Lithium-Ion Battery Seed

Table 1: Parameters needed to be set by the user.
Parameter	Value	Description
Q_B	12 Ah	Battery capacity
Ecell_init	3.9 V	Initial battery voltage
L_neg	30 μm	Thickness negative electrode
L_pos	55 μm	Thickness positive electrode
L_sep	30 μm	Thickness separator

This example utilizes the Initial Cell Charge Distribution global feature. This allows you to set the initial cell voltage (or initial cell state-of-charge (SOC)) as a model input. The feature computes the lithium concentrations (in the case of lithium-ion batteries) in the active electrode materials, cs, and balances the electrodes in the cell to each other. For further reading on this feature, see the Initial Cell Charge Distribution section in the Battery Design Module User’s Guide.

The next section contains a discussion that applies only to the battery management category of models (mentioned above), in which this template model has been used.

Battery Management

This application example is useful for investigation of the following in lithium-ion batteries under isothermal conditions:

•

Voltage,

•

polarization (voltage drop),

•

internal resistance,

•

state-of-charge (SOC), and

•

rate capability.

Note that one can always make the system nonisothermal with a Heat Transfer interface. In this manner, a sixth property, temperature, may be added to the list above.

Some of the listed properties play an important part in battery management systems (BMS) in, for instance, electric and hybrid electric vehicles (see Figure 1). The more properties that can be monitored accurately, the easier it is to manage the battery in order to maximize energy output and lifetime, and to guarantee safety.

Figure 1: Electric vehicle with key components within the battery management system visualized. As the flowchart shows to the right, the battery voltage is often monitored and from this the SOC is either computed or determined from empirical data. The information from the monitor determines how the control unit will regulate the battery.

For battery manufacturers, the same properties can be considered when optimizing the design of the battery, for example choice of materials and thickness of electrodes.

Several useful variables are available with the battery management models. For the SOCs of the electrodes, both “coulombic” and “at load” are defined in the Lithium-Ion Battery interface. The “coulombic” in contrast to “at load” omits the impact of any polarization in the battery. This means that the “coulombic” type is based on the average concentration in the particle and the “load” on the particle surface concentration.

SOC, coulombic, in each electrode:

(1)

SOC, at load, in each electrode:

(2)

The cell SOC can likewise by either “coulombic” or “at load”. The cell SOC, coulombic, is computed in the model as:

(3)

where the average cyclable lithium concentration in the electrode particles is inserted which is defined as:

(4)

Cell SOC, at load, is computed as:

(5)

where the cyclable lithium concentration at the surface of the electrode particles is inserted which is defined as:

(6)

The SOC definitions are furthermore used to compute the coulombic or at load open-circuit potential of each electrode and the corresponding open-circuit cell voltages.

Additionally, the model also sets up the local potential in the solid and electrolyte phases to calculate the cell voltage, Ecell, and the potential of each electrode, E, during load, as shown in Equation 7 and Equation 8.

(7)

(8)

Here, “cc” denotes the current collector boundary and “sep” the separator boundary.

The total polarization is determined in the model as well. It is calculated as the difference between the cell voltage and open-circuit cell voltage (coulombic).

(9)

In the same way, the electrodes’ polarization can be obtained as the difference between the electrode potential and open-circuit potential (coulombic).

Study Settings

In order for the Initial Cell Charge Distribution feature to function a Current Distribution Initialization study step is required.

Reference

1. M. Doyle, and Y. Fuentes, “Computer Simulations of a Lithium-Ion Polymer Battery and Implications for Higher Capacity Next-Generation Battery Designs,” J. Electrochem. Soc., vol. 150, no. 6, pp. A706–A713, 2003.

Battery_Design_Module/Batteries,_Lithium-Ion/li_battery_seed

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select . This study step automatically computes the initial potentials in the cell.

Click

Global Definitions

This model mainly uses the input of default parameters. However, the battery capacity and its initial voltage, together with the thicknesses of the electrodes and the separator are required to be set.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
Q_B	12[Ah]	43200 C	Battery capacity
Ecell_init	3.90[V]	3.9 V	Initial cell voltage

Add Material

The model has a graphite negative electrode, a LMO positive electrode, and a LiPF6 1:1 EC:DEC electrolyte. Import the materials from the Battery Material Library.

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click the right end of the split button in the window toolbar.

From the menu, choose .

In the tree, select .

Click the right end of the split button in the window toolbar.

From the menu, choose .

In the tree, select .

Click the right end of the split button in the window toolbar.

From the menu, choose .

In the toolbar, click

to close the window.

Definitions

Cell voltage probe

In the toolbar, click

and choose .

In the window for , type Cell voltage probe in the text field.

Locate the section. In the text field, type Ecell.

Geometry 1

Interval 1 (i1)

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

In the table, enter the following settings:


Lengths (m)
30e-6
30e-6
55e-6

Click

Definitions

Explicit selections are made in the model geometry.

Negative electrode

In the toolbar, click

In the window for , type Negative electrode in the text field.

Select Domain 1 only.

Separator

In the toolbar, click

Select Domain 2 only.

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

Positive electrode

In the toolbar, click

Select Domain 3 only.

In the window for , type Positive electrode in the text field.

Integration 1 (intop1)

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

Integration 2 (intop2)

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

Integration 3 (intop3)

Select the end-terminal boundary, that is, the positive electrode current collector, along with the rest of the electrode boundaries.

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

Select Boundary 4 only.

Integration 4 (pos_cc2)

Right-click and choose .

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

Select Boundary 1 only.

Integration 5 (neg_cc2)

Right-click and choose .

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

Select Boundary 2 only.

Integration 6 (neg_sep2)

Right-click and choose .

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

Select Boundary 3 only.

Materials

Material Link 1 (matlnk1)

In the window, under right-click and choose .

Material Link 2 (matlnk2)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Material Link 3 (matlnk3)

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Lithium-Ion Battery (liion)

Add the three typical battery domains in the Lithium-Ion Battery interface: a negative porous electrode, a positive porous electrode, and a separator.

Porous Electrode 1

For the negative electrode, select material properties where possible. Change the negative electrode particle radius. The initial concentration of lithium in graphite is calculated further on.

In the window, under right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Particle Intercalation 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the rp text field, type 2e-6[m].

Porous Electrode Reaction 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Porous Electrode 2

Select material properties for the positive electrode as well. Change the positive electrode particle radius. The initial concentration of lithium in LMO is calculated further on.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Particle Intercalation 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the rp text field, type 2e-6[m].

Porous Electrode Reaction 1

In the window, click .

In the window for , locate the section.

From the list, choose .

Separator 1

Since a liquid electrolyte is chosen, the battery model requires a separator.

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. From the list, choose .

Select the global feature Initial Cell Charge Distribution to allow either cell voltage or cell state-of-charge initially as input. The feature computes the initial lithium concentration in the electrode materials and balances the electrodes by computing the electrode material volume fraction in each electrode.

Initial Cell Charge Distribution 1

In the toolbar, click

and choose .

Since it is a lithium-ion battery chemistry with a negative carbon electrode, the default fractions in the Battery Cell Electrode Balancing section can be kept.

In the window for , locate the section.

In the Ecell,0 text field, type Ecell_init.

In the Qcell,0 text field, type Q_B.

Negative Electrode Selection 1

Select which model domains that represent the negative and positive electrode, respectively.

In the window, expand the node, then click .

Select Domain 1 only.

Positive Electrode Selection 1

In the window, click .

Select Domain 3 only.

Porous Electrode 1

To balance the electrodes in the cell and optimize the electrode material usage for the electrodes, revisit the Porous Electrode nodes and enter the electrode material volume fractions computed by the Initial Cell Charge Distribution feature.

In the window, under click .

In the window for , locate the section.

In the εs text field, type liion.epss_neg.

In the εl text field, type 1-liion.epss_neg.

Porous Electrode 2

In the window, click .

In the window for , locate the section.

In the εs text field, type liion.epss_pos.

In the εl text field, type 1-liion.epss_pos.

Electric Ground 1

Finish by setting the boundary conditions. Ground is set as reference at the leftmost boundary, the negative electrode current collector. A current is applied at the rightmost boundary, the positive electrode current collector. Set for instance the 1C discharge rate with the 1C current available with the Initial Cell Charge Distribution feature.

In the toolbar, click

and choose .

Select Boundary 1 only.

Electrode Current 1

In the toolbar, click

and choose .

Select Boundary 4 only.

In the window for , locate the section.

In the Is,total text field, type -liion.I_1C.