COMSOL 6.3 - Lithium-Ion Battery Base Model in 1D

This is a template base model containing the physics, geometry, and mesh of a lithium-ion battery.

The model is defined using the Lithium-Ion Battery interface, based on the Doyle–Fuller–Newman framework (Ref. 1). For a general introduction to the Lithium-Ion Battery interface, the user is recommended to first run the tutorial 1D Isothermal Lithium-Ion Battery, which is set up in a similar way.

This base model uses the global SOC and Initial Charge Distribution node to define the cell state-of-charge and initial charge inventory. The following tutorials, available in the Battery Design Module Application Library, make use of this base model:

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1D Lithium-Ion Battery Drive-Cycle Monitoring, which demonstrates how to run the model using a time-dependent current load curve

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Lithium-Ion Battery Rate Capability, which uses the base model to perform a range of discharge simulations at different rates. By modifying the cross-sectional capacity of the cell, an energy-optimized cell is compared to a power-optimized cell in a Ragone plot.

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Lithium-Ion Battery Internal Resistance, which simulates a hybrid pulse power characterization (HPPC) test and makes a full analysis of the different roots of the various voltage losses in the cell.

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Diffusion-Induced Stress in a Lithium-Ion Battery, which adds stresses and strains to the particles and in the negative electrode, and analyzes the mechanical stress that the particles are subjected to during a current load.

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Surrogate Model Training of a Battery Rate Capability Model, which is an application that uses the base model to compute data for training a deep neural network function. The application can be used to investigate the effect of battery electrode parameters on the rate capability of the battery.

Model Definition

The model is defined in 1D along the through-layer direction between the metal current collector foils of a lithium jelly roll. The geometry thus consists of one negative porous electrode, one separator and one positive porous electrode domain.

In this tutorial, we will investigate a 21,700 battery where it is assumed that 90% of the internal volume is occupied by the active jelly roll (electrode, separator, and current collector layers). Because of the 1D geometry, the current load of the battery model is formulated as a current density boundary condition with the unit of A/m2. The cell current is calculated using a 1C current variable I1C, cell (A), which is provided by the SOC and Initial Charge Distribution node. To convert from cell current (A) to cell current density (A/m2) on the jelly roll, the cell area is used. The cell area is computed as

(1)

where the length Lcell of the cell is calculated as

(2)

where Lccs is the sum of the thicknesses of the positive and negative current collector foils in the 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.

Materials

The battery model consists of the following materials:

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Negative electrode: Graphite (MCMB LixC6)

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Positive electrode: NMC 111 (Li1/3Mn1/3Co1/3O2)

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Electrolyte: 1.0 M LiPF6 in 3:7 EC:EMC

These materials are available from the Battery Material Library.

Electrode THICKNESS Balancing

The thickness of the positive electrode is set to 45 μm. The negative electrode thickness is calculated based on electrode balancing, using the following criteria:

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In order to avoid lithium plating during fast charging, the negative graphite electrode should have excess host capacity, so that an approximate negative electrode lithiation level of 80% is reached at 100% cell state of charge (SOC).

•

In order to avoid dissolution of the active electrode material and other harmful side reactions, the positive electrode potential is limited to about 4.23 V at 100% SOC, corresponding to a positive electrode lithiation level of 10%.

Based on the maximum Li concentration (

) and volume fractions (

) of the electrode materials, the thickness of the negative electrode may now be computed as

Physical Model

The Lithium-Ion Battery interface, used for defining the model, accounts for:

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Electronic conduction in the electrodes

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Ionic charge transport in the electrodes and electrolyte or separator

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Material transport in the electrolyte, allowing for the introduction of the effects of concentration on the ionic conductivity and concentration overpotentials

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Material transport within the spherical particles that form the electrodes, defined on an extra (pseudo) dimension

•

Butler–Volmer electrode kinetics using experimentally measured discharge curves for the equilibrium (half cell) potentials.

This tutorial model uses the global SOC and Initial Charge Distribution node to define the cell state-of-charge and initial charge inventory. This node is activated by enabling Define cell state-of-charge (SOC) and initial charge inventory on the interface top node. In this model, the cell voltages at 0% and 100% SOC are set to be defined from operational potential limits, and the initial cell charge distribution is defined by an initial cell SOC parameter. The total initial charge inventory of the cell is defined by the positive electrode host capacity. A formation loss is added in order to reduce the initial charge inventory, assuming that some charge inventory has been irreversibly lost prior to the start of the simulation.

The Lithium-Ion Battery interface defines and solves for the solid lithium concentration in the electrode particles, individually for each electrode. Based on the lithium concentration, the degree of lithiation, SOL (dimensionless), then relates the solid concentration levels to the maximum concentration of lithium atoms that the electrode material can host:

(3)

The individual degrees of lithiation for each electrode then in turns determine the local equilibrium potential for intercalation (the half cell potentials). During charge of a lithium-ion battery, cs in the negative electrode will increase, whereas cs in the positive electrode will decrease, with the rate being proportional to the battery current.

At open circuit of a fully relaxed cell, the cell voltage EOCV,cell can be expressed as

(4)

where Eeq,pos and Eeq,neg (V) are the equilibrium potentials, expressed as functions of the degrees of lithiation SOLpos and SOLneg (1) of the positive and negative electrode materials, respectively, based on the average cs variables of the corresponding electrode.

Unless the degrees of lithiation in the individual electrodes are coupled in some way, there exists an infinite number of combinations of values of SOLpos and SOLneg that fulfill the above equation. However, for an assembled battery cell, a change in SOLpos will always result in a corresponding change in SOLneg, and vice versa. The reason is that the total amount of lithium in the cell is conserved during cycling, resulting in a unique solution to the above equation.

In contrast to the individual electrode degrees of intercalation, which depend on the local concentrations of lithium, the state of charge (SOC) of a battery cell is typically defined on a global level as being proportional to the amount of charge passed when cycling between two corresponding open circuit voltage limits. The lower voltage limit corresponds to 0% SOC, and the upper voltage limit corresponds to 100% SOC. A cell state-of-charge variable is automatically calculated by the SOC and Initial Charge Distribution node.

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.

Battery_Design_Module/Lithium-Ion_Batteries,_Performance/lib_base_model_1d

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