Parameterization of battery models

Wolfram Language



This information is part of the Modelica Standard Library maintained by the Modelica Association.

A stack from BatteryStacks is built from Ns*Np identical cells, where Np describes the number of parallel connected cells and Ns the number of series connected cells.

The parameters of a stack built from Np*Ns identical cells are calculated as follows:

Description Cell Stack
Nominal OCV OCVmax OCVmax*Ns
End of discharge voltageOCVmminOCVmin*Ns
Capacity Qnom Qnom*Np
Inner resistance Ri Ri*Ns/Np

Cell parameters

The parameters of one cell are summarized in the parameter record cellData. Dependency of OCV on SOC can be chosen either linear (useLinearSOCDependency=true) or based on a look-up table.
By default, a linear OCV versus SOC characteristic is defined (like a capacitor), i.e. OCV_SOC[:,2]=[SOCmin,OCVmin/OCVmax; SOCmax,1].
The OCV versus SOC table has to be specified with 1st column = SOC values in ascending order, 2nd column = corresponding OCV values with respect to OCVmax.
Be careful using parameter smoothness for table interpolation, check the resulting characteristic.
Further dependencies of OVC (e.g. on temperature) are not taken into account, this would require a 2-dimensional table look-up.

Self-discharge is specified as discharge current Idis at SOC = SOCmax. From that values, a self-discharge conductance is calculated.
If self-discharge should be neglected, set Idis=0.

Linear temperature dependency of inner resistance can be specified by reference temperature T_ref and temperature coefficient alpha:
R = R_ref*(1 + alpha*(T - T_ref)).

Transient parameters

The parameter record for one cell of a transient battery model cellData extends from the basic cellData record, and adds the parameters of the additional RC-elements. These are specified by an array of parameter records rcData:

  • R .. Resistance of RC-element
  • C .. Capacitance of RC-element

The size of the array rcData has to be defined as parameter nRC. The parameters of these RC-elements are results of sophisticated measurements, e.g. cell impedance spectroscopy.
Temperature dependency of the resistors is assumed to be the same as inner resistance Ri.

Typical parameters of a Li-Ion cell

End of charge voltage   4.2 V
Nominal voltage   3.6 V
End of discharge voltageOCVmmin2.5 V

Capacity (i.e. nominal charge) Qnom, inner resistance Ri and short-circuit current Isc depend on the cell size.
Typical (estimated) values for a certain cell size are, as an example:

Capacity Qnom5 A.h
Inner resistance Ri 3 mΩ

Self-discharge rate is typically 1%/month.

Parameters of stacks built from a matrix of Ns x Np cells:

A stack from BatteryStacksWithSensors is built from Ns*Np cells arranged in a matrix, where Np describes the number of parallel connected cells and Ns the number of series connected cells. The parameters of such a stack are summarized in the parameter record stackData. Here the matrix of Ns x Np cell parameters records is compiled. The parameters of original cell data are propagated to all cells except those whose indices are specified in the array kDegraded[:,2]. For these degraded cells the parameters of degraded cell data are propagated.
Note: Any members of the parameter array kDegraded[:,2] outside the range 1≤kDegraded[:,1]≤Ns and 1≤kDegraded[:,2]≤Np are ignored.