COMSOL 6.3 - Lithium-Ion Battery Rate Capability

A battery’s possible energy and power outputs are critical to consider when deciding in which type of device it can be used.

A cell with high rate capability is able to generate a considerable amount of power, as it suffers from little polarization (voltage loss) even at high current loads. In contrast, a low rate-capability cell has the opposite behavior. The former cell type is said to be power optimized, while the latter type is energy optimized.

Characteristic for energy-optimized cells is that these have more capacity, and are thus able to supply more energy, but only for mild loads. Therefore, energy-optimized batteries are more suitable for portable electronics, for example, cell phones. The power energy-optimized ones fits, for example, power-demanding hybrid-electric vehicles better. The difference between these two types of cells is illustrated in Figure 1. This way of plotting energy versus power (or current if the cell voltage stays fairly constant throughout the load cycle) is also called a Ragone plot.

Figure 1: Comparison of energy outputs. Energy optimized cells (gray) can supply more energy but for lower current loads. Power optimized cells (black) work fine for higher power (current loads) but can only provide a fraction of the energy at low power.

This tutorial performs a rate capability investigation of two lithium-ion battery cell designs using the Lithium-Ion Battery interface.

You can also learn more about how to study rate capability with the Lithium-Ion Battery Internal Resistance tutorial, where the individual contributions to the voltage losses are analyzed more in detail.

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. Discharge curves are simulated for a range of current magnitudes (C-rates) for two different battery designs: an energy-optimized cell and a power-optimized cell. Changing from the energy-optimized case to the power-optimized case is done in the model by lowering the positive electrode thickness parameter from 60 μm to 25 μm. The negative electrode thickness is automatically reduced based on the correlation discussed in Lithium-Ion Battery Base Model in 1D.

The volumetric energy (J/m3) and power (W/m3) outputs during the discharge, starting from fully charged conditions, are calculated and investigated in a Ragone plot. A Global ODEs and DAEs interface is used to calculate the energy output according to Equation 1.

(1)

Where the length Lcell of the cell is calculated as

(2)

where Lccs is the sum both thickness of the positive and negative current collector foils in jelly roll. (The factor 1/2 stems from the configuration of a typical jelly roll where each metal foil is being coated on both sides by the same electrode layer.)

The power output is computed by dividing the energy with the total discharge time.

An Event interface is also used for implementing an accurate stop condition in the solver for when the cell voltage goes below a threshold level equal to the open circuit voltage at 0% cell state of charge.

Results and Discussion

Figure 2 shows the discharge curves of the energy optimized 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. At 10C the capacity utilization decrease is substantial; less than 10% of the available capacity has been utilized.

Figure 2: Solid lines: Cell voltages versus SOC during discharge at various C-rates of the energy-optimized cell. Dashed line: Corresponding open circuit voltage (OCV) versus SOC.

To investigate what could be the reason for the large capacity decrease at 10C, we plot the electrolyte salt concentration at the end of this discharge simulation in Figure 3. Toward the right in the figure a noticeable drop in electrolyte concentration is seen, and for the 25 rightmost micrometers, the concentration is close to 0. This region corresponds to the inner parts of the positive electrode in the model, and the reason for the depletion of lithium ions is the prolonged fast lithium intercalation rate, in combination with an insufficient lithium ion transport from the negative electrode through the separator.

Figure 3: Electrolyte concentration at the end of discharge at 10C of the energy-optimized cell.

The depletion of lithium ions will result in a very low local electrolyte conductivity, and this is manifested in Figure 4 where a corresponding steep potential drop is seen. This steep potential drop will result in the interior of the electrode not being utilized at all toward the end of discharge at high rates for the energy-optimized cell.

Figure 4: Electrolyte phase potential at the end of discharge at 10C of the energy-optimized cell.

Figure 5 shows the discharge curves for the power-optimized case, using half as thick electrodes as in the energy optimized case. These thinner electrodes now allows for utilizing about 60% of the available charge at the highest 10C discharge rate, as opposed to less than 10% for the energy-optimized case.

Figure 5: Solid lines: Cell voltages versus SOC during discharge at various C-rates of the power-optimized cell. Dashed line: Corresponding open circuit voltage (OCV) versus SOC.

Finally, the energy versus power Ragone plot is plotted in Figure 6. For power levels above around 200 W/m3, the power-optimized battery starts to outperform the energy-optimized cell.