Lithium-ion batteries exhibit capacity loss as a result of the combined degrading effects of calendaric and cyclic aging. In this study, we quantify the lifetime of large-format (180 Ah) commercial stationary-storage lithium iron phosphate-based lithium-ion cells by performing 1500 cycles of cyclic aging and ca. 850 days of calendaric aging. The aging tests were performed at two different temperatures (35 degrees C and 50 degrees C) to observe the effect of temperature on aging. The calendaric aging cells were stored at two different states of charge (SOC) (100 % and 75 %) to observe the effect of SOC. At the end of aging tests, the capacity loss of all cells at 50 degrees C exceeded those of all cells at 35 degrees C. Temperature was thus identified as major aging driver. The observed global activation energy over all investigated aging protocols was 37.3 kJ/mol. Furthermore, aging modes (loss of lithium inventory and loss of active material) were investigated by differential voltage analysis of the charge-discharge curves; for the cyclic aging cells, this was performed on the cycling data directly. The degradation mode analysis showed that loss of lithium inventory is mainly responsible for capacity loss.

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.

Capacity and internal resistance are key properties of batteries determining energy content and power capability. We present a novel algorithm for estimating the absolute values of capacity and internal resistance from voltage and current data. The algorithm is based on voltage-controlled models. Experimentally-measured voltage is used as an input variable to an equivalent circuit model. The simulation gives current as output, which is compared to the experimentally-measured current. We show that capacity loss and resistance increase lead to characteristic fingerprints in the current output of the simulation. In order to exploit these fingerprints, a theory is developed for calculating capacity and resistance from the difference between simulated and measured current. The findings are cast into an algorithm for operando diagnosis of batteries operated with arbitrary load profiles. The algorithm is demonstrated using cycling data from lithium-ion pouch cells operated on full cycles, shallow cycles, and dynamic cycles typical for electric vehicles. Capacity and internal resistance of a “fresh” cell was estimated with high accuracy (mean absolute errors of 0.9% and 1.8%, respectively). For an “aged” cell, the algorithm required adaptation of the model’s open-circuit voltage curve to obtain high accuracies.

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).

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.

Abstract 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.

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.

A balcony photovoltaic (PV) system, also known as a micro-PV system, is a small PV system consisting of one or two solar modules with an output of 100-600 Wp and a corresponding inverter that uses standard plugs to feed the renewable energy into the house grid. In the present study we demonstrate the integration of a commercial lithium-ion battery into a commercial micro-PV system. We firstly show simulations over one year with one second time resolution which we use to assess the influence of battery and PV size on self-consumption, self-sufficiency and the annual cost savings. We then develop and operate experimental setups using two different architectures for integrating the battery into the micro-PV system. In the passive hybrid architecture, the battery is in parallel electrical connection to the PV module. In the active hybrid architecture, an additional DC-DC converter is used. Both architectures include measures to avoid maximum power point tracking of the battery by the module inverter. Resulting PV/battery/inverter systems with 300 Wp PV and 555 Wh battery were tested in continuous operation over three days under real solar irradiance conditions. Both architectures were able to maintain stable operation and demonstrate the shift of PV energy from the day into the night. System efficiencies were observed comparable to a reference system without battery. This study therefore demonstrates the feasi-bility of both active and passive coupling architectures.

Mathematical modelling and numerical simulation have become standard techniques in Li-ion battery research and development, with the purpose of studying the issues of batteries, including performance and ageing, and consequently increasing the model-based predictability life expectancy. The efficient and fast charging of Li-ion batteries remains a delicate challenge for the automotive industry, being seriously affected by the formation of lithium metal on the surface of the anode during charge. This degradation process, lithium plating, is very damaging for the mechanical and chemical integrity of the battery, which not only sees its capacity lowered but could also incur serious damage and the risk of thermal runaway. It is very difficult to detect lithium plating in situ without a direct observation of the open cell, but it is possible to deduce its presence by analyzing the cell behavior during cycles of charge/discharge in critical conditions and detecting some peculiarities which have been shown to indicate plating. The most common hints are a voltage plateau due to lithium oxidation during discharge at constant temperature and a voltage drop due to re-intercalation of metallic lithium during heating of the cell. On the other hand, the absence of any evidence of changes in voltage should not be considered as proof of evidence of a complete absence of lithium plating. Following our development of a comprehensive modelling and simulation framework for a commercial 0.35 Ah high-power lithium-ion pouch cell with LCO/NCA blend cathode1, here we present an extended pseudo-3D (P3D) model2 in which a lithium plating reaction has been integrated and parameterized. The model is able to describe and predict both the equilibrium potentials and the non-equilibrium kinetics of the competing intercalation and plating reactions for arbitrary macroscopic operating conditions (C-rate, temperature, SOC). A relatively simple and common way to assess plating risk with P2D models is to compare the simulated local anode potential Δφ an with the thermodynamic plating condition of Δφ Li eq = 0 V, but this approach shows several pitfalls that have not been well discussed in literature, including the effects of temperature, pressure and ion concentration on the thermodynamics and kinetics of the plating reaction (see Figure 1a). An extra reaction, simulating explicitly the re-intercalation of the plated lithium, has also been included and can be freely switched on to simulate a case in which the cell is likely not showing macroscopic plating hints. The models allow the creation of operation maps (see Figure 1b) and an accurate spatiotemporal analysis of the competing reactions and lithium plating formation at the electrode-pair scale (1D, mesoscale) and intraparticle scale (1D, microscale) over a wide range of conditions. The governing equations for this model are implemented in an in-house multiphysics software. The electrochemistry model is based on the use of the open-source chemical kinetics code CANTERA, enabling the thermodynamically consistent description of the main and side reactions. To validate our extended model, we simulated and successfully reproduced our own experimental data on our modelling reference cell (0.35 Ah high-power lithium-ion pouch cell with LCO/NCA blend cathode - where no macroscopic plating hints are present) and the published experimental data from Ecker et al.3 (40 Ah high-power lithium-ion pouch cell with NMC cathode - where the plating hints are instead clearly visible). References S. Carelli, M. Quarti, M. C. Yagci and W. G. Bessler, J. Electrochem. Soc., 166(13), A2990-A3003 (2019). S. Carelli and W. G. Bessler, J. Electrochem. Soc., 167(100515) (2020). M. Ecker, Lithium Plating in Lithium-Ion batteries: An experimental and simulation approach, RWTH Aachen University (2016). Figure 1

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.

The accurate diagnosis of state of charge (SOC) and state of health (SOH) is of utmost importance for battery users and for battery manufacturers. State diagnosis is commonly based on measuring battery current and using it in Coulomb counters or as input for a current-controlled model. Here we introduce a new algorithm based on measuring battery voltage and using it as input for a voltage-controlled model. We demonstrate the algorithm using fresh and pre-aged lithium-ion battery single cells operated under well-defined laboratory conditions on full cycles, shallow cycles, and a dynamic battery electric vehicle load profile. We show that both SOC and SOH are accurately estimated using a simple equivalent circuit model. The new algorithm is self-calibrating, is robust with respect to cell aging, allows to estimate SOH from arbitrary load profiles, and is numerically simpler than state-of-the-art model-based methods.

Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.

This dataset contains the research data (code and measurement data) of the journal article: J. A. Braun, R. Behmann, D. Schmider, W. G. Bessler, "State of charge and state of health diagnosis of batteries with voltage-controlled models", Journal of Power Sources 544 (2022), 231828. Abstract: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. Intellectual property information:The Matlab codes and the research data provided here are under CC-BY-NC-4.0 license. Please note that the algorithms themselves are subject to industrial property rights, including, but not necessarily limited to, German patent DE102019127828B4 and international patent application WO2021073690A2. Any use of the codes and algorithms presented here is subject to these property rights. Overview of files:SOC_SOH_simple_model.m: Matlab script performing SOC and SOH diagnosis with the voltage-controlled "simple" equivalent circuit model. The script also reproduces the figures shown in the manuscript. SOC_SOH_simple_extended.m: Matlab script performing SOC and SOH diagnosis with the voltage-controlled "extended" equivalent circuit model. The script also creates figures of additional data not shown in the manuscript. Experimental_data_fresh_cell.csv: Tabulated experimental data (time, current, voltage, temperature) of the long-term experiment (99 h total with 1 s resolution) of a fresh lithium-ion cell. The cell is initally completely discharged. The data consist of full cycling, shallow cycling, and WLTP cycling. Experimental_data_aged_cell.csv: Tabulated experimental data (time, current, voltage, temperature) of the long-term experiment (85 h total with 1 s resolution) of a pre-aged lithium-ion cell. The cell is initally completely discharged. The data consist of full cycling, shallow cycling, and WLTP cycling. OCV_vs_SOC_curve.csv: Tabulated experimentally-derived open-circuit voltage (OCV) as function of state of charge (SOC). 1001 data points between SOC = 0 and SOC = 1 in increments of 0.001. readme.txt: Overview of files with a short description.

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.

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.

Passive hybridization refers to a parallel connection of photovoltaic and battery cells on the direct current level without any active controllers or inverters. We present the first study of a lithium-ion battery cell connected in parallel to a string of four or five serially-connected photovoltaic cells. Experimental investigations were performed using a modified commercial photovoltaic module and a lithium titanate battery pouch cell, representing an overall 41.7 W-peak (photovoltaic)/36.8 W-hour (battery) passive hybrid system. Systematic and detailed monitoring of this system over periods of several days with different load scenarios was carried out. A scaled dynamic synthetic load representing a typical profile of a single-family house was successfully supplied with 100 % self-sufficiency over a period of two days. The system shows dynamic, fully passive self-regulation without maximum power point tracking and without battery management system. The feasibility of a photovoltaic/lithium-ion battery passive hybrid system could therefore be demonstrated.

Simulation of Mechano-Electro-Thermal effects in Lithium-ion-batteries (SiMET) – Funded by the German Research Foundation (DFG) the research training group GRK 2218 “SiMET” bridges scales and disciplines to substantially advance models and experimentally validated simulation methods for improved scientific understanding and accelerated development processes of electrochemical energy storage batteries. More details can be found in the articles of this Special Issue.

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 are 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 the essential information needed for system integration. The study also provides complete and self‐consistent parameter sets for the use in cell models needed for performance prediction or state diagnosis.

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.

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.