Interpore 2023, Edinburgh, England, 22 - 25 May 2023, pp.465-466
Li-Ion batteries are widely used for energy storage mediums
because of their high volumetric and gravimetric energy capacities and proven mature
technology level suitable for mass production. However, they have one key
problem which is the heat generation during charging and discharging cycles. As
the cells are getting too hot or too cold, battery life and performance
decreases. If the heat generated from the batteries are not dissipated, there
is even risk of explosion. To model the thermal behavior of the battery package
one first needs to figure out the heat dissipated from a single cell, which can
be set as an heat source value for the thermal modeling for the battery
package. This can also be achieved with electrode scale continuum scale models,
where Li transport in electrolyte and charge balance and Li diffusion in porous
electrodes are modeled. However, electrode scale model would be over detailed
to combine with a system level model.
First, cell level 2^{nd} degree Thevenin’s
equivalent circuit model [1] was developed under Matlab (fig. 1 and fig.2).
Figure1. Thevenin’s equivalent circuit model concept
Figure2. Thevenin’s equivalent circuit model developed
under Matlab
The model requires Open Circuit Voltage (U_{oc}) vs State of Charge
(SOC) relationship as an input. The parameters Ro represents contact/ohmic
resistance of the cell, R1-C1 represents cell polarization, R2-C2 represents diffusion
process [2], which are determined by fitting terminal voltage (U_{t})-SOC measurement. Different
from the lead acid batteries the Li-Ion cells have exponential decrease in the
terminal voltage when the terminal voltage is approaching the cut-off voltage. To
mimic this behavior, the equivalent circuit components (R,C values) are not set
to constant values, they are varying as a function of SOC.
The developed Thevenin Model is able to calculate SOC, U_{oc}, U_{t}, state of health (SOH),
remaining capacity, useful capacity [3], thermal power and generated heat. The
main purpose of building an equivalent circuit model is to calculate thermal
power generated by the cell (Thermal_Power=(U_{oc}-U_{t})* I_current) [4,5].
Battery Package level simulation is carried out with setting
thermal power of Thevenin model as a heat source to model temperature
distribution. Thermal conductivity properties are taken from [6].
This is achieved with Comsol finite element simulation
software (fig. 3).
Figure
3. Temperature distribution within the battery package with active air cooling
Total system model is created to model system dynamics with
varying terminal current. Total system model is composed of Grid Connection,
Auxiliary Load, Power Control System, Power Management System, Convertors, HVAC
System, Battery Management System and Battery Package. The developed equivalent
circuit cell module is set in the heart of the battery package module. During
operation the main heat sources are battery packages. The temperature distribution
of the total system is calculated with FEM simulator.
The advantage of this approach is that the experimental data
can be perfectly fitted to the model data. The drawback of this approach is
that the heat that is generated during charge/discharge process is assumed to
be homogenously distributed at the outer surface of the cell.
REFERENCES
[1]
M. Chen and G. A. Rincon-Mora, “Accurate electrical battery model capable of
predicting runtime and I-V performance,” IEEE Transactions on Energy
Conversion, vol. 21, no. 2, pp. 504–511, Jun. 2006, doi:
10.1109/TEC.2006.874229.
[2]
N. Wassiliadis et al., “Revisiting the dual extended Kalman filter for battery
state-of-charge and state-of-health estimation: A use-case life cycle
analysis,” Journal of Energy Storage, vol. 19, pp. 73–87, Oct. 2018, doi:
10.1016/j.est.2018.07.006.
[3]
M. Rampazzo, M. Luvisotto, N. Tomasone, I. Fastelli, and M. Schiavetti,
“Modelling and simulation of a Li-ion energy storage system: Case study from
the island of Ventotene in the Tyrrhenian Sea,” Journal of Energy Storage, vol.
15, pp. 57–68, Feb. 2018, doi: 10.1016/j.est.2017.10.017.
[4] S. C. Chen,
C. C. Wan, and Y. Y. Wang, “Thermal analysis of lithium-ion batteries,” Journal
of Power Sources, vol. 140, no. 1, pp. 111–124, Jan. 2005, doi:
10.1016/j.jpowsour.2004.05.064.
[5] M. Muratori, “THERMAL
CHARACTERIZATION OF LITHIUM-ION BATTERY CELL,” PhD Thesis, POLITECNICO DI
MILANO, Milano, 2008.
[6] S. J. Drake, D. A. Wetz, J. K.
Ostanek, S. P. Miller, J. M. Heinzel, and A. Jain, “Measurement of anisotropic
thermophysical properties of cylindrical Li-ion cells,” Journal of Power
Sources, vol. 252, pp. 298–304, Apr. 2014, doi: 10.1016/j.jpowsour.2013.11.107.