Increased driving range and enhanced fast charging capabilities are two immediate goals of transport electrification. However, these are of competing nature, leading to increased energy and power demand respectively from the on-board battery pack. By fine-tuning the number of layers versus active electrode material of a lithium ion pouch cell, tailored designs targeting either of these goals can be obtained. Achieving this trade-off through iterative empirical testing of layer choices is expensive and often produces sub-optimal designs. This paper presents a model-based methodology for determining the optimal number of layers, maximising usable energy whilst satisfying specific acceleration and fast charging targets. The proposed methodology accounts for the critical need to avoid lithium plating during fast charging and searches for the optimal layer configuration considering a range of thermal conditions. A numerical implementation of a cell model using a hybrid finite volume-spectral scheme is presented, wherein the model equations are suitably reformulated to directly accept power inputs, facilitating rapid and accurate searching of the layer design space. We show how thermal management design can limit vehicle driving range at high charging temperatures. We highlight how electrode materials exhibiting increased solid phase diffusion rates are as equally important for extended range as developing new materials with higher inherent capacity. We illustrate for a plug-in hybrid vehicle, how the proposed methodology facilitates common module design of battery packs, thereby reducing the cost of derivative vehicle models. To facilitate model based layer optimisation, we provide the open-source toolbox, BOLD (Battery Optimal Layer Design).
Research into reduced-order models (ROM) for Lithium-ion batteries is motivated by the need for a real-time embedded model possessing the accuracy of physics-based models, while retaining computational simplicity comparable to equivalent-circuit models. The discrete-time realization algorithm (DRA) proposed by Lee et al. (2012, “One-Dimensional Physics-Based Reduced-Order Model of Lithium-Ion Dynamics,” J. Power Sources, 220, pp. 430–448) can be used to obtain a physics-based ROM in standard state-space form, the time-domain simulation of which yields the evolution of all the electrochemical variables of the standard pseudo-2D porous-electrode battery model. An unresolved issue with this approach is the high computation requirement associated with the DRA, which needs to be repeated across multiple SoC and temperatures. In this paper, we analyze the computational bottleneck in the existing DRA and propose an improved scheme. Our analysis of the existing DRA reveals that singular value decomposition (SVD) of the large Block–Hankel matrix formed by the system's Markov parameters is a key inefficient step. A streamlined DRA approach that bypasses the redundant Block–Hankel matrix formation is presented as a drop-in replacement. Comparisons with existing DRA scheme highlight the significant reduction in computation time and memory usage brought about by the new method. Improved modeling accuracy afforded by our proposed scheme when deployed in a resource-constrained computing environment is also demonstrated.
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