Expected cycle life vs. depth of discharge relationships of well-behaved single cells and cell strings

The present investigation is concerned with the factors which might influence the cycle life vs. depth of discharge relationship, taking into account the rate of loss of cell capacity, the amount of excess capacity built into the cells, and the penalty in capacity loss resulting from the use of deep depths of discharge. 'First principles' are used to develop a cell life model for somewhat arbitrary conditions. This model is then used to estimate the cycle life vs. depth of discharge relationships for 'well behaved' cells. The stochastic variations associated with groupings of single cells are then introduced to the battery pack cycle life model. The term 'well behaved' cell is used to describe a single cell which does not suffer any abrupt failure mode during the course of its operation. It gradually loses capacity for any number of the usual reasons at a rate which is the product of the fractional depth of discharge and a factor which is characteristic of the cell under consideration.