A zero-gap full cell for alkaline water electrolysis is equipped with two reference electrodes. The anode (NiO mesh), the cathode (Ni mesh), and the diaphragm are investigated simultaneously by analyzing the polarization curves and utilizing electrochemical impedance spectroscopy (EIS) and distribution of relaxation times (DRT) analysis. The shares of cell voltage are 44 % of the cathode, 23 % of the anode and 33 % of the diaphragm at 0.4 A/cm2. EIS and DRT analysis focus particularly on the diaphragm, revealing a complex behavior that cannot be described merely as an ohmic resistor as it is traditionally done. EIS shows that the total resistance of the diaphragm comprises an ohmic contribution and a polarization behavior. This behavior is attributed to a funnel effect of OH-ions through the diaphragm. The effect results in a change in the concentration profile near the diaphragm, leading to concentration polarization. To gain deeper insights, two equivalent circuit models with a focus on the diaphragm are developed to describe the behavior of the full cell. Both models showed that the diaphragm cannot be described by a simple ohmic resistance, and the resistance estimated by analyzing the polarization curve is a sum of multiple resistances.

The formation process affects lithium-ion battery (LIB) performance, safety, and lifetime, yet its optimization remains challenging due to complex material-process interactions. This study investigates the interplay between electrolyte composition and formation protocol using four carbonate-based electrolytes and two protocols in three-electrode cells during formation. Differential voltage analysis (DVA), incremental capacity analysis (ICA), and electrochemical impedance spectroscopy (EIS) reveal electrolyte-and protocol-specific differences in solid-electrolyte interphase (SEI) growth, interfacial kinetics, energy-, and active material loss. The DVA-derived SEI growth curves show electrolyte-dependent responses to the two formation protocols that qualitatively align with the electrolyte's solubility of SEI constituents, supporting an initial SEI growth via a near-shore aggregation mechanism. Furthermore, the SEI growth curves are utilized to parameterize a mechanistic SEI growth model. The model captures cell-specific capacity losses during formation and ten subsequent cycles, enabling quantitative assessment of transport limitations and interpretation of protocol-and electrolyte-induced differences. Overall, this work contributes to the understanding of electrolyte-protocol interactions and demonstrates a practical strategy to parameterize mechanistic SEI growth models.

Electrochemical impedance spectroscopy (EIS) is a widely used technique for characterizing lithium-ion batteries. Conventional EIS assumes that the battery operates as a linear time-invariant system. However, maintaining stationarity is challenging, particularly when a superimposed direct current (DC) bias is applied. This study systematically investigated the validity of impedance measurements with varying DC bias and excitation amplitudes, analyzing the resulting non-linear and non-stationary effects. To assess the validity of impedance spectra, we employed validation techniques including the Kramers-Kronig test, total harmonic distortion, and Lissajous analysis. Additionally, we conducted electrochemical simulations based on a pseudo-two-dimensional model to replicate and further interpret the observed effects. Our results demonstrate that DC bias introduces significant impedance drift, leading to compromised validity of impedance spectra. These effects are detected throughout all investigated validation techniques, indicating a high reliability and confidence in the techniques. By combining experimental measurements, simulations, and validation methods, this study provides deeper insights into the impact of DC bias on EIS. These findings are particularly relevant for the application of EIS in battery management systems, where reliable state estimation and fault diagnostics are essential. The results emphasize the need for real-time impedance validation to ensure accurate diagnostics in dynamic battery operation.

Experiments reveal that the electrodes of a commercial NFM || hard carbon sodium-ion battery undergo excessive sodiation and desodiation at low charge and discharge rates. These effects are observed during cycling, despite operating strictly within the manufacturer’s recommended voltage limits of 1.5V to 4.1V. The resulting increase in charge capacity originates from an additional phase transition in the cathode active material, which manifests itself electrochemically as a voltage plateau that delays reaching the cut-off voltage during charging. The occurrence of the phase transition at high cell voltages is verified by operando X-ray diffraction measurements. During the subsequent discharge, the reverse transition takes place. Unusual deep discharge is enabled by the combination of low overpotentials and the characteristic potential profile of the cell. These phenomena are reproducibly observed across multiple test sequences. To separate the effects of the individual electrodes on this full cell behavior, harvested electrodes from a commercial cell are assembled into an experimental three-electrode setup and analyzed by differential voltage analysis. Since the high-voltage phase transition is reported to involve irreversible processes, adapting characterization and cycling protocols (especially voltage limits) may improve long-term performance and facilitate future analyses.

Model-based development provides a systematic approach for investigating fuel cell (FC) and fuel cell system (FCS) operation. It places particular emphasis on understanding reaction kinetics, transport phenomena, and aging mechanisms as functions of operating conditions. Characterizing these processes by physical models requires effective and efficient parameter identification, i.e., the derivation of precise parameter information with minimal experimental effort. Conventional strategies for parameter identification in FC models have so far suffered in particular from high time and resource requirements, leading to considerable bottlenecks in FC model development and system characterization. Therefore, this paper proposes a generic, systematic workflow for equally effective and efficient parameter identification in nonlinear, parametric models. The approach is grounded in structural and practical identifiability analysis based on the Fisher information matrix. It incorporates existing prior knowledge about parameter values, thereby enabling the calculation of optimal experimental designs. The methodology is universally applicable to differentiable parametric models. We demonstrate its practical applicability for a proton exchange membrane FC under realistic measurement conditions using a zero-dimensional model with six unknown parameters. Compared to conventional Latin Hypercube Sampling, the proposed approach achieves parameter identification with a 74 % reduction in uncertainty or, conversely, saves 84 % of the experimental effort required to achieve the same accuracy. The framework enables experimenters to conduct measurement campaigns that are both maximally effective and efficient. All methodological implementations, data, and demonstration results are made publicly available to facilitate reproducibility and community adoption.

Sodium-ion batteries are emerging as a sustainable and cost-effective alternative to lithium-ion batteries for large-scale stationary energy storage. However, a key challenge of layered oxide cathodes, such as Image 1001 , is their structural instability under high-voltage operation. In particular, it is suspected that a voltage-induced phase transition accelerates degradation and limits long-term performance. This creates a central trade-off: expanding the voltage window is highly attractive from an application perspective, as it enables higher capacities and energy densities. However, it may also compromise cycle life by promoting structural degradation. In this study, we directly address this issue by linking the evolution of high-voltage phase transitions to the practical performance limits of sodium-ion layered oxide cathodes. Operando X-ray diffraction combined with electrochemical cycling analysis is first used to establish a mechanistic understanding of how these phase transitions develop during cycling. We then systematically evaluate their occurrence as a function of temperature and C-rate, quantifying their impact on capacity, energy, and power capability. Long-term cycling further reveals the effect of high-voltage operation on cycle life. Based on these findings, we propose an operating strategy that balances the gains in initial capacity, energy output, and power capability with the degradation risks associated with high-voltage operation.

The fabrication of solid-state batteries (SSBs) without the need for high-temperature sintering significantly requires less energy. The powder aerosol deposition (PAD) method enables direct film formation at room temperature, bypassing the conventional thermal densification step. This study presents an overview of recent advancements in the cycling properties of SSBs fabricated via PAD. Employing LiNi0.82Mn0.07Co0.11O2 (NMC) as cathode active material (CAM) and Li7La3Zr2O12 (LLZO) as solid electrolyte, a capacity of 141 mAh g-1 with 90 % capacity retention over 25 cycles is demonstrated with no thermal post-treatment applied after film fabrication. Based on these results, the role of LLZO as catholyte in the cathode layer is investigated. The findings suggest an electrochemical instability between nickel-rich NMC and LLZO during cycling. To enhance the capacity, the aggregated results are used to discuss various strategies for optimizing cathode layer design, particularly with respect to the composition and choice of the CAM.

The use of silicon-based secondary anode materials in blend anodes alongside graphite is becoming increasingly prevalent in commercial lithium-ion batteries also used more and more in automotive applications. In addition to the accelerated degradation of silicon due to its significant volume expansion, the crystalline phase transition of fully lithiated silicon results in alterations to the voltage profile during discharging. This study examines the impact of this phase transition on the operation and state estimation of battery cells using such silicon-containing graphite/SiOx blend anodes. A memory effect of trapping lithium in the crystalline phase occurs when the cell is subjected to partial cycling without being fully discharged. However, this effect can be cancelled out by a single deep discharge. To gain further insights, a variation in cycle numbers, state of charge range during cycling, charge and discharge current, and the operation temperature is conducted. In order to validate the findings, a variety of commercial and automotive cells and blend anode half-cells are analyzed.

Metallic lithium deposition (LD) is the key limiting factor for fast-charging of lithium-ion batteries, as it affects both safety and durability. The reliable detection of LD requires simple and rapid diagnostics, which has led to a widespread adaption of impedance-based LD detection methods in the literature. Most of these studies are largely phenomenological, offering limited insight into the underlying physicochemical mechanisms reflected in the impedance response. In contrast, this study takes an experimental approach by placing the cell under conditions where lithium deposition occurs as the main reaction. Thereby, a targeted analysis of its impact on impedance is enabled by slowly and homogeneously overcharging a graphite anode, which is combined with an oversized cathode in a three-electrode configuration. The setup allows to create controlled conditions from intercalation via the onset of LD to exclusively LD. The electrodes are analyzed using operando and ex-operando impedance measurements. Additionally, a distribution of relaxation times analysis is performed to gain deeper insight into the electrochemical processes under different LD conditions. This work thus bridges the gap between phenomenological detection methods and the fundamental understanding of LD, offering potential for an improved detection and prevention of LD and ultimately fast-charging of lithium-ion batteries. Conditions from intercalation via onset to mainly metallic lithium deposition created and systematically examined.Processes allocation by EIS & DRT.Recognition of fingerprints of metallic lithium deposition in SEI migration and charge-transfer processes.Validation and process assignment of operando-impedance results during lithium deposition.

Electrochemical impedance spectroscopy, a method for battery diagnostics, is used to estimate the internal temperature of a lithium-ion battery cell during highly dynamic load profiles. For the first time, a recurrent neural network is trained and evaluated with operando impedance data for temperature estimation. Furthermore, an approach is considered that guides the training process of the neural network by incorporating physical constraints. The model’s development based on an extensive series of measurements with different load profiles, tested under realistic conditions on large-format lithium-ion cells. The estimation accuracy of the data-driven approach is evaluated and compared against model-based methods, including the extended Kalman filter. An impedance correction model is proposed, which leads to a significant enhancement of the model-based estimation. The recurrent neural network under consideration achieves a mean square error of 1.07 °C for the investigated testing profiles in the temperature range up to 60 °C.

Battery packs, defined as interconnections of individual cells, are central to modern energy systems, yet their electrical and electrochemical behavior remains insufficiently understood. This review consolidates foundational principles, outlines challenges, and addresses fragmented knowledge that hinders further development at the pack level. A key challenge is the lack of harmonized and uniquely defined states, such as the state of charge and the state of health. To address this, we propose revised definitions and introduce state descriptors for more consistent and comparable pack-level analysis. We critically evaluate existing characterization methods, originally developed for single cells, and highlight their potential and limitations at the pack level. Many of these methods require further adaptation, and only their combination with harmonized state descriptors enables reliable and meaningful results. This work goes beyond identifying challenges by closing gaps in state descriptions, providing a foundation for future research, fostering reliable diagnostics, and supporting innovation in energy storage technologies.

Blend electrodes are used in lithium-ion batteries to increase the performance by combining two active materials, such as silicon (Si) or silicon oxide (SiOx) and graphite (Gr), for the negative electrode. In-depth knowledge of the complex interactions between the materials is essential to understand how inhomogeneities and local peaks of the intercalation current arise and how they can be prevented. This work presents a spatially resolved transmission line model developed to describe the electrochemical behavior of blend electrodes. Parameterization and model validation are carried out for a Gr/SiOx anode. Simulation results are used to investigate inhomogeneities in local states during lithiation at different C-rates. A special focus is put on stress indicators as precursors for accelerated ageing like local material-specific C-rates and spatial gradients of the degree of lithiation. Thus, the modeling approach is a tool for both the description of the properties of blend electrodes and for simulation-based balancing of the active materials' capacities within blend electrodes.

Proton exchange membrane electrolyzers (PEMEL) are considered a promising technology for intermittent generation of green hydrogen if connected to fluctuating energy sources and in volatile electricity markets. For an economic operation, a coupling of PEMEL with a battery energy storage system (BESS) is advantageous. In this work, optimized operating strategies of a grid connected PEMEL supported by a BESS are developed based on dynamic programming. Furthermore, a generic aging model is implemented to ensure that performance degradation is taken into account. The optimization is carried out for different hydrogen production targets per week based on day-ahead market electricity prices, system configurations with and without combined operation of electrolyzer and battery as well as aging effects. The results show that an optimized operating strategy can decrease the effective operating costs, i.e. electricity procurement costs and costs related to system degradation, of the considered use case by up to 7 %.

The distribution of relaxation times analysis is a powerful and non-destructive technique based on electrochemical impedance spectroscopy to analyze and identify electrochemical reactions and processes in batteries, fuel cells, and other electrochemical systems. However, there are inherent challenges to this analysis method that affect the accuracy of the results and impede their interpretation, particularly when capacitive, inductive or resistive-inductive characteristics are present. In this case, data truncation is often used, which leads to incorrectly identified time constants and polarization contributions as well as an ohmic offset. An approach that is capable of analyzing arbitrary spectra and determining the true ohmic offset is presented and applied to three algorithms to evaluate the influence of different regularization techniques: the generalized DRT analysis, the VanCittert algorithm and the separated sparse spike deconvolution. To validate the results, they are compared to the electrochemical system analysis (ELSA), which is a complementary data-driven method. It can be demonstrated that the proposed approach efficiently handles resistive-capacitive and resistive-inductive effects without requiring any non-negativity constraint for the parameters nor data truncation and without adding complexity.

Anodes with blended active materials, containing SiOx as a secondary material in addition to graphite, gain interest in research and commercial applications to increase the capacity of lithium-ion batteries. SiOx has the advantage of significantly higher specific capacity than graphite but the disadvantage of a reduced cycling and structural stability. To understand the processes involved for this type of blend anode, a detailed investigation of its electrochemical behavior is required. This work provides a non-destructive method for understanding the interaction between blend materials in cells containing silicon-based active material. This method helps to identify internal battery conditions and thereby optimize the battery performance. A cylindrical cell containing approximately 10 wt% of SiOx is used for electrochemical testing. By analyzing the voltage hysteresis, differences in the graphite lithiation are observable, which allows conclusions to be drawn about the SiOx lithiation. An increase in the charge rate leads to a decrease in graphite lithiation and consequently to an increase in SiOx lithiation. This effect is explained by the analysis of the pure material anode potentials. Validation of the effect is given by X-ray diffraction analysis to identify the state of graphite lithiation.

For the battery industry, quick determination of the ageing behaviour of lithium-ion batteries is important both for the evaluation of existing designs as well as for R&D on future technologies. However, the target battery lifetime is 8–10 years, which implies low ageing rates that lead to an unacceptably long ageing test duration under real operation conditions. Therefore, ageing characterisation tests need to be accelerated to obtain ageing patterns in a period ranging from a few weeks to a few months. Known strategies, such as increasing the severity of stress factors, for example, temperature, current, and taking measurements with particularly high precision, need care in application to achieve meaningful results. We observe that this challenge does not receive enough attention in typical ageing studies. Therefore, this review introduces the definition and challenge of accelerated ageing along existing methods to accelerate the characterisation of battery ageing and lifetime modelling. We systematically discuss approaches along the existing literature. In this context, several test conditions and feasible acceleration strategies are highlighted, and the underlying modelling and statistical perspective is provided. This makes the review valuable for all who set up ageing tests, interpret ageing data, or rely on ageing data to predict battery lifetime.

Electrochemical impedance spectroscopy (EIS) is widely used in electrochemistry, energy sciences, biology, and beyond. Analyzing EIS data is crucial, but it often poses challenges because of the numerous possible equivalent circuit models, the need for accurate analytical models, the difficulties of nonlinear regression, and the necessity of managing large datasets within a unified framework. To overcome these challenges, non-parametric models, such as the distribution of relaxation times (DRT, also known as the distribution function of relaxation times, DFRT), have emerged as promising tools for EIS analysis. For example, the DRT can be used to generate equivalent circuit models, initialize regression parameters, provide a time-domain representation of EIS spectra, and identify electrochemical processes. However, mastering the DRT method poses challenges as it requires mathematical and programming proficiency, which may extend beyond experimentalists’ usual expertise. Post-inversion analysis of DRT data can be difficult, especially in accurately identifying electrochemical processes, leading to results that may not always meet expectations. This article examines non-parametric EIS analysis methods, outlining their strengths and limitations from theoretical, computational, and end-user perspectives, and provides guidelines for their future development. Moreover, insights from survey data emphasize the need to develop a large impedance database, akin to an impedance genome. In turn, software development should target one-click, fully automated DRT analysis for multidimensional EIS spectra interpretation, software validation, and reliability. Particularly, creating a collaborative ecosystem hinged on free software could promote innovation and catalyze the adoption of the DRT method throughout all fields that use impedance data.

Interpreting impedance spectra of electrochemical systems using the distribution of relaxation times analysis remains an incompletely solved task. This study carefully examines various challenges related to the interpretation of resulting distributions of relaxation times using a closed-form lumped Doyle-Fuller-Newman model. First, the physical and phenomenological interpretation of peaks in the distribution of relaxation times are analyzed through a global sensitivity analysis. Second, the assignment of processes to specific ranges of time constants is investigated. Third, the use of half cells for the characterization of full cells is examined, and the clear limitations associated with the use of lithium metal counter electrodes are pointed out. Furthermore, the study provides first insights into the effects of distributed processes such as charge transfer, double-layer effects, and solid-state diffusion. Several prevailing interpretations in the literature are challenged and new insights and guidelines for interpreting distributions of relaxation times are offered.

Electrochemical impedance spectroscopy is a non-destructive experimental technique for the operando characterization of electrochemical systems. Here, we develop electrochemical system analysis (ELSA) as a data-driven, systems-theoretical approach to the analysis of measured impedance spectra. It solves the problem of finding an interpretable model description that explains given impedance data with high accuracy and without prior model assumptions. ELSA adopts the comprehensive analysis of the generalized distribution of relaxation time analysis and builds upon the data-driven and regularization-free Loewner method. ELSA systematically interprets the transfer function resulting from the Loewner method to reliably identify serial elements and resistive-capacitive and resistive-inductive processes with characteristic time constants. It also finds resonant elements by identifying conjugate complex poles. Based on the Shannon entropy of the residuals and the curvature of the locus, ELSA automatically and reproducibly identifies the minimal model order, thus avoiding overfitting. System characterization results are presented for different types of electrochemical power sources: batteries, fuel cells, and double-layer capacitors.

The Distribution of Relaxation Times (DRT) analysis gained considerable attention for its ability to reveal detailed information about complex electrochemical processes without requiring a priori knowledge. This review provides a comprehensive insight into different methods of the DRT analysis, their mathematical bases, and the latest approaches to acquiring and analyzing frequency and time domain data. The analysis is based on the deconvolution of frequency domain data into a distribution function of gains at (pre-specified) relaxation times in the time domain, which improves the spectral resolution and separability of electrochemical processes. It provides valuable information about different electrochemical processes on different time scales, making it particularly useful for the characterization of both materials and electrochemical systems. The DRT analysis can be applied to arbitrary spectra containing electromagnetic effects, resistive–capacitive processes, and solid-state diffusion. To enhance process identification, a post-processing step involving peak analysis with Gaussian or RQ-distribution peaks is presented and the assignment of peak patterns induced by distributed processes like solid-state diffusion is discussed. In addition, a step-by-step workflow for the DRT analysis is provided to guide researchers from data acquisition and validation techniques to calculation and interpretation of the distribution function.