Theory for the Battery Pack Interface
For the battery models of The Battery Pack Interface, refer to Theory for the Lumped Battery Interface. Individual battery models are created for each disjoint set of domains in the battery selection of the interface. All variables are given an additional suffix i, where the index i ranges from 1 to N, where N is the number of disjoint sets in the selection.
In the current conductors, the electric potential in the electrode phase ϕs (SI unit: V) is solved for using a charge balance based on Ohm’s law.
The current density, is (SI unit: A/m2), is defined as
where σs is the electric conductivity. The charge balance equation is expressed as
The joule heating source term Qh (SI unit: W/m3) is defined as
The battery models, which are formulated as global 0D equations, are coupled to ϕs on the current collector on the negative and positive connectors (δΩneg,i and δΩpos,i, respectively) separately for each battery i.
The coupling is achieved by defining two global electric potential degrees of freedom ϕs,neg,i,, ϕs,pos,i, and one degree of freedom for the individually applied battery current Iapp,i (SI unit: A) and then solving the following set of equations.
On the negative and positive connectors, if contact resistance is not included, the following applies,
If contact resistance Rc (SI unit: Ω·m2) is included on the negative and positive connectors, the following applies,
Additionally,
For all subnodes to the Batteries node, except the Thermal Event subnode, refer to Theory for the Lumped Battery Interface. The Thermal Event subnode is described below.
All the boundary condition subnodes of the Current Conductors node are similar to those described for the Current Distribution interfaces. See boundary nodes described in Shared Nodes for Battery Interfaces.
Thermal Event
The Thermal Event node can be used to define an event-based heat source. In addition, the event may also induce changes in the ohmic overpotentials (internal resistance) of the battery cells and/or induce cell short circuits.
Similarly to other nodes in the Battery Pack interface, individual events, heat sources and associated state variables are created for each battery cell (disjoint set of domains) in Thermal Event node selection.
To control the heat source released by the thermal event, an event time state variable tte (SI unit: s) is used. The initial value of the event time variable is set to inf. The thermal event is triggered by an Event condition, which could be when either the maximum or average cell temperature exceeds a corresponding maximum or average trigger temperature, or if the simulated time exceeds the explicit time that is specified.When the event is triggered, the event time variable tte is set to the current time t, in the case of maximum or average temperature event conditions. In the case of explicit time event condition, the event time variable tte is set to the specified explicit time texp. The event can only be triggered once per battery cell.
After the event has been triggered, the thermal event heat source Qh,te (SI unit: W) is added to the total sum of all heat sources for the battery cell. The heat source should be stated as a function of time elapsed after triggering of the event. Additionally, the heat sources due to the added ohmic overpotential and short circuit are also included appropriately.
Defining Temperature and SOC-Dependent Battery Parameters
This is applicable to the Lumped cell model. All battery parameters in the Battery Pack Interface, defined for instance in the Voltage Losses, Cell Equilibrium Potential and Thermal Event subnodes, need to be defined using global (nonspatially resolved) values. Individual parameter dependencies, (that is, per battery cell) on temperature and SOC are possible to define by the use of the bp.T_cell and bp.SOC (without a suffix) variables. In the parameter expressions, these variables are substituted internally to the corresponding global, but individually defined bp.T_cell_X and bp.SOC_X variables, where the suffix X denotes the cell number, ranging from 1 to the number of disjoint domains.
Note that bp.T_cell_X is defined as the average per cell of the temperature expression under Model Input of the Voltage Losses node for each cell number X. If Include concentration overpotential is active using Particle diffusion, bp.SOC is substituted for the local SOC in the generalized particle in the Diffusion time-constant parameter expression, and the average SOC in the particle for all other parameters.
Defining Temperature and DOC-Dependent Battery Parameters
This is applicable to the Two electrodes model. All battery parameters in the Battery Pack Interface, need to be defined using global (nonspatially resolved) values. Individual parameter dependencies, (that is, per battery cell) on temperature and DOC are possible to define by the use of the bp.T_cell, bp.DOC_neg, and bp.DOC_pos variables. In the parameter expressions, these variables are substituted internally to the corresponding global, but individually defined bp.T_cell_X, bp.DOC_neg_X, and bp.DOC_pos_X variables, where the suffix X denotes the cell number, ranging from 1 to the number of disjoint domains.
Note that bp.T_cell_X is defined as the average per cell of the temperature expression under Model Input of the Voltage Losses node for each cell number X. If Include concentration overpotential, negative is active using Particle diffusion, bp.DOC_neg is substituted for the local DOC in the generalized particle in the Diffusion time-constant parameter expression, and the average DOC in the particle for all other parameters. Similarly, If Include concentration overpotential, positive is active using Particle diffusion, bp.DOC_pos is substituted for the local DOC in the generalized particle in the Diffusion time-constant parameter expression, and the average DOC in the particle for all other parameters.