Battery pack

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Battery pack

Background
Benchmark ID	batteryPack_n151642m10q10
Category	misc
System-Class	AP-LTI-FOS
Parameters
nstates	151642
ninputs	10
noutputs	10
nparameters	2
components	A, B, C, E
Copyright
License	Creative Commons Attribution 4.0 International
Creator	Lucas Kostetzer (CADFEM)
Editor	Julia Vettermann
Location
https://zenodo.org/records/10820678

1 Motivation

Due to the increasing interest in electromobility detailed knowledge about the thermal system behavior of complete battery packs becomes crucial . Many aspects like power performance and aging characteristics depend on the temperature of the system. Thus the use of reduced models is important for a fast simulation of the system behavior over a long period of time.

2 Description

Model of the battery pack.

The battery pack consists of 10 cells and a water-cooled plate . The model has been generated and meshed in ANSYS. SOLID90 elements have been used for the finite element discretization of the battery cells. The flow problem has been modeled by FLUID116 elements, representing a one-dimensional pipe flow. Thereby SURF152 elements have been used to realize the convection between fluid and cooled plate. Thermal radiation and convection between battery pack and environment are neglected. The contact between the individual battery cells and between cells and cooled plate has been modeled with the help of the elements CONTA174 and TARGE170.

The ambient temperature as well as the fluid temperature at the entrance of the pipes has the given value of 0°C.

3 Data

The parametric system of order $n=151642$ with $m=10$ inputs and $q=10$ outputs is of the following form

$\begin{align} E\dot{T} & = (A + p_1 A_1 + p_2 A_2)T + Bu \\ y & = CT \end{align}$

with

$E \in \mathbb{R}^{n\times n}$	- capacity matrix
$A \in \mathbb{R}^{n \times n}$	- basic conductivity matrix
$A_1 \in \mathbb{R}^{n \times n}$	- part of conductivity matrix arising from convection
$A_2 \in \mathbb{R}^{n \times n}$	- part of conductivity matrix arising from heat flux
$B \in \mathbb{R}^{n\times m}$	- input map
$C \in \mathbb{R}^{q\times n}$	- output map
$T \in \mathbb{R}^n$	- state vector (temperature)
$u \in \mathbb{R}^{m}$	- input vector (heat generation rate of each battery cell)
$y \in \mathbb{R}^{q}$	- output vector (temperature at the center of each battery cell)

where $p_1$ is the heat transfer coefficient and $p_2$ is the mass flow in the pipes (FLUID116 elements with load heat flux).

All matrices can be downloaded from Zenodo. The battery pack is a benchmark for problems containing unsymmetric matrices.

In the original model the values $p_1=500\tfrac{W}{m^2 K}$ and $p_2=0.1\tfrac{W}{m^2}$ for the parameters have been used.

4 Origin

The model was created in ANSYS by Lucas Kostetzer (CADFEM). The export of the system matrices from ANSYS and the documentation for MOR Wiki were performed by Julia Vettermann.

5 Citation

To cite this benchmark, use the following references:

For the benchmark itself and its data:

 @misc{dataBatteryPack,
   author = {Lucas Kostetzer and Julia Vettermann},
   title = {Battery pack},
   howpublished = {hosted at {MORwiki} -- Model Order Reduction Wiki},
   year = 2024,
   doi = {10.5281/zenodo.10820678}
 }