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The significant market growth of stationary electrical energy storage systems both for private and commercial applications has raised the question of battery lifetime under practical operation conditions. Here, we present a study of two 8 kWh lithium-ion battery (LIB) systems, each equipped with 14 lithium iron phosphate/graphite (LFP) single cells in different cell configurations. One system was based on a standard configuration with cells connected in series, including a cell-balancing system and a 48 V inverter. The other system featured a novel configuration of two stacks with a parallel connection of seven cells each, no cell-balancing system, and a 4 V inverter. The two systems were operated as part of a microgrid both in continuous cycling mode between 30% and 100% state of charge, and in solar-storage mode with day–night cycling. The aging characteristics in terms of capacity loss and internal resistance change in the cells were determined by disassembling the systems for regular checkups and characterizing the individual cells under well-defined laboratory conditions. As a main result, the two systems showed cell-averaged capacity losses of 18.6% and 21.4% for the serial and parallel configurations, respectively, after 2.5 years of operation with 810 (serial operation) and 881 (parallel operation) cumulated equivalent full cycles. This is significantly higher than the aging of a reference single cell cycled under laboratory conditions at 20 °C, which showed a capacity loss of only 10% after 1000 continuous full cycles.
This article presents a comparative experimental study of the electrical, structural and chemical properties of large‐format, 180 Ah prismatic lithium iron phosphate (LFP)/graphite lithium‐ion battery cells from two different manufacturers. These cells are particularly used in the field of stationary energy storage such as home‐storage systems. The investigations include (1) cell‐to‐cell performance assessment, for which a total of 28 cells was tested from each manufacturer, (2) electrical charge/discharge characteristics at different currents and ambient temperatures, (3) internal cell geometries, components, and weight analysis after cell opening, (4) microstructural analysis of the electrodes via light microscopy and scanning electron microscopy, (5) chemical analysis of the electrode materials using energy‐dispersive X‐ray spectroscopy, and (6) mathematical analysis of the electrode balances. The combined results give a detailed and comparative insight into the cell characteristics, providing essential information needed for system integration. The study also provides complete and self‐consistent parameter sets for the use in cells models needed for performance prediction or state diagnosis.
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.
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.
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.
Mass transfer phenomena in membrane fuel cells are complex and diversified because of the presence of complex transport pathways including porous media of very different pore sizes and possible formation of liquid water. Electrochemical impedance spectroscopy, although allowing valuable information on ohmic phenomena, charge transfer and mass transfer phenomena, may nevertheless appear insufficient below 1 Hz. Use of another variable, that is, back pressure, as an excitation variable for electrochemical pressure impedance spectroscopy is shown here a promising tool for investigations and diagnosis of fuel cells.
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.
Electrochemical pressure impedance spectroscopy (EPIS) has recently been developed as a potential diagnosis tool for polymer electrolyte membrane fuel cells (PEMFC). It is based on analyzing the frequency response of the cell voltage with respect to an excitation of the gas-phase pressure. We present here a combined modeling and experimental study of EPIS. A pseudo-twodimensional PEMFC model was parameterized to a 100 cm2 laboratory cell installed in its test bench, and used to reproduce steady-state cell polarization and electrochemical impedance spectra (EIS). Pressure impedance spectra were obtained both in experiment and simulation by applying a harmonic pressure excitation at the cathode outlet. The model shows good agreement with experimental data for current densities ⩽ 0.4 A cm−2. Here it allows a further simulative analysis of observed EPIS features, including the magnitude and shape of spectra. Key findings include a strong influence of the humidifier gas volume on EPIS and a substantial increase in oxygen partial pressure oscillations towards the channel outlet at the resonance frequency. At current densities ⩾ 0.8 A cm−2 the experimental EIS and EPIS data cannot be fully reproduced. This deviation might be associated with the formation and transport of liquid water, which is not included in the model.
Model-based analysis of Electrochemical Pressure Impedance Spectroscopy (EPIS) for PEM Fuel Cells
(2019)
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, in particular fuel cells, offer an additional observable, that is, the gas pressure. The dynamic coupling of current or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have previously 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. First EPIS experiments on PEM fuel cells have recently been shown [3].
We present a detailed modeling and simulation analysis of EPIS of a PEM fuel cell. We use a 1D+1D continuum model of a fuel/air channel pair with GDL and MEA. Backpressure is dynamically varied, and the resulting simulated oscillation in cell voltage is evaluated to yield the ▁Z_( V⁄p_ca ) EPIS signal. Results are obtained for different transport situations of the fuel cell, giving rise to very complex EPIS shapes in the Nyquist plot. This complexity shows the necessity of model-based interpretation of the complex EPIS shapes. Based on the simulation results, specific features in the EPIS spectra can be assigned to different transport domains (gas channel, GDL, membrane water transport).
Electrochemical pressure impedance spectroscopy (EPIS) is an emerging tool for the diagnosis of polymer electrolyte membrane fuel cells (PEMFC). It is based on analyzing the frequency response of the cell voltage with respect to an excitation of the gas-phase pressure. Several experimental studies in the past decade have shown the complexity of EPIS signals, and so far there is no agreement on the interpretation of EPIS features. The present study contributes to shed light into the physicochemical origin of EPIS features, by using a combination of pseudo-two-dimensional modeling and analytical interpretation. Using static simulations, the contributions of cathode equilibrium potential, cathode overpotential, and membrane resistance on the quasi-static EPIS response are quantified. Using model reduction, the EPIS responses of individual dynamic processes are predicted and compared to the response of the full model. We show that the EPIS signal of the PEMFC studied here is dominated by the humidifier. The signal is further analyzed by using transfer functions between various internal cell states and the outlet pressure excitation. We show that the EPIS response of the humidifier is caused by an oscillating oxygen molar fraction due to an oscillating mass flow rate.
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 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.
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.
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).
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.
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.
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.
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”).
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)
Passive hybridization of battery cell and photovoltaic cell: modeling and experimental validation
(2017)
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.
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].
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.
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.
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.
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.
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.
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.
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.
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)
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.
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.