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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 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.
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.
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.
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.
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.
Oxidation of the nickel electrode is a severe aging mechanism of solid oxide fuel cells (SOFC) and solid oxide electrolyzer cells (SOEC). This work presents a modeling study of safe operating conditions with respect to nickel oxide formation. Microkinetic reaction mechanisms for thermochemical and electrochemical nickel oxidation are integrated into a 2D multiphase model of an anode‐supported solid oxide cell. Local oxidation propensity can be separated into four regimes. Simulations show that the thermochemical pathway generally dominates the electrochemical pathway. As a consequence, as long as fuel utilization is low, cell operation considerably below electrochemical oxidation limit of 0.704 V is possible without the risk of reoxidation.
In this article the high-temperature behavior of a cylindrical lithium iron phosphate/graphite lithium-ion cell is investigated numerically and experimentally by means of differential scanning calorimetry (DSC), accelerating rate calorimetry (ARC), and external short circuit test (ESC). For the simulations a multi-physics multi-scale (1D+1D+1D) model is used. Assuming a two-step electro-/thermochemical SEI formation mechanism, the model is able to qualitatively reproduce experimental data at temperatures up to approx. 200 °C. Model assumptions and parameters could be evaluated via comparison to experimental results, where the three types of experiments (DSC, ARC, ESC) show complementary sensitivities towards model parameters. The results underline that elevated-temperature experiments can be used to identify parameters of the multi-physics model, which then can be used to understand and interpret high-temperature behavior. The resulting model is able to describe nominal charge/discharge operation behavior, long-term calendaric aging behavior, and short-term high-temperature behavior during extreme events, demonstrating the descriptive and predictive capabilities of physicochemical models.
The measurement of the active material volume fraction in composite electrodes of lithium-ion battery cells is difficult due to the small (sub-micrometer) and irregular structure and multi-component composition of the electrodes, particularly in the case of blend electrodes. State-of-the-art experimental methods such as focused ion beam/scanning electron microscopy (FIB/SEM) and subsequent image analysis require expensive equipment and significant expertise. We present here a simple method for identifying active material volume fractions in single-material and blend electrodes, based on the comparison of experimental equilibrium cell voltage curve (open-circuit voltage as function of charge throughput) with active material half-cell potential curves (half-cell potential as function of lithium stoichiometry). The method requires only (i) low-current cycling data of full cells, (ii) cell opening for measurement of electrode thickness and active electrode area, and (iii) literature half-cell potentials of the active materials. Mathematical optimization is used to identify volume fractions and lithium stoichiometry ranges in which the active materials are cycled. The method is particularly useful for model parameterization of either physicochemical (e.g., pseudo-two-dimensional) models or equivalent circuit models, as it yields a self-consistent set of stoichiometric and structural parameters. The method is demonstrated using a commercial LCO–NCA/graphite pouch cell with blend cathode, but can also be applied to other blends (e.g., graphite–silicon anode).
Lithium-ion pouch cells with lithium titanate (Li4Ti5O12, LTO) anode and lithium nickel cobalt aluminum oxide (LiNi0.8Co0.15Al0.05O2, NCA) cathode were investigated experimentally with respect to their electrical (0.1C…4C), thermal (5 °C…50 °C) and long-time cycling behavior. The 16 Ah cell exhibits an asymmetric charge/discharge behavior which leads to a strong capacity-rate effect, as well as a significantly temperature-dependent capacity (0.37 Ah ∙ K−1) which expresses as additional high-temperature feature in the differential voltage plot. The cell was cycled for 10,000 cycles inbetween the nominal voltage limits (1.7–2.7 V) with a symmetric 4C constant-current charge/discharge protocol, corresponding to approx. 3400 equivalent full cycles. A small (0.192 mΩ/1000 cycles) but continuous increase of internal resistance was observed. Using electrochemical impedance spectroscopy (EIS), this could be identified to be caused by the NCA cathode, while the LTO anode showed only minor changes during cycling. The temperature-corrected capacity during 4C cycling exhibited a decrease of 1.28%/1000 cycles. The 1C discharge capacity faded by only 4.0% for CC discharge and 2.3% for CCCV discharge after 10,000 cycles. The cell thus exhibits very good internal-resistance stability and excellent capacity retention even under harsh (4C continuous) cycling, demonstrating the excellent stability of LTO as anode material.
One of the bottlenecks hindering the usage of polymer electrolyte membrane fuel cell technology in automotive applications is the highly load-sensitive degradation of the cell components. The cell failure cases reported in the literature show localized cell component degradation, mainly caused by flow-field dependent non-uniform distribution of reactants. The existing methodologies for diagnostics of localized cell failure are either invasive or require sophisticated and expensive apparatus. In this study, with the help of a multiscale simulation framework, a single polymer electrolyte membrane fuel cell (PEMFC) model is exposed to a standardized drive cycle provided by a system model of a fuel cell car. A 2D multiphysics model of the PEMFC is used to investigate catalyst degradation due to spatio-temporal variations in the fuel cell state variables under the highly transient load cycles. A three-step (extraction, oxidation, and dissolution) model of platinum loss in the cathode catalyst layer is used to investigate the cell performance degradation due to the consequent reduction in the electro-chemical active surface area (ECSA). By using a time-upscaling methodology, we present a comparative prediction of cell end-of-life (EOL) under different driving behavior of New European Driving Cycle (NEDC) and Worldwide Harmonized Light Vehicles Test Cycle (WLTC).
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.
The lifetime and performance of solid-oxide fuel cells (SOFC) and electrolyzer cells (SOEC) can be significantly degraded by oxidation of nickel within the electrode and support structures. This paper documents a detailed computational model describing nickel oxide (NiO) formation as a growing film layer on top of the nickel phase in Ni/YSZ composite electrodes. The model assumes that the oxidation rate is controlled by transport of ions across the film (Wagner's theory). The computational model, which is implemented in a two-dimensional continuum framework, facilitates the investigation of alternative chemical reaction and transport mechanisms. Model predictions agree well with a literature experimental measurement of oxidation-layer growth. In addition to providing insight in interpreting experimental observations, the model provides a quantitative predictive capability for improving electrode design and controlling operating conditions.
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).
Lithium–sulfur (Li/S) cells are promising candidates for a next generation of safe and cost-effective high energy density batteries for mobile and stationary applications. At present, most Li/S cells still suffer from relatively poor cyclability, capacity loss under moderate current densities and self-discharge. Furthermore, the underlying chemical mechanisms of the general discharge/charge behavior as well as Li/S-specific phenomena like the polysulfide shuttle are not yet fully understood. Here we present a thermodynamically consistent, fully reversible continuum model of a Li/S cell with simplified four-step electrochemistry, including a simple description of the polysulfide shuttle effect. The model is parameterized using experimental discharge curves obtained from literature and reproduces behavior at various current densities with fairly high accuracy. While being instructively simple, the presented model can still reproduce distinct macroscopic Li/S-cell features caused by the shuttle effect, e.g., seemingly infinite charging at low charge current densities, and suboptimal coulombic efficiency. The irreversible transport of active material from the cathode to the anode results in a voltage drop and capacity loss during cycling, which can also be observed experimentally.
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.
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.
Nickel cobalt aluminum oxide (NCA) based lithium-ion battery electrodes exhibit a distinct asymmetry in discharge/charge behavior towards high bulk stoichiometry (low state of charge). We show that basic electrochemical relationships, that is, the Nernst equation and the Butler-Volmer equation, are able to reproduce this behavior when a two-step reaction mechanism is assumed. The two-step mechanism consists of (1) lithium-ion adsorption from the electrolyte onto the active material particle surface under electron transfer, and (2) intercalation of surface-adsorbed lithium atoms into the bulk material. The asymmetry of experimental half-cell data of an NCA electrode cycled at 0.1 C-rate can be quantitatively reproduced with this simple model. The model parameters show two alternative solutions, predicting either a saturated (highly-covered) or a depleted surface for high bulk lithiation.