Battery Pack Discharge Control with Thermal Analysis

Thermal management is important in battery modeling. This example computes the temperature distribution in a battery pack during a 4C discharge. To ensure a constant output power and prevent extreme battery usage condition, the multiphysics model is coupled to a control diagram in Simulink. There, the current is automatically adjusted based on output power and the battery voltage. The maximum temperature in the battery pack is also monitored.

This models requires licenses for both the Battery Design Module and LiveLink™ for Simulink®.

Model Definition

The COMSOL model includes the electrochemical analysis of a battery cell coupled to a 3D thermal analysis of the battery stack. For a detailed description of the battery pack and the underlying COMSOL model, see the Thermal Distribution in a Pack of Cylindrical Batteries tutorial in the Battery Design Module Application Library.

The control system implemented in Simulink ensures a constant usage power and prevents possible battery damage. The control system consists of a PI controller to adjust the battery usage power to 180 W. The applied current in the battery is limited to a minimum value of −16.1 A and is stopped when the voltage reaches a minimum value of 12 V.

The cosimulation with COMSOL Multiphysics and Simulink is set up by exporting a COMSOL Cosimulation file from the COMSOL model and then adding this file to the COMSOL Cosimulation block in the Simulink simulation diagram. The input of the block consists of the applied current, provided by Simulink. The block has three outputs: the stack voltage, the temperature in the middle cell, and the power usage.

Figure 1 shows the full simulation diagram in Simulink.

Figure 1: Battery control diagram.

Results and Discussion

Figure 2 below shows the temperature in the battery stack. The maximum temperature is located in the middle of the stack, which corresponds to the third cell in the COMSOL model.

Figure 2: Temperature distribution in battery stack.

Figure 3 below shows the voltage of battery during usage. The voltage drops rapidly when the battery is fully charged and almost discharged; these are the regions that can cause most damage. Because it is not recommended to leave the battery in this region the applied current is cut when the voltage is below 10.2 V.

Figure 3: Voltage in battery stack.

Figure 4 below shows the applied voltage to ensure a usage power of 180 W. The current keep decreasing as the battery get discharged. The current is limited to −16 A to not damage the battery; this limit is reached after almost 700 s at full power. When the minimum allowed voltage is reached, the current is cut, here around 860 s.

Figure 4: Electric current in battery stack.

Figure 5 shows the usage power provided by the battery. You can notice the response time to reach full power caused by the PID controller, which is about 50 sec. Once the current is restricted to its maximum value, the usage power can no longer be enforced to a constant value and starts to drop until the current is cut.

Figure 5: Battery power.

Figure 6 shows the variation of the temperature in the third cell of the COMSOL model, which is used as output of the COMSOL Cosimulation block. The temperature keeps increasing until the power starts to drop, but the rise suddenly before the current is cut.

Figure 6: Maximum temperature in battery stack.

Setting Up the Cosimulation

Follow the workflow below to set up the cosimulation with COMSOL Multiphysics and Simulink:

Set up the COMSOL model and make sure that the study runs. Only studies with a single Stationary or Time Dependent study step are supported for cosimulation.

Save the COMSOL model. This step is important because the name of the model is needed to load the cosimulation file in Simulink.

Add the Cosimulation for Simulink feature node to the COMSOL model. Use this to define the inputs, outputs, and study for the cosimulation.

From the Cosimulation for Simulink feature node, export the file for cosimulation. Any location will work, but it is good practice to export this file to the location where the MPH-file has been saved.

Create or load the simulation diagram in Simulink, and add the COMSOL Cosimulation block.

Double-click the COMSOL Cosimulation block, and enter the name of the cosimulation file exported from COMSOL Multiphysics.

LiveLink_for_Simulink/Tutorials/battery_control_thermal

Modeling Instructions — COMSOL Desktop

Start this tutorial by opening the model Thermal Distribution in a Pack of Cylindrical Batteries from the Battery Design Module Application Library.

From the menu, choose .

From the Application Libraries root, browse to the folder Battery_Design_Module/Thermal_Management and double-click the file lumped_li_battery_pack_6s2p.mph.

Global Definitions

Battery Parameters

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Iapp	0[A]	0 A	Applied current

Component 1 (comp1)

In the window, expand the node.

Definitions (comp1)

E_OCP (int1)

In the window, expand the node, then click .

In the window for , locate the section.

Click .

dEdT (int2)

In the window, click .

In the window for , locate the section.

Click .

Lumped Battery (lb)

In the window, under click .

In the window for , locate the section.

In the Iapp text field, type Iapp.

Lumped Battery 2 (lb2)

In the window, under click .

In the window for , locate the section.

In the Iapp text field, type Iapp.

Lumped Battery 3 (lb3)

In the window, expand the node, then click .

In the window for , locate the section.

In the Iapp text field, type Iapp.

Study 1

Step 1: Time Dependent

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the text field, type 0 1e3.

Solution 1 (sol1)

In the window, expand the node.

Right-click and choose .

Save the COMSOL Model

From the menu, choose .

Browse to a suitable folder, enter the filename battery_control_thermal.mph, and then click .

Exporting the Cosimulation File

In the following configure the cosimulation, and export the file for cosimulation that will be loaded into Simulink.

Global Definitions

Cosimulation for Simulink 1

In the toolbar, click

In the window for , locate the section.

In the text field, type battery_control_thermal.

Locate the section. Click

In the table, enter the following settings:


Parameter name	Initial value	Unit
Iapp (Applied current)	0[A]	A

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


Expression	Unit	Name
lb.E_cell+lb2.E_cell+lb3.E_cell		V
Temp3		T
sqrt((Iapp*(lb.E_cell+lb2.E_cell+lb3.E_cell))^2)		Q

Locate the section. Find the subsection. Clear the check box.

Locate the section. Click This sets the current temperature plot (if a solution is available) as the thumbnail used for the COMSOL Cosimulation block inside Simulink.

Click