A design optimization methodology for Li+ batteries

• A formal design optimization methodology for functionally graded electrodes of Li+ batteries is developed.
• A multi-scale finite element model for predicting the power-storage characteristics of a full battery cell is presented.
• A multi-objective formulation is introduced to optimize the useable capacity over a range of discharge currents.
• The influence of spatially varying porosity and sizes of active particles on optimized electrodes is analyzed.
• The difference between considering a half-cell versus a full cell in the optimization process is shown.

Design optimization for functionally graded battery electrodes is shown to improve the usable energy capacity of Li batteries predicted by computational simulations and numerically optimizing the electrode porosities and particle radii. A multi-scale battery model which accounts for nonlinear transient transport processes, electrochemical reactions, and mechanical deformations is used to predict the usable energy storage capacity of the battery over a range of discharge rates. A multi-objective formulation of the design problem is introduced to maximize the usable capacity over a range of discharge rates while limiting the mechanical stresses. The optimization problem is solved via a gradient based optimization. A LiMn2O4 cathode is simulated with a PEO–LiCF3SO3 electrolyte and both a Li Foil (half cell) and LiC6 anode. Studies were performed on both half and full cell configurations resulting in distinctly different optimal electrode designs. The numerical results show that the highest rate discharge drives the simulations and the optimal designs are dominated by Li+ transport rates. The results also suggest that spatially varying electrode porosities and active particle sizes provides an efficient approach to improve the power-to-energy density of Li+ batteries. For the half cell configuration, the optimal design improves the discharge capacity by 29% while for the full cell the discharge capacity was improved 61% relative to an initial design with a uniform electrode structure. Most of the improvement in capacity was due to the spatially varying porosity, with up to 5% of the gains attributed to the particle radii design variables.