The Single Particle Battery Interface

The interface (

), found under the branch (

) offers a simplified (compared to, for instance, the Lithium-Ion Battery interface) approach to battery modeling. The basic assumptions used are valid when current distribution effects along the depth of the porous electrodes are negligible, and when the salt concentration gradients in the electrolyte do not cause significant changes of the local conductivity of the electrolyte. The validity of the assumptions and the applicability of the single particle approach depends on various battery parameters values such as electrode porosities and thicknesses, and the electrode-electrolyte chemistry, in relation to the current load. As a rule of thumb, the Single Particle Battery interface is typically applicable to battery currents up to 1C (currents corresponding to a full charge or discharge in one hour).

Due to the lower computational load of the single particle model, the interface is suitable for models including extended cycling for, for instance, life-time simulations and thermal simulations of battery packs.

The Single Particle Battery interface models the charge distribution in a battery using one separate single particle model each for the positive and negative electrodes of the battery. The core simplification of the single particle model is to treat the large number of individual electrode particles as a single particle, assuming that the reaction current distribution across the porous electrodes is uniform. The single particle formulation accounts for solid diffusion in the electrode particles and the intercalation reaction kinetics. The ohmic potential drop in the separator is also included in the model, using a lumped solution resistance term.

The single particle model is either solved in a global version, where all potential dependent variables are solved globally, or in a local version (available in 1D, 2D and 3D), where the variables are solved for locally in the same space dimension as the physics interface. The local version, which renders a significantly higher computational load, is suitable for modeling nonhomogeneous aging in cells where local differences in the model parameters (such as temperature) induce localized differences in the battery cell current density. It could also be used for modeling, for instance, cold start of a battery pack, where local currents will cause local heating with a positive feedback when the increased temperature raises the local electrolyte conductivity. Note that the global and local approach both require fairly low currents for the single particle approach to be valid, as described above. However, it is possible to set up the electrolyte solution resistance as a function of the applied current in order to provide a better representation even at higher values of current.

The local model contains both global and local variables. Conversion between local and global variables are done by integrating over the total cell volume.

The is the default physics interface name.

The is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the field. The first character must be a letter.

The default (for the first physics interface in the model) is spb.

This section is available in 1D, 2D, and 3D. The domain selection of the interface is used to calculate the battery volume.

Use the setting to specify the load of the battery. lets you specify the (A). lets you specify the settings that are required to apply a charge-discharge cycle, including constant current, constant voltage and rest periods. allows for specifying the (V) and lets you connect to the Electrical Circuits interface.

You may define the host capacities of the two electrodes (which in term will set the total capacity of the battery) either by the or the alternative. The for the cell capacity case, the electrode volume fractions are derived by setting explicit values for the in combination with the , which can be used to specify the relation in size between the two electrodes. The fractional volumes correspond to the relative thicknesses of the porous electrodes to the total thickness of the battery cell. (The volume fraction of the actual electrode materials within each electrode is defined in the Positive Electrode and Negative Electrode nodes.)

Use the setting (available in 1D, 2D, and 3D) to switch between a or definition of the dependent variables of the model. The difference between the global and local model is described above.

The settings of this section are used to specify the target initial solid concentration (state-of-charge) of the electrodes that will be solved for when the interface is solved with a Current Distribution Initialization step in the Study sequence. The initial charge distribution can then be used as initial conditions for a following Time Dependent study step in the Study.

sets the concentrations based on the cell capacity and the (1), sets the concentrations based on the cell capacity, and the lets you specify the state-of-charge of each electrode individually.

The can be used to reduce the amount of cyclable species in relation to the capacity specified in the Battery settings section. Use this setting to define irreversible losses of cyclable material, for instance due to solid-electrolyte-interface (SEI) formation in a lithium-ion battery.

This section is only visible if the is set to .

In certain cases the Butler–Volmer kinetics expression, used to define the electrode reactions, can be inverted in order to define the electrode overpotential as an analytical function of the current. The advantage of this is that the potential then does not have to be solved for explicitly as a dependent variable in the model, and the nonlinearities associated with the exponential Butler–Volmer expression can be avoided. This improves computational efficiency significantly. The inverse expression can be used only when

Enabling either the or will disable any subnodes to the corresponding electrode node and replace them with a single Lithium Insertion Reaction subnode.

This setting is available in 0D.

This setting is available in 1D. The setting is used to calculate the battery volume. See Cross-Sectional Area.

This setting is available in 2D. The setting is used to calculate the battery volume. See Out-of-Plane Thickness.

The setting on the physics interface node can be used to combine material library data for current densities and equilibrium potentials with an arbitrary reference electrode scale in the physics. The setting affects the electrode potentials used for model input into the materials node, as well as all equilibrium potential values output from the materials node.

Note that the setting will only impact how potentials are interpreted in communication between the physics and the node. If the option is not in use for equilibrium potentials or electrode kinetics, the setting has no impact.

This section is available when the is selected in the dialog box shown when the button (

) is clicked.

To display this section, click the button (

) and select in the dialog box. In this section you can set the of some of the dependent variables in the interface. The settings are normally only needed if the model is solved without an initial Current Distribution Initialization study step in the Study sequence. Also, you can set the check box . The check box is selected by default in 3D and is not selected by default in other space dimensions. Note that this check box is relevant only when coupling to heat transfer interfaces.

The section is only available in 1D, 2D, and 3D. The chosen will be used by the dependent variables when the is set to .