Much attention as been given to the study of Li-Ion batteries for their use in automotive applications such as Hybrid Electric Vehicles (HEV), Plug In Hybrid Electric Vehicles (PHEV), and pure Battery Electric Vehicles (BEV). The battery packs that are used in these applications are capable of delivering tens to hundreds of kilowatts for extended periods of time which requires packs made out of many batteries put in series to increase voltage, and also in parallel, to increase pack capacity. Hence, automotive battery packs are inherently large, distributed systems which must function as a system, subject to all the cells behaving as identically as possible. Due to the large number of cells (possibly hundreds) and the physical extent (large pack or multiple modules), cells-to-cells differences exist due to manufacturing differences, thermal gradients, possibly different aging histories, leading to the need for Battery Management Systems (BMS) to continuously balance the State of Charge (SoC) of all the cells. This thesis addresses the dynamic simulations of these large distributed battery systems to quantify the dynamic trajectories of each of the cells and the impact of pack topology, as well as statistical differences between cells, on the non-ideal behavior of the pack.
In this thesis, we present a battery pack model and simulation methodology in order to study some of the operation characteristics of different battery pack configurations, under different temperatures, different initial SoCs, and different current profiles. It is often assumed that the dynamic behavior of a battery pack can be approximated by a scaled up model of a single cell. Unfortunately, this assumption fails due to small manufacturing differences on each cell, the state of health (SoH) of each cell and non-uniform thermal conditions inside a battery pack.
We begin by deriving a computationally efficient analytical single cell battery dynamic model with scheduled parameters that are used in a larger pack. A general pack model is derived. We introduce a computationally efficient methodology to formulate and solve the system representing a full battery pack, while allowing each cell to have parameter variations.
Using the derived pack model and simulator and parameters identified experimentally for a single cell, a large number of simulations are carried out in parallel on a computing cluster to investigate the statistical behavior of the cell unbalance in the presence of appropriately distributed statistical variations in parameters (Monte-Carlo-like approach). From this vast array of simulations, appropriate statistical metrics of the divergence of the individual cell dynamic trajectories are then extracted and correlated to the statistics of the variability in input parameters. This information is invaluable for designing appropriate control algorithms in battery management systems (BMS), as well as to perform battery-pack diagnostics. We define metrics in order to quantify the SoC divergence between cells within the pack and current splits between the cells and strings in parallel. In addition, an example pack is presented with a simulated damaged cell in order to show the effect that one damaged cell has on an entire pack.