Impacts of cell topology, parameter distributions and current profile on the usable power and energy of lithium-ion batteries

In order to meet the energy and power requirements of large-scale battery applications, cells have to be connected in serial and parallel configuration. For the purpose of understanding the assembly of parallel-connected cells is referred to as logical cell. Caused by current and State of Charge (SoC) inhomogeneities between the serial and parallel cells, the usable power and energy will differ from the installed values. These differences are affected by the cell topology, cell parameter distributions and the current profile. The influences of these parameters are investigated by Monte Carlo simulations with Gaussian distributed cell parameters. The $5\sigma$ values of the usable power decrease almost logarithmically with increasing number of serial and parallel cells. The power is primarily limited by the logical cell with the highest current distribution, which in turn depends principally on the differences in cell parameters. In a battery the maximum difference of cell parameters statistically increase with the number of connected cells. Two further effects influence the usable energy. The Open Circuit Voltage (OCV) bending leads to a SoC balancing at the end of discharge. And the standard deviation of the logical cell capacity distribution decreases by square root with increasing number of parallel cells. These effetcs are leading to a higher usable energy by connecting the cells in parallel compared to a corresponding serial-connection, especially for discharging. Furthermore with increasing standard deviation of the cells resistance and capacity distributions a linear decrease of the usable power and energy is found.