J. Electrochem. Soc. 2015 volume 162, issue 9, A1849-A1857 Parameterisation of a Physico-Chemical Model of a Lithium-Ion Battery Part II: Model Validation Madeleine Ecker1,2, Stefan Käbitz1,2, Izaro Laresgoiti1,2, Dirk Uwe Sauer1,2,3 1 Chair for Electrochemical Energy Conversion and Storage Systems, Institute for Power Electronics and Electrical Drives (ISEA), RWTH Aachen University Jägerstrasse 17-19, 52066 Aachen, Germany 2 3 Juelich Aachen Research Alliance, JARA-Energy, Germany Institute for Power Generation and Storage Systems (PGS) @ E.ON ERC, RWTH Aachen University, Germany Corresponding author: Madeleine Ecker, Email: batteries@isea.rwth-aachen.de, Telephone: +49 241 80 96943 Fax: +49 241 80 92203 1 Abstract To draw reliable conclusions about the internal state of a lithium-ion battery or about ageing processes using physico-chemical models, the determination of the correct set of input parameters is crucial. In the first part of this publication, the complete set of material parameters for model parameterisation has been determined by experiments for a 7.5 Ah cell produced by Kokam. In this part of the publication, the measured set of parameters is incorporated into a physico-chemical model. Model results are compared to validation test results conducted on laboratory-made coin cells produced with materials obtained from the Kokam cell. The model is also compared to laboratory-made coin half cell experiments where anode or cathode materials obtained from the Kokam cell have been tested against metallic lithium as counter electrode, to prove the behaviour of the single electrodes. Finally, the model is scaled to reproduce the original Kokam cell and model results are validated by comparison with measurement results. The influence of temperature is considered as well. It is discussed, to which extent material parameters obtained by experimental investigation of laboratory coin cells can be transferred to commercial cells of the same material. The validity of physico-chemical models to describe cells is shown. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 2 Introduction There are different kinds of models to simulate lithium-ion batteries, each addressing different purposes. Electrical models, based on simple electric circuit diagrams, are usually used for battery management systems as they superior due to their high computing time efficiency [1]. Impedance-based models [2] are more complex, but are able to provide certain measures of extrapolation, as they map physical processes. They can be coupled to thermal models to design pack configurations and cooling systems [3]. They are also used in semi-empirical aging models aiming to predict lifetimes of batteries in real life applications [4]. Physicochemical models on the other hand are even more complex as they simulate the physical and chemical processes based on the fundamental physical principles. Usually, such models describe the migration and diffusion processes as well as the charge transfer kinetics. They are not only able to reproduce the voltage/current behaviour of a battery and to make extrapolations; they also display the internal state of a battery as potential or concentration distributions. Therefore, they can be used to gain a better understanding of the processes occurring inside a lithium-ion battery by providing much more information than just the terminal voltage. As they are parameterised by material properties, they help to optimise the material development process and they support purposed-designed cell development processes. The impact of changes in material properties on the system behaviour can be simulated with such models. Also, ageing mechanisms as lithium-plating [5], formation of solid electrolyte interfaces (SEI) [6] [7] or mechanical stresses [8] can be addressed. Physicochemical models are the only way to elaborate the performance of a battery cell before is even has been build. Several papers have been published developing physico-chemical simulation models that are based on the work of Newman and Tiedemann 1975 [9], amongst others: [10] [11] [12] [13] [14]. However, to the knowledge of the authors no work exists where a simulation model has been completely parameterised by parameters determined for the special material under consideration using samples taken from the test object. In most published models, a significant amount of parameters where derived from sometimes unsuitable literature sources or were even just roughly estimated. Only few comprehensive parameterisation efforts have been made. Doyle and Newman 1996 [11] validated a model based on measured values, but did not determine diffusion coefficients and kinetic parameters for their material. Less et al. 2012 [15] parameterised a half cell, but did not determine the kinetic parameters. In most papers dealing with physico-chemical models, values from supplementary literature sources have been taken, bearing the risk of different material properties, due to slight changes in the material. Smart et al. 2011 [16] for example showed that only small changes in the composition of the electrolyte can lead to high changes in the exchange current density of the system. Especially the parameters determining the cell kinetic are problematic, as either no reliable data are available in literature or the literature values of the parameters differ by several orders of magnitudes (see f. expl. the discussion of the diffusion coefficient in part I of this publication [17]). In some cases, assumptions have been made or model fitting has been performed to identify certain parameters. However, especially if conclusions about the internal state of the battery are to be drawn, the most important thing is to choose the correct set of parameters for the material under consideration. Shifting parameters against each other can lead to the same electrical behaviour, but changes the internal state of the battery completely. For investigation J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 of ageing effects, the true set of parameter is crucial. Therefore, a simple fitting for a high quantity of parameters is not the accurate method for parameter determination. In this work, a commercially available cell of unknown design and material content is considered. In the first part of this publication, the cell has been opened under argon atmosphere and all material parameters relevant to parameterise a physico-chemical model have been determined by experiment. Parts of the parameters have been determined building laboratory–made coin cells. In this part of the paper, the simulation model is introduced and all parameters measured in the first part are integrated into the model. A validation of the model including the measured parameters is given. Subsequently, it is discussed to which extent parameters obtained in laboratory cells can be transferred to commercial cells of the same material. 3 Experimental For model development, a commercial high energy pouch lithium-ion battery with 7.5 Ah manufactured by Kokam, labelled SLPB 75106100 has been used. The anode consists of graphite, the cathode of Li(Ni0.4Co0.6)O2 material. A detailed cell description can be found in the first part of this paper [17]. For model validation, coin cells have been built with materials extracted from the Kokam cell. Different types of laboratory cells were produced: • • coin full cells: consisting of anode (16 mm), cathode (16 mm) and separator (18 mm) coming from the Kokam cell together with 100 µl of LP50 of BASF. coin half cells: consisting either of anode or cathode (16 mm) and separator (18 mm) coming from the Kokam cell together with a metallic lithium foil (16 mm) as counter electrode and 100 µl of LP50 of BASF. No reference electrode has been used in this setup. After assembling, all cells were subject to additional initialisation cycles in order to restore the SEI. All electrochemical measurements on coin cells have been performed with a BaSyTec test device at 23 °C unless it is indicated differently. The open circuit potential (OCV) curve of the cells has been recorded during a stepwise charging process, where the OCV has been detected after a break of 5 h in each step. The validation tests for the 7.5 Ah Kokam cell have been performed with a cycling device by Digatron (ECO 10 A 0 – 6 V). Temperature was regulated with a climate chamber (Binder MK53 -40 °C to +180 °C). The temperature of the cell was logged using a temperature sensor on the cell surface. Additionally, the OCV curve for this cell has been recorded during a stepwise charging process, where the OCV has been detected after a break of 5 h in each step. 4 Simulation-Model In this section, a physico-chemical model will be introduced, that is able to simulate the electrical behaviour of the lithium- ion battery introduced in section 3. In a first step, the J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 complete dynamical model describing a full cell is introduced. For validation purposes, two modifications of this model have been implemented that are also discussed in the following. The models in question are a model describing a half cell (i.e. anode or cathode against metallic lithium as counter electrode) as well as a model neglecting all dynamic processes in the battery, only simulating the open circuit behaviour (model for electrode balancing determination). 4.1 Dynamic Cell Model The model relies on the governing physical and chemical processes in a lithium-ion battery, comprising diffusion and migration processes in the electrolyte and the solid material as well as the charge transfer process and has a 1D spatial resolution. The model is able to simulate the external accessible voltage Ubatt response of a battery to a given current Ibatt or vice versa as well as the time evolution of internal parameters of the battery like local potentials or concentration distribution of lithium ions in the electrolyte or the active material. It is based on the porous electrode theory originally derived by Newman and Tiedemann 1975 [9] [18]. Figure 1: Electrical network used in the physico-chemical cell model to describe the current distribution inside the cell. The model used in this work applies an electric circuit diagram to reproduce the current distribution inside the cell. The network is shown in Figure 1 and consists of different resistances and voltage sources imaging the physico-chemical processes. The elements of the network are not derived by regression fitting as it is known for impedance-based models, but represent the properties of the materials and are described by the corresponding physical and chemical equations. Elements of the network are the electronic resistance of the current collectors RCC and the electronic resistance of the active solid material RA, which are kept constant in the simulation. The charge transfer resistance RCT determines the reaction kinetics of the intercalation process and is calculated by applying the Butler-Volmer equation which describes the relation between reaction overpotential ηD and the current going into the reaction iD: dD R ct = d D = ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ ∙ D + (1 − ) ∙ − ( ∙ )∙ ∙ ∙ D ! (1) j0 is the exchange current density, α the transfer coefficient, z the charge number (for lithiumion battery z = 1), T the temperature, R the gas constant and F the Faraday constant. The contact area between electrode and electrolyte S is calculated by the total electrode volume J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 Velectrode, the porosity ε, the inactive part of the material, the volume of a single particle V1particle and the particle radius rparticle, following: S= #electrode ∙ (1 − () ∙ (1 − )*+,-). #1particle part ) 5 ∙ 4 ∙ 3 ∙ 4particle (2) The active material is assumed to consist of spherical particles The dependency of the exchange current density on the lithium concentration on the surface of the solid cs,sur and the lithium concentration in the electrolyte ce is described by [18]: 67 = 8 ∙ 97 ∙ (,:,max − ,s,sur )( ) ∙ ,s,sur ∙ ,@ (3) (cs,max-cs,sur) is the concentration of unoccupied sites in the intercalation lattice and k0 a proportionality factor. The temperature dependency of the exchange current density is modeled using Arrhenius equation: 67 (A) = 67 (A = 296.15[H]) ∙ Ja,j0 ∙M 5NO. P[Q] R (4) Ea,j0 is the activation energy of the charge transfer reaction and 296.15 K is the reference temperature the parameterisation measurements were conducted at [17]. Further on, the electrical network consists of a resistance RSEI describing the ionic conductivity of the SEI. This resistance is assumed to be zero for the pure electrical simulation and becomes more important if ageing effects are considered. In the pure electrical model, the effect of the SEI is incorporated in the charge transfer resistance. The voltage source U in the network represents the open circuit voltage of the considered electrode in dependency on the lithium concentration on the surface of the solid material. The open circuit voltage curves are measured for the cathode and anode using coin half cell setups (see [17]) and are implemented into the simulation model as look up tables. The electrochemical potential of the electrodes does not only depend on the concentration of lithium ions in the solid material as it is described by the voltage source U. It depends on the concentration of lithium ions in the electrolyte as well. For a cell in equilibrium (this means a constant concentration over the whole electrolyte), the contributions of the two electrodes sum up to 0 V. However, this is not the case in absence of equilibrium. This effect can be demonstrated by a concentration cell consisting of two equal electrodes in electrolytes of the same components, but different ion concentrations. There is a tendency for ions in the less concentrated electrolyte to dissolve and in the more concentrated one to plate on the electrode, which manifests in a potential difference between the two electrodes [19]. The resulting overpotential is commonly called ‘concentration overpotential’ ηC and is determined by Nernst equation according to [20]: C = T∙A ,I ∙ ln M R U∙8 ,II (5) This concentration overpotential due to concentration gradients in the electrolyte is described in the model by an additional voltage source in the network, labeled Uc applying equation (5). J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 The resistance RE reflects the ionic conductivity of the electrolyte inside the porous structure of the electrodes and is dependent on the lithium concentration in the electrolyte and on temperature. The concentration dependency of the bulk electrolyte σe has been measured in the first part of this publication [17] and can be described by Xe = 2.667 ∙ Z − 12.983 ∙ 5 + 17.919 ∙ + 1.726 (6) where σe is the electrolyte conductivity in [mS/cm] and x the salt concentration in [mol/l]. Equation (6) has been obtained by data fitting. The temperature dependency is modelled using the Arrhenius equation: Xe (A) = Xe (A = 296.15[H]) ∙ 296.15[H] ∙ A Ja,σe ∙M 5NO. P[Q] R (7) However, the conductivity of electrolyte in a porous structure differs from the conductivity of the bulk electrolyte. Therefore, an effective conductivity σe,eff can be introduced using the tortuosity factor κ and the porosity ε of the material. Xe, eff = Xe ∙ ( κ (8) The tortuosity factor describes the impact of the porous structure on mass transport and therefore strongly influences the lithium ion diffusion in the electrolyte as well as the ionic conductivity in a cell. The tortuosity factor κ is defined as the ration between the squared actual length of the way through the pore Leff going from point A to point B and the squared direct way L between the two points [21]. Finally, the resistance RE is calculated using the effective conductivity σe,eff, the thickness of the electrode coating d and the electrode surface A (determined by the length and width of the electrode): TE = b A ∙ Xe,eff (9) The resistance RS describing the ionic conductivity of the separator is calculated in the same way, combining equations (7) - (9) and (6) with the geometrical parameters of the separator. The double layer capacity of the battery is neglected in this model, as it only contributes to the voltage on very small time constants (in the range of ms). Ong et al. 1999 [22] integrated a double layer capacity into a physico-chemical model. They showed that a double layer capacity leads to a smoother transition toward the maximum potential at a given current. To solve the network, the elements of the electric circuit diagram have to be determined in each time step. For a given outer current, the current distribution and the resulting potentials in the network are calculated using the mesh current method. Figure 1 shows the spatial resolution of the electrical part of the model. Both electrodes are divided in 3 elements, each represented by a vertical line including the charge transfer and SEI resistance and the open circuit potential. The three different parts of each electrode has been marked by different shades of grey. The resolution is chosen as an example and can be increased on expense of J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 computing efficiency. If an electron comes from the outer circuit, it has to go through the current collector resistance, through the active material resistance of the first element and can then proceed in the active material to the next element closer to the separator or perform a charge transfer in the current element. Correspondingly, all paths above the charge transfer resistance represent electron transport; the paths below represent ion transport. As the elements of the electric circuit diagram depend on the lithium concentration on the surface of the solid material cs,sur as well as in the electrolyte ce, these concentrations have to be determined in each time step as well. Therefore, a model system is assumed, consisting of spherical active mass particles. The particles are assumed to have electrical contact but no inter-particle diffusion. Neglecting the effect of stress and anisotropic diffusion and assuming the active material to be a good electronic conductor (transport number t- ≈ 1), the diffusion in the solid material can then be described by Fick’s second law converted to spherical coordinates: d,s 1 d d,s = 5 ∙ Mds (,s ) ∙ 4 5 ∙ R d4 d4 d4 (10) r is the radius and Ds(cs) the concentration dependent diffusion constant of the solid material. On the surface of the particles the change in concentration is determined by diffusion as well as by the charge transfer current density jD, leading to the boundary condition: d,s 6D e =− d4 fg ds ∙ 8 and in the core: d,s e =0 d4 fg7 (11) Finally, to determine the concentration in the electrolyte the diffusion processes within the electrolyte have to be simulated. To model the porous electrode it is assumed that the space between the spherical particles is filled with inactive materials and electrolyte and has a certain tortuosity factor κ and a porosity ε. Therefore, the diffusion in this porous structure proceeds with an effective diffusion coefficient De,eff (similar to equation (8)) according to [21]). deff = d∙( κ (12) For battery systems usually concentrated solution theory is applied deviating from dilute solution theory by incorporating the interaction between the ions as well. This interaction is described by Stefan-Maxwell diffusion. Together with the Nernst-Planck equation and the continuity equation of mass and charge the Stefan-Maxwell diffusion can be used to derive an expression describing the change in lithium ion concentration with time in a binary electrolyte: d,e 1 1 − -7m = ∙ ∇kde,eff ∙ ∇,e l + ∙ + ∙ 6D d( 8∙( with zero flux at the current collectors: (13) J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 b,e e =0 b- ng7 and ngo (14) De,eff is the effective value of the apparent diffusion coefficient of the electrolyte in the porous structure (deviating from the one defined with respect to the solvent De0,eff) and t0+ is the transport number for Li+ in this electrolyte with respect to solvent velocity. It describes the contribution of the lithium ions to the total migration current. a is the ratio between the contact area between electrode and electrolyte and the considered volume. In equation (13), convection has been neglected and t0+ has been assumed to be constant with concentration. Furthermore, porosity has been assumed not to change with time. This is true, as long as no ageing of the system is considered and the porosity change due to the volume change is neglected. Due to the fact that in this work the transport of the solvent is not modelled and therefore the change in solvent concentration c0 is not known, it has been additionally assumed that dln(c0)/dln(ce) = 0. Therefore, equation (13) resembles the diffusion equation derived by dilute solution theory. A detailed derivation of transport equations in dilute and concentrated solution theory can be found in [19]. An application to a full-cell sandwich is also discussed in [10]. In each time step the diffusion equations of the active material and the electrolyte (equation (8) and (13), respectively) are solved using the finite difference method. For solid state diffusion the active mass particles are divided into 30 shells with constant volume. For simulation of the diffusion in the electrolyte, each electrode is divided into 18 volume elements, the separator into 6. Figure 2: Scheme of the active material concentration in anode and cathode directly after fabrication (upper figure) and in the charged state after the first initialisation cycles. For a charged cell csn,start and csp,start are used as start concentrations. The balancing of the system is determined by the start concentration of the anode csn,start and the cathode csp,start in the model. In Figure 2 the active material concentrations of cathode and anode are outlined for a cell directly after fabrication (upper figure) and in a charged state after the first formation cycles (lower figure). Prior to the first formation cycle, the anode consists of pure graphite (without lithium) and the cathode contains the maximum possible amount of lithium csp,max. Usually the lithium in Li(Ni0.4Co0.6)O2 - based cathode materials is J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 only used partly due to the low stability of lithium poor phases [23]. In the following, the used percentage of lithium in the cathode is called ‘utilisation’. During the first charge process, the lithium is deintercalated from the cathode and intercalated partly to the anode, the other part is irreversibly consumed in SEI formation (CSEI). Therefore, a cell in charged state has the following concentrations: ,sp,startg (1 − p-)q)r+-)s*) ∙ ,sp,max up ∙( ,sn, start = (p-)q)r+-)s* − tSEI ) ∙ ,sp, max ∙ u | ∙( vp )∙( vn )∙( (15) wxyz {@part,p ) (16) wxyz {@part,n ) V denotes the volumes of the electrode coatings, ε the porosities and inactivepart fraction of inactive material in the electrodes. For a cell in a discharged state one obtains: ,sp,startg (1 − tSEI ) ∙ ,sp,max (17) ,sn, start = 0 (18) The theoretical maximal concentration of an active material particle cs,max can be calculated by the density ρ and the molar mass M of the intercalation compound LiC6 or Li(Ni0.4Co0.6)O2: ,s,max = 4.2 } ~ (19) Dynamic Cell Model with one lithium-metal electrode The dynamic cell model for investigating one electrode in detail is generally similar to the full cell model described in section 4.1. However, instead of having an intercalation compound on the negative electrode, the anode is substituted by a lithium metal layer. On the positive electrode any material can be simulated, e.g. graphite, Li(Ni0.4Co0.6)O2,… Figure 3 displays the electric circuit diagram to model the half cell. Ubatt RCCp RA1p RA2p RA3p RA3n RCT1p RCT2p RCT3p RCT3n RSEI1p RSEI2p RSEI3p RSEI3n U1p U2p U3p RE1p Uc21p RE2p Uc32p RCCn U3n RE3p Ucs3p RS Figure 3: Electrical network used in the physico-chemical cell model with one lithium-metal electrode to describe the current distribution inside the cell. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 In difference to the intercalation compound the lithium layer has no porous structure filled with electrolyte, but consists of a single layer. Therefore, the lithium deposition reaction can only take place on the surface of the lithium layer directly at the separator, which is not the surface of a porous structure, but the pure geometrical area of the electrode. In the half cell model, no diffusion of lithium ions in the electrolyte occurs on the negative electrode and also no diffusion occurs inside the active material. The reaction on the negative electrode is a deposition reaction following the Butler-Volmer equation (1) with a concentration dependency of the exchange current density following: 67 = 8 ∙ 97 ∙ ,e (20) Also in this case the SEI resistance is assumed to be zero for the pure electrical model, but is incorporated in the charge transfer resistance. As in our setup, the lithium potential serves as reference potential, the voltage source U3n describing the lithium potential is zero. 4.3 Model for Cell Balancing Determination The model for cell balancing determination is a simplification of the full cell model described in section 4.1, where all dynamical processes have been neglected. Hence, the model consists of one active material particle for each electrode, where lithium can accumulate, without modelling the diffusion or the intercalation process itself. It serves as a tool to validate the balancing of the electrodes by comparing the simulated OCV curves with measured ones (see section 6). For each electrode, the open circuit voltage in dependency on the amount of intercalated lithium is provided. A given current directly changes the lithium content of the anode and cathode particle and therefore the OCV. The balancing of the two electrodes is determined by the utilisation of the cathode, the amount of formed SEI and the capacity of the active materials. Latter is calculated from the geometrical dimensions of the two electrodes, the theoretical capacity of the active materials, the amount of inactive material in the electrodes and their porosity (see equation (15) and (16). The parameters needed for model parameterisation are listed in Table 1. Abbreviation Description Unit Measured value wcell,p width of cathode of Kokam cell width of anode of Kokam cell length of cathode of Kokam cell length of anode of Kokam cell diameter cathode of coin cell diameter anode of coin cell thickness of cathode thickness of anode thickness of separator porosity of cathode porosity of anode porosity of separator inactive part of cathode inactive part of anode calculated maximal possible lithium concentration in an µm wcell,n hcell,p hcell,n diametercell,p diametercell,n Dxp Dxn Dxs εp εn εs inactivepart,p inactivepart,n csn,max Final model value Kokam cell 85·10³ Final model value coin cell - µm 87·10³ - 85·10³ µm 101·10³ - µm 103·10³ - µm µm µm µm µm % % % % % mol/dm ³ 16·10³ 16·10³ 54.5±0.5 73.7±1 19 29.6±0.7 32.9±0.5 50.8±2 39.17 40.37 31.92 101·10³ - 40 42.6 42 44.5 J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 OCVp anode particle calculated maximal possible lithium concentration in a cathode particle capacity loss due to initial SEI degree of utilization of cathode material OCV vs. x of cathode OCVn OCV vs. x of anode V Vmax Vmin maximal voltage minimal voltage V V csp,max CSEI utilisation mol/dm ³ 48.58 % 14 % 74 V See Figure 3-6 in [17] See Figure 3-5 in [17] 4.2 2.7 6.8 75 Table 1: Model parameter for the Model for cell balancing determination. The measured values as well as the values finally used in the coin cell and the Kokam cell simulation are listed. If no model value is given, the parameters have been used as measured originally. All parameters were measured at a temperature of 23 °C. 5 Model Parameterisation: Summary of the measured parameters In this section, the measured model parameters are summarised. The parameters have been measured in the first part of this publication [17]. Therefore, Kokam cells (SLPB 75106100) have been opened under argon atmosphere, the geometrical data have been measured and samples have been taken for further investigations. Hg-porosimetry has been conducted to determine porosity, particle radius as well as tortuosity of the electrodes and the separator. Conductivity and diffusion constants of the electrolyte as well as the electronic conductivity of the active material have been measured using the voltage response of the sample to an applied current. Finally, electrochemical measurements have been conducted on laboratory made coin cells, in order to determine open circuit voltage curves, diffusion coefficients and the charge transfer kinetics of the active materials as well as the balancing of the system. For all measurements, an electrolyte produced by BASF (LP50) has been employed. This electrolyte has been assumed to resemble most to the one of the original system, even if the exact composition of this system is unknown. In Table 1, the measured parameters determining the balancing of the system are given. In some cases a deviation from the measured parameter has been identified in order to obtain an agreement between experimental and simulation results. Therefore also the parameter values finally used for the simulation of the coin cell and the Kokam cell are listed. If no model value is given, the parameters have been used as measured originally. Deviations of the model parameter from the measured value are discussed in section 6. In Table 2, the parameters determining the dynamic behaviour of the system are given. Furthermore, the measured values as well as the values finally used in the coin cell and the Kokam cell simulation are listed and deviations are discussed in section 6. Abbreviation Description Unit Original values Final model values coin cell Final model values 7.5 Ah cell J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 rp rn κp κs κn Ds,p particle radius of cathode particle radius of anode tortuosity factor of cathode tortuosity factor of separator tortuosity factor of anode diffusion coefficient of cathode cm²/s Ds,n diffusion coefficient of anode cm²/s j0,p exchange current density of cathode at 50 % SOC exchange current density of anode at 50 % SOC exchange current density of lithium transfer coefficient of cathode transfer coefficient of anode transfer coefficient of lithium electronic conductivity of cathode electronic conductivity of anode diffusion coefficient of electrolyte transport number of electrolyte A/cm² 6.49±0.1 8.7±0.9 1.94±0.006 1.67±0.02 2.03±0.006 see Figure 3-9 in [17] see Figure 3-9 in [17] 2.23·10-4 A/cm² 7.05·10-5 5.39·10-4 A/cm² 2.04·10-3 - S/cm 0.527 0.489 0.492 0.681±0.44 S/cm cm²/s 0.14±0.03 2.4·10-6 S/cm J/mol literature value [24]: 0.26 See equation (6) 80.6·103 - J/mol 40.8·103 - J/mol 17.1·103 - J/mol 43.6·103 - J/mol 53.4·103 - J/mol 65.0·103 J/mol 17.1·103 j0,n j0,Li αp αn αLi σs,p σs,n De t0+ σe Ea,Dsp Ea,Dsn Ea,De Ea,j0p Ea,j0n Ea,j0Li Ea,σe ionic conductivity of electrolyte activation energy of diffusion coefficient of cathode activation energy of diffusion coefficient of anode activation energy of diffusion coefficient of electrolyte activation energy of exchange current density of cathode activation energy of exchange current density of anode activation energy of exchange current density of lithium activation energy of ionic conductivity of electrolyte µm µm 3.5 3.5 - 59.3·103 - Table 2: Model parameters for the dynamic model. The measured values as well as the values finally used in the coin cell and the Kokam cell simulation are listed. If no model value is given, the parameters have been used as measured originally. All parameters were measured at a temperature of 23 °C. 6 Model-Validation In this chapter, all parameters are incorporated into the models described in section 4. First of all, the model is validated by comparison of simulation results with measurements conducted on coin cells made from materials extracted from the Kokam cell. In a second step, the model results are compared with coin half cell measurements, in order to validate the behaviour of the single electrodes. The coin half cells have been built by materials extracted from the J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 Kokam cell with a metallic lithium foil as counter electrode. Finally, the model is scaled to simulate the full 7.5 Ah Kokam cell and the results are compared with measurement results at different temperatures. 6.1 Comparison with coin full cell measurements Validation tests have been performed, in order to compare model simulation results with measurements of coin cells made from materials retrieved from the 7.5 Ah Kokam cell. All measurements and the respective simulations have been conducted at 23 °C. The constant temperature value was applied to the model. Cell heating has been neglected in this section, which seems to be acceptable for the small coin cells. 3.5 1 Voltage [V] 4 2 Error [%] Voltage [V] 4 4.5 3 Simulation Measurement Error (a) 2 3.5 1 3 3 2.5 0 3 Simulation Measurement Error Error [%] 4.5 1 2 3 Discharge Capacity [mAh] 2.5 0 0 4 (b) 1 2 3 Discharge Capacity [mAh] 0 4 Figure 4: Comparison of a simulated and measured OCV curve of a coin full cell at 23 °C. The simulation error is displayed on the right axis. (a): Simulation performed with the measured set of model parameters, (b): Simulation performed with an adopted set of model parameters (see Table 1). First of all, OCV curves are used to compare with results obtained by the Model for cell balancing determination introduced in section 4.3. The Model for cell balancing determination has been developed to validate the balancing of the cell. In Table 1, all parameters needed to parameterise the Model for cell balancing determination are listed. All measured values are given to the model. Figure 4 (a) displays a comparison of the model results using the measured parameters with measurement results. The simulation result reproduces the measurement quite well. However, a detailed comparison with complementary parameterisation results of the cell balancing in the first part of this paper [17] shows some discrepancy with the simulation. According to the parameterisation experiments, the anode capacity should be smaller than stated in the simulation. The lithium content of the anode at full state of charge of the cell, for example, reveals a value of 0.71 in the simulation (xEoC,anode=0.71), but in the parameterisation experiments [17] a value of 0.75 has been measured. The anode adds only a small contribution to the voltage of the full cell, leading to only small deviations in the full cell voltage, even if the balancing is not correct (see Figure 4). However, the correct balancing of the anode is of great importance, especially for the simulation of ageing mechanisms at the anode, like SEI formation or lithium plating. In order to adapt the correct anode stoichiometry in the model, the inactive part of the anode and cathode material determined in [17] has been changed from 39.19 % to 40 % and from 40.37 % to 42.6 % for the cathode and the anode, respectively. The inactive part of the material is an arguable parameter that has high uncertainty in its determination (see [17]). Therefore, it seems to be justified to make these small changes. Additionally, the utilisation has been changed from 74 % to 75 %. Also this variation lies within the measurement J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 uncertainty. Figure 4 (b) displays a comparison of the model results using the adapted values with measurement results. The reproduction of the measurement is even better compared to the original set of parameter. The error of the simulation is below 1 %. Only at end of discharge the deviation rises slightly above 1 %. The original set, as well as the adapted set of parameters, are given in Table 1. 23°C Voltage [V] 4 3.5 4.5 3 (a) 23°C 1C 4 Voltage [V] 1C simulation 1C measurement 0.5C simulation 0.5C measurement 0.25C simulation 0.25C measurement 4.5 3.5 3 2.5 0 1 2 3 Time [h] 4 5 (b) Simulation Measurement 1 2 Time [h] 2.5 0 3 4 Figure 5: (a): Comparison of simulated and measured discharge curves of a coin full cell at 23 °C and different C rates. (b): Comparison of a simulated and measured charge-discharge curves at 23 °C and 1 C. The charge consists of a constant current, followed by a constant voltage phase. A break of 1 h has been made before discharge. All simulations have been performed without changes in the measured set of dynamical model parameters. The parameters determining the balancing have been adjusted according to the discussion above (the final model parameters used here are listed in Table 1and Table 2). 4.2 Simulation Measurement 4 3.85 Voltage [V] Voltage [V] 3.8 3.6 3.4 3.2 3 2.8 (a) 2.6 0 Simulation Measurement 3.9 3.8 3.75 3.7 23°C 3.65 2 4 6 Time [h] 8 10 12 4 (b) 4.5 5 Time [h] 5.5 6 Figure 6: Comparison of a simulated and measured pulse profile of a coin full cell at 23 °C. Pulses at different SOC, with different current rates (0.25 C, 0.5 C and 1 C) and different durations (10 S and 100 s) are compared. Figure (b) shows a zoom of figure (a) to display the pulses in more detail. All simulations have been performed without changes in the measured set of dynamical model parameters. The parameters determining the balancing have been adjusted according to the discussion above (the final model parameters used here are listed in Table 1 and Table 2). In a second step, all dynamic parameters measured in [17] and listed in Table 2 are implemented into the dynamical full cell model. The parameters determining the cell balancing have been chosen as discussed above. In Figure 5 (a), simulation results of discharge curves with different current rates at 23 °C are compared with experimental results J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 of a coin full cell. Without changing the measured set of dynamic parameters, the model shows a good agreement with the measured data. Also the 1 C charge-discharge curve (constant current charge, followed by a constant voltage phase, a 1 h break and a constant current discharge), shown in Figure 5 (b), can be reproduced by the model. Figure 6 shows the comparison of model end experimental results during a pulse profile. Pulses have been performed at different SOC, with different currents and different durations to test the performance of the model on short timescales and the relaxation behaviour. Graph (b) shows a zoom of graph (a), to analyse the pulses in more detail. Additionally, the short term behaviour of the cell can be reproduced well by the model using the same set of parameters. The maximum error occurring between simulation and measurement is 3.1 %. Higher deviations are only occurring at the end of the discharge. It is worse to keep in mind that the simulation results are obtained without fitting of parameters to the measured data. 6.2 Comparison with coin half cell measurements The comparison of simulation results with coin full cells only validates the behaviour of the complete system. However, especially for the simulation of ageing mechanisms the polarisation of the single electrodes is of great importance. Especially, since the anode only adds a small contribution to the full open circuit cell voltage. Thus, from investigation of the full cell behaviour, it is difficult to validate the polarisation of the anode itself. In order to validate the model with respect to the behaviour of the single electrodes, model results have been compared with measurements performed on coin half cells built with materials of the Kokam cell and metallic lithium foil as counter electrode. All measurements have been conducted at 23 °C. This constant temperature has been given to the model. Cell heating has been neglected as for the full cells. 1.4 1.2 1.4 Simulation Measurement τn=2.03 23°C (a) 0.8 0.6 0.8 0.6 0.4 0.4 0.2 0.2 0 0 23°C 1 Voltage [V] Voltage [V] 1 Simulation Measurement τn=3.5 1.2 1 2 3 Time [h] 4 5 0 0 6 (b) 1 2 3 Time [h] 4 5 6 Figure 7: Comparison of a simulated and measured discharge curve of a coin cell with a graphite and a lithium-metal electrode (graphite coin half cell) at 23 °C and 0.2 C. The simulations have been performed with the final parameter set discussed above (see Table 1 and Table 2). (a) displays the simulation performed with the originally measured tortuosity factor of the anode (τn=2.03). In (b), a higher value (τn=3.5) is used in the simulation. Figure 7 shows the 0.2 C discharge of the graphite coin half cell. Graph (a) shows the simulation result that has been obtained with the final parameter set discussed above (see Table 1 and Table 2). The comparison with the experimental result shows good agreement, but the different stages are not perfectly reproduced. There seem to be higher inhomogeneity in the real system compared to the simulation smearing the transitions. An increased tortuosity factor leads to slower electrolyte diffusion and therefore to increased inhomogeneity. An underestimation of the tortuosity factor using Hg-porosimetry can occur, J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 if small enough pores exist, where Hg cannot enter. Furthermore the approximation used to calculate the tortuosity factor is only valid for values smaller than 2.2. In graph (b), a higher value for the tortuosity factor of the anode (τn=3.5) has been used for the simulation. With a tortuosity factor of 3.5 for the anode material, the half cell behaviour can be reproduced significantly better. Re-simulation of the results of section 6.1 shows that the change in tortuosity factor of the anode does influence the full cell behaviour only marginal, but only changes the internal polarisation of the cell. As the final aim of the physico-chemical model is the simulation of ageing mechanisms, the mapping of the correct polarisation of the cell is of great importance. Therefore, the tortuosity factor of the anode has been set to 3.5 for the following simulations (see Table 2). 4.4 Simulation Measurement 4.2 Voltage [V] 4 3.8 3.6 3.4 3.2 3 2.8 0 23°C 2 4 Time [h] 6 8 Figure 8: Comparison of a simulated and measured discharge curve of a coin cell with a Li(Ni0.4Co0.6)O2 and a lithium-metal electrode (Li(Ni0.4Co0.6)O2 coin half cell) at 23 °C and 0.2 C. The simulations have been performed with the final parameter set discussed above (see Table 1 and Table 2). Figure 8 shows the 0.2 C discharge of a Li(Ni0.4Co0.6)O2 coin half cell. These simulation results have also been obtained with the final parameter set discussed above (see Table 1 and Table 2). Comparison with experimental results shows good agreement at beginning of the discharge. However, significant deviations occur in the final state of the discharge. The deviations are probably due to charge transfer limitations of the fully lithiated electrode which are not accurately taken account for in the model. Nonetheless, these deviations are not of much importance to the simulation of full cell configurations, as the cathode is usually not utilised in full state of charge in a full cell arrangement. 6.3 Reproducing the performance of the original commercial cell in full scale In this section, the model of the coin cell is scaled up to simulate the full commercially available 7.5 Ah Kokam cell in order to investigate, if parameters obtained from coin cell setups [17] can be transferred to the original system. The simulations are compared with validation experiments performed at different temperatures. The temperature on the surface of the cell, measured by a sensor, has been given to the model to include cell heating in the simulation. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 3 4 3 Simulation Measurement Error 2 3.5 1 0 3 0 -1 8 2.5 0 (b) 2 4 6 Discharge Capacity [Ah] Error [%] 1 2 4 6 Discharge Capacity [Ah] 4.5 2 3.5 2.5 0 (a) 3 Voltage [V] Voltage [V] 4 Simulation Measurement Error Error [%] 4.5 -1 8 Figure 9: Comparison of a simulated and measured OCV curve of a 7.5 Ah Kokam cell at 25 °C. The simulation error is displayed on the right axis. (a): Simulation performed with the measured set of model parameters, (b): Simulation performed with an adopted set of model parameters determining the balancing (see Table 1). The inactive parts of anode and cathode have been increased from 39.17 % to 42 % and from 40.37 % to 44.5 %, respectively, the oversize of the anode has been neglected and the capacity loss due to SEI has been decreased from 14 % to 6.8 %. First, an OCV curve at 25 °C is used to validate the balancing of the cell. Measurement results are compared with results obtained by the Model for cell balancing determination introduced in section 4.3. Figure 9 (a) displays a comparison of the model result using the measured parameter set (see Table 1) with measurement results. The graph shows that the capacity of the cell is not reproduced accurately by the model. Similar to the coin cell, the inactive part of the anode and cathode material determined in [17] has been adopted from 39.19 % to 42 % and from 40.37 % to 44.5 % for the cathode and the anode, respectively. As discussed before, the inactive part of the material is an arguable parameter that has high uncertainty in its determination which justifies the adaptation. A second set of parameters that had to be adopted in order to reproduce the OCV curve are the geometrical dimensions of the anode. To prevent lithium plating, the anode has been designed to be larger compared to the cathode (2 mm in width and 2 mm in length). Therefore, the anode is not completely covered by a cathode in the cell. It is feasible that the part of the anode that is not covered by a cathode is not completely used in the system. Therefore, the anode is assumed to have the same size as the cathode. Furthermore, the capacity loss due to SEI has been measured in a coin cell setup. Therefore, it is likely that during cell disassembling, removal of the coating and reassembling in a coin cell, the SEI of the anode material gets destroyed in some way and reforms during the first cycles in the coin cell to a SEI with a potentially different structure. The formation of a new structure is probable, as it is not clear, if the same electrolyte has been used for parameterisation measurement, as the one employed in the original system. The results of the first two formation cycles of coin full cells show that for these cells indeed about 6 % of the capacity go into a side reaction during the first two formation cycles. This leads to the fact that in a coin cell additional lithium is lost for the system, which is reflected in a higher value for CSEI (capacity loss due to SEI). Thus, the measured value of CSEI is lowered in the following. Figure 9 (b) shows the simulation result obtained using the discussed adaptation of the parameters which is summarised in Table 1. With the change in the inactive part of the material, the geometrical dimensions of the anode and the amount of lithium lost in SEI formation, the measured OCV curve can be reproduced perfectly. In the following J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 simulations, these parameters are used and addressed to as the final set of parameter determining the balancing. In a second step, all measured dynamic parameters of the Kokam cell listed in Table 2 are implemented into the dynamical cell model where the current is scaled according to the number of active material layers. Figure 10 (a) shows simulation results obtained with the measured set of dynamical model parameters (the anode tortuosity factor of the anode has been set to 3.5 as discussed before). The parameters determining the balancing have been adjusted according to the discussion above. The simulation is compared to a measured discharge curve with 1 C at 25 °C. The model reproduces the experimental results well, but an offset is visible at begin of discharge. This offset seems to be due to a deviation in the charge transfer, which has been determined in a coin cell setup. As discussed before, it is likely that during cell disassembling, removal of the coating and reassembling in a coin cell, the SEI of the anode material gets destroyed and reforms during the first cycles in the coin cell to a SEI with a potentially different structure, especially if a different electrolyte is used in the setup compared to the original system. With a different structure also the SEI resistance changes. As SEI is coupled to the charge transfer resistance in the model, a changed exchange current density of the anode due to changed SEI resistance is likely. Also Smart et al. 2011 [16] showed that changes in electrolyte composition lead to high changes in exchange current density of the anode due to differences in SEI formation, whereas the exchange current density of the cathode, is found to be only marginally affected by a change in electrolyte. In Figure 10 (b) simulation results obtained by changing the exchange current density of the anode from 7.05·10-5 A/cm² to 5.39·10-4 A/cm² are shown. All other parameters have been fixed as before. Even if the overall discharge curve does not give a better fit, the beginning of the discharge of 1 C discharge curve at 25 °C can now be reproduced well by the model. This is important for the short term behaviour of the cell, which is of great concern in applications like electric vehicles. Therefore, the new exchange current density is used for the following simulations. The final set of parameter for the 7.5 Ah Kokam cell are listed in Table 2. 2 4 3.6 3.4 1 3.2 3 (a) 2 3.6 3.4 1 3.2 3 original dynamic 2.8 parameters 2.6 1C 25°C 0 Simulation Measurement Error 3.8 Voltage [V] 3.8 Error [%] 4 Voltage [V] 4.2 Simulation Measurement Error Error [%] 4.2 2.8 0.5 1 Time [h] 0 1.5 2.6 0 (b) final dynamic parameters 1C 25°C 0.5 1 0 1.5 Time [h] Figure 10: Comparison of a simulated and measured discharge curve of a 7.5 Ah Kokam cell with 1 C at 25 °C. The simulation error is displayed on the right axis. (a): Simulation performed with the measured set of model parameters, (b): Simulation performed with an increased exchange current density of the anode from 7.05·10-5 A/cm² to 5.39·10-4 A/cm² (see Table 2). In both cases the parameters determining the balancing have been adjusted according to the discussion above. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 25°C Voltage [V] 4 3.5 4.5 25°C, 1C 4 Voltage [V] 1.3C simulation 1.3C measurement 1C simulation 1C measurement 0.5C simulation 0.5C measurement 0.25C simulation 0.25C measurement 4.5 3 3.5 3 Simulation Measurement 2.5 0 1 2 3 Time [h] (a) 4 2.5 0 5 1 (b) 2 Time [h] 3 4 Figure 11: (a): Comparison of simulated and measured discharge curves of the 7.5 Ah Kokam cell at 25 °C and different C rates. (b): Comparison of a simulated and measured chargedischarge curves at 25 °C and 1 C. The charging process consists of a constant current, followed by a constant voltage phase. A break of 1 h has been made before discharge. All simulations have been performed with the final set of parameters listed in Table 1 and Table 2. The final set of parameter is used to simulate discharge curves at different C rates, charge and discharge curves as well as pulse profiles. In Figure 11 (a), simulation results of discharge curves with different current rates at 25 °C are compared with experimental results of a 7.5 Ah Kokam cell. The model shows a good agreement with the measured data. Likewise, the 1 C charge-discharge curve (constant current charge, followed by a constant voltage phase, a 1 h break and a constant current discharge), shown in Figure 11 (b) can be reproduced by the model. Figure 12 shows the comparison between model and experimental results during a 1 C discharge to 50 % SOC followed by a pulse profile using pulses with different currents and of different durations. The relaxation after the discharge is reproduced well by the model. Also the short term behaviour of the cell during the pulses can be reproduced by the model. The maximum error occurring between simulation and measurement is 2.3 %. Finally, also the simulation results of pulses at different SOC have been compared with experimental data. The results are shown in Figure 13. Here, the model is also able to simulate the long term discharge curves as well as the short term pulses of the cell, which a maximal error of 2.6 %. 4.3 25°C 4.2 Simulation Measurement 3.85 Simulation Measurement Voltage [V] Voltage [V] 4.1 4 3.9 3.8 3.75 3.8 3.7 3.7 3.6 0 (a) 2 4 Time [h] 6 8 4 (b) 4.5 Time [h] 5 5.5 Figure 12: Comparison of a simulated and measured pulse profile after a 1 C discharge to 50 % SOC of the 7.5 Ah Kokam cell at 25 °C. Pulses with different current rates (0.25 C, 0.5 C, 1 C and 1.3 C) and different durations (10 S and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail. All simulations have been performed with the final set of parameters listed in Table 1 and Table 2. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 4.5 Simulation Measurement 4 3.5 Simulation Measurement 3.9 Voltage [V] Voltage [V] 25°C 3.85 3.8 3.75 3 0 5 (a) 10 15 Time [h] 20 25 6 7 (b) 8 9 Time [h] 10 Figure 13: Comparison of a simulated and measured pulse profile of the 7.5 Ah Kokam cell at 25 °C. Pulses at different SOC, with different current rates (0.25 C, 0.5 C, 1 C and 1.3 C) and different durations (10 s and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail. All simulations have been performed with the final set of parameters listed in Table 1 and Table 2. To validate the Arrhenius approach and the activation energies determined, also simulation results at different temperatures have been compared with experimental data. As discussed in [17], uncertainties occurred in the determination of the activation energy of solid state diffusion depending on the method. Therefore, these two values have been left as a free fitting parameter, starting with the values from EIS measurement. The best results are obtained using the values of Ea,Dn = 59.3 kJ/mol for graphite and EaDp = 80.6 kJ/mol for the Li(Ni0.4Co0.6)O2 material. The measured activation energies as well as literature values and the values obtained by model fitting are summarised in Table 3. GITT EIS Literature Best fitting value Graphite 48.9 kJ/mol 40.8 kJ/mol 35 kJ/mol [25] 59.3 kJ/mol Li(Ni0.4Co0.6)O2 31.7 kJ/mol 80.6 kJ/mol - 80.6 kJ/mol Table 3: Activation energies for solid state diffusion coefficients obtained by different measurement techniques, literature and model fitting. The resulting activation energy of the Li(Ni0.4Co0.6)O2 material agrees with the result obtained by the EIS measurement. The one of the graphite material is somewhat higher compared to the one obtained by EIS and GITT and also compared to the literature value. However, the activation energy of solid state diffusion of the graphite has been adopted according to the best fit result. All other parameters have been fixed as before (see Table 1 and Table 2). J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 4 Voltage [V] 3.8 3.6 3.4 3.2 -10°C 4 3.8 3.6 3.4 3.2 3 3 2.8 2.8 2.6 0 1.3C simulation 1.3C measurement 1C simulation 1C measurement 0.5C simulation 0.5C measurement 0.25C simulation 0.25C measurement 4.2 Voltage [V] 40 °C simulation 40 °C measurement 25 °C simulation 25 °C measurement 0 °C simulation 0 °C measurement -10 °C simulation -10 °C measurement 4.2 1C 0.5 (a) 1 1.5 Time [h] 2.6 0 1 2 3 4 5 Time [h] (b) Figure 14: (a): Comparison of simulated and measured discharge curves of the 7.5 Ah Kokam cell with 1 C at different temperatures. (b): Comparison of simulated and measured discharge curves of the 7.5 Ah Kokam cell at -10 °C and different C rates. All simulations have been performed with the final set of parameters listed in Table 1 and Table 2. Figure 14 (a) shows measured and simulated discharge curves conducted with 1 C at different temperatures. The temperature dependency of the exchange current density seems to be reproduced accurately. No severe offset occurs at begin or during discharge. The solid state diffusion of the anode limits the capacity obtained at end of discharge. The new value of the activation energy seems to be reasonable, as the capacities are predicted quite well at different temperatures. The solid state diffusion of the cathode only models the shape of the discharge curve. The activation energy obtained by EIS seems to be the proper value, as also the shapes of the curves are reproduced well for different temperatures. Overall, the model is able to simulate the temperature dependency of the battery. Simulation Measurement 4.2 4.2 4 Voltage [V] Voltage [V] 4 Simulation Measurement 3.8 3.6 3.8 3.6 3.4 3.4 -10°C 3.2 0 (a) 2 4 Time [h] 6 8 4 (b) 4.5 Time [h] 5 5.5 Figure 15: Comparison of a simulated and measured pulse profile after a 1 C discharge to 50 % SOC of the 7.5 Ah Kokam cell at -10 °C. Pulses with different current rates (0.25 C, 0.5 C, 1 C and 1.3 C) and different durations (10 S and 100 s) are compared. (b) shows a zoom of (a) to display the pulses in more detail. All simulations have been performed with the final set of parameters listed in Table 1 and Table 2. In the following, the low temperature behaviour is investigated in more detail. Figure 14 (b) displays measured and simulated discharge curves with at -10 °C with different current rates. The dependency on current rate at low temperature is reproduced perfectly by the model. Figure 15 investigates the relaxation and short term behaviour of the cell at -10 °C. Again, a simulation of a 1 C discharge to 50 % SOC followed by a pulse profile using pulses with different currents and of different durations is compared to experimental results. Also for low J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 temperature the model is able to reproduce the relaxation after the discharge as well as the short term behaviour of the cell during the pulses. 7 Conclusions In the first part of this publication [17], all parameters necessary to fully parameterise a physico-chemical model have been determined experimentally for a 7.5 Ah pouch cell produced by Kokam. The measured values are summarised in Table 1 and Table 2. The model parameters have been used for a model validation using coin cells as well as 7.5 Ah cells of the same material. The model is able to reproduce discharge curves at different current rates as well as pulse profiles with only small adjustments of the measured parameters. The adjustment can be justified by measurement uncertainty. Additionally, the results obtained by coin half cell measurements can be reproduced with sufficient accuracy by the model. Finally, the model has been scaled to reproduce the 7.5 Ah cell. The model results have been compared with discharge curves at different current rates and temperatures as well as pulse profiles. The activation energy of the solid state diffusion has been identified to be a critical parameter, as different measurement techniques reveal values deviating strongly from each other. Fitting model to experimental results suggests that activation energies obtained by electrochemical impedance spectroscopy are more suitable for model parameterisation. The comparison of model and validation test results also revealed that additional SEI has been formed in the coin cell, probably due to SEI destruction during the disassembling/assembling process. Therefore, the amount of lithium irreversibly lost in the SEI as well as the exchange current density (also dependent on the SEI) measured by coin cells had to be adjusted to simulate the 7.5 Ah cell. With these adjustments, the model is able to reproduce the current dependency as well as the temperature dependency of the cell during usage. The results show that a physico-chemical model of a commercial available cell can be parameterised using coin cell measurements. With the derived set of parameters, the model is able to make quantitative predictions about the internal state of the battery during cycling. Furthermore, it can also be used to draw conclusions about ageing processes occurring in the cell, and it can be used to predict the performance of batteries made from the characterised materials in arbitrary cell designs. 8 Acknowledgement This work has been performed in the framework of the research initiatives “Modellierung von Lithium-Plating”, “HGF Energie Allianz” and “KVN”. “Modellierung von Lithium-Plating” with the IGF-number LN 15 was a project of the Research Association FKM, Lyon Straße 18, 60528 Frankfurt am Main and was financed via the AiF within a program to promote industrial research (IGF) by the Federal Ministry of Economic Affairs and Energy based on a decision by the German Bundestag. “HGF Energie Allianz” was funded by Impuls- und Vernetzungsfond der Helmholtz-Gemeinschaft e.V. “KVN” was funded by the German Federal Ministry for Education and Research, funding number 13N9973. Responsibility for the content of this publication lies with the authors. J. Electrochem. Soc. 2015 volume 162, issue 9, A1836-A1848 9 Bibliography [1] W. Waag, C. Fleischer, and D. U. Sauer, J. Power Sources, 258, 321 (2014) [2] S. Buller, Impedance-Based Simulation Models for Energy Storage Devices in Advanced Automotive Power Systems. PhD thesis, RWTH Aachen, ISEA (2003) [3] M. Fleckenstein, O. Bohlen, M. A. Roscher, and B. Bäker, J. Power Sources, 196, 4769 (2011) [4] J. Schmalstieg, S. Käbitz, M. Ecker, and D. U. Sauer, J. Power Sources, 257, 325 (2014) [5] P. Arora, M. Doyle, and R. E. White, J. Electrochem. Soc., 146, 3543 (1999) [6] P. Ramadass, B. Haran, P. M. Gomadam, R. White, and B. N. Popov, J. Electrochem. Soc., 151, A196 (2004) [7] J. Christensen and J. Newman, J. Electrochem. Soc., 151, A1977 (2004) [8] S. Renganathan, G. Sikha, S. Santhanagopalan, and R. E. White, J. Electrochem. Soc., 157, A155 (2010) [9] J. Newman and W. Tiedemann, AIChE J., 21, 25 (1975) [10] T. F. Fuller, M. Doyle, and J. Newman, J. Electrochem. Soc., 141, 1 (1994) [11] M. Doyle, N. J., A. S. C. N. Gozdz, A. S.Gozdz, and J.-M. Tarascon, J. Electrochem. Soc., 143, 1890 (1996) [12] P. Arora, M. Doyle, A. S. Gozdz, R. E. White, and J. Newman, J. Power Sources, 88, 219 (2000) [13] M. Doyle and Y. Fuentes, J. Electrochem. Soc., 150, A706 (2003) [14] Y. Ji, Y. Zhang, and C.-Y. Wang, J. Electrochem. Soc., 160, A636 (2013) [15] G. B. Less, J. H. Seo, S. Han, A. M. Sastry, J. Zausch, A. Latz, S. Schmidt, C. Wieser, D. Kehrwald, and S. Fell, J. Electrochem. Soc., 159, A697 (2012) [16] M. C. Smart and B. V. Ratnakumar, “J. Electrochem. Soc., 158, A379–A389 (2011) [17] M. Ecker, K. D. Tran, P. Dechent, S. Käbitz, A. Warnecke, and D. U. Sauer, “Parameterisation of a physico-chemical model of a lithium-ion battery, part i: Determination of parameters,” submitted to J. Electrochem. Soc.. [18] W. van Schalkwijk and B. Scrosati, Advances in Lithium-Ion Batteries. Springer, (2002) [19] N. J. and K. E. Thomas-Alyea, Electrochemical Systems. Wiley-Interscience (2004) [20] J. Garche and C. Dyer, Encyclopedia of Electrochemical Power Sources. No. 2 in Encyclopedia of Electrochemical Power Sources, Elsevier (2009) [21] N. Epstein, Chem. Engineering Science, 44, 777 (1989) [22] I. J. Ong, J. Electrochem. Soc., 146, 4360 (1999) [23] B. L. Ellis, K. T. Lee, and L. F. Nazar, Chem. Materials, 22, 691 (2010) [24] A. Nyman, M. Behm, and G. Lindbergh, Electrochim. Acta, 53, 6356 (2008) [25] T. Kulova, A. Skundin, E. Nizhnikovskii, and A. Fesenko, Russian J. Electrochem., 42, 259 (2006)