Optimal Graded Electrode Design of Lithium-Ion Batteries with Simultaneous Optimization Approach
Authors: Qi Yanbo , Jang Taejin , Ramadesigan Venkatasailanathan , Schwartz Daniel T. , Subramanian Venkat R. 
Published: February 2020

The first attempt to improve battery performance through model-based design optimization was made by W. Tiedemann and J. Newman in 19751. V. Ramadesigan et al.2
developed optimal spatially varying porosity for porous electrodes by considering ohmic resistance model in the electrode. They also introduced the idea of using graded electrode to further improve the performance.
Since the introduction of the pseudo-2D (P2D) model by the Newman group, many efforts have been made in utilizing the P2D model in battery design. S. Golmon et al.3 extended the P2D model by incorporating the mechanical stress-strain relationship and developed a systematic framework to formulate the multi-objective and multi-design-parameter optimization problem with adjoint sensitivity analysis4. S. De and his coworkers5 used a reformulated model developed by P. Northrop et al.,6 which greatly improved the computational efficiency, and performed optimization of multiple design parameters including the thickness and porosity of the positive and negative electrodes to maximize the specific energy of the cell. N. Xue et al.7 applied the gradient-based algorithm framework to optimize the cell design to maximize the energy density with specific power density requirements. C. Liu et al. developed a multi-objective optimization framework to optimize for minimizing degradation, maximizing specific energy and power at the same time by varying the conductivity, particle sizes, electrode thickness, and porosity for both electrodes.8 They also considered the degradation mechanism and the long-term performance for design.
Y. Dai and V. Srinivasan revisited the idea of using graded electrodes to achieve better performance.9 They concluded that no significant improvement was observed by using the graded electrode design from their simulation. Later, Z. Du et al. examined the effects of several design parameters, including graded porosity, on the performance of thick electrodes by simulation. They proposed several continuously changing porosity profile in opposed to the more practical layered approach, and confirmed Dai and Srinivasan’s conclusion that graded electrode design can only increase the performance slightly.10

We have successfully applied the simultaneous optimization approach to a secondary current distribution electrode model recently, which enables faster optimization and direct control on the state variables11. The effect of including graded electrode in design was also discussed. Single objective optimization such as reducing the overall electrode resistance provides a modest 4-6% reduction in resistance. Multiple objective optimization (simultaneously minimizing electrode resistance, the overpotential variance, and the overpotential average) shows that multilayer designs open up a much richer feasible design space for achieving multiple goals.
The limitation of the model in the past paper is that it does not take into account the concentration gradient in the system and the intercalation/deintercalation in the electrodes, which are key processes in a lithium-ion system and are captured by the P2D model.
In this work, we will first apply the simultaneous optimization approach to a P2D model and compare its performance with the sequential approach. We will also explore the application of the graded electrode design to the P2D model and identify the benefits if any.

Acknowledgements

The authors are thankful for the financial support by the Clean Energy Institute at the University of Washington and the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy through the Advanced Battery Materials Research (BMR) Program (Battery500 Consortium).

References

W. Tiedemann and J. Newman, Journal of the Electrochemical Society, 122, 1482 (1975).

V. Ramadesigan, R. N. Methekar, F. Latinwo, R. D. Braatz and V. R. Subramanian, Journal of The Electrochemical Society, 157, A1328 (2010).

S. Golmon, K. Maute and M. L. Dunn, International Journal for Numerical Methods in Engineering, 92, 475 (2012).

S. Golmon, K. Maute and M. L. Dunn, Journal of Power Sources, 253, 239 (2014).

S. De, P. W. C. Northrop, V. Ramadesigan and V. R. Subramanian, Journal of Power Sources, 227, 161 (2013).

P. W. C. Northrop, V. Ramadesigan, S. De and V. R. Subramanian, Journal of The Electrochemical Society, 158, A1461 (2011).

N. Xue, W. Du, a. Gupta, W. Shyy, a. Marie Sastry and J. R. R. a. Martins, Journal of the Electrochemical Society, 160, A1071 (2013).

C. Liu and L. Liu, Journal of The Electrochemical Society, 164, E3254 (2017).

Y. Dai and V. Srinivasan, Journal of The Electrochemical Society, 163, A406 (2015).

Z. Du, D. L. Wood, C. Daniel, S. Kalnaus and J. Li, Journal of Applied Electrochemistry, 47, 405 (2017).

Y. Qi, T. Jang, V. Ramadesigan, D. T. Schwartz and V. R. Subramanian, Journal of The Electrochemical Society, 164, A3196 (2017).