Is There a Benefit in Employing Graded Electrodes for Lithium-Ion Batteries?

Abstract

Literature reports show both benefits and negligible impact when including graded electrodes in battery design, depending upon the exact model and conditions used. In this paper, we use two different optimization approaches for a secondary current distribution porous electrode model with nonlinear kinetics to confirm that computed solutions are correct. We use these confirmed optimal solutions to probe several ways that graded porosity can improve electrode performance. Single objective optimization such as reducing the overall electrode resistance using a graded electrode design provides a modest 4-6% reduction in resistance for typical lithium-ion battery parameters. Multiple objective optimization-for example, simultaneously considering electrode resistance and the overpotential variance and eventually the overpotential average as well-shows that multilayer designs open up a much richer feasible design space for achieving multiple goals. The ultimate answer to the value of graded electrodes will be the techno-economic analysis that links the benefits of an expanded optimal design space to the detrimental costs associated with manufacturing multilayer electrodes. An open-access executable code that can give optimal porosity distribution of any specified chemistry and detailed explanation of the two approaches can be found on the Subramanian group's website. Modeling and mathematical optimization can significantly improve the efficiency of battery design, helping to meet the growing demands for various applications. The idea of using modeling for battery design was first introduced by Tiedemann and Newman in 1975. 1 They used an ohmically limited porous electrode model to maximize the cell's effective capacity by changing the electrode thickness and porosity. Newman later applied the reaction-zone model to maximize the specific energy of the system, taking mass into consideration as well.2 For these two models, the objective function can be directly related to the design variables, thus the optimum can be obtained by simply observing the plot or from the analytical solution. They further optimized the thickness and porosity of a lithium iron phosphate 3 electrode, where they maximized the specific energy using the Ragone plots. Ramadesigan et al.4 went one step further by including the linear electrode kinetics to minimize the internal resistance of the electrode. They used control vector parameterization (CVP) to minimize the ohmic resistance in the positive electrode by varying porosity.With the development of battery modeling, more physical processes have been included, and one of the most popular physics based models is the pseudo-2-Dimensional (P2D) model developed by the Newman group. 5 The P2D model involves a set of nonlinear partial differential equations (PDEs) that can only be solved numerically. Therefore, a numerical optimization approach is required to perform optimization on the system. Du et al. proposed a surrogate-modelbased approach, 6 and later developed a sophisticated framework based on th...

Combining composition graded positive and negative electrodes for higher performance Li-ion batteries

“…Using simulation, grading of the type explored here has been suggested to modify and homogenize the spatial distribution of the electrode overpotential [31]. The experimental work here provides cell data consistent with this prior suggestion and for the first time quantifies the marked benefits of grading by experiment.…”

“…We expect that changing the local conductive carbon fraction may change the local electronic conductivity (and resistance), and thus may have a direct, homogenizing effect on the local overpotential and active material utilization. Some simulation-based studies have suggested this may be a promising line of enquiry [31], and building on recent developments in manufacturing capability for graded electrodes [28], we now investigate the effect of micro-scale composition grading in detail and in full cells. We design, manufacture and assess the performance of carefully controlled heterogeneous, graded electrode structures with the aim of promoting greater uniformity in overpotential distribution, and reaction rates across the electrode thickness.…”

Myth and Reality of a Universal Lithium‐Ion Battery Electrode Design Optimum: A Perspective and Case Study

“…[ 42 ] In a recent study, Qi et al also optimized a cathode for reduced resistance. [ 38 ] However, they reported only a 4.4% resistance reduction.…”

Model-Based Investigation of Porosity Profiles in Graphite Anodes Regarding Sudden-Death and Second-Life of Lithium Ion Cells

“…Focusing on the minimization of the ohmic resistance of a porous electrode, Ramadesigan et al [25] optimized a spatially varying porosity profile. Qi et al [26] applied a multi-objective optimization to a layered porosity profile for optimally balancing the ohmic resistance, the average overpotential and the standard deviation of the overpotential.…”