1D Lithium-Ion Battery Drive-Cycle Monitoring

This application shows how a battery cell subjected to a hybrid electric vehicle drive cycle can be investigated using the Lithium-Ion Battery interface in COMSOL.

In Figure 1, an example of an electric vehicle with three critical components of a simplified battery management system is displayed. When the vehicle runs according to a specific drive cycle, the temperature and voltage of the battery will vary and be monitored. This tells the monitoring unit, usually with the help of some type of algorithm, the state-of-charge (SOC) of the battery, and decides, for instance, whether the battery is empty or full. In those two cases, the control unit will stop the discharge and charge, respectively. Monitored elevated temperature can also trigger the control unit.

Figure 1: Electric vehicle with key components within the battery management system visualized. As the flowchart to the right shows, the battery voltage and temperature are monitored and act as inputs to the control unit.

What the Lithium-Ion Battery interface can do here is to predict the battery behavior or make comparisons between computed and monitored properties. So the simulations will in fact act as either a pre-monitoring step of the battery or a tool to understand the battery behavior during the cycle better. The latter is possible, since the model setup includes the physical properties and can therefore calculate some properties that are difficult to measure, for instance:

•

internal resistance and polarization in each part of the battery cell,

•

more accurate cell SOC, and

•

SOC of each electrode material.

At the same time, the model setup opens up the possibility to vary many battery design parameters. For instance, materials and thickness of electrodes can easily be changed to evaluate its effect on the overall performance.

In this example, the advanced monitoring possibilities of the Lithium-Ion Battery interface are highlighted.

Model Definition

The model is set up for a graphite/LMO battery cell. The materials are available from the Battery Material Library and mainly default settings are selected. The model domains consist of:

•

Negative porous electrode: Graphite (MCMB LixC6) active material and electronic conductor.

•

Separator.

•

Positive porous electrode: LMO (LiMn2O4) active material, electronic conductor, and filler.

•

Electrolyte: 1.0 M LiPF6 in EC:DEC (1:1 by weight).

This battery cell assembly gives a cell voltage around 4 V, depending on the state-of-charge (SOC) of the cell.

The Lithium-Ion Battery interface accounts for:

•

electronic conduction in the electrodes,

•

ionic charge transport in the electrodes and electrolyte/separator,

•

material transport in the electrolyte, allowing for the introduction of the effects of concentration on ionic conductivity and concentration overpotential, and

•

material transport within the spherical particles that form the electrodes, and

•

Butler-Volmer electrode kinetics using experimentally measured discharge curves for the equilibrium potential.

Drive cycle data containing C-rate versus time is imported and used as current load in the model. The drive cycle contains C-rates up to 20C and can be that of a typical hybrid electric vehicle. In Figure 2, the cycle is displayed with the C-rate recalculated to current (1C equals 12 A).

Figure 2: Drive cycle used in the model.

The initial cell voltage is set to 3.9 V, using the Initial Cell Charge Distribution feature.

More battery parameters and additional variable definitions used here are found in the Lithium-Ion Battery Seed application.

Results and Discussion

In Figure 3 the cell voltage and electrode potentials are shown. The cell voltage varies between 3.6 V and 4.25 V, while the open-circuit voltage varies considerably less. Of the two electrodes, the positive electrode potential varies slightly more than the negative electrode during the cycle, approximately 0.3 V. For prolonged lifetime and better safety, the battery should operate only within a specific voltage span. Since the upper and lower voltage limits for this battery cell chemistry are 4.2 V and 3.3 V, respectively, the battery design seems to fulfill this requirement.

Figure 3: Cell voltage and open-circuit cell voltage, together with electrode potential during drive cycle.

The polarization gives an indication of the internal resistance and, normally, a large polarization reduce the battery lifetime and causes increased heat generation. The polarization during the pulse is displayed in Figure 4. Note that the sign of the polarization quickly changes when the current load shifts between charge and discharge.

Figure 4: Total polarization during drive cycle.

The SOC is monitored in Figure 5. It shows that the cell and materials seem to be far from exhausted. The cell SOC is well within 0-100 %, the positive electrode is within 65-80 % (SOC window 17.5-100 %), and the negative electrode within 14-29 % (SOC window 0- 98%). This causes less strain on the battery and improves the stability of the system.

Figure 5: SOC of cell and electrodes at load during drive cycle.

Considering the results, this type of battery design seems suitable for the drive cycle.

For further reading on polarization and rate-capability, see Lithium-Ion Battery Rate Capability and Lithium-Ion Battery Internal Resistance.

Battery_Design_Module/Batteries,_Lithium-Ion/li_battery_drive_cycle

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select in the tree.

Click

In this tutorial, we will run the battery model you just loaded versus a specified drive cycle. First for 100 s, then for 600 s.

Global Definitions

A hybrid electric vehicle drive cycle, C-rates vs. time, is imported from a text file.

Interpolation 1 (int1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click

Browse to the model’s Application Libraries folder and double-click the file li_battery_drive_cycle_data.txt.

Click

Find the subsection. In the table, enter the following settings:


Function name	Position in file
driving	1

Locate the section. In the table, enter the following settings:


Argument	Unit
Column 1	s

Click

Definitions (comp1)

Load the variables from a text file. Additionally, use the imported C-rate to create a current variable.

Variables 1

In the window, expand the node.

Right-click and choose .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file li_battery_management_variables.txt.

In the table, enter the following settings:


Name	Expression	Unit	Description
I_drive	-liion.I_1C*driving(t)	A	Drive cycle current

(The internally defined liion.I_1C variable used above defines the constant current required to completely charge or discharge the battery in 1 hour. The variable is defined by the node.)

Lithium-Ion Battery (liion)

Electrode Current 1

In the window, under click .

In the window for , locate the section.

In the Is,total text field, type I_drive.

Porous Electrode 1

In the nodes of the features, it is useful to enable fast assembly in the particle dimension option. This option enables an alternative method for assembling of the diffusion equation in the particle dimension, that typically decreases computation time for 1D models. Note that the same diffusion equations are solved for regardless of assembly method. Additionally, specify the reference exchange current density for the electrode kinetics in the nodes.

Particle Intercalation 1

In the window, expand the node, then click .

In the window for , click to expand the section.

Select the check box.

Porous Electrode Reaction 1

In the window, click .

In the window for , locate the section.

In the i0,ref(T) text field, type i0ref_neg.

Particle Intercalation 1

In the window, expand the node, then click .

In the window for , locate the section.

Select the check box.

Porous Electrode Reaction 1

In the window, click .

In the window for , locate the section.

In the i0,ref(T) text field, type i0ref_pos.

Study 1

Step 2: Time Dependent

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,1,100).

Solution 1 (sol1)

In the toolbar, click

Set the to to ensure that sudden transients in the drive cycle are resolved by the time-dependent solver. Also, enable the nonlinear controller to improve handling of sudden load changes.

In the window, expand the node, then click .

In the window for , click to expand the section.

From the list, choose .

Select the check box.

The problem is now ready for solving.

In the toolbar, click

Results

Probe Plot Group 6

A probe plot of the battery voltage versus time is plotted automatically during the simulation:

In the window, under click .

In the toolbar, click

Study 1

Step 2: Time Dependent

Increase the solver time to 600 s.

In the window, under click .

In the window for , locate the section.

In the text field, type range(0,1,600).

In the toolbar, click

Results

Create Figure 2 to illustrate the current during the drive cycle.

Current

In the toolbar, click

and choose .

In the window for , type Current in the text field.

Locate the section. Select the check box.

In the associated text field, type Current (A).

Global 1

Right-click and choose .

In the window for , click in the upper-right corner of the section. From the menu, choose .

Click to expand the section. Clear the check box.

In the toolbar, click

Cell and Electrode Voltages

Create Figure 3 to display the electrode potentials and the cell voltage. For comparison, include the open-circuit cell voltage (at load, concentration gradient in the electrode particles accounted for).

In the toolbar, click