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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 451 records · Page 25

Enabling off-highway diesel engine downsizing and performance improvement using electrically assisted turbocharging

Internal combustion engine (ICE) downsizing through various turbocharging configurations is generally known by the powertrain design community as an effective means to reduce frictional losses, increase waste heat recovery, and improve fuel efficiency while increasing engine power density. However, often is the case that turbocharging strategies, including variable geometry turbochargers, and regulated two-stage turbochargers, incur the performance tradeoff between transient response and fuel economy (pumping losses) at high engine speeds. For off-highway vehicles having particularly transient and high-powered duty cycles, efforts to improve this tradeoff and increase operational flexibility have turned to evaluating various electrified air system architectures. In this study, a 4.5 L diesel-ICE configured with an electrically driven compressor (eBooster ® ) is placed in series with a conventional turbocharger and integrated into a 48 V mild-hybrid powertrain architecture. The objective of this powertrain configuration is to enable engine downsizing by 34%, replacing the current 6.8 L ICE platform with the hybridized 4.5 L ICE concept. The commercial 1-D simulation software GT-SUITE is used for powertrain system development and system optimization. Development and validation of the GT-SUITE model and air system controls is concurrently supported through experimental data collection. The simulation model development includes using machine learning methods for optimizing exhaust gas dilution, injection timing, and eBooster ® power to improve steady-state and transient brake-specific fuel consumption while minimizing criteria pollutant emissions. It was found that total specific fluid consumption over the standardized non-road transient engine duty cycle could be reduced by 18% over the current 6.8 L engine by using an optimized eBoosted 4.5 L engine. The hybridized 4.5 L engine concept concurrently showed sufficient transient response capability and nearly an order of magnitude reduction in duty cycle total soot production.

25 ENERGY STORAGE↗

A multiscale cohesive law for carbon fiber networks

Better predictive models of mechanical failure in low-weight heat shield composites would aid material certification for missions with aggressive atmospheric entry conditions. In this study, we develop such a model for the rapid engineering analysis of the failure limits of phenolic impregnated carbon ablator (PICA) - a leading heat shield material whose structural component is a carbon fiber network. We hypothesize inelastic deformation failure mechanisms and model their behavior using molecular dynamics simulations to calculate the binding energy. We then upscale this binding energy to the macroscale using a renormalization argument. The approach delivers insightful and reasonably accurate macroscale predictions that compare favorably to experiments. In application, the model is validated for a particular variety of PICA by comparison to experiment and would then be used to study design scenarios in different entry conditions.

36 MATERIALS SCIENCE↗

Extremum-Seeking-Based Ultra-local Model Predictive Control and Its Application to Electric Motor Speed Regulation

Electric vehicle (EV) market is rapidly expanding. As a critical component of EV, an electric motor needs to accurately follow a reference speed signal while respecting the electrical current constraint for safety. Those requirements are usually formulated as a model predictive control (MPC) problem. However, the performance of traditional model-based MPC depends on the accuracy of the system model, which may not always be guaranteed in reality. Therefore, we utilize a data-driven, model-free predictive control strategy, called ultra-local MPC (ULMPC), to control the speed of an electric motor. To further enhance the control performance of ULMPC, we employ the extremum-seeking control (ESC) to tune the control gain of the ULMPC online. Simulation and hardware experiments demonstrate the enhancement of the extremum-seeking-based ULMPC over a constant-gain ULMPC.

Zhou, Yujing↗

STRUCTURE AND PROPERTIES STUDY ON ENERGY MATERIALS: THERMOELECTRIC MATERIAL TETRAHEDRITE AND LITHIUM ION CONDUCTOR LiPON

Development of efficient energy materials is critical in order to ease the energy demand and reduce our dependence of fossil fuel. Thermoelectric materials are promising due to their capability of generating electrical power by recovering waste heat. The performance of thermoelectric materials is quantified by a dimensionless figure of merit zT, which depends on their properties such as electrical conductivity, Seebeck coefficient and thermal conductivity. Tetrahedrites, a copper antimony sulfosalt mineral, typified by Cu12-xMxSb4S13, where M is a transition metal element such as Ni, Zn, Fe or Mn, have great potential for thermoelectric application due to their relatively high zT (close to 1 at 700 K), earth-abundance, environmental friendliness, favorable electrical properties, and most importantly intrinsic low lattice thermal conductivity (less than 1 W m-1 K-1) in wide temperature. In addition to energy recovery, reliable energy storage devices are also emerging to relieve the energy demand and improve the efficiency of consuming energy resources. Lithium-ion batteries are known to be reliable and successful electrochemical energy storage devices and appliable in various aspects, including laptops, smartphones and electrical vehicles. Lithium phosphorous oxynitride (LiPON) are widely used as thin-film solid-state electrolytes in Li-ion battery, which is the only demonstrated solid-state electrolyte that is quite stable in direct contact with Li metal at potentials from 0-5 V. However, the structure of LiPON, the effects of N doping, and the origin of its good electrochemical stability remains inconclusive.In this thesis, reliable modeling techniques accompanied with experimental tools, are applied to study the thermoelectric material tetrahedrite and the ionic conductor LiPON, in order to study their structural and dynamical properties. Accurate and efficient density-functional theory (DFT) and density-functional tight-binding (DFTB) methods, combined with molecular dynamics (MD) simulations are utilized in order to investigate the structures and properties of these energy materials. The incoherent and coherent atomic dynamics study of tetrahedrite Cu10.5NiZn0.5Sb4S13 provides the origin of softening upon cooling by investigate the motion of Cu12e at different temperatures. The dynamic structure factors in the longitudinal and transverse direction will also be discussed. The Cu movement of Cu-rich tetrahedrite Cu14Sb4S13 is revealed by Cu self-diffusivity, nuclear density map and "nudged elastic band" (NEB). Moreover, we investigate the effect of simulation cell size and basis sets on the DFT-based MD simulation results using tetrahedrite Cu10Zn2Sb4S13 thermoelectric as a model material, showing the advantage of larger cell by accessing smaller Q range. In addition, the low-temperature structural properties of Cu12Sb4S13 is measured by neutron diffraction, which indicates that no cubic to tetragonal transition occurs at metal-semiconductor transition (MST) temperature. Thermoelectric properties such as Seebeck coefficient, electrical resistivity and electrical thermal conductivity will also be investigated. DFTB method is implemented to study the structure and transport properties of Li3PO4 and LiPON, while the exploration of N doping effect is included. Lastly, the LiPON/Li interphase will be revealed in order to study the origin of electrochemical stability

25 ENERGY STORAGE↗

STRUCTURE AND PROPERTIES STUDY ON ENERGY MATERIALS: THERMOELECTRIC MATERIAL TETRAHEDRITE AND LITHIUM ION CONDUCTOR

Development of efficient energy materials is critical in order to ease the energy demand and reduce our dependence of fossil fuel. Thermoelectric materials are promising due to their capability of generating electrical power by recovering waste heat. The performance of thermoelectric materials is quantified by a dimensionless figure of merit zT, which depends on their properties such as electrical conductivity, Seebeck coefficient and thermal conductivity. Tetrahedrites, a copper antimony sulfosalt mineral, typified by Cu 12-x MxSb 4 S 13 , where M is a transition metal element such as Ni, Zn, Fe or Mn, have great potential for thermoelectric application due to their relatively high zT (close to 1 at 700 K), earth-abundance, environmental friendliness, favorable electrical properties, and most importantly intrinsic low lattice thermal conductivity (less than 1 W m -1 K -1 ) in wide temperature. In addition to energy recovery, reliable energy storage devices are also emerging to relieve the energy demand and improve the efficiency of consuming energy resources. Lithium-ion batteries are known to be reliable and successful electrochemical energy storage devices and appliable in various aspects, including laptops, smartphones and electrical vehicles. Lithium phosphorous oxynitride (LiPON) are widely used as thin-film solid-state electrolytes in Li-ion battery, which is the only demonstrated solid-state electrolyte that is quite stable in direct contact with Li metal at potentials from 0-5 V. However, the structure of LiPON, the effects of N doping, and the origin of its good electrochemical stability remains inconclusive. In this thesis, reliable modeling techniques accompanied with experimental tools, are applied to study the thermoelectric material tetrahedrite and the ionic conductor LiPON, in order to study their structural and dynamical properties. Accurate and efficient density-functional theory (DFT) and density-functional tight-binding (DFTB) methods, combined with molecular dynamics (MD) simulations are utilized in order to investigate the structures and properties of these energy materials. The incoherent and coherent atomic dynamics study of tetrahedrite Cu 10.5 NiZn 0.5 Sb 4 S 13 provides the origin of softening upon cooling by investigate the motion of Cu12e at different temperatures. The dynamic structure factors in the longitudinal and transverse direction will also be discussed. The Cu movement of Cu-rich tetrahedrite Cu 14 Sb 4 S 13 is revealed by Cu self-diffusivity, nuclear density map and “nudged elastic band” (NEB). Moreover, we investigate the effect of simulation cell size and basis sets on the DFT-based MD simulation results using tetrahedrite Cu1 0 Zn 2 Sb 4 S 13 thermoelectric as a model material, showing the advantage of larger cell by accessing smaller Q range. In addition, the low-temperature structural properties of Cu 12 Sb 4 S 13 is measured by neutron diffraction, which indicates that no cubic to tetragonal transition occurs at metal-semiconductor transition (MST) temperature. Thermoelectric properties such as Seebeck coefficient, electrical resistivity and electrical thermal conductivity will also be investigated. DFTB method is implemented to study the structure and transport properties of Li 3 PO 4 and LiPON, while the exploration of N doping effect is included. Lastly, the LiPON/Li interphase will be revealed in order to study the origin of electrochemical stability.

Li, Junchao↗

Hybrid Energy Management with Real-Time Control of a High-Power EV Charging Site

Decarbonization of transportation systems is driving higher capacity energy storage and faster charging power requirements in electric vehicles (EVs). Given the potential advantages - such as increased efficiency, reduced inverter capacity, and less total cable mass - there is a demand in the industry for more DC distribution for high-power charging (HPC) hubs. However, the cost-effective, adaptive, and robust operation of the DC-coupled HPC hub necessitates a robust site energy management system (SEMS). Validating SEMS operation using a digital twin of an HPC hub in a real-time simulator (RTS) platform is crucial before field deployment. In this study, we propose a hybrid energy management site controller designed to achieve high-level, long-term operational objectives while managing low-level power sharing control between hub assets. We develop a centralized model predictive controller (MPC) to optimize hub operating points and use these points to update the droop parameters of the site energy storage system (ESS). This approach ensures the hub follows an optimal operating point while maintaining the flexibility to respond to load surges. We tested and verified our proposed approach both offline and on a Controller Hardware-in-the-loop (C-HIL) simulation platform integrated with a SEMS framework, demonstrating real-time site operation and validating a cost-effective and robust site controller.

ADVANCED PROPULSION SYSTEMS↗

Accelerating Battery Simulations by Using High Performance Computing and Opportunities with Machine Learning

The US Department of Energy (DOE) estimates that the battery pack cost of $60 per kilowatt-hour while increasing the driving range to over 300 miles and vehicle charging under 15 min or less would enable mass penetration of electric vehicles in the USA by 2030. These projections are based on the currently available high-density cell chemistry combined with a system level design and optimized electrodes. Electrodes for current state-of-the-art lithium-ion cell technology are fabricated from electrode slurry comprising of active material, polymeric binder, and conductive diluent such as carbon black that are coated on metal current collectors such as copper and aluminum. Given these challenging requirements for development of electrical energy storage devices for future transportation needs, a predictive simulation capability which can accelerate design by considering performance and safety implications of different geometry, materials, and chemistry choices is required. In this chapter, we discuss our state-of-the-art three-dimensional modeling framework, providing examples on battery performance and safety simulations. We also present approaches to use machine learning in the context of large datasets that are becoming available.

Allu, Srikanth↗

A statistical mechanics approach to macroscopic limits of car-following traffic dynamics

Herein we study the derivation of macroscopic traffic models from car-following vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic description. We consider the superposition of Follow-the-Leader (FTL) interactions and relaxation towards a traffic-dependent Optimal Velocity (OV) and we show that the resulting macroscopic models depend on the relative frequency between these two microscopic processes. If FTL interactions dominate then one gets an inhomogeneous Aw–Rascle–Zhang model, whose (pseudo) pressure and stability of the uniform flow are precisely defined by some features of the microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is comparable to that of FTL interactions then one gets a Lighthill–Whitham–Richards model ruled only by the OV function. We further confirm these findings by means of numerical simulations of the particle system and the macroscopic models. Unlike other formally analogous results, our approach builds the macroscopic models as physical limits of particle dynamics rather than assessing the convergence of microscopic to macroscopic solutions under suitable numerical discretisations.

97 MATHEMATICS AND COMPUTING↗

A Misalignment Tolerant Magnetic Coupler Design and Implementation for Wireless Charging of Unmanned Aerial Vehicles (UAVs)

Wireless power transfer technology is getting more attention these days as a part of expanded battery charging infrastructure and network at a wide range of power levels. Charging Unmanned aerial vehicles (UAVs) is one wireless charging application, and charging their batteries can be challenging because they have short flight times and are frequently charged. For wireless charging of UAVs, the misalignment performance of the magnetic coupler pads is critical because landing on a charging pad at a perfectly aligned position is difficult and can be time-consuming. Different coil shapes and system structures have been proposed in the literature to overcome this challenge. A new design with a high misalignment tolerance is needed; therefore, to fill this gap, a wireless power transfer system has been designed for a 250 W UAV battery charging system with a new magnetic coupler design. A 3D model of the proposed design was created, and finite element simulations were performed. To prove the proposed design, the magnetic coupler prototypes were developed, and experimental results are presented herein. The misalignment tolerance of the proposed system was observed for various rotational positions of the secondary coil, from 0° to 360°. The results demonstrate that DC–DC efficiency varies between 80% and 85% within full 360° rotation of the receiver coil. This result enables the proposed system to address the misalignment problem for wireless charging of UAVs.

UAVs↗

Standard model physics and the digital quantum revolution: thoughts about the interface

Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. Here, from the perspective of three domain science theorists, this article compiles thoughts about the interface on entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A Sensorless Coil Detection Scheme based on Dead-Time Effect in Dynamic Wireless Power Transfer Systems

The detection of electric vehicles in dynamic wireless power transfer (DWPT) systems is important to reduce the standby losses and comply with the electromagnetic-field emission guidelines recommended by the International Commission for Non-Ionizing Radiation Protection. This paper discusses a novel sensorless coil detection scheme, which exploits the phenomenon of voltage-polarity reversal/notches caused by the dead-time effect in the full-bridge inverter. The variations in the system impedance and dead-time effects are collectively exploited to detect the receiver coil in the DWPT system. The proposed coil detection scheme is accomplished at low excitation voltage, which reduces the inverter standby losses. The theoretical analysis of the notch occurrence and open-loop simulation results are presented using a DWPT model developed in the piecewise linear electrical circuit simulation software.

Kavimandan, Utkarsh↗

A Unified Design Theory for Multi-Port Polyphase Transformers Enabling Scalable Power-Multiplexed EV Fleet Charging Systems

This paper presents a unified analytical design theory for multi-port polyphase transformers, targeting scalable and isolated high-power Electric Vehicle (EV) fleet charging systems with power multiplexing capability. As fleet electrification accelerates, conventional one-to-one charger architectures face significant challenges in infrastructure cost, peak power demand, and low utilization of installed power electronics. Power-multiplexed charging architectures, which dynamically distribute power from a shared pool of converter modules across multiple vehicles, have emerged as a promising solution. However, such architectures require scalable, isolated multi-port power interfaces capable of routing energy among multiple inputs and outputs, whose design remains complex and dependent on iterative modeling. To address this gap, the proposed theory provides closed-form expressions for self-inductance, leakage inductance, and mutual coupling terms for arbitrary multi-phase, multi-port transformer structures. The formulation enables direct synthesis of isolated multi-input and multi-output resonant converter systems without reliance on geometry-specific finite-element analysis or extensive parameter extraction. This capability is particularly critical for power-multiplexed systems, where modular converter structures must interface with multiple vehicles while maintaining galvanic isolation and flexible power allocation. The effectiveness of the proposed framework is demonstrated through the design of a 360 kW multi-phase system operating over a 700–900 VDC input and 400–1250 VDC output range. PLECS simulation results confirm accurate prediction of system behavior and validate the applicability of the approach to multi-port, power-multiplexed charging scenarios. The proposed method significantly reduces design complexity while enabling scalable, cost-effective, and fully utilized EV fleet charging infrastructure.

Asa, Erdem [ORNL] (ORCID:0000000190884812)↗

Dynamic Queue Prediction at Signalized Intersections with Fusing Sensory Information and Connected Vehicles

Queue length is one of the most essential metrics for indicating traffic conditions at signalized intersections. Most existing studies mainly focus on queue length estimation in a retrieving way which cannot effectively predict the future state of vehicle in queue. This paper proposes an innovative dynamic queue prediction model in a vehicle-infrastructure cooperative way. The proposed dynamic queue predictor can customize the queue prediction using the trajectories of preceding vehicles from radar detection with varying information from loop detectors and connected vehicles (CVs). The dynamic queue prediction accuracy can be further improved with at least one present CV in the same cycle. With the accurate dynamic queue prediction, we present a case study of Queue-Aware Eco-Approach and Departure (QEAD) to provide an online optimal vehicle trajectory considering both the signal status and preceding vehicle's future status in queue. The proposed framework and algorithms are of pragmatic significance and one of its advanced features is the ability to work under low penetration rate of CVs. The test using Next Generation SIMulation (NGSIM) dataset and a case study in VISSIM microscopic simulation show promising results.

Ye, Fei↗

Ensuring reliable connectivity to cellular-connected UAVs with up-tilted antennas and interference coordination

To integrate unmanned aerial vehicles (UAVs) in future large-scale deployments, a new wireless communication paradigm, namely, the cellular-connected UAV has recently attracted interest. However, the line-of-sight dominant air-to-ground channels along with the antenna pattern of the cellular ground base stations (GBSs) introduce critical interference issues in cellular-connected UAV communications. In particular, the complex antenna pattern and the ground reflection (GR) from the down-tilted antennas create both coverage holes and patchy coverage for the UAVs in the sky, which leads to unreliable connectivity from the underlying cellular network. To overcome these challenges, in this paper, we propose a new cellular architecture that employs an extra set of co-channel antennas oriented towards the sky to support UAVs on top of the existing down-tilted antennas for ground user equipment (GUE). To model the GR stemming from the down-tilted antennas, we propose a path-loss model, which takes both antenna radiation pattern and configuration into account. Next, we formulate an optimization problem to maximize the minimum signal-to-interference ratio (SIR) of the UAVs by tuning the up-tilt (UT) angles of the up-tilted antennas. Since this is an NP-hard problem, we propose a genetic algorithm (GA) based heuristic method to optimize the UT angles of these antennas. After obtaining the optimal UT angles, we integrate the 3GPP Release-10 specified enhanced inter-cell interference coordination (eICIC) to reduce the interference stemming from the down-tilted antennas. Our simulation results based on the hexagonal cell layout show that the proposed interference mitigation method can ensure higher minimum SIRs for the UAVs over baseline methods while creating minimal impact on the SIR of GUEs.

3GPP↗

Automated Signal Timing Plan Reconstruction Using High-Resolution Event-Based Controller Data for Digital Twins

Transportation digital twins are essential tools for evaluating emerging technologies such as connected and automated vehicles, adaptive traffic signal control, and mobility optimization strategies. Realistic digital twins require accurate emulation of real-world signal controllers and detailed signal timing plans. However, signal timing plans are often unavailable or difficult to access, forcing researchers and modelers to rely on assumed fixed timings or halt their analysis. To overcome this challenge, we present a method that directly estimates signal timing plan parameters using high-resolution, event-based data from traffic signal controllers. The proposed method extracts key parameters, including cycle length, offset, phase sequence, coordinated phases, phase-specific minimum and maximum green durations, vehicle extensions, and splits under coordination. A rule-based deterministic signal timing reconstruction algorithm based on traffic signal operation rules, such as those outlined in the Signal Timing Manual, is developed and validated. We evaluate this method, which uses high-resolution controller event logs and verified signal timing plans, on 94 signalized intersections in Nashville, Tennessee, demonstrating their ability to generate accurate, simulation-ready signal timing plans for tools such as SUMO and Vissim.

Saroj, Abhilasha [ORNL] (ORCID:0000000191178063)↗

Stochastic Home Energy Management Systems with Varying Controllable Resources

This paper studies the performance of a model predictive control (MPC) algorithm in a home energy management system (HEMS) as the set of controllable resources varies and under both a constant and a time-of-use (TOU) electricity price structure. The set of controllable resources includes residentially-owned photovoltaic (PV) panels, a home battery system (HBS), an electric vehicle (EV), and a home heating, ventilation, and air conditioning (HVAC) system. The HEMS optimally schedules the set of controllable resources given user preferences such as indoor thermal comfort and electricity cost sensitivity. The home energy management system is built on a chance constrained, MPC-based algorithm, where the chance constraint ensures the indoor thermal comfort is satisfied with a high probability given uncertainty in the outdoor temperature and solar irradiance forecasts. Simulation results for varying sets of controllable resources under two different electricity price structures demonstrate the variation in the HEMS control with respect to HBS operation, electricity cost, and grid power usage.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Impact Modeling and Testing of Pouch and Prismatic Cells

Understanding battery response under impact is critical to improve the safety of electrified vehicles. Nevertheless, predicting the impact behaviors of batteries is not straightforward since a battery cell usually contains hundreds of thin layers with dramatically different material properties and multiple physical processes occur simultaneously during cell deformation. Here we utilized both empirical tests and numerical models to capture the failure process of pouch and prismatic cells in various impact scenarios. In each test, a cell was hit once by an indenter dropped from a certain height. During which the cell penetration, loading force, voltage and temperature were monitored to characterize the cell’s response. Meanwhile, numerical models were developed to capture the coupled mechanical, electrical, electrochemical and thermal responses of batteries. In these models, the cell bulk was treated as a homogeneous part to achieve computational efficiency required by large-scale simulations, and it was represented by the geologic cap model that allows both shear and compaction deformation. Simulation results showed agreement with experimental data in essential features of cell behaviors during impact. Details of the test setup, model development and cell failure behaviors are presented in this paper. Additionally, capabilities, limitations and future improvement of the battery safety modeling are discussed.

25 ENERGY STORAGE↗

Understanding implications of cathode architecture on energy density of solid-state batteries

Next generation solid-state batteries (SSB) will need to leverage high voltage cathodes, as well as metallic anodes to achieve the realistic performance targets necessary to replace liquid electrolyte-based batteries in cutting-edge applications including electric vehicles. However, limitations arising from mass and charge transports, kinetics and chemo-mechanical degradation at the electrode | electrolyte interface limit the performance of present day SSBs. Optimizing composite cathode architecture, which is an integral part of solid-state batteries, is vital to realize the high-energy density and high-performance goals for next-generation solid-state batteries. Additionally, cathode architecture needs to be optimized for high loadings of active material, well-percolated ion and electron transport pathways and increased resilience against electrochemical stresses. This paper provides a first report of framework for geometric modeling of composite cathode architectures and evaluates the impact of cathode architecture on cell-level energy density using hierarchical models. Packing around primary and secondary active material particles are simulated for a range of active material particle size and solid electrolyte size distributions in the composite cathode. Impact of packing architecture on processing parameters of a given cathode composition and thickness, as well as on achievable energy density is evaluated for a range of commonly used solid electrolyte and cathode materials. Overall, the proposed framework offers a facile exploratory methodology for establishing initial metrics for scalable processing of practical and competent SSBs.

25 ENERGY STORAGE↗