40 Chapter 4 Calculating the Number of Cells Needed The first thing we need to do is to figure out how many cells will be needed to meet the basic voltage and current requirements of the pack design. Beginning with the desired pack voltage you can easily calculate the number of cells (assuming that you have a desired cell to work with) needed to create that system voltage. The system voltage is generally based on the voltage needs of the electric motor(s) in the system. Once this target voltage is known it is a simple enough matter to determine how many cells are needed in series to generate that voltage by dividing the pack voltage (V p ) by the cell voltage (V c ):
V p /V c = number of series cells For example, for a desired 350-V pack and using a 3.6-V NMC (lithium nickel manganese cobalt oxide)-based cell, it would require 350 V/3.6 V = 97.2 cells, for simplicity round down to 96 cells. Similarly, to achieve a 350-V pack using a 3.2-V LFP (lithium iron phosphate) cell you would need (350 V/3.2 V) 109 cells. Again for simplicity you may decide to use either 108 or 110 cells. Or using a 2.2-V LTO (Lithium Titanate) cell you would need (350 V/2.2 V) 159 cells, or rounded to 160 cells in order to reach the desired voltage.
One of the reasons to round up or down here is also to end up with an even number of cells which will allow you to divide them equally in the modules that will make up the pack. This also allows you to use a single, or at least a common, module design in your pack. Going back to the NMC example, with 96 cells required we could manage this with 8 modules of 12 cells each or 4 modules of 24 cells each. If we rounded up to 98 we would have to use 7 modules of 14 cells each.
The other consideration that must be taken into account when determining how many cells and modules will be used in the design is the type of cell supervision circuit (CSC), also called a voltage temperature monitor (VTM), board that is used and how many cells it can monitor. The CSC will be discussed in more detail in Chapter 8 on Battery Management Systems, but for the purposes of this chapter we can say that it is important to know how many cells your CSC boards can manage; current technology ranges from 12 to 16 cells.
So if your CSC can only manage 12 cells, then the module must include no more than 12 cells which means we will need 8 modules to achieve the 96 cell total and 350-V pack voltage level. Calculating the Pack Energy and Capacity To then calculate the pack energy (E p ), let us assume that a 25-kWh pack is desired, we would multiply the pack voltage (V p ) by the capacity (I p ). This of course assumes that you know the needed capacity, or current, of the pack. E p = V p Ч I p