Javier Gazzarri, MathWorks
No thermal management and asymmetrical heat transfer boundary conditions create a thermal gradient in this 8s 2p Li-ion battery module. As a result, battery cells degrade unevenly. Capacity fades more rapidly in cells that are at higher temperatures. This is an undesirable condition since it leads the module into imbalanced SOC conditions.
The battery cell block is modeled using an equivalent circuit with temperature effects, and a provision for capacity fade and internal resistance increase, both functions of cycle count and temperature.
The module is cycled with a square wave of constant power in both charge and discharge. Current changes direction based on minimum and maximum cell battery state of charge (SOC).
Individual cell capacity is continuously calculated and results show how the higher the temperature, the higher the aging rate.
In this example, we model a lithium ion battery pack with an 8S2P topology. Each battery cell is parameterized to represent the electrical behavior of a 1.5 Amp hour, 18,650 commercially available cell, whose data sheet we digitized and turned into equivalent circuit parameters, using a web app that calculates the internal resistance and its temperature dependence, based on constant current discharge curves. Individual battery cells exchange heat with one another by conduction. The top two cells expel heat to the environment by convection. And the bottom two cells are thermally insulated.
In addition to the datasheet information that characterizes the electrical behavior, I added a few assumed degradation-related parameters to simulate the effect of long term cycling and performance, as well as degradation dependence on temperature. It is important to emphasize that these degradation rates are not real since aging information was not available in the datasheet, and that they are extremely exaggerated so that significant degradation can take place in a short amount of time for demonstration purposes.
The Simscape electrical battery block has provisions for the increase in internal resistance and decrease in capacity as a function of cycle count. What is interesting to note in this case, is that effective cycle count will not be uniform throughout the pack because of the non-uniform temperature that will induce different degradation rates. The pack is cycled with a square wave of 300 watts in both charge and discharge. Switching between charge and discharge is based on the SOC of the pack reaching the lower and upper threshold. The total simulation time is 100 hours.
Because of the asymmetrical thermal layout of the system, the temperature of each individual cell evolves differently. Cells at the top are colder than cells at the bottom, which means that their rate of aging is also different from one another, i.e. their capacity and internal resistance are different. This divergent evolution of the cell degradation effectively means that each cell develops a cycle life that is different from those of the cells around it. So here, we can see that the effective cycle counts off the hotter cells is larger than that of the colder cells because their capacity degrades more quickly.
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