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Solid Oxide Fuel Cells (SOFCs) are regarded as a promising technology for economic power generation due to their high efficiency and large fuel flexibility. Durability is a severe hurdle towards their deployment. The near future targets in respect to Degradation Rate (DR) are about 0.1% kh−1, which needs improved monitoring and diagnostics. This work aims at introducing a new approach based on Differential Analysis of the i-V curves, named DiVA. It operates with the Differential Resistance Rd and its evolution during long term testing. Two new performance indicators are introduced. Since derivatives are more sensitive to small deviations, the Differential Resistance Analysis (DRA) ensures increased sensitivity and information capability in respect to degradation monitoring and diagnostics, which is demonstrated on a small stack during thermal cycling conditions – before and after the first thermal cycle, on button cells tested up to 9000 h, as well as on button cells operating in fuel cell and in electrolysis mode. The results show that DRA is several times more sensitive in comparison with the classical DR evaluation based on registration of the voltage decrease at constant current.

Solid Oxide Fuel Cells (SOFCs) are a promising technology that can provide efficient and clean energy production. The general barriers hindering their market entry are durability, i.e. resistance to aging, and costs. In parallel to the deeper insight into the different degradation sources and improved understanding of ageing factors and their interactions, work towards higher accuracy for the assessment and monitoring of real-world fuel cell ageing in necessary. The requirements for operational stability formulate the parameter “degradation rate” (DR). Most often long term durability tests are performed at constant current load and the decrease of the voltage is used for its definition. In this work a new approach based on analysis of the volt-ampere characteristics, named Differential Resistance Analysis (DRA), is presented. It operates with the differential resistance, i.e. with the derivative of the voltage in respect to the current (dU/dI = Rd) which is more sensitive to small deviations and thus increases the sensitivity of the analysis. Two performance indicators are derived (Rd, min and ∆U*) with differing selectivity: ∆U* is more sensitive to activation losses and Rd, min - to transport hindrances. The application of the DRA is demonstrated on examples from measurements in fuel cell and in reverse (fuel cell/electrolyzer) mode, as well as on modeling data. The results show that the method is at least 10 times more sensitive to DR evaluation in comparison with the classical approach.

A new concept of a high temperature fuel cell based on a dual H+ and O2- conducting membrane was successfully developed recently (“IDEAL-Cell”, FET-Energy/FP7, 2008-2011). It operates in the range of 600-700 °C, and was shown to be superior of standard SOFCs and PCFCs at equivalent overall thickness. It is based on the junction between the anodic part of a PCFC and the cathodic part of a SOFC through a mixed H+ and O2- conducting porous composite ceramic membrane, avoiding all disadvantages associated to the presence of water at the electrodes. In the initial configuration, the porous mixed conductivity central membrane was made of a composite BCY15/YDC15, in which the active sites lay along the triple contact lines (TPB) between the protonic conducting phase (BCY15), the anionic conducting phase (YDC15) and the gas phase in the pores. During the course of the European project cited above, it was discovered and modeled that, in addition to be a protonic conductor, BCY15 was also an excellent oxygen conductor at 600-700 °C provided that it is fed with oxygen. Therefore, a second generation of dual membrane cell was developed in which YDC15 is replaced by BCY15, leading to a strongly simplified cell, much easier to shape and sinter, with potentially higher performances, i.e. the TPB become full active surfaces, magnifying the number of active sites; i.e. the dual membrane being solely made of BCY15, the tortuosity of the conductive phase is strongly diminished and its volume fraction increased, hence the electric resistance becomes much lower. As a whole, this so-called “monolithic concept” (for the cell is almost essentially made of a single BCY15 phase) improves the chemical and mechanical compatibility, increases the global cell conductivity and represents an important step towards simplifying the technology for industrialization. Moreover this new concept shows a good reversibility between the SOFC and SOEC modes; since this cell is based on 3 separate compartments (oxygen at the cathode, hydrogen at the anode, water at the dual central membrane), the dynamic of the device when shifting from one mode to the other is very high (no need to adjust the gas mixture at electrodes). The present work proposes to further increase the electrochemical properties of this monolithic dual membrane high temperature fuel cell by studying the catalytic properties on the mixed H+ and O2- conducting membrane with or without addition of Pt nanoparticles or Ni foam, which have been evaluated by impedance spectroscopy and polarization measurements. These additions led to slight adjustments of the shaping parameters to obtain flat and comparable samples. Finally, the electrochemical performances of the different configurations of the monolithic cell have been evaluated in real operating conditions via a dedicated 3-chamber set-up named Real Life Tester (RLT℗). Results show satisfactorily OCV and good performances for all samples, but a rapid degradation for the configuration with Ni foam probably due to aqueous electrochemical corrosion.

Steam electrolysis by means of reversible Fuel Cells is a promising concept for compensating the intermittency of renewable energy sources. Several tests on SOFC stacks operated in reverse mode (SOEC) reported faster degradation than in power production mode. Although not completely clarified, the degradation mechanisms appear partly related to the higher steam concentration at the electrode compartments. This work introduces a novel type of cell with dual anionic-protonic conductivity, which allows the separation of the steam compartment from the electrodes compartments. The concept is presented together with a set of experimental results pointing out the potential advantages of this approach. © The Electrochemical Society.

Water behavior studies were performed in porous ceramic media based on proton conducting yttrium-doped barium cerate BaCe0.85Y0.15O3-α (BCY15), which is a component of a new high-temperature dual membrane fuel cell (dmFC) design. Complex permittivity measurements were carried out on porous samples at room temperature. A new phenomenon was observed during wetting—a gigantic enhancement of the real component of the capacitance at lower frequencies. A possible explanation is the formation of semi-liquid layer with dipole structure on the pores walls, which is supposed to be organized also at operating temperatures. Since the electrochemically active volumetric layer facilitates the water formation, it should improve the operation of the dmFC by decreasing its resistance, which is experimentally confirmed. This phenomenon can be of importance also for classical proton conducting solid oxide fuel cells, as well as for operation in electrolyzer mode.

International audience; This paper reports impedance studies of a dual membrane fuel cell - an innovative design based on the idea for a junction between an oxygen ion conducting cathode/electrolyte part and proton conducting anode/electrolyte part through a mixed oxygen ion and proton conducting porous membrane. Thus oxygen, hydrogen and water are located in three independent chambers. This concept allows avoiding all the severe pitfalls connected to the presence of water at electrodes in both SOFC and PCFC. The performed measurements of the 3 compartments and the data analysis are improved by introducing some specialized approaches and techniques, which are discussed. The impedance contribution in the proof of the new concept is also presented.

This work presents results of a measurement setup which was constructed for understanding the performance contributions of the individual compartments and reactions taking place in the patented concept of IDEAL-Cell (described in detail in[1]). By inserting a third measurement point at the central membrane of an ideal cell it was possible to measure the cell in three different modes corresponding to hydrogen, oxygen compartment and the full cell. Recorded maximum power densities of (~4, ~7, 11, 16) mW/cm² at (600, 650, 700, 750) °C in H2-O2 atmosphere respectively were observed which were similar to the values of proof of concept ideal cell samples tested so far. Moreover in our setup it was possible to record higher maximum power densities for the hydrogen (proton conducting) compartment which was (~14, 22, 33*, ~38*) mW/cm² at (600, 650, 700, 750) °C.

This paper reports impedance studies of the cathode/electrolyte behaviour in solid oxide fuel cells (SOFC), based on comparative investigation of half-cells with yttria stabilized zirconia (YSZ) electrolyte and different cathode materials: lanthanum strontium manganite (LSM), and composite LSM/YSZ with low ionic conductivity as well as the electron conducting Ag, Pt and Au. For improved impedance data analysis the technique of the differential impedance analysis is applied. It ensures structural and parametric identification without preliminary assumptions about the working model. It is found that despite the low ionic conductivity of LSM, the cathode reaction of the oxide cathode materials is a two-step process including: (i) charge transfer with activation energy of the resistivity E a increasing with the temperature and (ii) transport of oxygen ions through the bulk of the electrode (rate-limiting stage) with E a independent on the temperature. For the metal (electron conducting) electrodes, the reaction behaviour is described with one step process with higher E a at higher temperatures. The activation energy of the electrolyte conductivity decreases with the increase of the temperature. The observed changes in E a for the electrolyte and the cathode reaction (the charge transfer step for the LSM-based electrodes) appear in the same temperature interval. This interesting coincidence suggests for correlation between the bulk (electrolyte) and surface conduction properties. Approaches for improvement of both the ionic conductivity and the supply with electrons in LSM should be also searched.

In the high current density regime, the performance of SOFCs is limited by concentration overpotentials, which are particularly significant at the anode side where a competition occurs between incoming hydrogen and outgoing water. In standard SOFCs where the anode is made of YSZ and Ni, this becomes crucial when the demand for reactants exceeds the capacity of the porous cermet anode to supply them by gas diffusion mechanisms. A delicate compromise should be found between maintaining a high level of activation in the anode, i.e. high density of triple phase boundaries (TPB), favored by a distribution of small interconnected pores with high tortuosity and small grains size, and high gas permeability, favored by a distribution of large interconnected pores with low tortuosity, while the percolation of both electronic and anionic conductivity phases is maintained. The present work aims at determining experimentally anodes gas permeability as a function of the experimentally determined percolation, tortuosity and volume fraction of the pores, assuming that the diffusion of gases is described by the Darcy Law. Anodes with varying porosity ensured by different quantities of the pore former were obtained by cold pressing and sintering. SEM image analysis, mercury intrusion porosimetry and permeability measurements for different gases were performed. The obtained results show that permeability increases with the volume fraction of the pore former. However, non-linearity as a function of the gases molecular weight is observed and discussed as a function of the mean free path and thus of possible mixed Darcy and Knudsen diffusion.

In this study the technique of the Differential Impedance Analysis (DIA) is applied for distinction of two models which give similar impedance diagrams presented with slightly depressed semi-circles—two time-constants Voigt model with high degree of mixing and one time-constant model in which the capacitance is replaced with constant phase element (CPE). Those two models are often used for impedance investigations of solid state. The applicability of the recognition procedure is confirmed on synthetic models as well as on real samples of yttria-stabilized zirconia (YSZ) and Er-doped BaTiO 3 .

This work shows the enhanced capability of differential impedance analysis (DIA) for recognition of CPE behavior. It is based on the procedure of a secondary DIA, which analyses the frequency dependence of the local operating model parameters' estimates in the zones where there is no adequacy between the object and the local estimator. The new algorithm is successfully examined on synthetic models of CPE, Warburg, Randles, Randles with CPE modification, simple Faradaic reaction with CPE capacitance, as well as on real data obtained on yttrium iron garnet single crystals and yttria stabilized zirconia single crystals.

A new concept of a high temperature fuel cell based on a porous dual-conducting (H+ and O2-) central membrane was successfully developed as part of a European project (“IDEAL-Cell”, FET-Energy/FP7, 2008-2011). This additional layer ensures the connectivity between both SOFC cathode/electrolyte and PCFC electrolyte/anode “water-free” compartments so that the system operates with three independent chambers. During the development of this concept, it was discovered that BCY15, used so far as a protonic conductor, exhibited a very significant anion conduction at operating temperature under oxygen atmosphere, opening up the route for a simplified and more efficient configuration; since then, BCY15 is used in all the constituent layers to lead to the so-called monolithic concept. Therefore the porous dual-conducting central membrane is made of a single BCY15 phase instead of a composite mixture of a proton conductor (i.e. BCY15) and an anion conductor (i.e. YDC15). This CM is thus sandwiched between 2 BCY15 electrolytes with a BCY15 + Ni anode on one side and a LSCF48 + BCY15 cathode on the other side. Recent works proved that electrical performances of the monolithic configuration at 600°C are higher than those measured for standard SOFCs and PCFCs at equivalent geometry. The present work aims at presenting the first results of the manufacturing and electrochemical testing of a two-cells short stack specifically designed with 3 independent chambers in which central membrane (CM) supported monolithic cells are integrated. The supported-CMs were fabricated by using BCY15 and a polymer PMMA as a pore former agent. The CMs were sintered at 1400°C for 5 hours under static air leading to a porosity content of around 50 ± 3 vol. %. The electrolytes were then deposited onto the CMs by tape casting from an ethanol-based suspension containing BCY15 and 1 wt. % of ZnO, and were sintered at 1350°C for 3 hours. Anode ink containing 60 vol. % BCY15, 40 vol. % NiO and 10 wt. % of graphite was deposited on one electrolyte and sintered at 1350°C for 3 hours. Cathode ink containing 50 vol. % BCY15, 50 vol. % LSCF48 and 10 wt. % of graphite was deposited on the other electrolyte and sintered at 1100°C for 3 hours to avoid delamination and creeping. This processing sequence leads to flat cells having a total thickness lower than 1 mm. 2 cells were integrated in a specifically designed short stack made of INOX 440C, and sealed with Thermoculite 866 LS. The electrochemical performances of the short-stack have been measured in real operating conditions via a dedicated 3-chamber set-up named Real Life Tester (RLT), and compared to those of single cells operated under the same conditions. Results are discussed in terms of cells geometry and microstructure, and stack design improvements are proposed.

Permittivity Spectroscopy is a branch of the Impedance Spectroscopy specially tuned for measurements and analyses of dielectrics permittivity properties. The present paper presents experimental results on permittivity properties of composite objects in which a polarizable dielectric is distributed in a fine non-polarizable matrix (solid or liquid) measured in frequency range 1 MHz down to 0.01 Hz. Two types of objects are studied - water in porous functional ceramics and lubricating oils. In both systems gigantic enhancement of the effective capacitance is observed. The first series of experiments was performed on porous membranes of yttrium doped barium cerate, which is a proton conducting ceramics with hydrophilic properties. At a given level of watering the measured capacitance is sharply increasing (3 to 5 orders of magnitude) in the lower frequency range. The second example covers permittivity study of lubricating oils, where the increase is 2-3 orders of magnitude. The phenomenon of gigantic enhancement of the effective capacitance could be related to a formation of dipole volume structures induced by the external alternating electrical field.

International audience; Recently a new design of solid oxide fuel cell (SOFC) named dual membrane fuel cell (dmFC) has been introduced and proved. It is based on the introduction of three independent compartments for hydrogen, oxygen and water, which eliminate the dilution of the fuel or the oxidizer respectively in the SOFC construction or in its proton conducting (pSOFC) modification. Due to the registered sufficient mixed ionic conductivity of BaCe0.85Y0.15O2.925 (BCY15), a simplified modification in respect to shaping technology and construction is introduced. It's performance is better than the one of pSOFC cell produced with the same material and shaping procedure: 76 mW/cm2 (dmFC thickness 1.1 mm) against 71 mW/cm2 (pSOFC thickness 0.66 mm) at 700 °C. Impedance measurements carried out down to 1 mHz ensure information about the water formation and behaviour in the separate central membrane compartment of the dmFC design, which brings to performance improvements, registered also in electrolyser mode of operation.

The purpose of this study is to compare the investigations of amorphous magnetic ribbons combining the usual structural methods with physical impedance spectroscopy (PIS) and X-ray photoelectron spectroscopy (XPS). The samples are commercially available rapidly quenched ribbons for torroidal transformers. Two types of ribbons were thermally treated below the temperature of amorphous–crystalline phase transition. Two binding energies of B 1 s electrons are determined by XPS in one of the as-quenched ribbons, which show impedance time constant spectra without dispersion. The other ribbon, possessing only one value of binding energy of the B 1 s electron (B I state) in a rapidly as-quenched state, undergoes transition to a still amorphous state but acquires high electromagnetic losses and show another value of the binding energy of the B 1 s electron (B II state) after the heat-treatment procedure. This latter type of ribbons show structural impedance spectra containing various time constant values.

The nanosized Co, B, H, particles synthesized by the ‘tea’ and ‘antigravity’ methods using a borohydride reduction process have been subjected to structure and composition studies by X-ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM) and selected area diffraction (SAD). The amounts of the elements Co, B, O2, H2 and C as mean volume values, and surface values for the as-prepared particles, as well as after Ar+ etching to a depth of about 15 nm and 30 nm from the initial particle surface, are determined. About 1.5 atoms of cobalt per atom of boron correspond to samples obtained by the ‘antigravity’ method. The binding energy (BE) of 1s electrons of boron atoms has only one value. These particles are angular and are in the typical nanocrystalline state. In the case of samples prepared by the ‘tea’ method, two atoms of cobalt per atom of boron are found. The presence of two kinds of BE (B1 and B11) of 1s electrons of boron atoms in the particles obtained by the ‘tea’ method is observed and almost equal amounts of these two states are established in the spectrum. The particles' shape and structure are typical of the amorphous state. The fact that there is one peak when the ‘antigravity’ method is applied, in contrast to the two peaks with the ‘tea’ method indicates the presence of a metal amorphous state in the latter case.

The effect of tap water contaminants on the kinetics of the hydrogen evolution reaction on a nickel electrode in 1 mol dm(-3) KOH was investigated by galvanostatic polarization and electrochemical impedance spectroscopy techniques. It was found that the tap water contaminants lead to an increase in the overpotential of the hydrogen evolution reaction, especially at low temperatures. The combination of electrochemical techniques, as well as physicochemicals such as SEM and EDAX ones, confirmed that the contaminants are specifically adsorbed and blocked the available electrode surface for the reaction. It was concluded that they do not participate in an electrochemical reaction in the potential region where HER occurs. Besides the short term negative impact on the rate of hydrogen evolution, a 55 h test revealed that the overpotential shows a steady increase over time in presence of tap water contaminants, while in absence of these contaminants the overpotential is constant. Copyright (C) 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.

This paper presents results for the conductivity of BaCe0.85Y0.15O2-δ (BCY15) measured by electrochemical impedance spectroscopy in wet hydrogen and in Air, as well as test results from the application of the material in a new dual membrane fuel cell configuration (“IDEAL Cell”), in which the water is produced and evacuated through a separate chamber. The conductivity of dense BCY15 in wet hydrogen atmosphere at 700 °C is 2.0 10-2 S/cm. The measured values in air are of the same order. Preliminary tests of the material in the new cell design, where the three types of conductivity (protonic, oxide ion and mixed) are used in different cell compartments, are successfully performed.

Most electrochemical objects are intrinsically nonstationary or contain valuable evolving phenomena. This paper presents the essentials of the theory of Nonstationary Impedance Spectroscopy (NIS) including the ideas of nonstationary and instantaneous impedance, the new mathematical background and the main approach to the development of nonstationary impedance models. The practical issues for the application of the new techniques are discussed.

During the last years the method of the Electrochemical Impedance Spectroscopy has been intensively developed. It is the most powerful electrochemical method, because of it unique ability to investigate the structure and the properties of the objects in a wide frequency range. The Capacitive Impedance Spectroscopy (CIS) is of special interest. The further development of this principle is given in the current work. It gives an opportunity to investigate the electric properties of different kinds of materials. A special measuring system is developed for this purpose. A modern computer techniques with a special data analyze software is also described.

IDEAL-Cell is a new concept of a high temperature fuel cell operating in the range 600-700 °C. It is based on the junction between the anode part of a PCFC and the cathode part of a SOFC through a mixed H+ and O2- conducting porous ceramic membrane. This concept, extensively described in the present paper, aims at avoiding all the severe pitfalls connected with the presence of water at the electrodes in both SOFC and PCFC concepts. Spark Plasma Sintering samples were designed specifically for proving the IDEAL-Cell concept. The first electrochemical results obtained at 600 °C under hydrogen on millimeter thick samples show that IDEAL-Cell behaves like a high temperature fuel cell. It is estimated that the overall efficiency of this new concept should greatly surpass that of standard SOFCs and PCFCs and that the material constraints, especially in the case of interconnect materials, should significantly decrease.

Electrochemical impedance spectroscopy is one of the most informative tools for investigating of the complicated processes in electrochemical power sources. The interest arises from the unique advantage of the method's capability to separate and characterize, in a single measurement, the different steps involved in a complex process. Impedance spectroscopy finds a variety of applications for studies of different energy sources – batteries, fuel cells, supercapacitors, and other systems – and has different targets – studies of basic kinetic processes, materials research, quality control, matching, and diagnostics. The principle of the method and a set of useful techniques providing for reliable experiments and data interpretation are described. The selection of the measurement setup configuration and details of the experimental program are discussed. Techniques for correction of the errors due to cable inductance and to possible time evolution of the object are described. The unique method for soft computing – differential impedance analysis, which corresponds to the nature of power sources – is also explained. Examples of experimental data – raw and processed – illustrate the recommended techniques and their application in different studies.

The IDEAL-Cell concept is based on the junction between a PCFC anode/electrolyte section and a SOFC cathode/electrolyte section, through a mixed proton and oxide ion conducting porous ceramic membrane, operating in the temperature range 600-700{degree sign}C. Recombination of ions takes place within the junction, or central membrane (CM), and water vapor is evacuated through open porosity. The first results on the fabrication of multilayered samples reproducing the IDEAL-Cell structure are reported here, together with electrochemical tests carried out on selected samples in order to evaluate the performances of the chosen materials and to demonstrate the feasibility of this innovative concept of fuel cell. Stable OCV and power generation were obtained in the multilayered structures. Anomalies on the I/V curves and impedance measurements under large perturbation could be considered as proofs of water formation inside the central membrane.

The oxygen reduction (OR) mechanism at the Sr-doped LaMnO3 (LSM) and yttria stabilized zirconia (YSZ) composite cathode for high temperature solid oxide fuel cells is still uncertain, despite of the great deal of work carried out over the last years about this system. In previous works, we tested a half-cell (with a YSZ electrolyte pellet) in a typical three-electrode configuration: It was observed that the portion of the composite cathode volume involved in the reaction depends on the operating temperature. Moreover, we analyzed part of the impedance data by the differential impedance analysis, which does not need a preliminary working hypothesis. The results suggested that significant limitations in the oxygen ion transport occur in the LSM pure material, which are not observed in the composite YSZ/LSM cathode. In this study, we investigate the behavior of the LSM/YSZ system in a Ni/YSZ cermet anode-supported half-cell with yttria stabilized zirconia (8YSZ) electrolyte and a screen printed LSM/YSZ composite cathode. The aim is to individuate and characterize the cathodic contribution from the overall impedance response, varying the partial pressure of the reactant gases, to obtain additional information about the OR mechanism from the p(O2) dependence. By a possible interpretation of the oxygen reaction mechanism, a comparative study of the cathode behavior with previous results is performed.

Identification of the appropriate model is the aim of experimental data analysis. Some principal problems of the classical approach for parametrical identification are discussed. A new method for structural identification where the working model is derived from the experimental results is developed. Some recent results which expand the applicability of the method are also given.

The optimization of Ni-YSZ anodes is an important step in obtaining electrically efficient anode supported SOFCs. Despite the continuous studies concerning optimization of the anode reduction conditions, degradation phenomena, oxidation-reduction cycling behaviour and microstructural changes, the anode reduction continues to be an active field for deeper insight [1,2], since as a final stage of the cell preparation, it offers an opportunity for optimization in respect to mechanical stability, electronic conductivity, catalytic activity and gas permeation. This is additionally complicated due to the counter-flow of the fuel and exhaust water vapour. This study combines two approaches – impedance spectroscopy and gas permeability studies that ensure experimental information about the main processes occurring during anode reduction: (i) formation of a new microstructure influencing the diffusive mass transfer and (ii) development of an electrically conductive network. The gas permeability studies [3] are carried out on anode pellets at room temperature before and after reduction performed at different conditions (temperature, reduction atmosphere). The observed changes are discussed and compared with SEM microstructural analysis. The impedance measurements are carried out directly during the reduction of button cells, segmented cells and NiO-YSZ anode pellets and thus the reduction process is studied during its evolution. The influence of the reduction conditions, including the duration of the process, is discussed in respect to the formation of an optimal Ni network with good electrical connectivity and catalytic activity. The presented figure shows two impedance diagrams measured on a segment from segmented fuel cell in different stages of the reduction process . Acknowledgement:The research leading to these results has received funding from the European Union's Seventh Framework Programme (FP7/2007-2013) Fuel Cells and Hydrogen Joint Undertaking (FCH-JU-2013-1) under grant agreement No 621207. References S.-W. Baek, J. Bae, Internat. J. Hydrogen energy 36 (2011) 689 B. Liu, Y. Zhang, B. Tu, Y. Dong, M. Cheng, J. Power Sources 165 (2007) 14 E. Mladenova, D. Vladikova, Z. Stoynov, A. Chesnaud, A. Thorel, M. Krapchanska, Bulg. Chem. Communic. 3 (2013) 366 Figure 1

The successful application of the Impedance Spectroscopy for measurement and quality control of batteries should obey a number of specific requirements, correspondent to the nature of the batteries as objects under investigation. Batteries are nonlinear and non-stationary large statistical systems with distributed parameters in macro- and micro-scale. Processes of charge and mass-transfer take place in their electrodes, changing the chemistry and the habitus of the active electrode materials. Starting with the very first successful measurement of a small Lead-acid battery in 1976 [1], we developed a set of complementary techniques providing for reliable measurements of battery impedances, data handling and analysis. The techniques for inductive errors evaluation and correction, for the 4-Dimentional data treatment [2] of the evolving battery State of Charge will be discussed in details. Special attention will be given to the interpretation of the battery impedance as a property of a fuzzy system with un-known parameters distribution. The Differential Impedance Analysis which solves this problem and the related Spectral Transforms are powerful tools for batteries evaluation and quality control [3]. These techniques will be illustrated with practical examples of impedance measurements of large industrial Lead-acid and Li-ion batteries and stacks fabricated by different technologies and for different purposes. Some related side phenomena as: (i) presence and destruction of the passive layer; (ii) increased inductance of stacks as well as impedance observation of local in-homogeneities in Li-ion batteries will be also discussed. References 1. M. Keddam, Z. Stoynov, H. Takenouti, J. Appl. Electrochem. 7 (1977) 539. 2. Z. Stoynov in: C. Julien, Z. Stoynov (Eds.), Materials for Lithium- ion Batteries, Kluver Academic Publishers, 3/85 (2000) 359. 3. Z. Stoynov and D. Vladikova, in Encyclopedia of Electrochemical Power Sources, edited by U. Garche ( Elsevier, 2009) pp. 632-642.

The problems of non-stationary electrochemical impedance spectroscopy are discussed by an analysis of the errors of the classical Fourier transform applied in non-stationary conditions. The essentials of the theory of generalized Fourier transform, called rotating transform, capable of handling non-stationary signals, are described. The application of the rotating transform to impedance analysis of non-stationary electrochemical systems is emphasized.

The problem of non-stationarity plays an important role in the development of impedance spectroscopy. The main reason is due to the fact that most electrochemical systems possess an intrinsic non-stationary nature. Instantaneous impedance is the theoretical basis for solving this problem. The present paper is devoted to an experimental technique for estimation of the instantaneous impedance. On the basis of the four-dimensional approach the experimental design for measuring the instantaneous impedance is described in detail. A special technique is proposed for validation of the modelling, based on the a posteriori evaluation of the model flexibility.

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The impedance study of non-stationary systems is of a great interest to electrochemistry concerning the investigation of real objects in low and infra low frequency ranges. The method described in this paper requires the measurement of a consecutive series of impedance diagrams during the time of the system evolution. The analysis of this four-dimensional data set is based on the hypothesis of a continuum of the state and parameter spaces. This approach allows the estimation of the non-stationary transfer function of the system presented by its instantaneous impedance projections. The method described is applied to simulated data and the validity of the non-stationary estimation is verified.

Structural simulation is a new approach to modeling of more complex electrochemical systems, the impedance of which is hard to present in an explicit analytical form. This method is based on the parameters and structure of the impedance model only and eliminates the solution of the impedance equations. It renders possible the simulation of complex models with variation of both their parameters and structures and provides a complete computerization of the simulation process.

The main problem in parameter estimation of electrochemical systems is related to their significant response in a very large frequency range. Using the classical least-squares method leads to the solution of “ill-conditioned” matrices. To avoid this problem, a model reduction method has been developed for parametrical identification of electrochemical systems in the frequency domain. According to this approach, the system is represented by reduced lumped parameter submodels. Parameter estimation of these submodels is consecutively performed using simple least-squares estimators on the basis of the impedance data reduced for the participation of the previous submodels. For more efficient computer handling of the models, a matrix description of the electrochemical impedances is introduced. A number of simulated models and measured data are identified showing the applicability of this method.