Lithium-Ion Battery Internal Resistance

The cell voltage during the first 10 s 10C discharge and 10 s relaxation is shown in Figure 3. Compared to the open-circuit cell voltage, polarization is present in all four cases.

In Figure 3, it is shown that the lowered initial cell SOC (40%) lowers the voltage all through the pulse. The material properties affected by the cell SOC are the open-circuit potentials (OCP) of the electrodes and the electrochemical reaction rate in this model. However, the changes seem to be mainly due to the OCPs, since the magnitude of the OCPs differ significantly between 40% and 60% cell SOC.

Figure 3: Cell voltage behavior for the different designs during the first 20 s of the pulse. (SOC0 equals initial cell SOC.)

The cell voltage increases considerably when the positive active material particle size is decreased, showing that a major part of the internal resistance originates from there in the original design. In contrast, the lowered porosity in the positive electrode shows that the electrolyte part of the positive electrode requires a quite high porosity (0.4) to efficiently transport lithium ions.

In Figure 4, the total polarization, which is equal to the difference between the cell voltage and open-circuit voltage, is shown. The polarization seems to depend on both instantaneous and time-dependent internal resistances. The former gives an immediate voltage drop when the current is turned on or off, the latter increases the drop more slowly, and is the only resistance that is observed during the relaxation period. The instantaneous behavior has to do mainly with ohmic resistances, such as conductivity, and the time-dependent one with slow mass transport processes, for example, diffusion, in the electrolyte and the active materials. The calculated internal resistance is calculated from Ohm’s law at the end of the 10C discharge, as shown in Equation 2.

(2)

The resistances calculated for the different cases are (in the order presented in the plot legends, top down): 2.0 m⋅Ω. 2.1 m⋅Ω., 1.4 m⋅Ω., and 4.1 m⋅Ω.

Figure 4: Total polarization (EOCV,cell-Ecell) in the different designs during the first 20 s of the pulse.

In Figure 5 and Figure 6, the potentials and OCPs are shown for the two electrodes. The internal resistance in both electrodes is almost the same. The polarization, given by the difference in potential and open-circuit potential, is approximately 10 mV in both electrodes..

Figure 5: Positive electrode potential during the first 20 s of the pulse.

Figure 6: Negative electrode potential during the first 20 s of the pulse.

The energy efficiency of the battery during the pulse should be considerably less than 100% due to the polarization. Both the discharge and charge give considerable polarization, as shown in Figure 7. The energy efficiency is calculated from Equation 1 and becomes (in the order presented in the plot legends, top down): 90.8 %, 89.9 %, 93.4 % and 87.8 %.

Figure 7: Cell voltage behavior for the different battery designs during the whole pulse.

Reference

1. M. Doyle, J. Newman, A.S. Gozdz, C.N. Schmutz, and J.M. Tarascon, “Comparison of Modeling Predictions with Experimental Data from Plastic Lithium Ion Cells,” J. Electrochem. Soc., vol. 143, no. 6, pp. 1890–1903, 1996.

2. A. Nyman, T. G. Zavalis, R. Elger, M. Behm, and G. Lindbergh, “Analysis of the Polarization in Li-Ion Battery Cell by Numerical Simulations,” J. Electrochem. Soc., vol. 157, no. 11, pp. A1236–A1246, 2010.

Battery_Design_Module/Batteries,_Lithium-Ion/li_battery_internal_resistance

Modeling Instructions

Application Libraries

From the menu, choose .

In the window, select in the tree.

Click

Global Definitions

The rate capability of three battery parameters are tested: the initial cell state-of-charge (SOC), the porosity, and particle size of the positive electrode. These are added to the global parameters to enable parameter variation. Replace the initial cell voltage to initial cell state-of-charge, since the former is no longer needed.

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
SOCcell_init	0.6	0.6	Initial cell state-of-charge
rp_pos	2e-6[m]	2E-6 m	Particle size positive electrode
epsl_pos	0.4	0.4	Porosity positive electrode
smooth	1e-3	0.001	Rectangle pulse smoothing factor

Definitions (comp1)

Load the variables from a text file.

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.

Piecewise 1 (pw1)

Set up the pulse with a Piecewise function. The pulse is 10 s of discharge, followed by 10 s of relaxation, and 10 s of charge.

In the toolbar, click

and choose .

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

Locate the section. From the list, choose .

From the list, choose .

In the text field, type smooth.

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


Start	End	Function
0	10	-1
10	20	0
20	30	1

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

Click

Variables 1

Set up the current pulse in the variable list.

In the window, click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Unit	Description
I_pulse	10liion.I_1Cpulse(t)	A	10 C pulse test

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 I_pulse.

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. Also, introduce the parameters that are to be varied, into the interface.

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.

Porous Electrode 2

In the window, under click .

In the window for , locate the section.

In the εl text field, type epsl_pos.

Particle Intercalation 1

In the window, expand the node, then click .

In the window for , locate the section.

In the rp text field, type rp_pos.

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.

Initial Cell Charge Distribution 1

Change the initial battery setting from initial cell voltage to cell state-of-charge and enter the SOCcell_init parameter that is investigated.

In the window, under click .

In the window for , locate the section.

From the list, choose .

In the SOCcell,0 text field, type SOCcell_init.

Component 1 (comp1)

The cumulative energy input and output is calculated with a Global equation.

From the menu, choose .

Add Physics

Go to the window.

In the tree, select .

Click in the window toolbar.

From the menu, choose .

Cumulative Energy Output and Input

In the window for , type Cumulative Energy Output and Input in the text field.

Global Equations 1

In the window, expand the node, then click .

In the window for , locate the section.

In the table, enter the following settings:


Name	f(u,ut,utt,t) (1)	Initial value (u_0) (1)	Initial value (u_t0) (1/s)	Description
Wout	Woutt-abs(pos_cc(I_pulse))Ecell(pos_cc(I_pulse)<0)	0	0
Win	Wint-abs(pos_cc(I_pulse))Ecell(pos_cc(I_pulse)>0)	0	0