Battery Pack Design Criteria and Selection 43 energy is which number they are looking for usable energy or total energy. If the customer has already calculated the efficiency of their vehicle then they may be referring to a need for a total energy of 25 kWh less the 20% that is not usable from the system design and not in fact 25 kWh of usable energy, which will require a larger system in order to deliver that much usable energy. So with all of these things in mind, and assuming that we need the larger 31.25 kWh pack, we can recalculate the capacity of the cells in order to achieve these goals using the formula:
E p /V p = I p Where E p equals the total pack energy in kWh and I p represents the pack current in Ah, and V p represents the pack voltage that we are calculating here. So using the formula for this example we find: 31 . 25 kWh/350 V = 90 Ah cell In this example, we would need 96 cells that are 3.7 V each and at 90 Ah in capacity to achieve the 350 V and 31.25 kWh of total energy. This distinction between total energy and usable energy is an important one because virtually all lithium-ion batteries available today are not capable of using 100% of their available energy in consideration with safety, life and performance requirements.
Calculating System Power With those basic calculations in mind we can also dig a bit deeper and begin looking at how much power the system can provide. In addition to the formula’s shown above which are based on Ohm’s Law it is also possible to use several derivations of this to calculate power and to use power (in Watts) in your calculations. In this instance, we are combining Ohm’s Law with Joule’s Law in order to create a formula for determining electrical power (in Watts again). System power can be calculated by using the formula: P = I 2 Ч R Where P represents the power in watts (W), I 2 represents the square of the current in Amperes, and R represents the resistance in Ohms.
Similar to Ohm’s Law this formula can be cross-calculated to form the following three base formulas for calculating power: P = I 2 Ч R R = P/I 2 I 2 = P/R For example, if the cell that we are using has an internal resistance of 7 m Ω , then we can calculate the power for each cell as follows: ( 90 Ah ) 2 Ч 7 m Ω = 648 W per cell