From Variability and Aging Rate Spread to Quantification of Failure Rates in Lithium-Ion Packs
Authors: Dechent Philipp , Schoeneberger Ilka , Hust Friedrich Emanuel , Sauer Dirk Uwe 
Published: February 2020

One of the most important components of an electric vehicle is its energy storage system. Unfortunately, it has also proven to be the most expensive component, which is limiting the vehicle’s performance, for example range or power, for a given cost target. If higher spreads and poorer cell quality can be coped within the system, costs can be lowered by decreasing the number of cells rejected in production.
The aim of the research provided is to optimize system topologies for individual applications in order to find suitable cells, avoid oversizing of battery systems and to give forecasts of lifetime and quantifiably failure rates for battery packs build on cell measurements while decreasing cost. On that account a simulation tool chain was developed to incorporate variability and aging rate spreads in the system design process. With the simulation tool battery topologies can be simulated with different varying usage profiles, cell parameter spreads and varying aging rates.
Previous analysis on the impact of variations in commercial lithium-ion battery systems on aging, showed the important role of spreads in cell parameters of the batteries. Cell aging is usually simulated with models with parameters determined by accelerated aging tests, usually consisting of large test set with different operating points. Aging due to high temperatures and charge levels and aging due to cycling is combined to assess the capacity after a given usage profile. In order to decrease the impact of measurement errors all aging parameters are determined on the average of multiple cells. Furthermore, in state-of-the-art simulations, variation from cell-to-cell is not considered, although tests showed a heavy influence.
As part of our research, a modeling framework was developed which makes it possible to simulate the electrical and thermal behavior of batteries as well as their aging behavior in different configurations. Thereby, the electrical behavior of the battery can be approximated by an electrical equivalent circuit, which is determined by electrochemical impedance spectroscopy, pulse current parameterization, and relaxation measurement. The thermal model receives the heat loss calculated from the electrical simulation and uses it to calculate the temperature distribution within the battery cell and pack. The feedback of the temperature distribution to the electrical model is given by lookup tables of the electrical elements depending on the cell temperature.
The layout of the equivalent circuit framework is flexible for different configurations. Thus, it is also possible to adopt a spread of the parameters within the equivalent circuit diagram for individual cells of a simulated pack. For example, initial capacity distributions obtained by end-of-line testing or from literature can be used. In addition, aging rates from aging tests can be assigned to each cell to take variations in aging speed into account.
Together with load profiles, usage pattern and lifetime requirements topologies can be simulated multiple times as part of a Monte Carlo simulation with cell properties derived from the aging rate distributions and initial spread distributions. Subsequently the topology needs to be evaluated to verify if the requirements, especially for mandatory lifetime, are met.
If the targets cannot be fulfilled, the topology can be changed. For example, another cell might be used, or the target adjusted, and simulations are repeated. A useful instance for example is the assessment of maximum cell variation for a given application as 800 V EVs, to still reach the lifetime expectations. The same cell might be used, but the initial selection for grading and tolerances during production must be stricter.

Figure 1