Thermal-Electric Battery Simulation Setup and Guidelines

The battery solution is set up with a hierarchical connectivity structure of packs, modules and cells. The core unit is the battery cell, which will be characterized by its specific properties, for example, cathode chemistry and shape. These cell units are connected in series and parallel to form a module, that is, a group of cells, with a desired power output. Finally, the modules are assembled into a pack, with modules connected in series and parallel. These packs are where the overall electrical input/output is provided to the solution.

Battery Packs

SimLab interface: The battery pack panel,shown in Figure 1, provides the module arrangement as well as the electrical input to the pack.

The arrangement of the modules in serial and parallel determines how current will distribute through the pack. These are given nSmP arrangement, where n is the number of modules in series and m is the number of modules in parallel. As an example, a pack built from four serially connected modules, for example, 4S1P, is shown in Figure 2. An alternative pack with two parallel banks of four serially connected modules is shown in Figure 3.

Note: For consistency with the labeling at the module level, the module numbering is parallel first.

Different types of electrical input can be included as an input to the battery pack using the electrical_input_type command. Although all inputs are done at a pack level these are then distributed to the cell level to ensure consistency of the electrical solution. These are summarized in the following sections.

In general, when the electrical input is provided at the pack level this is required to be distributed to the cell level based on electrical connectivity as well as individual cell properties.

Overview of cell current calculation

If the pack current output $I^k$ is provided as an input, this is required to be distributed to the cell level, since the cells are the source of the voltage that drives the current. To facilitate this distribution in a pack, consistency between the charge conservation solution and ECM models must be maintained. For a 2^nd order ECM model, the solution update for the polarization resistor current is given by,

Where $I_{\varphi }$ is the current flux on the negative terminal of the battery (from the charge conservation PDE solution), $R_1$ and $R_2$ are the polarization resistance of the 1^st and 2^nd order RC pairs respectively, $C_1$ and $C_2$ are the polarization capacitance of the 1^st and 2^nd order RC pairs respectively, $I_{R_1}^k$ , $I_{R_2}^k$ , ${\text{I}}_{{\text{R}}_1}^{\text{k}+1}$ , ${\text{I}}_{{\text{R}}_2}^{\text{k}+1}$ are diffusion resistor current at time step k and k+1, and $\text{Δ}t$ is the time step size.

For example, for a 2s2p pack the electrical circuit diagram would be as shown in Figure 2.

Where $I_j^k U_j^k$ , and $R_j$ are the current, fixed voltage (for example, for second order: $U_j^k={\text{V}}_{\text{ocv}}-$ ${\text{V}}_1-$ ${\text{V}}_2$ ) and ohmic resistance in cell $j$ , respectively. To determine the current, $I_j^k$ the voltage, $U^k$ , across a bank of parallel connected cells (PCU), can be determined based on the charging/discharging current ( $I^K$ ) and the cell electrical properties, for example,

The updated cell current, $I_j^k$ , is then used as a boundary flux in the solution of the charge conservation equation for electrically conducting components connected to the negative terminal of the battery.

The battery solution supports both generic charging and discharging, including constant; piecewise linear; and cubic spline. Constant current discharge would be used for typical testing scenarios. Piecewise linear and cubic spline are used for experimental data such as a driving cycle, for example, NEDC or US06.

These are typically known from a battery specification sheet.

AcuSolve input

BATTERY_PACK( "4S2P battery module" ) {
    number_of_parallel_modules = 2
    number_of_serial_modules = 4
    electrical_input_type = current
    current_type = piecewise_linear
    current_curve_fit_values = Read( "time_current.txt" )
    current_curve_fit_variable = time
}

0               0.66809696
9.61104062      0.66809696       
12.5842409      0.66809696
13.34691228     15.37136268
…

Figure 3 shows a typical NEDC driving profile with current input.

Figure 4 shows a typical cell voltage and soc response form this current input applied to a battery pack.

Supports both generic charging and discharging, these include: constant; piecewise_linear; cubic_spline; and c-rate profiles. As with current, constant c-rate discharge would be used for typical testing scenarios. Piecewise linear and cubic spline are used for experimental data such as a driving cycle.

AcuSolve input

BATTERY_PACK( "4s2p battery module" ) {
    number_of_parallel_modules = 2    
    number_of_serial_moudles = 4
    electrical_input_type = c_rate
    c_rate = 1
}

Charging profiles include CC-CV (Constant Current-Constant Voltage) or CP-CV (Constant Power-Constant Voltage) methods.

In CC-CV charging, the process begins with a constant current (or c-rate) until reaching a specified voltage limit, and then switches to constant voltage charging. The simulation terminates when the current drops to a pre-defined level, for example, cut off current or maximum state of charge. In AcuSolve this is given as a fraction of the original input current. The switch between constant current and constant voltage is defined by the maximum voltage provided on the battery specification data sheet. This is set in the BATTERY_MODULE command (see Battery Module).

In CP-CV charging begins by applying a constant power, shifting to constant voltage once the voltage limit is reached. The termination criteria for CP-CV charging are the same as those for CC-CV.

A typical CC-CV or CP-CV charging current, voltage and soc curve are shown in Figure 5 and Figure 6.

Sign convention

For charging profiles the current is always negative, since the sign convention in AcuSolve discharge current is positive.

SimLab input

An example of a typical CC-CV input is shown in Figure 7.

AcuSolve input format

Power input can be provided as a constant power or a profile (piecewise linear and cubic spline). In this approach the power in the pack is calculated.

where ${\text{U}}_{\text{T}}\left(\text{t}\right)$ is the pack voltage (determined from the cell and module connectivity) and $i\left(\text{t}\right)$ is the pack current at time t. Using the above equation, it is possible to determine the cell current using an iterative approach based on the input power and known open circuit and polarization voltages.

AcuSolve input format

Constant voltage (CV) is charging with constant voltage. The input module voltage divided by the number of parallel cells should be between the minimum and maximum cell voltage.

AcuSolve input format

Battery Module

SimLab input

An example of the battery module input in SimLab is shown in Figure 8.

The identification of the electrical bodies, for example, cells, allows for identification of a cell in a pack based on the module number and cell numbering. For example, if the label is M2S1P4, this means that the cell in the pack belongs to module 2 and is the 4th cell in the first parallel bank connected in series. These bodies are added under a separate sub-assembly with a user-given name.

AcuSolve input format

BATTERY_MODULE( "M1" ) {
    number_of_parallel_cells = 7
    number_of_serial_cells = 12
    maximum_cell_voltage = 4.2
    minimum_cell_voltage = 3
    maximum_cell_state_of_charge = 0.95
    minimum_cell_state_of_charge = 0.15
    number_of_parallel_connected_units = 1
    battery_pack = "BatteryPack_1"
}

The number of BATTERY_MODULE commands depend on the number of modules defined in the BATTERY_PACK command (see Battery Packs).

The number_of_parallel_connected_units can generally be ignored as it has no effect on the solution if the initial state of charge of all the cells in a module is identical. At present, this feature is supported for current and power input. Details of this feature are outlined in Cell Electrical Connectivity, Cell Numbering, and Battery Components.

Battery Model

The BATTERY_MODEL specifies the ECM parameters for an individual battery. In the ECM approach, the electric behavior, for example, the voltage-current response, is modeled using a phenomenological electric circuit approach. The parameters for this electric circuit need to be provided, for example, as a function of soc and temperature, in order to model the heat generated from a battery. For example, a 2nd order ECM, that is, two RC pairs, requires the input of the following parameters: capacity, $V_{OCV}$ , ${\text{R}}_0,{\text{R}}_1, {\text{R}}_2,{\text{C}}_1$ , ${\text{C}}_2$ and optionally entropic heat.

The capacity of a battery cell. The coulomb value will be exported as Ah (Amp-hr).

Open circuit voltage is the voltage established between positive and negative terminals when the current is zero, this is, the circuit is open. The type includes Constant, Linear and Bilinear, whereas Constant is a constant open circuit voltage,for Linear, a table can be created which defines the state of charge (soc) versus voltage plot values. For Bilinear, Voltage is specified as a function of both soc and temperature.

Ohmic resistance in the ECM model represents the internal resistance of battery components. The type includes Constant, Linear and Bilinear, whereas Constant is a constant ohmic resistance, for Linear, a table can be created which defines the state of charge (soc) versus resistance plot values. For Bilinear, resistance is specified as a function of both soc and temperature.

Polarization resistance and capacitance in the ECM model describe the dynamic behavior of the battery, for example, ion transport and charge transfer.

Entropic heat coefficient is the derivative of open circuit potential with respect to temperature. It represents reversible heat generation in the battery cell. The type includes Constant, Linear and Bilinear.

BATTERY_MODEL( "CircuitModel" ) {
    battery_model_type = first_order_ecm
    ohmic_resistance_type = piecewise_linear
    ohmic_resistance_curve_fit_values = Read("SIMLAB.DIR/ro.fit" )
    ohmic_resistance_curve_fit_variable = soc
    open_circuit_voltage_type = piecewise_linear
    open_circuit_voltage_curve_fit_values = Read( "SIMLAB.DIR/ocv.fit" )
    open_circuit_voltage_curve_fit_variable = soc
    polarization_resistance1_type = piecewise_linear
    polarization_resistance1_curve_fit_values = Read( "SIMLAB.DIR/r1.fit" )
    polarization_resistance1_curve_fit_variable = soc
    polarization_capacitance1_type = piecewise_linear
    polarization_capacitance1_curve_fit_values = Read( "SIMLAB.DIR/c1.fit" )
    polarization_capacitance1_curve_fit_variable = soc
    battery_capacity = 2.5
}

SimLab interface

In SimLab, all of the above mentioned ECM parameters can be entered via the Circuit Model panel, shown in Figure 11.

Electrical Output Variables

For electrically conducting components the following output variables are provided:

Electric potential

For battery packs the electric potential is determined based on the solution of charge conservation combined with the voltage generated by the cells.

Current density

The current density is taken directly from the solution of charge conservation and is given by

$$\text{i}=-\sigma \nabla \varphi$$

where $\sigma$ is the thermal conductivity, representing the reciprocal of the resistivity provided to AcuSolve as an input.

Joule heat density

Joule heat density is the thermal energy generated due to the passage of current (electrical energy).

$$q_J=\sigma {\left|\nabla \varphi \right|}^2$$

Electrical Boundary Conditions

For a well-defined problem, the charge conservation equation requires a reference voltage in the system. Following the sign convention where current is considered positive during discharge, a battery pack is arranged such that the reference voltage is a conductive pathway connected to the negative terminal of a battery. An illustration of this arrangement is depicted in Figure 9. In this configuration, the reference voltage (0V) is applied to the busbar connected to the negative terminal of the first battery pair (S1P1 & S1P2). The final busbar, linked to the positive terminals of the second battery pair (S2P1 & S2P2), automatically calculates the current based on charge conservation and the input provided to the battery pack (described in the Battery Packs section).

SimLab interface

The boundary conditions are defined in SimLab using the voltage and current panels (Figure 10):

AcuSolve input format

The voltage and current conditions for the charge conservation equation are set under the SIMPLE_BOUNDARY_CONDITION section. The following snippets of the input file show these definitions.

SIMPLE_BOUNDARY_CONDITION(  "Voltage" ) {
    surface_sets = { "Voltage_PartBody.4_1_tet_tria3" }
    type = wall
    ...
    electric_potential_type = value
    electric_potential = 0.0
}

SIMPLE_BOUNDARY_CONDITION(  "Current" ) {
    surface_sets = { "Current_PartBody.3_1_tet_tria3" }
    type = wall
    ...
    electric_current_from_module = on
}

Cell Electrical Connectivity, Cell Numbering, and Battery Components

Typically, battery modules and packs have cell labeling in the format mSnP where m is the serial position and n is the parallel position. An example of a 2s2p configuration is given in Figure 12.

The number of parallel and serial cells, number_of_parallel_cells and number_of_serial_cells, respectively, are defined by their electrical connectivity first in the parallel direction and then in the serial direction. As an example, a pouch module made of 8 cells connected in a 4s2p configuration would have four pairs of parallel serially connected parallel cells: 1&2, 3&4, 5&6, and 7&8. This setup is shown in Figure 13.

For a cylindrical module with 48 cells in an 8s6p configuration (shown in Figure 14), banks of six parallel connected cells, for example, 1-6 or 7-12, are connected in series. For example, cells 1-6 are connected in series to cells 7-12.

Moreover, each time a new module is created, the cell numbering restarts from one in the AcuSolve input file.

The current collector is explicitly modeled only in the MSMD approach. In the single potential model, the jellyroll is a homogenized region representing the anode, cathode, separator, and current collector. The tab connects to this homogenized region in this modeling approach. Some examples cell structures are shown in Figure 15. The geometry can also include the fall details of the cell such as the current interrupt device (CID). A mock-up of such a geometry is shown in Figure 16. In this case the components would be defined as:

• The +tab set to tab_positive
• CID bottom disk, CID top disk and Terminal would be set to busbar
• Jellyroll is set to battery_cell

As an example, two 2s2p battery modules connected in series would be labeled as follows:

BATTERY_COMPONENT_MODEL( "M1S1P1" ) {
    component_type = battery_cell
    cell_id = 1
    battery_module = "Module_1"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M1S1P2" ) {
    component_type = battery_cell
    cell_id = 2
    battery_module = "Module_1"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M1S2P1" ) {    
    component_type = battery_cell
    cell_id = 3
    battery_module = "Module_1"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M1S2P2" ) {
    component_type = battery_cell
    cell_id = 4
    battery_module = "Module_1"
    isoc = 0.95
}

BATTERY_COMPONENT_MODEL( "M2S1P1" ) {
    component_type = battery_cell
    cell_id = 1
    battery_module = "Module_2"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M2S1P2" ) {
    component_type = battery_cell
    cell_id = 2
    battery_module = "Module_2"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M2S2P1" ) {
    component_type = battery_cell
    cell_id = 3
    battery_module = "Module_2"
    isoc = 0.95
}
BATTERY_COMPONENT_MODEL( "M2S2P2" ) {
    component_type = battery_cell
    cell_id = 4
    battery_module = "Module_2"
    isoc = 0.95
}

SimLab interface

In the SimLab interface, the components within a battery pack are labeled using the Classify parts panel, as illustrated in Figure 17.

The last panel, Cell Naming Order, assigns labels to battery modules within a pack using the standard mSnP convention. Additionally, each module in the pack is identified similarly. For instance, in a battery pack with two modules, the location of the battery in the second parallel and serial position would be M2S2P2.

The number_of_parallel_connected_unit is how many parallel connected unit (PCUs) you have in the configuration. Conceptually a PCU and a SCU is demonstrated in Figure 18.

For example, in a 4s2p case, where the number_of_parallel_connected_units = 1, 2 or 4. The corresponding electrical connection of the battery cells would be represented by the circuits shown in Figure 19.

The importance of understanding this connectivity is related to how current distributes through the battery pack when cells (and therefore modules) connected in parallel have cells of differing states. For instance, with a single PCU, it is essential for voltage to be uniform across each cell in the circuit to ensure conservation. This principle also applies to modules connected in parallel. In the AcuSolve battery solution, a rudimentary controller is integrated to balance cell voltages, thereby automatically calculating the current based on the solution derived from charge conservation in the busbars, tabs, and the properties of the cells.