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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.
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 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 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.
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.
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.
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.
Lithium-ion battery cells exhibit a complex and nonlinear coupling of thermal, electrochemical,and mechanical behavior. In order to increase insight into these processes, we report the development of a pseudo-three-dimensional (P3D) thermo-electro-mechanical model of a commercial lithium-ion pouch cell with graphite negative electrode and lithium nickel cobalt aluminum oxide/lithium cobalt oxide blend positive electrode. Nonlinear molar volumes of the active materials as function of lithium stoichiometry are taken from literature and implemented into the open-source software Cantera for convenient coupling to battery simulation codes. The model is parameterized and validated using electrical, thermal and thickness measurements over a wide range of C-rates from 0.05 C to 10 C. The combined experimental and simulated analyses show that thickness change during cycling is dominated by intercalation-induced swelling of graphite, while swelling of the two blend components partially cancel each other. At C-rates above 2 C, electrochemistry-induced temperature increase significantly contributes to cell swelling due to thermal expansion. The thickness changes are nonlinearly distributed over the thickness of the electrode pair due to gradients in the local lithiation, which may accelerate local degradation. Remaining discrepancies between simulation and experiment at high C-rates might be attributed to lithium plating, which is not considered in the model at present.
Silicon (Si) has turned out to be a promising active material for next‐generation lithium‐ion battery anodes. Nevertheless, the issues known from Si as electrode material (pulverization effects, volume change etc.) are impeding the development of Si anodes to reach market maturity. In this study, we are investigating a possible application of Si anodes in low‐power printed electronic applications. Tailored Si inks are produced and the impact of carbon coating on the printability and their electrochemical behavior as printed Si anodes is investigated. The printed Si anodes contain active material loadings that are practical for powering printed electronic devices, like electrolyte gated transistors, and are able to show high capacity retentions. A capacity of 1754 mAh/gSi is achieved for a printed Si anode after 100 cycles. Additionally, the direct applicability of the printed Si anodes is shown by successfully powering an ink‐jet printed transistor.
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.
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.
The formation of secondary phases in the porous electrodes is a severe mechanism affecting the lifetime of solid oxide fuel cells (SOFC). It can occur via various chemical mechanisms and it has a significant influence on cell performance due to pore clogging and deactivation of active surfaces and triple-phase boundary (TPB). We present a modeling and simulation study of nickel oxide formation (reoxidation) and carbon formation (coking) within the SOFC anode. We use a 2D continuum model based on a multi-phase framework [Neidhardt et al., J. Electrochem. Soc., 159, 9 (2012)] that allows the introduction of arbitrary solid phases (here: Ni, YSZ, NiO, Carbon) plus gas phase. Reactions between the bulk phases are modeled via interface-adsorbed species and are described by an elementary kinetic approach. Published experimental data are used for parameterization and validation. Simulations allow the prediction of cell performance under critical operation conditions, like (i) a non-fuel operation test, where NiO formation is taking place (Figure 1a), or (ii) an open circuit voltage (OCV) stability test under hydrocarbon atmosphere, where solid carbon is formed (Figure 1b). Results are applied for enhanced interpretation of experimental data and for prediction of safe operation conditions.
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).
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.
Simulation-based degradation assessment of lithium-ion batteries in a hybrid electric vehicle
(2017)
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.
Compact solid discharge products enable energy storage devices with high gravimetric and volumetric energy densities, but solid deposits on active surfaces can disturb charge transport and induce mechanical stress. In this Letter, we develop a nanoscale continuum model for the growth of Li2O2 crystals in lithium–oxygen batteries with organic electrolytes, based on a theory of electrochemical nonequilibrium thermodynamics originally applied to Li-ion batteries. As in the case of lithium insertion in phase-separating LiFePO4 nanoparticles, the theory predicts a transition from complex to uniform morphologies of Li2O2 with increasing current. Discrete particle growth at low discharge rates becomes suppressed at high rates, resulting in a film of electronically insulating Li2O2 that limits cell performance. We predict that the transition between these surface growth modes occurs at current densities close to the exchange current density of the cathode reaction, consistent with experimental observations.
In the dual membrane fuel cell (DM-Cell), protons formed at the anode and oxygen ions formed at the cathode migrate through their respective dense electrolytes to react and form water in a porous composite layer called dual membrane (DM). The DM-Cell concept was experimentally proven (as detailed in Part I of this paper). To describe the electrochemical processes occurring in this novel fuel cell, a mathematical model has been developed which focuses on the DM as the characteristic feature of the DM-Cell. In the model, the porous composite DM is treated as a continuum medium characterized by effective macro-homogeneous properties. To simulate the polarization behavior of the DM-Cell, the potential distribution in the DM is related to the flux of protons and oxygen ions in the conducting phases by introducing kinetic and transport equations into charge balances. Since water pressure may affect the overall formation rate, water mass balances across the DM and transport equations are also considered. The satisfactory comparison with available experimental results suggests that the model provides sound indications on the effects of key design parameters and operating conditions on cell behavior and performance.
Pressure dynamics in metal-oxygen (metal-air) batteries: a case study on sodium superoxide cells
(2014)
Electrochemical reactions in metal–oxygen batteries come along with the consumption or release of gaseous oxygen. We present a novel methodology for investigating electrode reactions and transport phenomena in metal–oxygen batteries by measuring the pressure dynamics in an enclosed gas reservoir above the oxygen electrode. The methodology is exemplified by a room-temperature sodium–oxygen battery forming sodium superoxide (NaO2) in an electrolyte of diethylene glycol dimethyl ether (diglyme) and sodium trifluoromethanesulfonate (NaOSO2CF3, NaOTf). The experiments are supported by microkinetic simulations with a one-dimensional multiphysics continuum model. During galvanostatic cycling over 30 cycles, a constant oxygen consumption/release rate is observed upon discharge/charge. The number of transferred electrons per oxygen molecule is calculated to 1.01 ± 0.02 and 1.03 ± 0.02 for discharge and charge, respectively, confirming the nature of the oxygen reaction product as superoxide O2–. The same ratio is observed in cyclic voltammetry experiments with low scan rate (<1 mV/s). However, at higher scan rates, the ratio increases as a result of oxygen transport limitations in the electrolyte. We introduce electrochemical pressure impedance spectroscopy (EPIS) for simultaneously analyzing current, voltage, and pressure of electrochemical cells. Pressure recording significantly increases the sensitivity of impedance toward oxygen transport properties of the porous electrode systems. In addition, we report experimental data on the diffusion coefficient and solubility of oxygen in electrolyte solutions as important parameters for the microkinetic models.
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.
In this paper we present a model of the discharge of a lithium–oxygen battery with aqueous electrolyte. Lithium–oxygen batteries (Li–O2) have recently received great attention due to their large theoretical specific energy. Advantages of the aqueous design include the stability of the electrolyte, the long experience with gas diffusion electrodes (GDEs), and the solubility of the reaction product lithium hydroxide. However, competitive specific energies can only be obtained if the product is allowed to precipitate. Here we present a dynamic one-dimensional model of a Li–O2 battery including a GDE and precipitation of lithium hydroxide. The model is parameterized using experimental data from the literature. We demonstrate that GDEs remove power limitations due to slow oxygen transport in solutions and that lithium hydroxide tends to precipitate on the anode side. We discuss the system architecture to engineer where nucleation and growth predominantly occurs and to optimize for discharge capacity.
Die Erfindung betrifft eine Photovoltaik-Stromversorgungsvorrichtung, insbesondere vom öffentlichen Stromnetz unabhängige Photovoltaik-Stromversorgungsvorrichtung, mit einem positiven (204) und einem negativen (206) Lastanschluss für den Anschluss einer elektrischen Last, mit einer Mehrzahl von photovoltaischen Zellen (104) und einer wiederaufladbaren Batterie (5), welche wenigstens zwei in Serie geschaltete Batteriezellen (112) umfasst. Nach der Erfindung sind die photovoltaischen Zellen (104) zu einer der Anzahl der Batteriezellen (112) entsprechenden Anzahl von seriell verbundenen Teilstrings (108) verschaltet und jeder Teilstring (108) ist mit einem positiven Teilstringanschluss mit einem Pluspol und mit einem negativen Teilstringanschluss mit einem Minuspol einer zugeordneten Batteriezelle (112) oder mehreren zugeordneten parallel geschalteten Batteriezellen (112) verbunden. Dabei kann jeder Teilstring (108) zwischen dem positiven und negativen Teilstringanschluss eine maximale Leerlaufspannung erzeugen, die kleiner oder gleich einer vorgegebenen Ladeschlussspannung der zugeordneten Batteriezelle (112) oder der zugeordneten parallel geschalteten Batteriezellen (112) ist. Weiterhin betrifft die Erfindung eine Schaltungsanordnung zum Laden einer wiederaufladbaren Batterie, die zur Realisierung einer derartigen Photovoltaik-Stromversorgungsvorrichtung geeignet ist.
Proton Exchange Membrane Fuel Cells (PEMFC) are energy efficient and environmentally friendly alternatives to conventional energy conversion systems in many yet emerging applications. In order to enable prediction of their performance and durability, it is crucial to gain a deeper understanding of the relevant operation phenomena, e.g., electrochemistry, transport phenomena, thermodynamics as well as the mechanisms leading to the degradation of cell components. Achieving the goal of providing predictive tools to model PEMFC performance, durability and degradation is a challenging task requiring the development of detailed and realistic models reaching from the atomic/molecular scale over the meso scale of structures and materials up to components, stack and system level. In addition an appropriate way of coupling the different scales is required.
This review provides a comprehensive overview of the state of the art in modeling of PEMFC, covering all relevant scales from atomistic up to system level as well as the coupling between these scales. Furthermore, it focuses on the modeling of PEMFC degradation mechanisms and on the coupling between performance and degradation models.
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.
Passive hybridization of battery cell and photovoltaic cell: modeling and experimental validation
(2017)
On the Fundamental and Practical Aspects of Modeling Complex Electrochemical Kinetics and Transport
(2018)
Numerous technologies, such as batteries and fuel cells, depend on electrochemical kinetics. In some cases, the responsible electrochemistry and charged-species transport is complex. However, to date, there are essentially no general-purpose modeling capabilities that facilitate the incorporation of thermodynamic, kinetic, and transport complexities into the simulation of electrochemical processes. A vast majority of the modeling literature uses only a few (often only one) global charge-transfer reactions, with the rates expressed using Butler–Volmer approximations. The objective of the present paper is to identify common aspects of electrochemistry, seeking a foundational basis for designing and implementing software with general applicability across a wide range of materials sets and applications. The development of new technologies should be accelerated and improved by enabling the incorporation of electrochemical complexity (e.g., multi-step, elementary charge-transfer reactions and as well as supporting ionic and electronic transport) into the analysis and interpretation of scientific results. The spirit of the approach is analogous to the role that Chemkin has played in homogeneous chemistry modeling, especially combustion. The Cantera software, which already has some electrochemistry capabilities, forms the foundation for future capabilities expansion.
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–oxygen cells with nonaqueous electrolyte show high overpotentials during charge, indicating asymmetric charge/discharge reaction mechanisms. We present a kinetic modeling and simulation study of the lithium–oxygen cell cycling behavior. The model includes a multistep reaction mechanism of the cell reaction (2Li + O2 ⇄ Li2O2) forming lithium peroxide by precipitation, coupled to a 1D porous-electrode transport model. We apply the model to study the asymmetric discharge/charge characteristics and analyze the influence of a redox mediator dissolved homogeneously in the liquid electrolyte. Model predictions are compared to experimental galvanostatic cycling data of cells without and with 2,2,6,6-tetramethylpiperidinyloxyl (TEMPO) as redox mediator. The predicted discharge behavior shows good agreement with the experimental results. A spatiotemporal analysis of species concentrations reveals inhomogeneous distributions of dissolved oxygen and reaction products within the cathode during discharge. The experimentally observed charge overpotentials as well as their reduction by using a redox mediator can be qualitatively reproduced with a partially irreversible reaction mechanism. However, the proposed models fail to reproduce the particular shape of the experimental charge curve with continuously increasing charge overpotential, which implies that part of the reaction mechanism is still open for investigation in future work.
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)
Lithium‐ion battery cells are multiscale and multiphysics systems. Design and material parameters influence the macroscopically observable cell performance in a complex and nonlinear way. Herein, the development and application of three methodologies for model‐based interpretation and visualization of these influences are presented: 1) deconvolution of overpotential contributions, including ohmic, concentration, and activation overpotentials of the various cell components; 2) partial electrochemical impedance spectroscopy, allowing a direct visualization of the origin of different impedance features; and 3) sensitivity analyses, allowing a systematic assessment of the influence of cell parameters on capacity, internal resistance, and impedance. The methods are applied to a previously developed and validated pseudo‐3D model of a high‐power lithium‐ion pouch cell. The cell features a blend cathode. The two blend components show strong coupling, which can be observed and interpreted using the results of overpotential deconvolution, partial impedance spectroscopy, and sensitivity analysis. The presented methods are useful tools for model‐supported lithium‐ion cell research and development.
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.
Modelling detailed chemistry in lithium-ion batteries: Insight into performance, ageing and safety
(2018)
Combined heat and power production (CHP) based on solid oxide fuel cells (SOFC) is a very promising technology to achieve high electrical efficiency to cover power demand by decentralized production. This paper presents a dynamic quasi 2D model of an SOFC system which consists of stack and balance of plant and includes thermal coupling between the single components. The model is implemented in Modelica® and validated with experimental data for the stack UI-characteristic and the thermal behavior. The good agreement between experimental and simulation results demonstrates the validity of the model. Different operating conditions and system configurations are tested, increasing the net electrical efficiency to 57% by implementing an anode offgas recycle rate of 65%. A sensitivity analysis of characteristic values of the system like fuel utilization, oxygen-to-carbon ratio and electrical efficiency for different natural gas compositions is carried out. The result shows that a control strategy adapted to variable natural gas composition and its energy content should be developed in order to optimize the operation of the system.
Modeling and Simulation the Influence of Solid Carbon Formation on SOFC Performance and Degradation
(2013)
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.
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.
Battery degradation is a complex physicochemical process that strongly depends on operating conditions. We present a model-based analysis of lithium-ion battery degradation in a stationary photovoltaic battery system. We use a multi-scale multi-physics model of a graphite/lithium iron phosphate (LiFePO4, LFP) cell including solid electrolyte interphase (SEI) formation. The cell-level model is dynamically coupled to a system-level model consisting of photovoltaics (PV), inverter, load, grid interaction, and energy management system, fed with historic weather data. Simulations are carried out for two load scenarios, a single-family house and an office tract, over annual operation cycles with one-minute time resolution. As key result, we show that the charging process causes a peak in degradation rate due to electrochemical charge overpotentials. The main drivers for cell ageing are therefore not only a high state of charge (SOC), but the charging process leading towards high SOC. We also show that the load situation not only influences system parameters like self-sufficiency and self-consumption, but also has a significant impact on battery ageing. We assess reduced charge cut-off voltage as ageing mitigation strategy.
Battery degradation is a complex physicochemical process that strongly depends on operating conditions and environment. We present a model-based analysis of lithium-ion battery degradation in smart microgrids, in particular, a single-family house and an office tract with photovoltaics generator. We use a multi-scale multi-physics model of a graphite/lithium iron phosphate (LiFePO4, LFP) cell including SEI formation as ageing mechanism. The cell-level model is dynamically coupled to a system-level model consisting of photovoltaics, inverter, power consumption profiles, grid interaction, and energy management system, fed with historic weather data. The behavior of the cell in terms of degradation propensity, performance, state of charge and other internal states is predicted over an annual operation cycle. As result, we have identified a peak in degradation rate during the battery charging process, caused by charging overpotentials. Ageing strongly depends on the load situation, where the predicted annual capacity fade is 1.9 % for the single-family house and only 1.3 % for the office tract.