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Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power

Electrochemistry-based Battery Modeling for Prognostics

Batteries are used in a wide variety of applications. In recent years, they have become popular as a source of power for electric vehicles such as cars, unmanned aerial vehicles, and commericial passenger aircraft. In such application domains, it becomes crucial to both monitor battery health and performance and to predict end of discharge (EOD) and end of useful life (EOL) events. To implement such technologies, it is crucial to understand how batteries work and to capture that knowledge in the form of models that can be used by monitoring, diagnosis, and prognosis algorithms. In this work, we develop electrochemistry-based models of lithium-ion batteries that capture the significant electrochemical processes, are computationally efficient, capture the effects of aging, and are of suitable accuracy for reliable EOD prediction in a variety of usage profiles. This paper reports on the progress of such a model, with results demonstrating the model validity and accurate EOD predictions.

battery

Modeling a Li/SOCl2 battery for design purposes

A generalized code applicable to many different electrochemical systems and geometric designs is discussed. The code is to be set up so that physical property data such as thermal conductivity, viscosity, density, and configuration (e.g. physical dimensions) are the input data. Thus, by changing these parameters many different battery configurations can be handled. The outputs, as a function of time and space, are voltage, current, temperature, pressure, velocity, and species concentration.

Ernst, D. W.

Exploring the Model Design Space for Battery Health Management

Battery Health Management (BHM) is a core enabling technology for the success and widespread adoption of the emerging electric vehicles of today. Although battery chemistries have been studied in detail in literature, an accurate run-time battery life prediction algorithm has eluded us. Current reliability-based techniques are insufficient to manage the use of such batteries when they are an active power source with frequently varying loads in uncertain environments. The amount of usable charge of a battery for a given discharge profile is not only dependent on the starting state-of-charge (SOC), but also other factors like battery health and the discharge or load profile imposed. This paper presents a Particle Filter (PF) based BHM framework with plug-and-play modules for battery models and uncertainty management. The batteries are modeled at three different levels of granularity with associated uncertainty distributions, encoding the basic electrochemical processes of a Lithium-polymer battery. The effects of different choices in the model design space are explored in the context of prediction performance in an electric unmanned aerial vehicle (UAV) application with emulated flight profiles.

Saha, Bhaskar

Usage-based Lifing of Lithium-Ion Battery with HybridPhysics-Informed Neural Networks

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs).The ability to model and forecast the remaining useful life of these batteries enables UAV reliability assurance. Building accurate models for battery state of charge and state of health based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. Un-fortunately, these simplifications lead to residual discrepancy between model predictions and observed data. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations.

Lithium-ion Battery

A Prognostics Framework for Battery Health Monitoring Integrated with Thermal Modeling

Urban Air Mobility (UAM) promises to revolutionize transportation in major cities, offering passenger travel, cargo delivery, and emergency medical services through a network of electric vertical takeoff and landing (eVTOL) aircraft. However, the limited range of current eVTOLs, due to the low specific energy of lithium-ion batteries along with a possibility of thermal runaway conditions poses significant safety concerns, leading to potentially compromising operational safety. To address this critical challenge, researchers are actively evaluating the impact of flight and environmental conditions on onboard lithium-ion battery health. This involves carefully assessing the performance of battery packs under laboratory and operational conditions for developing models to estimate future health using prognostics framework. This study examines the effectiveness of evaluating battery degradation leading to catastrophic failures under varying operational conditions in laboratory. These are captured using physics based models of underlying phenomenons and integrated into the prognostics framework. A fully charged battery undergoes controlled discharge cycles at varying C-rates based on the simulated power draw profile, with current and voltage, temperature data recorded throughout the experiment. The observed data provides valuable insights into how different operating conditions and mission profiles affect battery performance. This information is crucial for developing strategies to optimize battery systems, enhance range, and ultimately ensure the safe and reliable operation of UAM vehicles.

Thermal Modeling

A Prognostics Framework for Battery Health Monitoring Integrated with Thermal Modeling

Urban Air Mobility (UAM) promises to revolutionize transportation in major cities, offering passenger travel, cargo delivery, and emergency medical services through a network of electric vertical takeoff and landing (eVTOL) aircraft. However, the limited range of current eVTOLs, due to the low specific energy of lithium-ion batteries along with a possibility of thermal runaway conditions poses significant safety concerns, leading to potentially compromising operational safety. To address this critical challenge, researchers are actively evaluating the impact of flight and environmental conditions on onboard lithium-ion battery health. This involves carefully assessing the performance of battery packs under laboratory and operational conditions for developing models to estimate future health using prognostics framework. This study examines the effectiveness of evaluating battery degradation leading to catastrophic failures under varying operational conditions in laboratory. These are captured using physics based models of underlying phenomenons and integrated into the prognostics framework. A fully charged battery undergoes controlled discharge cycles at varying C-rates based on the simulated power draw profile, with current and voltage, temperature data recorded throughout the experiment. The observed data provides valuable insights into how different operating conditions and mission profiles affect battery performance. This information is crucial for developing strategies to optimize battery systems, enhance range, and ultimately ensure the safe and reliable operation of UAM vehicles.

Thermal Modeling

Modeling for Battery Prognostics

For any battery-powered vehicles (be it unmanned aerial vehicles, small passenger aircraft, or assets in exoplanetary operations) to operate at maximum efficiency and reliability, it is critical to monitor battery health as well performance and to predict end of discharge (EOD) and end of useful life (EOL). To fulfil these needs, it is important to capture the battery's inherent characteristics as well as operational knowledge in the form of models that can be used by monitoring, diagnostic, and prognostic algorithms. Several battery modeling methodologies have been developed in last few years as the understanding of underlying electrochemical mechanics has been advancing. The models can generally be classified as empirical models, electrochemical engineering models, multi-physics models, and molecular/atomist. Empirical models are based on fitting certain functions to past experimental data, without making use of any physicochemical principles. Electrical circuit equivalent models are an example of such empirical models. Electrochemical engineering models are typically continuum models that include electrochemical kinetics and transport phenomena. Each model has its advantages and disadvantages. The former type of model has the advantage of being computationally efficient, but has limited accuracy and robustness, due to the approximations used in developed model, and as a result of such approximations, cannot represent aging well. The latter type of model has the advantage of being very accurate, but is often computationally inefficient, having to solve complex sets of partial differential equations, and thus not suited well for online prognostic applications. In addition both multi-physics and atomist models are computationally expensive hence are even less suited to online application An electrochemistry-based model of Li-ion batteries has been developed, that captures crucial electrochemical processes, captures effects of aging, is computationally efficient, and is of suitable accuracy for reliable EOD prediction in a variety of operational profiles. The model can be considered an electrochemical engineering model, but unlike most such models found in the literature, certain approximations are done that allow to retain computational efficiency for online implementation of the model. Although the focus here is on Li-ion batteries, the model is quite general and can be applied to different chemistries through a change of model parameter values. Progress on model development, providing model validation results and EOD prediction results is being presented.

Prognostics

Enabling Mission Flexibility to Battery Driven Deep Space Endeavors With Generalized Battery-Health-Monitoring Using Physics-Based and Data-Driven Reduced-Order Models

The needs and requirements for an electrochemical energy storage for deep space exploration is well explored. It is often understood that different mission sites and environmental conditions require different battery chemistries or technologies. Additionally, various engineering solutions are deployed to overcome specific chemical challenges. One often overlooked need is the “health” monitoring of an electrochemical storage system. The term generalized health monitoring, as envisioned in this work, refers to the monitoring of various aspects such as electrode health, electrolyte health, reaction pathway health, cooling system health, sensor health, and BMS health [1]. Generalized health monitoring allows mission leads, engineers, and scientists to incorporate flexibility in mission designs, make on-the-fly mission changes, and extend the duration of science missions. Moreover, it enables automation and data-driven decision-making without compromising safety and performance. Recently, our group developed a hierarchy of thermal reduced-order models (TROM) by combining a physics-based modeling approach and data-driven model reduction techniques applied to flight data [2]. The resulting TROMs were found to be not only accurate but also identifiable from the flight data. Consequently, the coefficient of variance of the model parameters is small over the course of hundreds of flights, allowing for monitoring the parameter evolution trajectories as the battery ages and degrades. These parameters constitute the metrics of the generalized health of a battery. Monitoring their evolution allows such models to be used for anomaly detection and prognostics, improving early detection of abnormal behavior and thus enabling timely maintenance, longer battery life, and enhanced battery safety. For this presentation, the practicality of the thermal model will be validated on a pack of 14cells under various topology configurations such as 1S14P, 2P7S, 7S2P, and 1P14S. It is well known that manufacturing and non-uniform aging lead to variability in the performance of a cell, which is exacerbated by cell balancing during active load. Additionally, in extreme scenarios, the paramount objective is to complete the mission, regardless of the stresses on the battery. Topology-induced balancing issues further stress the battery. The goal of this study is to determine if the noise (identifiability) in the reduced-order thermal model parameters is sensitive to topology, cell spacing, cooling strategy, and manufacturing or age variability. The variability in cells is considered by assuming a multimodal distribution for microscopic parameters of a cell (such as porosity, tortuosity, reaction kinetics, volumetric thermal conductivity, and volumetric heat capacity). The compounded effect of manufacturing variability, topological selection, cooling strategies, and cell balancing ages each cell in a battery differently. The study aims to clarify whether the challenge in extracting maximum information depends on the minimum number of sensors or models used for data extraction.

Automation

A Parametric Battery Model for the Conceptual Design of Electric Aircraft

Electric aircraft conceptual designs usually have an assumed specific power and specific energy for the aircraft’s energy storage system that dictates the total capacity and the peak power available. The specific energy and power are inherently linked to the state-of-charge and discharge rate from which they were derived; therefore, they will not directly correspond to the diverse circumstances encountered in various aircraft missions and flight segments. These parameters turn the battery system into a black box, disregard potential electrical restrictions, and disallow the aircraft and battery to be optimized as a system. Peering into this box, this study highlights the importance of incorporating a parametric battery model into the conceptual design workflow by splitting high-level terms such as power into voltage and current and investigating their variability during the discharge process. Through the modeling of these more detailed parameters, this methodology shows the feasibility of using low states-of-charge for contingency operations, including the end of the reserve mission, expanding the amount of usable capacity for electric aircraft. Stark differences in aircraft capabilities can arise between varying fidelity battery models due to late-mission, high-power flight operations. This parametric battery model effectively captures these differences by evaluating the limitations that arise within the individual battery cells and the aircraft powertrain. This paper shows that the unusable charge of a battery is set by the balked landing power requirement and can realistically range from 5% to 44% based on assumptions. This sets the analog to unusable fuel capacity in aircraft with liquid fuel systems. Needing only aircraft- and mission-level inputs and only seconds of run time, this model is a prime fit for the fast, accurate exploration of the electric aircraft conceptual design space.

Battery

Optimal Battery Charging for Damage Mitigation

Our control philosophy is to charge the NiH2 cell in such a way that the damage incurred during the charging period is minimized, thus extending its cycle life. This requires nonlinear dynamic model of NiH2 cell and a damage rate model. We must do this first. This control philosophy is generally considered damage mitigating control or life-extending control. This presentation covers how NiH2 cells function, electrode behavior, an essentialized model, damage mechanisms for NiH2 batteries, battery continuum damage modeling, and battery life models. The presentation includes graphs and a chart illustrating how charging a NiH2 battery with different voltages and currents affects damages the battery and affects its life. The presentation concludes with diagrams of control system architectures for tracking battery recharging.

Hartley, Tom T.

Physics-Based Modeling and Simulation of Emerging Battery Technologies for Aerospace

Recently there is a growing interest in the aviation sector to reduce air and noise pollution. Electrochemical energy storage devices such as batteries coupled with a distributed electric propulsion system can reduce noise concerns as well as emissions and allow the concept of Urban Air Mobility to come to fruition. The battery performance needs to improve considerably compared from current state-of-art Li-ion battery (about 200Wh/Kg) to realize all-electric passenger jet for short flights (up to 690 miles). NASA is exploring lithium-oxygen battery chemistry to power hybrid (battery powered electrical system) and all-electric aircraft for short distance and long-distance flights. Li-O2 is one of the advanced Li-ion technologies that promise to provide specific energy of more than 750Wh/Kg. For this presentation, we present our work on improving power density of Li-O2 batteries through the use of multiphysics simulations. Next, a path is outlined to port these model to simulate performance for a new battery chemistry for space application, Li-CO2. Li-CO2 uses carbon dioxide as the active material instead of oxygen. Although this technology is in its early development, the offers two benefits: it can be used as a CO2 scrubber, as oxygen is one of the by-products on charging, and as a backup or a standalone battery for various Mars or Venus missions, where the carbon dioxide content in the atmosphere is high and need battery to operate at higher temperatures.

Mehta, Mohit

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. The transient finite-element analysis is done using TACS, and the cell-discharge battery model uses OpenMDAO and dymos. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

Battery Pack Shape Optimization using Transient Heat Conduction Coupled with Cell-Discharge Analysis

Battery electric systems exhibit significant time-dependence, especially when evaluated in the context of an aircraft mission profile with continually changing power demands. Additionally, when evaluating battery-powered aircraft concepts, it is important to accurately compute the temperature of the batteries and properly characterize the thermal response of the system. The temperature of the batteries has a significant impact on cell performance, in addition to safety considerations of maintaining battery temperatures below their operating limit. Because of these considerations, battery models for preliminary design and optimization of aircraft should include the capability to accurately compute the temperature distribution within the battery pack. Furthermore, battery pack designs should be as light-weight as possible to maximize the pack energy density, while also considering battery temperature limits. Here, we demonstrate a simultaneous trajectory and shape optimization of a battery pack concept, using a transient heat transfer finite element model coupled with a time-varying cell-discharge battery model to provide this capability. Including the transient finite element problem in the loop enables accurate temperatures that can be passed back to the cell discharge model, while the cell discharge model can supply the finite element model with time-varying heat boundary conditions to the finite element problem, further benefiting the fidelity of the thermal response of the batteries. We first demonstrate the coupling capability between the battery cell-discharge model and the transient finite-element heat transfer through an optimization which computes the optimal current profile for the battery pack while ensuring the battery temperatures remain below their operational limit. We then build on this optimization by adding shape optimization to the problem, which allows us to consider a composite objective function which also minimizes the mass of the battery pack, while also producing an optimal current discharge profile.

Optimization

Design and Analysis of Battery Thermal Management Systems

Thermal management of battery cell packs is a critically needed technology. The purpose of this work is to design new and improved Battery Thermal Management Systems (BTMS) for use in electric airplanes. The BTMS should be 3D printable and hold twelve to sixteen 18650 batteries. To minimize aircraft’s weight, an actively air-cooled battery pack was chosen to avoid the excess weight of water-cooled and phase change material (PCM) cooled packs. As a result, significant changes were made to remove all metal in the pack and replace it with lower density polymer matrix composites (PMCs) which can be additively manufactured. Two air cooled battery pack configurations (traditional propeller fans & bladeless fans) were designed, modeled, and compared. These packs were first modeled in SolidWorks 2021 3D CAD, then imported into COMSOL MultiPhysics to be studied using the “Heat Transfer in Solids and Fluids” module. The design with the bladeless fans eliminated the need to use high conductivity heavy metal to remove unwanted thermal energy. These bladeless fans were designed entirely out of PMCs. This thermal pack design weighs 0.04 kg less than that of the traditional propeller fans design and has increased the battery pack energy density by 8.25 Wh/kg.

Thermal Management System for Battery Packs

Li-ion Battery Aging with Hybrid Physics-Informed Neural Networks and Fleet-wide Data

In this work, we propose a hybrid model for Li-ion battery discharge and aging prediction that leverages fleet-wide data to predict future capacity drops.The model is built upon an hybrid approach merging physics-based and empirical equations, as well as neural network models in a recurrent neural network cell. The hybrid physics-informed neural network can predict voltage discharge cycles given the loading profile, and estimate the used capacity of the battery under random-loading conditions by tracking aging parameters connected to the residual capacity of the battery. By merging information on the battery aging parameters with existing fleet-wide aging data, the model can predict the future residual capacity of the battery that is being monitored, and therefore enable predictions of voltage discharge curves far ahead in the battery life cycle. We validated the approach using the NASA Prognostics Data Repository Battery data-set, which contains experimental data on Li-ion batteries discharged at random loading conditions in a controlled environment. The approach also allows the identification of discrepancies between the battery aging trend and the trend observed at the fleet level, so that batteries behaving differently from the rest of the fleet can be subject to closer monitoring and further testing to refine predictions.

PINN

Performance of Two Battery Prognostic Applications used by Two Octocopters for Safe Low Altitude Autonomous Flight Operations

This paper addresses the problem of building trust in online predictions of the remaining available flying time for two different electric Unmanned Aerial Vehicles (eUAVs) powered by lithium-ion-polymer batteries. Flight tests for various automation research missions for the two vehicles were monitored using two on-board battery health management applications to make predictions of the remaining flying time (RFT) for each eUAV and to predict the state of the battery. Playback of the voltage, current and temperature profiles of the battery discharge were used to assess the accuracy of the estimation of the voltage and the charge states of the models as well as the estimate of the RFT. The reference ground truth values were the observed landing time and the measured battery pack resting pack voltage 20 minutes after the flight. The predicted RFT, state of charge (SoC), and state of energy (SoE) were compared with the observed results. Noise values of one standard deviation from the mean values of the internal charge states of the battery model during a reference run were used to vary the states during simulation. One application used an equivalent circuit model of the electrical dynamics of the battery pack, and the other application used a reduced-order electrochemistry model. The variation of the model state components was compared to the variation in the estimate of the RFT and the variation in the SoE to estimate a confidence factor. Variation in the estimates caused by factors affecting the off-line laboratory parameter identification experiments is considered. Variation in the estimates due to environmental factors are discussed.

Assurance

Battery Cell Thermal Runaway Calorimeter

We currently have several methods for determining total energy output of an 18650 lithium ion cell. We do not, however, have a good method for determining the fraction of energy that dissipates via conduction through the cell can vs. the energy that is released in the form of ejecta. Knowledge of this fraction informs the design of our models, battery packs, and storage devices; (a) No longer need to assume cell stays together in modeling (b) Increase efficiency of TR mitigation (c) Shave off excess protection.

Darcy, Eric