COMSOL 6.4 - Power Losses in a Lithium-Ion Battery

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Power Losses in a Lithium-Ion Battery

This tutorial analyzes the power losses in a lithium-ion battery during a Hybrid Pulse Power Characterization (HPPC) test. The model is a continuation of the Lithium-Ion Battery Rate Capability tutorial, where the total discharge energy was compared between an energy-optimized and a power-optimized battery.

Many physical battery properties affect the polarization and rate capability of a battery cell, for instance:

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the thicknesses of the electrodes and separator layers,

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the porosity of the electrodes and separator layers,

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the active material particle size in the electrodes,

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the choice of active electrode material,

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other material choices, for example, the electrolyte and electronic conductor, and

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the degree of lithiation of the electrode material due to several material properties being dependent on the intercalation state.

The power losses can typically be decreased by using thinner separator and electrode layers, higher porosities, and smaller active material particles. However, minimizing the power losses often results in a decreased capacity of the battery, since when using thinner or more porous electrodes, the relative amount of active electrode material in the cell decreases.

Figure 1: Selection of design parameters in a cell and their relation to power losses. Upward pointing arrows indicate increase, downward pointing decrease. For example, the power capability of a cell decreases with decreased porosity and increased particle size.

The choice of active materials is important as well. Some materials are able to transport intercalated lithium efficiently even at high current loads. Additionally, the electrolyte is also important; for example, polymer batteries are seldom used in high-power applications since these contain a nonliquid electrolyte with poor lithium-ion transport properties.

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.

This tutorial investigates the power losses in a battery subjected to a 10 A discharge pulse for 10 s, followed by a 20 s rest, followed by a 10 A charge for 10 s. The losses are analyzed both for an energy-optimized and a power-optimized cell, featuring positive-electrode thicknesses of 60 μm and 25 μm, respectively. The battery model is parameterized in such a way that when changing the positive-electrode thickness parameter, the negative-electrode layer thicknesses change correspondingly, as discussed in Lithium-Ion Battery Base Model in 1D. Both cells are assumed to fit into a 21700 canister of fixed volume, which means the active cell area, Acell, varies with the thickness parameter; again, see Lithium-Ion Battery Base Model in 1D.

A Load Cycle node is used to define a load cycle comprising a 10 A charge for 10 s, followed by a 20 s rest, followed by a 10 A discharge for 10 s. The initial state of charge is 50 s.

Computing Power Losses

The Lithium-Ion Battery interface automatically defines various power loss variables. These are derived locally in the model geometry from physical gradients and interfacial changes in the Gibbs free energy of the transported and reacting species (ions, intercalated lithium, and electrons) in the cell.

As an example, the local power loss due to electron conduction in a domain, ploss,s (W/m3) is defined as

(1)

where is is the electronic current vector (A/m2) and ϕs the electrode phase potential (V).

In addition to the current-conduction power loss defined above, power loss variables are also computed for:

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Electrolyte transport — the power losses associated with ion transport

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Kinetic activation — the power losses associated with the charge transfer processes occurring at the electrode surfaces

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Particle intercalation — the power losses associated with diffusion of intercalated (atomic) lithium in the solid electrode particles

How these are computed is documented in the theory chapter for the Lithium-Ion Battery interface. It should be noted that the power loss variables may sometimes be identical to the heat source variables (also computed automatically by the interface), but are generally not the same, since the heat source variables consider changes in enthalpy rather than the Gibbs free energy.

The interface also defines integrated power loss variables, which for this 1D example is computed as

(2)

for the total electron conduction loss.

Integrated total loss variables per model tree feature node (, , and so on) are also available.

Results and Discussion

Figure 2 shows the cell voltage and corresponding C-rates for the two cell configurations. The C-rates are slightly higher for the power-optimized (positive electrode thickness of 25 μm) battery compared to the energy-optimized (positive electrode thickness of 60 μm) battery. The reason for this is that the total current and volume are fixed, in combination with the energy-optimized battery having a higher capacity. The polarization (voltage deviation from the rest voltage) is however still higher for the energy-optimized cell, despite the slightly lower C-rate.

Figure 2: Cell voltage and current C-rates versus time.

Figure 3 shows the local power losses in the energy-optimized cell (left) and the power-optimized cell (right) at 1 s (top) and 9 s (bottom) into the discharge pulse, whereas Figure 4 shows the corresponding power losses integrated over the whole cell during the course of the whole simulation. The power losses stemming from electron conduction are fairly small and both the distribution and magnitude of the losses stays more or less constant during each pulse. The kinetic activation losses also stay fairly constant during each pulse. When it comes the electrolyte transport and particle intercalation losses, however, these increase significantly during each pulse. This is related to the buildup of concentration gradients during each pulse. During the rest period (between t = 10 s and 30 s in Figure 4), the electrode and activation losses are close to zero, whereas the electrolyte and particle intercalation losses show a slow relaxation behavior as the concentration gradients get reduced. The power losses are generally higher for the energy-optimized cell, with the electrolyte transport-related losses being the main contributor, when integrated over all domains.

Figure 3: Local power losses stemming from electrolyte transport (blue lines), kinetic activation (green lines), particle intercalation transport (red lines) and electron conduction in the electrodes (cyan lines) in the energy-optimized cell (left) and the power-optimized cell (right) at 1 s (top) and 9 s (bottom) into the discharge pulse.

Figure 4: Cell-integrated power losses in the energy-optimized (left) and the power-optimized cell (right).

Figure 5 shows the power losses integrated separately over the negative electrode, the separator and the positive electrode. For this model, the power loss contributions from the two electrodes are dominating over the separator.

Figure 5: Power losses integrated per component; the negative electrode (blue lines), the separator (green lines) and the porous electrode (red lines) domains in the energy-optimized (left) and the power-optimized cell (right).

Finally, Figure 6 compares the total sum of all power losses for the energy and power-optimized cases.

Figure 6: Total power losses for the energy optimized (green line) and the power optimized (blue line) cell.

1. 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/Lithium-Ion_Batteries,_Performance/lib_power_losses

Modeling Instructions

Application Libraries

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From the menu, choose .

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In the window, select > > in the tree.

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In this tutorial we will perform an HPPC (hybrid pulse power characterization) test on the battery model you just loaded. The combined discharge–rest–charge load profile will be applied at 50% state of charge.

Global Definitions

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In the window, under click .

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In the window for , locate the section.

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In the table, enter the following settings:


Name	Expression	Value	Description
soc_init	50[%]	0.5	Initial SOC

Parameters - Pulse

Add a second group of parameters from a text file.

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In the toolbar, click

and choose > .

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In the window for , type Parameters - Pulse in the text field.

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Locate the section. Click

.

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Browse to the model’s Application Libraries folder and double-click the file lib_power_losses_parameters.txt.

Lithium-Ion Battery (liion)

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In the window, expand the > node, then click .

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In the window for , locate the section.

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Select the checkbox.

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In the window, expand the node.

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Right-click and choose .

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the Iset text field, type -I_pulse.

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Locate the section. Select the checkbox.

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In the tmax text field, type t_pulse.

Lithium-Ion Battery (liion)

In the window, expand the > node, then click > > .

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the tmax text field, type t_rest.

In the window, click .

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In the toolbar, click

and choose .

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In the window for , locate the section.

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In the Iset text field, type I_pulse.

Porous Electrode - Negative

Proceed as follows to enable computation of the intercalation power losses in the electrode particles:

Particle Intercalation 1

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In the window, expand the > > node, then click .

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In the window for , locate the section.

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From the list, choose .

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Click to expand the section. Select the checkbox.

Particle Intercalation 1

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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Locate the section. Select the checkbox.

Step 2: Time Dependent

Specify the initial and final time of the simulation in the times list.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type 0 2*t_pulse+t_rest.

Parametric Sweep

Add a parametric sweep varying the positive electrode thickness parameter. This will perform the HPPC simulation both for a power optimized and an energy-optimized battery. When varying the L_pos parameter, the negative electrode thickness is automatically updated based on the correlation defined in the node.

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In the toolbar, click

.

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In the window for , locate the section.

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In the table, enter the following settings:


Parameter name	Parameter value list	Parameter unit
L_pos (Positive electrode thickness)	25 60	um

Solution 1 (sol1)

Enable to store all steps taken by the time-dependent solver. This will produce smooth plots when visualizing the results.

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In the toolbar, click

.

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In the window, expand the node, then click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

.

Voltage and C Rate

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In the toolbar, click

.

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In the window for , type Voltage and C Rate in the text field.

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Locate the section. From the list, choose .

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Click to expand the section. From the list, choose .

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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Click to expand the section. Find the subsection. Clear the checkbox.

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Find the subsection. In the text field, type Voltage, .

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Click to expand the section. From the list, choose .

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In the table, enter the following settings:


Legends
L<sub>pos</sub>=25 \mu m
L<sub>pos</sub>=60 \mu m

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In the window, right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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Click to expand the section. From the list, choose .

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Find the subsection. From the list, choose .

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Locate the section. Find the subsection. Clear the checkbox.

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Find the subsection. In the text field, type C rate, .

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From the list, choose .

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In the table, enter the following settings:


Legends
L<sub>pos</sub>=25 \mu m
L<sub>pos</sub>=60 \mu m

Voltage and C Rate

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In the window, click .

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In the window for , locate the section.

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Select the checkbox.

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In the table, select the checkbox for .

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Locate the section. From the list, choose .

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In the toolbar, click

.

Local Power Losses

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In the toolbar, click

and choose .

Create a plot of the local power losses as follows:

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In the window for , type Local Power Losses in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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In the list box, select .

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From the list, choose .

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In the text field, type 1.

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Click to expand the section. From the list, choose .

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In the text area, type Local Power Losses, L<sub>pos</sub> = eval(L_pos*1e6) \mu m, t=eval(t) s.

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Right-click and choose .

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In the window for , locate the section.

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From the list, choose .

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Click in the upper-right corner of the section. From the menu, choose > > > .

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Locate the section. From the list, choose .

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Select the checkbox. In the associated text field, type Electrolyte.

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Locate the section. From the list, choose .

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In the text field, type x.

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From the list, choose .

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Click to expand the section. Select the checkbox.

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Find the subsection. Clear the checkbox.

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Select the checkbox.

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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

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In the toolbar, click

.

Local Power Losses

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In the window, click .

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In the window for , locate the section.

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Select the checkbox. In the associated text field, type Power loss (kW/m<sup>3</sup>).

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Locate the section. From the list, choose .

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In the toolbar, click

.

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Locate the section. In the list box, select .

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In the toolbar, click

.

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In the text field, type 9.

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In the toolbar, click

.

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In the list box, select .

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In the toolbar, click

.

Cell-Integrated Power Losses

There are also corresponding predefined variables available that are integrated for all domains. To plot these cell-integrated variables, proceed as follows:

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In the toolbar, click

.

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In the window for , type Cell-Integrated Power Losses in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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In the list box, select .

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Locate the section. From the list, choose .

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In the text area, type Cell-Integrated Power Losses, L<sub>pos</sub> = eval(L_pos*1e6) \mu m.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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


Expression	Unit	Description
liion.P_loss_l	W	Electrolyte

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Click to expand the section. Find the subsection. Clear the checkbox.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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


Expression	Unit	Description
liion.P_loss_act	W	Kinetic

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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


Expression	Unit	Description
liion.P_loss_inter	W	Particle

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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In the toolbar, click

.

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


Expression	Unit	Description
liion.P_loss_s	W	Electronic

Cell-Integrated Power Losses

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In the window, click .

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In the window for , locate the section.

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Select the checkbox. In the associated text field, type Power loss (W).

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Locate the section. From the list, choose .

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In the toolbar, click

.

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Locate the section. In the list box, select .

Component Power Losses

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In the toolbar, click

.

Furthermore, there are integrated variables for the total losses of each domain node that you plot as follows:

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In the window for , type Component Power Losses in the text field.

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Locate the section. From the list, choose .

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From the list, choose .

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In the list box, select .

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Locate the section. From the list, choose .

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In the text area, type Component Power Losses, L<sub>pos</sub> = eval(L_pos*1e6) \mu m.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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Click to expand the section. Select the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
Negative

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In the window, right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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Locate the section. Select the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
Separator

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In the toolbar, click

.

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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Locate the section. From the list, choose .

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In the table, enter the following settings:


Legends
Positive

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Select the checkbox.

Component Power Losses

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In the window, click .

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In the window for , locate the section.

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Select the checkbox. In the associated text field, type Power loss (W).

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Locate the section. From the list, choose .

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In the toolbar, click

.

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Locate the section. In the list box, select .

Total Power Loss

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In the toolbar, click

.

Finally, plot the total of all power losses.

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In the window for , type Total Power Loss in the text field.

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Locate the section. From the list, choose .

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Locate the section. From the list, choose .

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Right-click and choose .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > > .

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Locate the section. Find the subsection. Clear the checkbox.

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From the list, choose .

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In the table, enter the following settings:


Legends
L<sub>pos</sub>=25 \mu m
L<sub>pos</sub>=60 \mu m

Total Power Loss

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

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In the toolbar, click

.