Semi-Empirical Modeling of Capacity Fade: A Practical Approach for Battery Pack Manufacturers
Authors: Wilke Stephen , Schweitzer Ben , Khateeb Siddique , Al-Hallaj Said 
Published: February 2020

Lithium ion batteries are rapidly increasing in usage for stationary energy storage projects, and market forecasts predict continued accelerating growth in these fields. For industrial and grid applications, customer requirements and return-on-investment goals necessitate long system lifetime (10-15 years) and a guaranteed number of cycles or total energy throughput. Battery pack manufacturers must design their systems to reliably meet these life requirements while minimizing cost. However, for most pack assemblers the prerequisite information on cell ageing is neither available from the cell supplier nor easily obtainable via testing. Given the rapid development of new materials and cell model lines, it becomes an enormous task for pack manufacturers to conduct comprehensive in-house testing of all candidate cells.

In order to make industrial lithium ion batteries feasible and competitive, system manufacturers must reduce costs by leveraging the newest state-of-the-art cell technology and independently ensuring it fulfills the lifetime requirements. This latter task must be accomplished using a manageable scope of cell lifetime testing that keeps up with the rapid pace of new cell development (12 months). Appropriate modeling can be used to extrapolate testing results to the projected lifetime target, but such models must be reliably accurate so as to reduce the high level of uncertainty and risk associated with constructing systems using newly released cells.

Toward these ends, we have developed and implemented a semi-empirical modeling approach [1, 2] that is practical and effective for a small pack manufacturing company. The model incorporates a limited set of cell degradation mechanisms to predict capacity fade. Based on a specific product application, grid-tied frequency regulation, an experimental matrix was designed to elucidate the effects of temperature, depth-of-discharge (DOD), time, and energy throughput on calendar and cycle ageing. The focus on one usage profile helped to reduce the number of pertinent independent variables and required tests. Cell storage testing was performed at 25, 35, 45, and 55°C, and cycle tests were conducted with DOD of 10, 20, 40, 60, and 80%. The semi-empirical model was constructed using a mathematical framework reflective of the physics-based ageing mechanisms for SEI growth [3] and particle fracture [4, 5], fitted to the experimental dataset. Good agreement between the model predictions and test results for capacity fade are shown for two different state-of-the-art 18650 cell models.

This semi-empirical model demonstrates how a pack manufacturer can successfully assess the lifetime performance of new cell technologies for applications with strict lifetime requirements, while addressing risk and supporting product warranty. The physical basis of the modeling approach yields reliable predictions, and its simple formulation reduces the required testing and timeline for completion. When used on a number of newly released cells, this model approach becomes a useful tool to guide cell selection, battery system oversizing, and thermal management requirements [6], which can all lead to reductions in battery cost.

References

[1]   S. Santhanagopalan, K. Smith, J. Neubauer, K. Gi-heon, and A. Pesaran, Design and Analysis of Large Lithium-Ion Battery Systems, Artech House, Boston (2015).

[2]   J. Schmalstieg, S. Käbitz, M. Ecker, and D. U. Sauer, J. Power Sources, 257, 325–334 (2014).

[3]   M. Broussely, et al., J. Power Sources, 146, 90–96 (2005).

[4]   J. Wang, et al., J. Power Sources, 269, 937–948 (2014).

[5]   M. Safari, M. Morcrette, A. Teyssot, and C. Delacourt, J. Electrochem. Soc., 157, A713–720 (2010).

[6]   B. Schweitzer, S. Wilke, S. Khateeb, and S. Al-Hallaj, J. Power Sources, 287, 211–219 (2015).