio levels; recommends energy efficiency measures; and prioritizes buildings for net-zero energy retrofits. Thanks to interoperability with the DOE's Standard Energy Efficiency Data (SEED) platform, BETTER is supporting U.S. jurisdictions to prepare buildings for retrofit at speed, scale, and low cost to comply with energy policies. This paper discusses the use of BETTER and SEED by one of the branches of the California state government to streamline a retrofit program across 455 public non-residential buildings to align with state goals to reduce greenhouse gas emissions. It describes the organization's challenge to reduce energy consumption across a geographically diverse, aging portfolio; explores how BETTER and SEED improved workflow efficiency; presents preliminary results, including avoiding audit costs of $3.28 million and developing the groundwork for retrofit projects estimated to prevent emission of 2,271 t CO2e annually; and provides guidance for other jurisdictions seeking similar results.

BETTER↗
DOE OSTI2025

Finite Element Analysis of the TRUST Nonlinear Dynamics Testbed

This paper builds on prior work conducted within the Los Alamos National Laboratory (LANL) Testbeds to Reduce Uncertainty in Simulations and Tests (TRUST) program. Specifically, it builds on finite element (FE) modeling efforts for the TRUST program’s Nonlinear Dynamics (ND) testbed. Historically, the FE model for the ND testbed has exclusively utilized a Lanczos eigensolver that linearly extracts the system’s natural frequencies. This paper investigates the Abaqus 2024’s explicit dynamic solver, which implements a central difference explicit solver. The central difference method used in Abaqus can capture nonlinear material responses in structural dynamic simulations making it suitable for the ND FE model.

42 ENGINEERING↗
DOE OSTI2025

Measurement of off-shell Higgs boson production in the $H^*\rightarrow ZZ\rightarrow 4\ell$ decay channel using a neural simulation-based inference technique in 13 TeV pp collisions with the ATLAS detector

A measurement of off-shell Higgs boson production in the $H^*\to ZZ\to 4\ell$ decay channel is presented. The measurement uses 140 fb −1 of proton–proton collisions at $\sqrt{s} = 13$ TeV collected by the ATLAS detector at the Large Hadron Collider and supersedes the previous result in this decay channel using the same dataset. The data analysis is performed using a neural simulation-based inference method, which builds per-event likelihood ratios using neural networks. The observed (expected) off-shell Higgs boson production signal strength in the $ZZ\to 4\ell$ decay channel at 68% CL is $0.87^{+0.75}_{-0.54}$ ($1.00^{+1.04}_{-0.95}$ ). The evidence for off-shell Higgs boson production using the $ZZ\to 4\ell$ decay channel has an observed (expected) significance of 2.5σ (1.3σ). The expected result represents a significant improvement relative to that of the previous analysis of the same dataset, which obtained an expected significance of 0.5σ. When combined with the most recent ATLAS measurement in the $ZZ\to 2\ell 2\nu$ decay channel, the evidence for off-shell Higgs boson production has an observed (expected) significance of 3.7σ (2.4σ). The off-shell measurements are combined with the measurement of on-shell Higgs boson production to obtain constraints on the Higgs boson total width. The observed (expected) value of the Higgs boson width at 68% CL is $4.3^{+2.7}_{-1.9}$ ($4.1^{+3.5}_{-3.4}$ ) MeV.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A new biogeochemical modelling framework (FLaMe-v1.0) for lake methane emissions on the regional scale: development and application to the European domain

This study presents a new physical-biogeochemical modelling framework for simulating lake methane (CH 4 ) emissions at regional scales. The new model, FLaMe-v1.0 (Fluxes of Lake Methane), rests on an innovative, computationally efficient lake clustering approach that enables the simulation of CH 4 emissions across a large number of lakes. Building on the Canadian Small Lake Model (CSLM) that simulates the lake physics, we develop a suite of biogeochemical modules to simulate transient dynamics of organic Carbon (C), Oxygen (O 2 ), and CH 4 . We first test the performance of FLaMe-v1.0 by analyzing physical and biogeochemical processes in two theoretical lakes with characteristics that can be considered representative for many lakes (an oligotrophic, deep lake driven by cold climate versus a eutrophic, shallow lake driven by warm climate). Next, we evaluate the model by comparing simulated and observed timeseries of CH 4 emissions in four well-surveyed lakes. We then apply FLaMe-v1.0 at the European scale to evaluate simulated diffusive and ebullitive lake CH 4 fluxes against in-situ measurements in both boreal and central European regions. Finally, we provide a first assessment of the spatio-temporal variability in CH 4 emissions from European lakes with a surface area comprised between 0.1–1000 km 2 (n= 108 407, total area = 1.33 × 105 km 2 ), indicating a total emission of 0.97 ± 0.23 Tg CH 4 yr −1 , with the uncertainty constrained by combining FLaMe-v1.0 and machine learning techniques. Moreover, 30 % and 70 % of these CH 4 emissions are through diffusive and ebullitive pathways, respectively. Annually averaged CH 4 emission rates per unit lake area during 2010–2016 have a South-to-North decreasing gradient, resulting in a mean over the European domain as 7.39 g CH 4 m −2 yr −1 . Our simulations reveal a strong seasonality (with ice-blocking effects accounted for) in European lake CH 4 emissions, with nearly ten times higher emissions during late summer than during winter. This pronounced seasonal variation highlights the importance of accounting for the sub-annual variability in CH 4 emissions to accurately constrain regional CH 4 budgets. In the future, FLaMe-v1.0 could be embedded into Earth System Models to investigate the feedback between climate warming and global lake CH 4 emissions.

Maisonnier, Manon [Free Univ. of Brussels (Belgium↗
DOE OSTI2024

New U.S. Data Tools are Playing a Crucial Role in Decarbonizing Buildings at Speed, Scale, and Low Cost

Preparing buildings for retrofits traditionally requires expensive on-site audits or time- intensive simulation models. As a result, the majority of buildings fail to pursue cost-saving retrofits. To address these barriers, the U.S. Department of Energy (DOE) has introduced the Building Efficiency Targeting Tool for Energy Retrofits (BETTER)—a new, free, on-line tool that utilizes a data-driven analytical engine and user-friendly web interface to automatically analyze a building’s monthly energy usage in response to weather conditions. The tool benchmarks a building’s electric and fossil energy usage against peers; estimates energy, cost, and emissions reductions at the building and portfolio levels; recommends energy efficiency measures; and prioritizes buildings for net-zero energy retrofits. Thanks to interoperability with the DOE’s Standard Energy Efficiency Data (SEED) platform, BETTER is supporting U.S. jurisdictions to prepare buildings for retrofit at speed, scale, and low cost to comply with energy policies. This paper discusses the use of BETTER and SEED by one of the branches of the California state government to streamline a retrofit program across 455 public non-residential buildings to align with state goals to reduce greenhouse gas emissions. It describes the organization’s challenge to reduce energy consumption across a geographically diverse, aging portfolio; explores how BETTER and SEED improved workflow efficiency; presents preliminary results, including avoiding audit costs of $3.28 million and developing the groundwork for retrofit projects estimated to prevent emission of 2,271 t CO2e annually; and provides guidance for other jurisdictions seeking similar results.

Li, han↗
DOE OSTI2025

Multiphysics simulation of recent experiments on alkali‐silica reaction expansion in reinforced concrete members

Alkali‐silica reaction (ASR) is an important degradation process that causes volumetric expansion and damage in concrete, and is affected significantly by the local temperature, moisture and stress conditions that often vary across the regions of a structure. Numerical simulation is essential to predict the progression and effects of ASR on the performance of structures. Because of the interactions between thermal and moisture transport and mechanical deformation, it is important for numerical models to represent all these physical phenomena and the coupling between them. Simulations of ASR in reinforced concrete (RC) structures are further complicated by the need to capture interactions between concrete and embedded reinforcing bars. Here, this paper describes the implementation of a scalable, coupled‐physics ASR model for simulating RC structures and assesses the ability of that model to predict ASR‐induced expansion in recent laboratory tests on RC block and beam specimens. These laboratory tests and the simulation approach were selected because of their applicability to RC structural‐scale simulations. This validation study helps builds confidence the ability of this approach to model ASR expansion in large, complex RC structures, which is a current high‐priority need.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A prototype cooling blanket for mitigating occupant overheating risk in a hot indoor environment: Modeling and assessments

Conventional ways of cooling a room or an entire house for occupant thermal comfort during summer consume a significant amount of energy and are vulnerable to overheating risk during power outages that lead to loss of cooling system operations. This study investigates a low-power cooling blanket, as a Personal Cooling System (PCS), that covers the upper human body for direct cooling during a five-day heat wave in a single-family house. A modeling framework is developed for evaluating the thermal and energy performance of the cooling blanket, which builds upon the co-simulation of three models: a house energy model, a personal thermal comfort model, and a cooling blanket model. Simulation results show that under the power outage scenario, the cooling blanket can greatly reduce the occupant heat stress with a reduction of daily hours of exceedance (discomfort hours defined as TSV>2) by up to 17.2 h (a 95.3 % improvement from the baseline power outage without the blanket). The cooling blanket, equipped with an innovative electrocaloric heat pump (COP as high as 10.1) consumes 6.31 W and can be operated by a portable battery for several days. The cooling blanket consumes only 0.28 % of the electricity of a central air-conditioning system running to provide cooling for the whole house during the five-day heatwave period. The findings justify further research of electrocaloric wearable PCS as low-power effective cooling to ensure thermal survivability of occupants during extreme indoor environments.

Electrocaloric heat pump↗