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. The model is based on the Lithium-Ion Battery Base Model in 1D.

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:

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

•

The individual degrees of lithiation of each electrode material

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The individual electrode potentials

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.

Model Definition

The model is set up in 1D for a graphite/NMC battery cell. A more detailed description of the model can be found in Lithium-Ion Battery Base Model in 1D.

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. Figure 2 shows the drive cycle.

Figure 2: Drive cycle, defined as C-rate versus time.

The Modeling Instructions shows how to open up the base model and apply the load cycle to the battery model. First a shorter 60 s simulation is performed, and the preliminary analysis of the results indicate too low potentials in the negative electrode (an indication of lithium plating susceptibility). The battery is then made more power optimized by using thinner electrodes, and the simulation is then recomputed for 600 s. The results of the final simulation is discussed in the next section.

Results and Discussion

Figure 3 shows the cell voltage, and the corresponding open circuit voltage and the current levels (on the secondary y-axis) versus time. The cell voltage varies between 3.3 V and 4.1 V, while the open-circuit voltage (OCV), the voltage the cell would relax to if left at open circuit for a longer time, varies considerably less.

Figure 3: Cell voltage and open-circuit cell voltage, together with charge/discharge current C-rate.

Figure 4 shows the total polarization, computed as the difference between the cell OCV and the cell voltage under load, and the current load. The two curves exhibit a dynamically changing nonlinear relationship with respect to each other. This stems from the contributions from several different phenomena to the total cell polarization of the cell. In the Lithium-Ion Battery Rate Capability and the Lithium-Ion Battery Internal Resistance we will look more into the origin of these potential losses.

Figure 4: Total polarization and load.

The SOC and the corresponding degrees of lithiation in each electrode are shown in Figure 5.

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

The load cycle is not charge-neutral, resulting in an increase of the cell SOC from 25% to about 40% at the end of the simulation.

The degree of lithiation levels will impact the corresponding electrode potentials, in combination with the different contributions to the cell polarization. Figure 6 shows the potential in the positive electrode at two locations during the simulation: At the boundary between the separator and the electrode, and at the boundary between the electrode and the current collector. Analyzing these potentials is important since too high positive electrode potentials may result in gassing or decomposition of the electrode host material. Generally the potentials vary more at the electrode-separator boundary compared to the electrode-current collector boundary. This is a result from the nonhomogeneous current distribution in the cell.

Figure 6: Positive electrode potentials.

Similarly, Figure 7 shows the corresponding negative electrode potentials. At the separator, a negative electrode potential below 0 V is spotted for some 20C charge pulses. This will result lithium plating, which in turn may result in accelerated battery aging and capacity loss. A conclusion from this work is hence that for a battery with this configuration, the BMS system would likely have to protect the battery in some way from excessively large (>10C) charging currents.

Figure 7: Negative electrode potentials.

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 60 s, then for 600 s.

Global Definitions

Create hybrid electric vehicle drive cycle, defined in terms of C-rates vs. time, by importing a text file to a interpolation polynomial.

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
load_function	1

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


Argument	Unit
Column 1	s

Click

Lithium-Ion Battery (liion)

Electrode Current Density 1

Modify the current density boundary condition to make use of the interpolation function you just created.

In the window, expand the node, then click .

In the window for , locate the section.

In the in,s text field, type I_1C*load_function(t).

Porous Electrode - Negative

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 (for this model by about 20%). Note that the same diffusion equations are solved for regardless of assembly method.

Particle Intercalation 1

In the window, expand the node, then click .

In the window for , click to expand the section.

Select the check box.

Particle Intercalation 1

In the window, expand the node, then click .

In the window for , locate the section.

Select the check box.

Global Definitions

Parameters 1

Modify the parameter for the initial state-of-charge of the battery. This will impact the initial solid concentration levels (degrees of lithiation) defined in the child nodes to the nodes.

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
soc_init	0.25	0.25	Initial SOC

Study 1

Step 1: Time Dependent

The model is now ready for solving. First set the solver to run a simulation 60 s of cycling time only.

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the text field, type range(0,1,60).

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. Set the initial step of the solver manually to avoid a too large initial time step. Also, enable the nonlinear controller to improve handling of sudden load changes.