EVS 28 KINTEX , Korea , May 3-6 , 2015 Optimization of Li-Ion batteries through modelling techniques

Battery performance and lifetime constitute a bottleneck for electric vehicles and stationary electric energy storage systems to penetrate the market. Electrochemical or physics based battery models are one of the engineering tools to enhance their performance. These models should enable us to optimize the cell design and the battery management system. In this study we evaluate the ability of the much used Porous Electrode Model (PEM) to predict the effect of changing cathode density in the overall performance of a Li-Ion cell. We conclude that the PEM is well capable of predicting battery discharge capacities for cells with changing cathode density.


Introduction
Until today battery development, new battery designs and the optimization of existing designs are accomplished by build and break cycles.As a consequence battery development is an extremely time consuming process.However software could be used in the first stages of product design.For Li-Ion Batteries (LIBs) this is not yet implemented in a successful manner.Virtual design of these electrochemical systems remains a challenge.Not long after LIBs were commercialised by Sony, Newman and his group [1][2] proposed a mathematical abstraction, of which we refer to as Porous Electrode Theory (PET) [3], which is able to predict battery performance given certain design and material specifications of the cell.In contrast to common thermodynamics which is able to describe the equilibrium state of an electrochemical system PET attempts to predict the dynamic behaviour of LIBs.Although PET captures many physical phenomena, such as concentrated electrolyte transport and solid state diffusion, which limit the macroscopic performance of a cell, the accurate and exact prediction of performance parameters remains cumbersome.Not to mention the evolution of these parameters over the cycle life of a cell.Further research on this topic is ongoing [3][4][5].Our group is interested in the ability of PET to predict the influence of cell design parameters on battery performance.In this work cathode density is investigated.

Experimental part
In order to assess the capability of a model to predict the influence of multiple design parameters it is self-evident to conduct an experiment in which one design parameter is altered and all others are kept constant.The cathode density was chosen to evaluate the ability of a PET model to predict the influence of the cathode density on the constant current discharge capacity.The cathode density is interesting parameters to investigate because it does not affect the cost of a cell -the same amount of active material is used-but can have a clear impact on its performance as will be shown.In total 10 cells with an NMC positive electrode and graphitic negative electrode were made of which 5 cells with 14% higher cathode density.After formation and preconditioning all cells were subjected to the same characterization tests to determine the discharge capacities.The capacities were determined based on a constant current discharge until the cells reached the cut off voltage (2,7V) and after the cells were charged until 100% SoC.100% SoC is defined as the state of a cell which is reached after a constant current charge of 0,5C until the End-of-Charge-Voltage (V max = 4.2V) is reached followed by constant voltage charge until the current drops below 0,01C.By proceeding in this manner, polarization at the end of the charge regime is limited.After a relaxation period of 30min a discharge current of respectively 0,5, 1, 2, 3, 4 and 5C is applied.During all experiments the cells were put in a climate chamber keeping the temperature at 25°C. Figure 1 shows the result of this experiment.The discharge capacities are given relative to their 0,04C discharge capacity.From this figure we conclude that the influence of a higher cathode density becomes apparent only at higher than 3C.
This indicates that at low rates the anode is rate limiting.At higher C-rates the cathode limits the available capacity: from simulation results we see that LiPF 6 salt cannot penetrate to the back of the cathode, close to the current collector, fast enough in order to keep the intercalation reaction going.As a consequence the AM near the back of the electrode remains unused.Not surprisingly the effect of a higher cathode density becomes clear.A higher cathode density lowers the volume fraction of electrolyte (or porosity) and hence lowers the penetration of electrolyte.At low rates cells with higher cathode density seem to have a slightly higher discharge capacity.The reason is that a higher packaging of particles results in higher electronic conductivity of the electrode matrix.

Model description
Porous Electrode Theory (PET) is well derived by Newman [1][2] and much advanced by many researchers [3][4][5].Here we give a short overview of the PET model used in our simulation.

Reaction kinetics
Along with many other electrode reactions dominated by electrical charge transfer, the chemical reaction at the electrode/electrolyte interface in LIBs is described by a Butler-Volmer equation: Were η is the overpotential and α a and α c are the transfer coefficients.Both charge transfer coefficients are taken to be 0,5.i 0 is the exchange current density given by, with k the rate constant and c s,max the maximum concentration of lithium in the intercalation host.

Mass transport in the active material
Transport of lithium ions in the crystal lattice of most active materials can be described by Fick's first [4], Were D s is the chemical diffusion coefficient.Given the morphologically complexity of porous electrodes and difference in synthesis of the active material, published values of D s for NMC and graphite show a wide variety of values.However, from these publications a trend in the dependency on c s and order of magnitude can be derived.For NMC a linear dependence on the filling fraction is appropriate see reference Where D s,0 is the diffusion coefficient at infinite dilution and x=c s /c s,max .Also for graphite it remains challenging to determine the chemical diffusion coefficient.For these simulations we made use of data from Markevich et al. [7] which are based on Galvanosatic Intermittent Titration Technique.As in most homogenized models of LIBs the diffusion in the particles of active material is simplified to a one-dimensional diffusion in spherical particles of the same size distributed along the thickness of the electrode.

Ion transport in concentrated binary solutions
It is assumed that concentrated solution theory [1] is suitable to describe the transport of the solvated Li + and PHF 6 -ions in the mixture of organic esters.The interested reader is referred to reference [1], [4], for an elaborate derivation.The result is a set of two equations which the describe free-flow ion transport of a binary concentrated solution, With c e and Φ e respectively the concentration of the salt in the electrolyte and potential in the electrolyte.D e is the salt diffusion coefficient, κ the electrolyte conductivity, it's assumed that exact variation of the state variables, salt concentration and electrolyte potential, is not needed to describe the macroscopic output of a cell.In other words volume-averaging is used on the equations to obtain at a set of homogenized equations.This simplifies the characterization of complex porous electrodes to the average quantities called porosity and tortuosity.The free-flow transport properties of the electrolyte are altered using the Bruggeman relationship: These transport equations can be simplified further on given that the main transport direction of Lithium ions is perpendicular to the current collector surface.The result is a set of two onedimensional homogenized equations describing ion transport in the electrolyte [1].

Potential distribution in the electrodes
The potential distribution in the solid electrode matrix is determined Ohms law Using conservation of charge expressed in its local form yields With σ s the electronic conductivity of the electrode material.Equations ( 3) and (9) describe each electrode equations ( 5) and ( 6) describe the potential distribution and salt concentration in both electrodes and separator.A summary of the input parameters for the model is given in table 1.An increased cathode density will result in a lower volume fraction of electrolyte and a thicker electrode.The Open Circuit Potential (OCP) is a material dependent input parameters.The OCP of intercalation hosts changes as a function of the concentration of Li-Ions.To measure the OCP of the graphitic negative electrode and NMC positive electrode two coin cells were charged and discharged at a C/40 current rate.Lithium metal, which has a stable chemical potential was used as a counter electrode.To determine the concentration of lithium in both electrodes in the full cell at the start of discharge the OCP curves were used: the difference of both OCP curves of the coin cells, balanced with the appropriate mass ratios, should fit the OCP curve of the full cell.

Results and discussion
In this work the model is judged on its ability to simulate the terminal cell voltage for constant current discharge curves.To show an example of the output result of the model, a plot of the experimental and simulated constant current 5C discharge curves is given in figure 2. As can be seen both simulated discharge curves overestimated the discharge capacity with around 6% SoC compared to their experimental counterparts.However the general trend of the curves is satisfying to judge its ability to predict the influence on increased cathode density.The difference between the experimental discharge curve is insignificant until 60% SoC.From then on the polarization from the cell with a higher cathode density increases significant.As a result the discharged capacity is, on average, 6,2% SoC when the cells reach the cut-off voltage.For the simulated cells a similar trend occurs: the virtual cell with higher cathode density reaches the cut-off voltage '7,0% SoC sooner' then the one with a higher cathode density.Over the whole SoC range the simulated discharge curve of the cell with a higher cathode density shows a slightly lower voltage.We believe this is a consequence of underestimation of the electronic conductivity of electrodes with higher density.
In figure 3 this comparison of experimental discharge curves versus simulated discharge curves is summarized by repeating the data from figure 1 and adding the predictions of simulated discharge curves.For example the result for the 5C rate can directly be derived from figure 2. As can be seen there is a general overestimation of the discharge capacities by the simulation.The relative effect of a higher cathode density, however, is well predicted qualitatively.As discussed the effect of the higher cathode density becomes apparent current rates higher than 3C also in the simulation.However at 4C the effect is still underestimated by the simulation whereas at 5C the difference in discharge capacity is well predicted.

Conclusion
In order to enhance the performance of current state-of-the-art Li-Ion batteries accurate battery models are required.These models should be able to simulate the output voltage and provide us with reliable prediction in function of battery design parameters.From this work we concluded that the PET model shows good promise to deal with this problem.Although results are hopeful, they are not satisfying in terms of accuracy.In this regard we refer to the general trend were the PET model, overestimates the discharge capacities at rates higher then 0,5C.Especially if we are looking to the next step, which is path dependant life cycle predictions, an accurate prediction of current-voltage curves is essential.
Chairman of the International Program Committee of the International Electric, Hybrid and Fuel Cell Symposium (EVS24).
Prof. Dr. Ir. Van den Bossche Peter graduated as an electromechanical engineer from the Vrije Universiteit Brussel and defended his PhD at the same institution with the thesis "The Electric Vehicle: raising the standards".He is currently lecturer at the engineering faculties of the Vrije Universiteit Brussel, and in charge of co-ordinating research and demonstration projects for electric vehicles in collaboration with the international associations CITELEC and AVERE.His main research interest is electric vehicle standardization, in which quality he is involved in international standards committees such as IEC TC69, of which he is Secretary, and ISO TC22 SC21.

Figure 1 :
Figure 1: Discharge capacity at multiple current rates relative to the 0,04C discharge capacity for two different cell designs.The yellow bars indicate the average capacity of the cells with low cathode density; the green bars indicate the average capacity of cells with a high cathode density.The error bars have width of 2 times the standard deviation.
The subscript s is used to indicate the solid phase.For most used Lithium Metal Oxides, D s shows a strong dependence on the concentration of lithium ions, making it indispensable to model D s as a function of the composition (local SoC or c s ) [6].

Figure 2 :
Figure 2: Two experimental (full lines) and two simulated (dotted lines) 5C discharge curves of a cell with low cathode density versus a cell with a 14% higher cathode density

Figure 3 :
Figure 3: Discharge capacity at multiple current rates relative to the 0,04C discharge capacity for two different cell designs: low cathode density and high cathode density.The dotted curves are both predictions based on simulation results, the full lines are experimental results.

Table 1 :
Material and cell design parameters, inputs for the model