The simultaneous optimization approach enables fast and convenient control of state variables and design variables in order to achieve goals such as minimizing the overall resistance and overpotential variation in nonlinear models of porous electrodes.¹ Use of simultaneous optimization also lets one assess design considerations such as employing a graded electrode, but of course, the benefit depends on the formulation of the problem. For example, single objective optimization of the overall electrode resistance based on use of a graded porosity results in a modest 4-6% resistance reduction for typical lithium ion battery electrode material properties. In contrast, 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 these goals.

We apply the same simultaneous optimization approach to a more complicated nonlinear battery model, the pseudo-2D (P2D) model, where electrolyte transport processes and solid-state intercalation/deintercalation transport and kinetics in the electrodes are captured.² The P2D model was developed by the Newman group³ and has become one of the most widely accepted electrochemical battery model in literature.

Functionally graded materials have properties that change with position, and are an emerging area for design.⁴ Here we propose to explore the multi-objective performance of batteries with optimal spatial gradients in porosity and functional materials. As a result, the battery electrode, chemistry, composition, and other properties can all change with electrode thickness or within the particle to produce a functionally graded electrode. The inclusion of functionally graded materials to our graded electrode design further broadens the application of our simultaneous optimization design frame work. We first show how to modify the standard P2D model to accommodate property gradient (e.g. diffusivity change within a particle), and then build the simultaneous optimization framework, to find the optimal property distribution together with the porosity distribution.

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

1. Y. Qi, T. Jang, V. Ramadesigan, D. T. Schwartz and V. R. Subramanian, Journal of The Electrochemical Society, 164, A3196 (2017).
2. T. J. Y. Qi, V. Ramadesigan, D. T. Schwartz, and V. R. Subramanian, ECS Meeting Abstracts, Multiscale Modeling, F02 (2018).
3. T. F. Fuller, M. Doyle and J. Newman, Journal of the Electrochemical Society, 141, 1 (1994).
4. A. Neubrand and J. Rödel, Zeitschrift für Metallkunde, 88, 358 (1997).