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A two-dimensional single-phase model is developed for the steady-state and transient analysis of polymer electrolyte membrane fuel cells (PEMFC). Based on diluted and concentrated solution theories, viscous flow is introduced into a phenomenological multi-component modeling framework in the membrane. Characteristic variables related to the water uptake are discussed. A Butler–Volmer formulation of the current-overpotential relationship is developed based on an elementary mechanism of electrochemical oxygen reduction. Validated by using published V–I experiments, the model is then used to analyze the effects of operating conditions on current output and water management, especially net water transport coefficient along the channel. For a power PEMFC, the long-channel configuration is helpful for internal humidification and anode water removal, operating in counterflow mode with proper gas flow rate and humidity. In time domain, a typical transient process with closed anode is also investigated.
The state-of-the-art electrochemical impedance spectroscopy (EIS) calculations have not yet started from fully multi-dimensional modeling. For a polymer electrolyte membrane fuel cell (PEMFC) with long flow channel, the impedance plot shows a multi-arc characteristic and some impedance arcs could merge. By using a step excitation/Fourier transform algorithm, an EIS simulation is implemented for the first time based on the full 2D PEMFC model presented in the first part of this work. All the dominant transient behaviors are able to be captured. A novel methodology called ‘configuration of system dynamics’, which is suitable for any electrochemical system, is then developed to resolve the physical meaning of the impedance spectra. In addition to the high-frequency arc due to charge transfer, the Nyquist plots contain additional medium/low-frequency arcs due to mass transfer in the diffusion layers and along the channel, as well as a low-frequency arc resulting from water transport in the membrane. In some case, the impedance spectra appear partly inductive due to water transport, which demonstrates the complexity of the water management of PEMFCs and the necessity of physics-based calculations.
A balcony photovoltaic (PV) system, also known as a micro-PV system, is a small PV system consisting of one or two solar modules with an output of 100–600 Wp and a corresponding inverter that uses standard plugs to feed the renewable energy into the house grid. In the present study we demonstrate the integration of a commercial lithium-ion battery into a commercial micro-PV system. We firstly show simulations over one year with one second time resolution which we use to assess the influence of battery and PV size on self-consumption, self-sufficiency and the annual cost savings. We then develop and operate experimental setups using two different architectures for integrating the battery into the micro-PV system. In the passive hybrid architecture, the battery is in parallel electrical connection to the PV module. In the active hybrid architecture, an additional DC-DC converter is used. Both architectures include measures to avoid maximum power point tracking of the battery by the module inverter. Resulting PV/battery/inverter systems with 300 Wp PV and 555 Wh battery were tested in continuous operation over three days under real solar irradiance conditions. Both architectures were able to maintain stable operation and demonstrate the shift of PV energy from the day into the night. System efficiencies were observed comparable to a reference system without battery. This study therefore demonstrates the feasibility of both active and passive coupling architectures.
Ziel der Investitionsmaßnahme Enerlab 4.0 war die Bereitstellung einer umfangreichen in-operando und post-mortem Diagnostik für dezentrale Energieerzeuger und -Speicher, z. B. Batteriezellen und Photovoltaikzellen. Diese sind wichtige Komponenten für verschiedene Bereiche der Industrie 4.0 – von autonomen Sensoren über energieautarke Produktion bis hin zur Qualitätskontrolle. Zu diesem Zweck wurde die apparative Ausstattung der Hochschule Offenburg erweitert, und zwar sowohl für in-operando Diagnostik (elektrische Zyklierer, Impedanzspektrometer, Temperaturprüfschränke) als auch für post-mortem Diagnostik (Glovebox, Probenpräparationen für vorhandene Werkstoffanalytik und chemische Analytik). Be-reits vorhandene Geräte aus anderen laufenden oder abgeschlossenen Projekten wurden in die neue Infrastruktur integriert. Im Ergebnis entstand ein modernes und leistungsfähiges Batterie- und Photovoltaiklabor, welches in zahlreichen laufenden und neuen Vorhaben genutzt wird.
Die Erfindung betrifft ein Verfahren und eine Vorrichtung zur Bestimmung des Ladezustandes (SOC) einer aufladbaren Batterie (106) eines vorgegebenen Batterietyps oder eines damit in einem physikalischen Zusammenhang stehenden Parameters, insbesondere einer in der Batterie enthaltenen Restladungsmenge Q, wobei das Verfahren mittels eines spannungsgeführten Batteriemodells (102) arbeitet, welches für die betreffende Batterie (106) oder einen entsprechenden Batterietyp parametriert wird. Es muss lediglich die Batteriespannung Umess gemessen und dem Batteriemodell (102) als Eingangsgröße zur Verfügung gestellt werden. Weiterhin betrifft die Erfindung ein Verfahren und eine Vorrichtung zur Bestimmung des Gesundheitszustandes (SOH) einer Batterie (102), wobei das Batteriemodell (102), das auch zur Bestimmung des SOC verwendet wird, einen modellierten Batteriestrom Imodliefert. Aus diesem können modellierte Ladungsmengen während Lade- und Entladephasen der Batterie (106) bestimmt und mit gemessenen Ladungsmengen, die aus dem gemessenen Batteriestrom Imessbestimmt werden, verglichen werden. Da das Batteriemodell (102) nicht altert, kann hierdurch der SOH der Batterie bestimmt werden.
Im Batterielabor der Hochschule Offenburg wurde ein neues Verfahren zur Bestimmung von Ladezustand und Gesundheitszustand von Lithium-Ionen-Batterien entwickelt. Es beruht auf der Auswertung von Spannungs- und Strommessungen mit einem mathematischen Batteriemodell. Das Verfahren ist genauer und robuster als Standardverfahren, die auf Ladungszählung beruhen. Zudem ist es numerisch einfacher umzusetzen als andere modellbasierte Verfahren. Wir demonstrieren die Methode mit einer Heimspeicherzelle und einer Elektrofahrzeugzelle.
Die Erfindung betrifft ein Verfahren und eine Vorrichtung zur Bestimmung des Ladezustandes (SOC) einer aufladbaren Batterie (106) eines vorgegebenen Batterietyps oder eines damit in einem physikalischen Zusammenhang stehenden Parameters, insbesondere einer in der Batterie enthaltenen Restladungsmenge Q, wobei das Verfahren mittels eines spannungsgeführten Batteriemodells (102) arbeitet, welches für die betreffende Batterie (106) oder einen entsprechenden Batterietyp parametriert wird. Es muss lediglich die Batteriespannung Umess gemessen und dem Batteriemodell (102) als Eingangsgröße zur Verfügung gestellt werden. Weiterhin betrifft die Erfindung ein Verfahren und eine Vorrichtung zur Bestimmung des Gesundheitszustandes (SOH) einer Batterie (102), wobei das Batteriemodell (102), das auch zur Bestimmung des SOC verwendet wird, einen modellierten Batteriestrom Imodliefert. Aus diesem können modellierte Ladungsmengen während Lade- und Entladephasen der Batterie (106) bestimmt und mit gemessenen Ladungsmengen, die aus dem gemessenen Batteriestrom Imessbestimmt werden, verglichen werden. Da das Batteriemodell (102) nicht altert, kann hierdurch der SOH der Batterie bestimmt werden.
The invention relates to a method and to a device for determining the state of charge (SOC) of a rechargeable battery (106) of a specified battery type or a parameter physically related thereto, in particular a remaining charge amount Q contained in the battery, the method operating by means of a voltage-controlled battery model (102), which is parameterized for the battery (106) in question or a corresponding battery type. It is merely necessary to measure the battery voltage Umess and to provide said battery voltage to the battery model (102) as an input variable. The invention further relates to a method and to a device for determining the state of health (SOH) of a battery (102), wherein the battery model (102) also used to determine the SOC provides a modeled battery current Imod. Modeled charge amounts during charging and discharging phases of the battery (106) can be determined from said modeled battery current and can be compared with measured charge amounts, which are determined from the measured battery current Imess. Because the battery model (102) does not age, the SOH of the battery can thereby be determined.
Ziel des Projekts STABIL war die Vorhersage der Alterung und Verbesserung der Lebensdauer von mobilen und stationären Lithium-Ionen-Batterien. Batterien sind zentrale Komponenten der Elektromobilität und der stationären Speicherung von regenerativem Strom. Die im Stand der Technik unzureichende Lebensdauer der Batterie ist heute wesentlicher Kostentreiber. Im Projekt wurde daher in einem skalenübergreifenden und interdisziplinären Ansatz das Verhalten von einzelnen Batteriezellen und ganzen Batteriesystemen unter zwei unterschiedlichen systemischen Randbedingungen untersucht.
Ziel des LiBaLu-Teilprojekts Modellierung und Simulation war die Unterstützung der Elektroden- und Zellentwicklung mit Hilfe umfangreicher Computersimulationen im Sinne des computergestützten Engineering (CAE). Zwei verschiedene Schwerpunkte standen im Mittelpunkt der Untersuchungen. Zum einen wurde das mechanistische Verständnis der komplexen Elektrochemie in Lithium-Luftbatterien durch mikrokinetische Modelle aufgeklärt. Auf Basis von postulierten Mehrschrittmechanismen wurden makroskopische Eigenschaften (Entlade-/Ladekennlinien, Zyklovoltammogramme) vorhergesagt und mit experimentellen Daten der Projektpartner verglichen. Zum anderen wurde das Design der Prototypzelle mit Hilfe numerischer Simulationen untersucht und optimiert. So konnten z. B. optimale Schichtdicken oder die Rolle von Gastransportlimitierungen identifiziert werden.
Fast charging of lithium-ion batteries remains one of the most delicate challenges for the automotive industry, being seriously affected by the formation of lithium metal in the negative electrode. Here we present a physicochemical pseudo-3D model that explicitly includes the plating reaction as side reaction running in parallel to the main intercalation reaction. The thermodynamics of the plating reaction are modeled depending on temperature and ion concentration, which differs from the often-used assumption of a constant plating condition of 0 V anode potential. The reaction kinetics are described with an Arrhenius-type rate law parameterized from an extensive literature research. Re-intercalation of plated lithium was modeled to take place either via reverse plating (solution-mediated) or via an explicit interfacial reaction (surface-mediated). At low temperatures not only the main processes (intercalation and solid-state diffusion) become slow, but also the plating reaction itself becomes slower. Using this model, we are able to predict typical macroscopic experimental observables that are indicative of plating, that is, a voltage plateau during discharge and a voltage drop upon temperature increase. A spatiotemporal analysis of the internal cell states allows a quantitative insight into the competition between intercalation and plating. Finally, we calculate operation maps over a wide range of C-rates and temperatures that allow to assess plating propensity as function of operating condition.
Passive hybridization refers to a parallel connection of photovoltaic and battery cells on the direct current level without any active controllers or inverters. We present the first study of a lithium-ion battery cell connected in parallel to a string of four or five serially-connected photovoltaic cells. Experimental investigations were performed using a modified commercial photovoltaic module and a lithium titanate battery pouch cell, representing an overall 41.7 W-peak (photovoltaic)/36.8 W-hour (battery) passive hybrid system. Systematic and detailed monitoring of this system over periods of several days with different load scenarios was carried out. A scaled dynamic synthetic load representing a typical profile of a single-family house was successfully supplied with 100 % self-sufficiency over a period of two days. The system shows dynamic, fully passive self-regulation without maximum power point tracking and without battery management system. The feasibility of a photovoltaic/lithium-ion battery passive hybrid system could therefore be demonstrated.
Simulation-based degradation assessment of lithium-ion batteries in a hybrid electric vehicle
(2017)
Batteries typically consist of multiple individual cells connected in series. Here we demonstrate single-cell state of charge (SOC) and state of health (SOH) diagnosis in a 24 V class lithium-ion battery. To this goal, we introduce and apply a novel, highly efficient algorithm based on a voltage-controlled model (VCM). The battery, consisting of eight single cells, is cycled over a duration of five months under a simple cycling protocol between 20 % and 100 % SOC. The cell-to-cell standard deviations obtained with the novel algorithm were 1.25 SOC-% and 1.07 SOH-% at beginning of cycling. A cell-averaged capacity loss of 9.9 % after five months cycling was observed. While the accuracy of single-cell SOC estimation was limited (probably owed to the flat voltage characteristics of the lithium iron phosphate, LFP, chemistry investigated here), single-cell SOH estimation showed a high accuracy (2.09 SOH-% mean absolute error compared to laboratory reference tests). Because the algorithm does not require observers, filters, or neural networks, it is computationally very efficient (three seconds analysis time for the complete data set consisting of eight cells with approx. 780.000 measurement points per cell).
The accurate diagnosis of state of charge (SOC) and state of health (SOH) is of utmost importance for battery users and for battery manufacturers. State diagnosis is commonly based on measuring battery current and using it in Coulomb counters or as input for a current-controlled model. Here we introduce a new algorithm based on measuring battery voltage and using it as input for a voltage-controlled model. We demonstrate the algorithm using fresh and pre-aged lithium-ion battery single cells operated under well-defined laboratory conditions on full cycles, shallow cycles, and a dynamic battery electric vehicle load profile. We show that both SOC and SOH are accurately estimated using a simple equivalent circuit model. The new algorithm is self-calibrating, is robust with respect to cell aging, allows to estimate SOH from arbitrary load profiles, and is numerically simpler than state-of-the-art model-based methods.
Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.
Lithium-ion batteries exhibit slow voltage dynamics on the minute time scale that are usually associated with transport processes. We present a novel modelling approach toward these dynamics by combining physical and data-driven models into a Grey-box model. We use neural networks, in particular neural ordinary differential equations. The physical structure of the Grey-box model is borrowed from the Fickian diffusion law, where the transport domain is discretized using finite volumes. Within this physical structure, unknown parameters (diffusion coefficient, diffusion length, discretization) and dependencies (state of charge, lithium concentration) are replaced by neural networks and learnable parameters. We perform model-to-model comparisons, using as training data (a) a Fickian diffusion process, (b) a Warburg element, and (c) a resistor-capacitor circuit. Voltage dynamics during constant-current operation and pulse tests as well as electrochemical impedance spectra are simulated. The slow dynamics of all three physical models in the order of ten to 30 min are well captured by the Grey-box model, demonstrating the flexibility of the present approach.
Grey-box modelling combines physical and data-driven models to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling, as differential equations given by physical laws and neural networks can be combined in a single modelling framework. This simplifies the simulation and optimization and allows to consider irregularly-sampled data during training and evaluation of the model. We demonstrate this approach using two levels of model complexity; first, a simple parallel resistor-capacitor circuit; and second, an equivalent circuit model of a lithium-ion battery cell, where the change of the voltage drop over the resistor-capacitor circuit including its dependence on current and State-of-Charge is implemented as NODE. After training, both models show good agreement with analytical solutions respectively with experimental data.
Lithium-ion batteries show strongly nonlinear behaviour regarding the battery current and state of charge. Therefore, the modelling of lithium-ion batteries is complex. Combining physical and data-driven models in a grey-box model can simplify the modelling. Our focus is on using neural networks, especially neural ordinary differential equations, for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis for the grey-box model. Unknown parameters and dependencies are then replaced by learnable parameters and neural networks. We use experimental full-cycle data and data from pulse tests of a lithium iron phosphate cell to train the model. Finally, we test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.
The lifetime of a battery is affected by various aging processes happening at the electrode scale and causing capacity and power fade over time. Two of the most critical mechanisms are the deposition of metallic lithium (plating) and the loss of lithium inventory to the solid electrolyte interphase (SEI). These side reactions compete with reversible lithium intercalation at the graphite anode. Here we present a comprehensive physicochemical pseudo-3D aging model for a lithium-ion battery cell, which includes electrochemical reactions for SEI formation on graphite anode, lithium plating, and SEI formation on plated lithium. The thermodynamics of the aging reactions are modeled depending on temperature and ion concentration, and the reactions kinetics are described with an Arrhenius-type rate law. The model includes also the positive feedback of plating on SEI growth, with the presence of plated lithium leading to a higher SEI formation rate compared to the values obtained in its absence at the same operating conditions. The model is thus able to describe cell aging over a wide range of temperatures and C-rates. In particular, it allows to quantify capacity loss due to cycling (here in % per year) as function of operating conditions. This allows the visualization of aging colormaps as function of both temperature and C-rate and the identification of critical operation conditions, a fundamental step for a comprehensive understanding of batteries performance and behavior. For example, the model predicts that at the harshest conditions (< –5 °C, > 3 C), aging is reduced compared to most critical conditions (around 0–5 °C) because the cell cannot be fully charged.
This article presents the development, parameterization, and experimental validation of a pseudo-three-dimensional (P3D) multiphysics aging model of a 500 mAh high-energy lithium-ion pouch cell with graphite negative electrode and lithium nickel manganese cobalt oxide (NMC) positive electrode. This model includes electrochemical reactions for solid electrolyte interphase (SEI) formation at the graphite negative electrode, lithium plating, and SEI formation on plated lithium. The thermodynamics of the aging reactions are modeled depending on temperature and ion concentration and the reactions kinetics are described with an Arrhenius-type rate law. Good agreement of model predictions with galvanostatic charge/discharge measurements and electrochemical impedance spectroscopy is observed over a wide range of operating conditions. The model allows to quantify capacity loss due to cycling near beginning-of-life as function of operating conditions and the visualization of aging colormaps as function of both temperature and C-rate (0.05 to 2 C charge and discharge, −20 °C to 60 °C). The model predictions are also qualitatively verified through voltage relaxation, cell expansion and cell cycling measurements. Based on this full model, six different aging indicators for determination of the limits of fast charging are derived from post-processing simulations of a reduced, pseudo-two-dimensional isothermal model without aging mechanisms. The most successful aging indicator, compared to results from the full model, is based on combined lithium plating and SEI kinetics calculated from battery states available in the reduced model. This methodology is applicable to standard pseudo-two-dimensional models available today both commercially and as open source.
This article presents the development, parameterization, and experimental validation of a pseudo-three-dimensional (P3D) multiphysics model of a 350 mAh high-power lithium-ion pouch cell with graphite anode and lithium cobalt oxide/lithium nickel cobalt aluminum oxide (LCO/NCA) blend cathode. The model describes transport processes on three different scales: Heat transport on the macroscopic scale (cell), mass and charge transport on the mesoscopic scale (electrode pair), and mass transport on the microscopic scale (active material particles). A generalized description of electrochemistry in blend electrodes is developed, using the open-source software Cantera for calculating species source terms. Very good agreement of model predictions with galvanostatic charge/discharge measurements, electrochemical impedance spectroscopy, and surface temperature measurements is observed over a wide range of operating conditions (0.05C to 10C charge and discharge, 5°C to 35°C). The behavior of internal states (concentrations, potentials, temperatures) is discussed. The blend materials show a complex behavior with both intra-particle and inter-particle non-equilibria during cycling.
Aqueous lithium–oxygen batteries are promising candidates for electric energy storage. In this paper we present and discuss a multiphase continuum model of an aqueous lithium–oxygen single cell including reactions and transport in a porous gas diffusion electrode (GDE). The model is parameterized using in-house half-cell experiments and available literature data on aqueous electrolytes. We validate our transport model with cyclic voltammetry and electrochemical impedance spectroscopy measurements over a wide range of temperatures (25, 40, 55 °C) and electrolyte concentrations (0.1–2 M). We observe very good agreement between simulations and measurements during oxygen reduction conditions. A sensitivity analysis of the validated model demonstrates the influence of the porous structure on GDE performance and gives directions for the future development of electrodes.
Seven cell design concepts for aqueous (alkaline) lithium–oxygen batteries are investigated using a multi-physics continuum model for predicting cell behavior and performance in terms of the specific energy and specific power. Two different silver-based cathode designs (a gas diffusion electrode and a flooded cathode) and three different separator designs (a porous separator, a stirred separator chamber, and a redox-flow separator) are compared. Cathode and separator thicknesses are varied over a wide range (50 μm–20 mm) in order to identify optimum configurations. All designs show a considerable capacity-rate effect due to spatiotemporally inhomogeneous precipitation of solid discharge product LiOH·H2O. In addition, a cell design with flooded cathode and redox-flow separator including oxygen uptake within the external tank is suggested. For this design, the model predicts specific power up to 33 W/kg and specific energy up to 570 Wh/kg (gravimetric values of discharged cell including all cell components and catholyte except housing and piping).
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products (e.g., fuel cells, metal/air cells, electrolyzers) offer an additional observable, that is, the gas pressure. The dynamic coupling of current and/or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have introduced the term electrochemical pressure impedance spectroscopy (EPIS) [1,2]. EPIS shows a particular sensitivity towards transport processes of gas-phase or dissolved species, in particular, diffusion coefficients and transport pathway lengths. It is as such complementary to standard EIS, which is mainly sensitive towards electrochemical processes. This sensitivity can be exploited for model parameterization and validation. A general analysis of EPIS is presented, which shows the necessity of model-based interpretation of the complex EPIS shapes in the Nyquist plot (cf. Figure). We then present EPIS simulations for two different electrochemical cells: (1) a sodium/oxygen battery cell and (2) a hydrogen/air fuel cell. We use 1D or 2D electrochemical and transport models to simulate current excitation/pressure detection or pressure excitation/voltage detection. The results are compared to first EPIS experimental data available in literature [2,3].
The DMFC is a promising option for backup power systems and for the power supply of portable devices. However, from the modeling point of view liquid-feed DMFC are challenging systems due to the complex electrochemistry, the inherent two-phase transport and the effect of methanol crossover. In this paper we present a physical 1D cell model to describe the relevant processes for DMFC performance ranging from electrochemistry on the surface of the catalyst up to transport on the cell level. A two-phase flow model is implemented describing the transport in gas diffusion layer and catalyst layer at the anode side. Electrochemistry is described by elementary steps for the reactions occurring at anode and cathode, including adsorbed intermediate species on the platinum and ruthenium surfaces. Furthermore, a detailed membrane model including methanol crossover is employed. The model is validated using polarization curves, methanol crossover measurements and impedance spectra. It permits to analyze both steady-state and transient behavior with a high level of predictive capabilities. Steady-state simulations are used to investigate the open circuit voltage as well as the overpotentials of anode, cathode and electrolyte. Finally, the transient behavior after current interruption is studied in detail.
Passive hybridization of battery cell and photovoltaic cell: modeling and experimental validation
(2017)
Modelling detailed chemistry in lithium-ion batteries: Insight into performance, ageing and safety
(2018)
Lithium-ion batteries show a complex thermo-electrochemical performance and aging behavior. This paper presents a modeling and simulation framework that is able to describe both multi-scale heat and mass transport and complex electrochemical reaction mechanisms. The transport model is based on a 1D + 1D + 1D (pseudo-3D or P3D) multi-scale approach for intra-particle lithium diffusion, electrode-pair mass and charge transport, and cell-level heat transport, coupled via boundary conditions and homogenization approaches. The electrochemistry model is based on the use of the open-source chemical kinetics code CANTERA, allowing flexible multi-phase electrochemistry to describe both main and side reactions such as SEI formation. A model of gas-phase pressure buildup inside the cell upon aging is added. We parameterize the model to reflect the performance and aging behavior of a lithium iron phosphate (LiFePO4, LFP)/graphite (LiC6) 26650 battery cell. Performance (0.1–10 C discharge/charge at 25, 40 and 60°C) and calendaric aging experimental data (500 days at 30°C and 45°C and different SOC) from literature can be successfully reproduced. The predicted internal cell states (concentrations, potential, temperature, pressure, internal resistances) are shown and discussed. The model is able to capture the nonlinear feedback between performance, aging, and temperature.
Muli-scale thermos-electrochemical modelling of aging mechanisms in an LFP/graphite lithium-ion cell
(2017)
We present an electrochemical model of a lithium iron phosphate/graphite (LFP/C6) cell that includes combined aging mechanisms: (i) Electrochemical formation of the solid electrolyte interphase (SEI) at the anode, leading to loss of lithium inventory, (ii) breaking of the SEI due to volume changes of the graphite particles, causing accelerated SEI growth, and (iii) loss of active material due to of loss percolation of the liquid electrolyte resulting from electrode dry-out. The latter requires the introduction of an activity-saturation relationship. A time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours). The combined modeling and simulation framework is able to predict calendaric and cyclic aging up to the end of life of the battery cells. The aging parameters are adjusted to match literature calendaric and cyclic aging experiments, resulting in quantitative agreement of simulated nonlinear capacity loss with experimental data. The model predicts and provides an interpretation for the dependence of capacity loss on temperature, cycling depth, and average SOC. The introduction of a percolation threshold in the activity-saturation relationship allows to capture the strong nonlinearity of aging toward end of life (“sudden death”).
One of the practical bottlenecks associated with commercialization of lithium-air cells is the choice of an appropriate electrolyte that provides the required combination of cell performance, cyclability and safety. With the help of a two-dimensional multiphysics model, we attempt to narrow down the electrolyte choice by providing insights into the effect of the transport properties of electrolyte, electrode saturation (flooded versus gas diffusion), and electrode thickness on a single discharge performance of a lithium-air button cell cathode for five different electrolytes including water, ionic liquid, carbonate, ether, and sulfoxide. The 2D distribution of local current density and concentrations of electrochemically active species (O2 and Li+) in the cathode is also discussed w.r.t electrode saturation. Furthermore, the efficacy of species transport in the cathode is quantified by introducing two parameters, firstly, a transport efficiency that gives local insight into the distribution of mass transfer losses, and secondly, an active electrode volume that gives global insight into the cathode volume utilization at different current densities. A detailed discussion is presented toward understanding the design-induced performance limitations in a Li-air button cell prototype.
Modeling and simulation play a key role in analyzing the complex electrochemical behavior of lithium-ion batteries. We present the development of a thermodynamic and kinetic modeling framework for intercalation electrochemistry within the open-source software Cantera. Instead of using equilibrium potentials and single-step Butler-Volmer kinetics, Cantera is based on molar thermodynamic data and mass-action kinetics, providing a physically-based and flexible means for complex reaction pathways. Herein, we introduce a new thermodynamic class for intercalation materials into the open-source software. We discuss the derivation of molar thermodynamic data from experimental half-cell potentials, and provide practical guidelines. We then demonstrate the new class using a single-particle model of a lithium cobalt oxide/graphite lithium-ion cell, implemented in MATLAB. With the present extensions, Cantera provides a platform for the lithium-ion battery modeling community both for consistent thermodynamic and kinetic models and for exchanging the required thermodynamic and kinetic parameters. We provide the full MATLAB code and parameter files as supplementary material to this article.
Practical bottlenecks associated with commercialization of Lithium-air cells include capacity limitation and low cycling efficiency. The origin of such losses can be traced to complex electrochemical side reactions and reactant mass transport losses[1]. The efforts to minimize such losses include exploration of various electrolytes with additives[2], and cell component geometry and material design. Given the wide range of options for such materials, it is almost impractical to experimentally setup and characterize all those cells. Consequently, modeling and simulation studies are efficient alternatives to analyze spatially and temporally resolved cell behavior for various combinations of materials[3]. In this study, with the help of a two-dimensional multi physics model, we have focused on the effect of electrode and electrolyte interaction (electrochemistry), choice of electrolyte (species transport), and electrode geometry (electrode design) on the performance of a lithium-air button cell. Figure1a shows the schematics of the 2D axisymmetric computational domain. A comparative analysis of five different electrolytes was performed while focusing on the 2D distribution of local current density and the concentration of electro-chemically active species in the cell, that is, O2and Li+. Using two different cathode configurations, namely, flooded electrode and gas diffusion electrode (GDE)[4] at different cathode thickness, the effect of cell geometry and electrolyte saturation on cell performance was explored. Further, a detailed discussion on electrode volume utilization (cf. Figure1b) is presented via changes in the active volume of cathode that produces 90% of the total current with the cell current density for different combinations of electrolyte saturations and cathode thickness.
The durability of polymer electrolyte membrane fuel cells (PEMFC) is governed by a nonlinear coupling between system demand, component behavior, and physicochemical degradation mechanisms, occurring on timescales from the sub-second to the thousand-hour. We present a simulation methodology for assessing performance and durability of a PEMFC under automotive driving cycles. The simulation framework consists of (a) a fuel cell car model converting velocity to cell power demand, (b) a 2D multiphysics cell model, (c) a flexible degradation library template that can accommodate physically-based component-wise degradation mechanisms, and (d) a time-upscaling methodology for extrapolating degradation during a representative load cycle to multiple cycles. The computational framework describes three different time scales, (1) sub-second timescale of electrochemistry, (2) minute-timescale of driving cycles, and (3) thousand-hour-timescale of cell ageing. We demonstrate an exemplary PEMFC durability analysis due to membrane degradation under a highly transient loading of the New European Driving Cycle (NEDC).
Simulation-based degradation assessment of lithium-ion batteries in a hybrid electric vehicle
(2017)
The insufficient lifetime of lithium-ion batteries is one of the major cost driver for mobile applications. The battery pack in vehicles is one of the most expensive single components that practically must be excluded from premature replacement (i.e., before the life span of the other components end). Battery degradation is a complex physicochemical process that strongly depends on operating condition and environment. We present a simulation-based analysis of lithium-ion battery degradation during operation with a standard PHEV test cycle. We use detailed multiphysics (extended Newman-type) cell models that allow the assessment of local electrochemical potential, species and temperature distributions as driving forces for degradation, including solid electrolyte interphase (SEI) formation [1]. Fig. 1 shows an exemplary test cycle and the predicted resulting spatially-averaged SEI formation rate. We apply a time-upscaling approach to extrapolate the degradation analysis over long time scales, keeping physical accuracy while allowing end-of-life assessment [2]. Results are presented for lithium-ion battery cells with graphite/LFP chemistry. The behavior of these cells in terms of degradation propensity, performance, state of charge and other internal states is predicted during long-term cycling. State of health (SOH) is quantified as capacity fade and internal resistance increase as function of operation time.
Lithium-ion batteries exhibit a well-known trade-off between energy and power, which is problematic for electric vehicles which require both high energy during discharge (high driving range) and high power during charge (fast-charge capability). We use two commercial lithium-ion cells (high-energy [HE] and high-power) to parameterize and validate physicochemical pseudo-two-dimensional models. In a systematic virtual design study, we vary electrode thicknesses, cell temperature, and the type of charging protocol. We are able to show that low anode potentials during charge, inducing lithium plating and cell aging, can be effectively avoided either by using high temperatures or by using a constant-current/constant-potential/constant-voltage charge protocol which includes a constant anode potential phase. We introduce and quantify a specific charging power as the ratio of discharged energy (at slow discharge) and required charging time (at a fast charge). This value is shown to exhibit a distinct optimum with respect to electrode thickness. At 35°C, the optimum was achieved using an HE electrode design, yielding 23.8 Wh/(min L) volumetric charging power at 15.2 min charging time (10% to 80% state of charge) and 517 Wh/L discharge energy density. By analyzing the various overpotential contributions, we were able to show that electrolyte transport losses are dominantly responsible for the insufficient charge and discharge performance of cells with very thick electrodes.