Lithium-Ion Battery Rate Capability

The current loads applied on the cell are 0.01C, 0.1C, 0.5C, 1C, 2C, 5C, and 10C. At discharge the initial cell voltage is set at the upper cut-off voltage, 4.1 V, and at charge to the lower cut-off voltage, 3.3 V, for the MCMB/LMO battery cell. In Figure 2, the cell voltage for the discharge loads is shown for the MCMB/LMO cell. A clear increase in polarization (voltage drop) with increased load is observed. Compared to the open-circuit voltage curve, the capacity utilization decreases considerably with increased load as well.

Figure 2: Cell voltage during 0.01C, 0.1C, 1C, 2C, 5C, and 10C discharge current load for the MCMB/LMO battery cell.

For the LTO/NMC battery cell, the initial cell voltage is set to the upper cut-off voltage, 3.2 V, at discharge and to the lower cut-off voltage, 0.5 V, at charge. In Figure 3, the cell voltage for the discharge loads is shown for the LTO/NMC cell. The observed increase in polarization with current load is slightly higher for this battery design. Less capacity is also discharged.

Figure 3: Cell voltage during 0.01C, 0.1C, 1C, 2C, 5C, and 10C discharge current load for the LTO/NMC battery cell.

Figure 4 is a Ragone plot displaying both battery designs’ energy versus power output. The shape of the plot is characteristic for batteries. With increased energy output less power is obtained and vice versa. The shape of the Ragone plot can change drastically if the battery design is altered. A comparison of the MCMB/LMO and LTO/NMC data shows that the energy density is considerably lower in the LTO/NMC cell. This is mainly explained by the lower cell voltage of the cell (see Figure 2 and Figure 3). Improved rate capability would shift the slope further to the right along the x-axis, at the same time as the whole curve is shifted downward. The LTO/NMC cell has, despite the lower energy density, also worse rate capability. The rather small change in energy density with current load (~10%) for both cells indicates that both are rather power-optimized. To achieve better rate capability other design features than electrode chemistry can be changed, this is described in the Lithium-Ion Battery Internal Resistance application.

Figure 4: Ragone plot for the MCMB/LMO and LTO/NMC battery cells.

The charge behavior is normally harder to put into the context of rate capability. This is illustrated for the MCMB/LMO battery cell in Figure 5. The polarization is slightly more pronounced compared to discharge. However, most striking is that the charged capacity is considerably lower than the discharged capacity (less of SOC window is utilized). This mainly has to do with the shape of the open-circuit potential curves of the electrode active materials. The low capacity usage normally means that the active electrode material can handle peaks of medium-high current load, where the cell voltage exceeds that of a fully charged cell (>4.1 V), given that the voltage is within the stability window of the electrolyte.

Figure 5: Cell voltage during 0.01C, 0.1C, 1C, 2C, 5C, and 10C charge current load for the MCMB/LMO battery cell.

The cell voltage at charge load for the LTO/NMC cell is displayed in Figure 6. The charged capacity is also lower than the discharged capacity for this cell design, however, the polarization is in the same magnitude as for the discharge.

Figure 6: Cell voltage during 0.01C, 0.1C, 1C, 2C, 5C, and 10C charge current load for the LTO/NMC battery cell.

Battery_Design_Module/Batteries,_Lithium-Ion/li_battery_rate_capability

Modeling Instructions

Root

From the menu, choose .

Browse to the model’s Application Libraries folder and double-click the file li_battery_seed.mph.

Global Definitions

Add parameters for controlling the C-rate as well as the upper and lower cut-off voltages for the battery cell.

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
a	1	1	C-factor for C-rate calculation
Ecell_up	4.1[V]	4.1 V	Upper cut-off voltage
Ecell_low	3.3[V]	3.3 V	Lower cut-off voltage

Also modify the parameter value for Ecell_init as follows:

In the table, enter the following settings:


Name	Expression	Value	Description
Ecell_init	if(a>0,Ecell_low,Ecell_up)	3.3 V	Initial cell voltage

Definitions (comp1)

Load the variables from a text file.

Variables 1

In the window, under 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.

Lithium-Ion Battery (liion)

Electrode Current -Current Load Rates

In the window, under click .

In the window for , type Electrode Current -Current Load Rates in the text field.

Locate the section. In the Is,total text field, type liion.I_1C*a.

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