Tutorial of a Lithium-Ion Battery
The following tutorial defines a three-dimensional model of a lithium-ion battery pouch cell. In the pouch battery cell design, all current flows through the cell “tabs”, and as the cell size and power increases, the voltage gradients in the metal foil current collectors may come into play, resulting in a nonuniform current distribution and electrode utilization in the cell. A nonuniform utilization results in suboptimal use of the battery electrodes and may also result in nonuniform and accelerated electrode aging.
The aim of the tutorial is to get acquainted to the most common features in the Lithium-Ion Battery interface for battery modeling, and to investigate the current distribution and electrode utilization in a large format lithium-ion battery pouch cell.
(A more common, and computationally more favorable, approach for battery modeling is often to define the model geometry in 1D. Tutorials featuring more conventional geometries are available in the Battery Design Module Application Library.)
The model defines and solves the current and material balances in the lithium-ion battery. The intercalation of lithium inside the particles in the porous electrodes is solved using a fourth independent variable r for the particle radius (x, y, and t are the other three). The reaction kinetics and the intercalation are coupled to the material and current balances at the surface of the particles. The model equations are found in the Battery Design Module User’s Guide. The model was originally formulated for 1D simulations by John Newman and his coworkers at the University of California at Berkeley. The original 1D model is popularly known as pseudo-2D model (or P2D model) in literature, for our 3D case the corresponding popular name would be P4D.
Model Definition
The cell geometry is shown in the figure below. Note that all plots are scaled 100 times in the z direction due to the high aspect ratio of the geometric features.
Model geometry, scaled 100 times in the z direction.
The geometry defines one foil-to-foil unit cell, stacking five layers in the z direction:
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Negative metal current collector foil: 10 mm, Cu (due to symmetry, half of this thickness is used in the model geometry)
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Negative electrode: 60 mm, graphite
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Separator: 30 mm
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Positive electrode: 60 mm, LMO
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Positive metal current collector foil: 10 mm, Al (due to symmetry, half of this thickness is used in the model geometry)
The electrolyte is LiPF6 dissolved in the organic solvents EC and EMC at a 3:7 ratio.
Symmetry is assumed along the center of the cell.
The positive and negative current terminals are located opposite to each other (but may easily be placed on the same side by altering the Geometry node in the model).
The Lithium-Ion Battery interface is used to set up the physics, using material data from the Battery material library. After finishing the modeling instructions later the part of the model tree defining the materials and physics will look as below.
Figure 6: Part of the model tree defining the materials and physics.
The Particle Intercalation subnodes to the Porous Electrode nodes model the solid lithium concentration in an additional particle dimension (extra dimension).
The SOC and Initial Cell Charge Distribution node is used to set the initial cell state of charge.
An Electrode Ground boundary condition is used on the negative tab whereas an Electrode Current boundary condition defines the cell current exiting the cell on the positive tab.
A time-dependent solver is used to simulate the charging from a 20% to 90% cell state of charge at a rate of 4 C. (A 1 C rate corresponds to the charge or discharge current required to fully charge or discharge the battery in 1 h).
Results and Discussion
The figure below shows the simulated cell voltage vs time.
Cell voltage vs time.
The two following figures show the potential distribution in the negative and positive metal foils (current collector and tab) at the end of the 4C charge.
Potential distribution in the negative metal foil at the end of the 4C charge.
Potential distribution in the positive metal foil at the end of the 4C charge.
The potential variation is about 5 mV in the negative current collector and 9 mV in the positive current collector at the 4C charge current. For a 1C charge current the corresponding potential variation would be below 2 mV (results not shown here).
The two figures below show the electrolyte current magnitude of the separator at the beginning and end of the 4C charge, respectively. This provides a measure of the electrode utilization for a given time. The current distribution varies about 6% in the separator plane over time. For 1C, the variation would be generally smaller (results not shown here). Initially, the separator current density is higher close to the tabs whereas toward the end of the charge, the current density is higher in the central parts of the cell.
Current density magnitude of the separator at the beginning of the 4C charge.
Current density magnitude of the separator at the end of the 4C charge.
The following instructions show how to formulate, solve, and reproduce this model.