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Three-dimensional performance and lifetime model for lithium-ion batteries -spatially-resolved models are required for accurate simulation of large-sized cells!
Abstract
Performance, safety and lifetime of Li-ion batteries are closely connected topics, which are strongly influenced by electrical and thermal inhomogeneities occurring during operation inside the system. These inhomogeneities might impact large-sized automotive cells over complete life cycles significantly; however current lifetime models are not able to consider these effects. This work introduces a new spatially-resolved lifetime modeling concept for Li-ion batteries consisting of a spatially-resolved thermo-electrical model and a semi-empirical ageing model for more accurate performance and lifetime simulation of large-sized cells. Simulations carried out for cylindrical cell types show significant thermal and electrical gradients between inner and outer cell, which force a strongly inhomogeneous degradation of the cell’s active mass. This yields a redistribution of currents and impedance with increasing lifetime. Lifetime prognosis carried out on the new modeling approach points out its advantages for large-sized cell simulation towards conventional one-node models.
... A higher temperature for example causes a faster aging and therefore a faster increase in the inner resistance, affecting the electrical performance of the battery. These relations have been investigated in [10] but lacking a profound parameterization of the developed model using aging test results. This work will focus on the parameterization of the aging model by experimental data using extended aging test results. ...
For a reliable integration of batteries into the vehicle, knowledge about battery behavior and especially the lifetime of the battery in the application is indispensible. This work aims at the development of a lifetime prediction approach based on an aging model for lithium-ion batteries. Extended accelerated lifetime tests are performed at different temperatures and states of charge (SOC) to investigate the impact of these conditions on the impedance rise and capacity loss. The results are used to find mathematical expressions describing the impact of storage time, temperature and voltage on aging, to build up a model coupling an impedance-based electric-thermal part with a semi-empirical (physically motivated) aging model. Based on these models different drive cycles, use patterns and management strategies can be analyzed with regard to their impact on the lifetime. This is an important tool for vehicle designers and for the implementation of business models. The strength of this paper is the good data basis and the detailed modeling approach.
... A higher temperature for example causes a faster aging and therefore a faster increase in the inner resistance, affecting the electrical performance of the battery. These relations have been investigated in [13] but lacking a profound parameterization of the developed model using aging test results. This work will focus on the parameterization of the aging model by experimental data using extended aging test results. ...
Battery lifetime prognosis is a key requirement for successful market introduction of electric and hybrid vehicles. This work aims at the development of a lifetime prediction approach based on an aging model for lithium-ion batteries. A multivariable analysis of a detailed series of accelerated lifetime experiments representing typical operating conditions in hybrid electric vehicle is presented. The impact of temperature and state of charge on impedance rise and capacity loss is quantified. The investigations are based on a high-power NMC/graphite lithium-ion battery with good cycle lifetime. The resulting mathematical functions are physically motivated by the occurring aging effects and are used for the parameterization of a semi-empirical aging model. An impedance-based electric-thermal model is coupled to the aging model to simulate the dynamic interaction between aging of the battery and the thermal as well as electric behavior. Based on these models different drive cycles and management strategies can be analyzed with regard to their impact on lifetime. It is an important tool for vehicle designers and for the implementation of business models. A key contribution of the paper is the parameterization of the aging model by experimental data, while aging simulation in the literature usually lacks a robust empirical foundation.
In this work, a physico-chemically motivated impedance-based and real-time capable lithium-ion battery model is introduced and parametrized according to cells from a Tesla Model S. The work is divided into three parts. In the first part, electrochemical properties of the cell are derived. The second part describes the deduction of a generic electrical and thermal model. Both models form the foundation of the so-called ISEAFrame, a simulation framework for energy storage systems. Three test cases for the simulation framework are discussed in the third part.
In the first part, experiments on automotive cells of a Tesla Model S were conducted. A car module was disassembled and several hundred lithium-ion cells were extracted. A cell tear-down analysis was performed to investigate single components. From the active materials, several half-cells were constructed and electrochemically tested. It was found that one major factor affecting the relaxation behavior of the full-cell was instigated by the negative electrode. The relaxation is assumed to be caused by redistribution of lithium inside the graphitic electrode caused by potential differences between particles. Further experiments were conducted on the full-cells. 27 cells were connected in parallel and slowly charged and discharged to better understand the voltage response of parallel-connected cells. During the experiment, current and voltage of each specimen were logged. It could be shown that the change of voltage (dV/dQ) in the batteries was the main influencer for the redistribution of currents.
The second part focuses on modelling the electro-thermal behavior of batteries. An implementation of a generic electrical and thermal model was derived and implemented in C++. The model is capable to be executed on real-time systems. The electrical model is an input-/output-based model. The current is used as input and voltage, heat and other internal states are used as output. The model consists of a time-variant differential-algebraic system that is linearized in each time step. The electrical network is based on lumped parameters and can be represented by a unidirectional and acyclic graph (tree). The parameters of the network can be varied according to the behavior of the battery and are dependent on state of charge, temperature as well as other states. From the tree representation, the Kirchhoff equations are derived. These equations form the basis of a state-space model that describes physical and chemical processes by means of a voltage response. In addition to the real-time capable C++ model, a transcoder has been developed that translates a single simulation scenario from an intermediate representation into other target languages such as Matlab or Simulink. The thermal model is input-/output-driven as well. Heat is treated as the input and temperature is the output. The heat is fed in by the electrical model and conducted over a set of finite volumes that are representing the battery and its cooling. The temperature is fed back to the electrical network and thus modifying the electrical network’s elements.
In the last part, three different test cases are discussed. The three test cases are exploring the capabilities of the developed simulation framework and its limitations. First of all, an in-depth look is taken at the half-cell graphite anode against lithium. Several relaxation measurements are simulated and compared to the experimental results of the first part of this work. In the second part, simulations of the full-cell are compared to experiments at different states of charge and different temperatures. Finally, a simulation of the whole Tesla Model S module is compared to experiments that have been conducted.
The developed simulation framework has been published and can be accessed via https://github.com/FHust/ISEAFramework.
The technical and commercial success of hybrid-electric vehicles (HEV) and plug-in hybrid-electric vehicles (PHEV) is strongly related to the security, cost and lifetime of the traction battery. Energy and power performances of Li-ion systems are impacted during ageing with a reduction of capacity and an increase of internal impedance. Ageing phenomena occurring in Li-ion batteries are the consequences of combined effect of cycling current, temperature and state-of-charge (SOC). Temperature is one of the most important factors conditioning power performances and ageing of the battery systems. Thermal effects occurring inside cylindrical cells have to be considered in OD battery models for security issues and cycle life optimization through minimization of ageing mechanisms. Most of Li-ion ageing mechanisms have been experimentally identified and described in literature. Ageing models developed in literature generally consider the classical Solid Electrolyte Interphase (SEI)s growth mechanism occurring at the negative carbonaceous electrode. On the one hand, high order pseudo-ID electrochemical models are predictive and reproduce in a good way the evolutions of capacity and power loss during ageing. On the other hand, OD semi-empirical ageing models require lots of experimental data for calibration and are most of the time not predictive with respect to various operating conditions during cycle life of the battery systems. It is then clear that advances in modeling are required to account for physics-based ageing kinetics in zero-dimensional electro-thermal models. In this work, an original OD single electrode electrochemical model taking into account the ageing mechanism of negative electrode surface layer growth via electrolyte diffusion is developed and coupled with a OD impedance-based electro-thermal model. Physics-based first correlations between capacity decrease and impedance increase is proposed. Calibration and validation of the full OD coupled model are pe- - rformed on experimental data for a commercial cylindrical LiFePO4/Carbone 2.3 Ah cell. The ageing model is then used to discuss impact of temperature and State-Of-Charge on PHEV duty cycles.
In future car concepts, namely hybrid electric vehicles (HEV) and full electric vehicles (EV), the battery
system will be stressed more than in conventional car concepts. Especially the thermal stress will be very
high. Since temperature has a strong impact on battery performance and ageing, a detailed knowledge
about the thermal properties and the temperature depending on the load profiles is necessary. Hence,
thermal measurements and simulation models are essential for development and design of future storage
systems. Current thermal models mostly only consider the complete battery, although a battery system is
often affected by its weakest point, e.g. thermal hotspots and inhomogeneities. For a better understanding
of the battery a new model approach has been developed: a combined thermal and electrical model with a
high spatial resolution. Since Lithium-ion batteries are the most promising technology the model has been
developed for a cylindrical Li-ion cell type, but the general model approach also covers other battery
technologies and geometries. By means of simulation it is shown that a combined thermo-electrical
battery model is suitable to display the interaction between thermal and electrical properties inside a
battery.
The passivating solid electrolyte interphase (SEI) layer forms at the surface of the negative-electrode active material in
lithium-ion cells. A continuum-scale mathematical model has been developed to simulate the growth of the SEI and transport
of lithium and electrons through the film. The model is used to estimate the film growth rate, film resistance, and irreversible
capacity loss due to film formation. We show that film growth at the negative electrode is faster for charged batteries than
for uncharged batteries and that higher electron mobility in the film leads to faster growth. If electron mobility is low,
the rate of film growth is limited by transport of electrons through the film, and the rate decreases as the thickness increases.
We examine the dependence of film resistance upon both film thickness and defect concentration in the film. We also show that
the concentration polarization in the film increases as it grows at open circuit, even though the concentration gradient may
decrease. © 2004 The Electrochemical Society. All rights reserved.
This paper presents a systematic approach to employ electrochemical impedance spectroscopy for determining model structure and parameters of a simulation model for a VRLA battery. It focuses on the interpretation of the impedance data in terms of equivalent circuit models and describes the Matlab/Simulink implementation of the model as well as its time-domain verification. Furthermore, the advantages and limits of the impedance-based model as well as the possible simplifications are discussed.
Different types of commercially available electrochemical double layer capacitors (EDLCs) were analysed in accelerated ageing tests by impedance spectroscopy. From these measurements the parameters of an impedance model were determined. The characteristic change of the impedance parameters is discussed and an ageing model for EDLCs is developed.
The authors develop two-dimensional and three-dimensional simulation codes of the transient response of the temperature distribution in the lithium ion secondary battery during a discharge cycle. At first, a two-dimensional simulation code for a cylindrical battery is developed, and the simulation results for a commercially available small size battery are compared with the corresponding experimental results. The simulation results of the transient temperature and voltage variations coincide very well with the experimental results. The simulation result of the temperature difference between the center of the battery body and the center of the battery side is also in reasonable agreement with the experimental result. Next, the authors develop a three-dimensional simulation code and perform numerical simulations for three large size prismatic batteries with the same capacity and different cross sectional shapes. It is made clear that selecting the battery with the laminated cross section has a remarkable effect on the suppression of the temperature rise in comparison with the battery with square cross section, whereas the effect of the lamination on the suppression of the temperature unevenness is unexpectedly small. These results indicate the accuracy and usefulness of the developed simulation codes.
This paper reports a modeling approach for the scale-up of a lithium-ion polymer battery (LIPB). A comparison of the experimental discharge curves with the modeling results confirmed that the parameters used to model a small-scale LIPB could be applied to a large-scale LIPB provided the materials and composition of the electrodes as well as the processes for manufacturing the batteries were the same. The potential and current-density distribution on the electrodes of a LIPB were predicted as a function of the discharge time using the finite element method. In addition, the temperature distributions of the LIPB were calculated based on the modeling results of the potential and current-density distributions. The temperature distributions from the model were in good agreement with the experimental measurements.
Some of the aging mechanisms occurring in Li ion batteries, either on rest or on cycling, are described from long-term storage or cycling data. Generally, the most critical part of the cell is the negative electrode/electrolyte interface. Stability of the solid electrolyte interface (SEI), more generally of the passivating layer, must be insured by proper material choice and additives. Excessive growth induces with time a capacity loss corresponding to the lithium corrosion, and a reduction of power capability of the electrode, from the active surface area degradation. In a worst case, reduction of charge rate capability may lead to local lithium plating during cycling, strongly aggravating the capacity fading. When the SEI is correctly built, with low electronic conductivity, the negative electrode stability can be very stable, as described by long-term aging (more than 4 years) at higher temperature than ambient. Vinylen carbonate is confirmed as outstanding additive. At elevated temperature, high SOC induces side reactions at the positive interface, involving electrolyte components oxidation. The results are an increase of cell impedance, and possible slow CO2 evolution. Presence of lithium carbonate greatly enhanced the gas formation. The observed impedance increase indicates a reduction of the active surface area, in agreement with solid deposit. When properly designed with an appropriate choice of active materials and electrolyte, the Li ion system can provide a very long service.
Extended cycle- and calendar-life testing of lithium-ion cells has shown the effect of aluminum concentration in the cathode on the area-specific impedance versus time behavior of the cell. In cells with a LiNi0.8Co0.15Al0.05O2 (5% Al) cathode, the change in mechanism from t1/2 to t occurred at about 35 weeks. Increasing the aluminum concentration to 10% (LiNi0.8Co0.1Al0.1O2) delayed the change for, approximately, an additional 30 weeks. The factors affecting the rate of increase during the parabolic and linear portions of the curve depended on cathode composition and particle size. The difference in the time it took for the change in mechanism was related to the cathode composition.
Lithium-ion cells with 5-Ah capacity were fabricated using a spinel
as a cathode active material, graphitized carbon as an anode active material, and 1 M
as an electrolyte. In order to improve the calendar life of the cell, we investigated the degradation mechanism by measuring
the thickness of the solid electrolyte interphase (SEI) on anode active material. The SEI thickness was measured by focused
ion beam, scanning electron microscope, and X-ray photoelectron spectroscopy. The thickness of the SEI was initially
, and after storage for 392 days at 25 and 40°C, the thickness was 0.15 and
, respectively. The capacity decreased with increase in the thickness of SEI, because Li in the cell is consumed by forming
SEI. The amount of Li consumption was estimated theoretically assuming that SEI is formed by a reaction between intercalated
Li and the electrolyte in SEI on the negative carbon surface, and a diffusion of the electrolyte in the SEI is the rate-determining
step of the reaction. The theoretical equation showed a good agreement with experimental capacity fade at 25, 40, and 60°C
for the storing days up to 380 days. A voltage decrease of the cell after 1-s at 20 A of discharge current was measured to
estimate roughly the increase of the cell internal resistance during storage. The increase of SEI resistance was estimated
by the theoretical equation and compared with the experimental voltage drop data after 1-s discharge. However, the theoretical
data was not in a good agreement with the experimental data. The reason is that the charge-transfer resistance on the anode
also increases during storage. Another reason is the resistance change of the cathode during the storage.
The potential and current density distribution on the electrodes of a lithium-polymer battery were studied by using the finite element method. The effect of the configuration of the electrodes such as the aspect ratio of the electrodes and the size and placing of current collecting tabs as well as the discharge rates on the battery performance was examined to enhance the uniformity of the utilization of the active material of electrodes. The results showed that the aspect ratio of the electrodes and the size and placing of current collecting tabs have a significant effect on the potential and current density distribution on the electrodes to influence the distribution of the depth of discharge on the electrodes, thus affecting the uniform utilization of the active material of electrodes.
A series of cylindrical 18650 lithium-ion cells with an MAG-10|1.2 M LiPF6 ethylene carbonate (EC):ethyl methyl carbonate (EMC) (w:w=3:7)|LixNi0.8Co0.15Al0.05O2 configuration were made and tested for power-assist hybrid electric vehicle (HEV) applications under various aging conditions of temperature and state-of-charge (SOC). The cells were intermittently characterized for changes in power capability, rate capacity, and impedance as aging progressed. The changes of these properties with temperature, as depicted by Arrhenius equations, were analyzed. We found that the degradation in power and capacity fade seems to relate to the impedance increase in the cell. The degradation follows a multi-stage process. The initial stage of degradation has an activation energy of the order of 50–55 kJ/mol, as derived from power fade and C1 capacity fade measured at C/1 rate. In addition, microcalorimetry was performed on two separate unaged cells at 80% SOC at various temperatures to measure static heat generation in the cells. We found that the static heat generation has an activation energy of the order of 48–55 kJ/mol, similar to those derived from power and C1 capacity fade. The correspondence in the magnitude of the activation energy suggests that the power and C1 capacity fades were related to the changes of the impedance in the cells, most likely via the same fading mechanism. The fading mechanism seemed to be related to the static heat generation of the cell.
The rechargeable lithium-ion battery has been extensively used in mobile communication and portable instruments due to its many advantages, such as high volumetric and gravimetric energy density and low self-discharge rate. In addition, it is the most promising candidate as the power source for (hybrid) electric vehicles and stationary energy storage. For these applications in durable equipment, the long-term cycling and storage behaviour becomes of increasing interest. In this paper, the mechanisms of lithium-ion battery ageing are reviewed and evaluated.
Impedance spectroscopy is a promising tool for the modeling and diagnosis of industrial batteries. This paper discusses methodological questions connected with the measurement and interpretation of the impedance of such batteries, especially nonlinearity, voltage drift, stability, reproducibility, half-cell measurements, model structure and parameter extraction with respect to quantities like state of charge (SOC). On the basis of this discussion, a specialized impedance spectroscope for industrial batteries has been developed, as well as modifications of the standard electrochemical impedance spectroscopy (EIS) algorithm. A mini-cycle technique is suggested that gains additional information compared to classical measurements with continuous dc current offset. Impedance spectra from lead/acid batteries for different dc currents, SOCs, and temperatures are presented and analyzed. Reference-electrode measurements allow for separation of the half-cell impedances. Emphasis is placed on the limits of experimental reproducibility due to “history” of the battery.
To handle the complexity of modern automotive power nets, simulation-based design methods are important and suitable models of all system components including the battery as a main part are therefore mandatory. However, simulation models of energy storage devices are difficult to obtain. In particular, batteries are time-variant and strongly non-linear. An impedance-based modeling approach has been applied that copes with these characteristics and offers the development and parameterization of powerful models covering a wide dynamic range. As an example, this paper outlines the development of a NiMH battery model. Besides the impedance-based part of the model, the influences of the typical hysteresis effect of NiMH batteries is described in detail and an empirical modeling approach is introduced. The presented model is already successfully used by an automotive manufacturer which reflects the applicability of the modeling approach.
To understand further the thermal abuse behavior of large format Li-ion batteries for automotive applications, the one-dimensional modeling approach formulated by Hatchard et al. [T.D. Hatchard, D.D. MacNeil, A. Basu, J.R. Dahn, J. Electrochem. Soc. 148(7) (2001) A755–A761] was reproduced. Then it was extended to three dimensions so we could consider the geometrical features, which are critical in large cells for automotive applications. The three-dimensional model captures the shapes and dimensions of cell components and the spatial distributions of materials and temperatures, and is used to simulate oven tests, and to determine how a local hot spot can propagate through the cell. In simulations of oven abuse testing of cells with cobalt oxide cathode and graphite anode with standard LiPF6 electrolyte, the three-dimensional model predicts that thermal runaway will occur sooner or later than the lumped model, depending on the size of the cell. The model results showed that smaller cells reject heat faster than larger cells; this may prevent them from going into thermal runaway under identical abuse conditions. In simulations of local hot spots inside a large cylindrical cell, the three-dimensional model predicts that the reactions initially propagate in the azimuthal and longitudinal directions to form a hollow cylinder-shaped reaction zone.
In this work, the long term calendar life of lithium ion cells for satellite and standby applications has been studied in experiments where the capacity evolution is tracked as a function of storage temperature. Cells containing either LiCoO2 and LiNixMyO2 positives coupled with a graphite negative were float charged at 3.8 or 3.9 V. This study focused on losses at the negative electrode and the data were fit to a model which involved a rate-determining step governed by electronic conductivity of the solid electrolyte interphase (SEI) layer, following Arrhenius’ law as a function of temperature. When nickel-based positives are used, a “lithium reserve” exists on the negative and this property enhances the calendar life for long life applications.
Test results and life modeling of special calendar- and cycle-life tests conducted on 18650-size generation 1 lithium-ion battery cells were presented. The test consisted of a once per day discharge and charge pulse, which was designed to produce minimal impact on the cell but yet establish its performance over a period of time. Results indicated that the discharge and regen resistances increased non-linearly as a function of the test time. The magnitude of the resistances depended on the temperature and states-of-change at which the test was conducted.
Inhomogeneous temperature and current distribution in lithium-ion batteries -Analysis based on a coupled thermo-electrical simulation model, 8th AABC
- J B Gerschler
- J Kowal
- D U Sauer
J. B. Gerschler, J. Kowal, D. U. Sauer. Inhomogeneous
temperature and current distribution in lithium-ion batteries -Analysis based on a coupled thermo-electrical simulation model,
8th AABC, Tampa (FL), USA, 12.-16.5.2008.
Impedance-Based Loss Calculation and Thermal Modeling of Electrochemical Energy Storage Devices for Design Considerations of Automotive Power Systems
- D Linzen
D. Linzen. Impedance-Based Loss Calculation and Thermal
Modeling of Electrochemical Energy Storage Devices for Design
Considerations of Automotive Power Systems, PhD thesis,
RWTH Aachen University, December 2005
Calculation of Spatially-Resolved Impedance -Using Lead-Acid as Example
- J Kowal
J. Kowal. Calculation of Spatially-Resolved Impedance -Using Lead-Acid as Example, PhD thesis, RWTH Aachen
University, June 2010
Mathematical modeling of the capacity fade of Li-ion cells
Mathematical modeling of the capacity fade of Li-ion cells, J.
Power Sources 123 (2003), 230 -240
Solid Diffusion Model for Ageing of Lithium-Ion Batteries
- H J Ploehn
- P Ramadass
- R E White
H. J. Ploehn, P. Ramadass, R. E. White. Solid Diffusion
Model for Ageing of Lithium-Ion Batteries, J. Electrochem. Soc.
151 (3), 2004, A456 -A462
RWTH Aachen University Email: friedrich.hust@isea.rwth-aachen.de Friedrich Hust studies industrial engineering with his major in Electrical Power Engineering at the RWTH Aachen University
- Cand
- Wirt
Cand. Wirt.-Ing. Friedrich Hust
Institute for Power Electronics and Electrical
Drives (ISEA), RWTH Aachen University
Email: friedrich.hust@isea.rwth-aachen.de
Friedrich Hust studies industrial engineering
with his major in Electrical Power
Engineering at the RWTH Aachen
University. Since 2008 he is working as a
student assistant at the ISEA.