44 Chapter 4 or 648 W/ ( 90 Ah ) 2 = 7 m Ω per cell or 648 W/7 m Ω = 92 Ah per cell Using this first formula (P = I 2 Ч R) we can also replace current with voltage to develop another set of formulas for calculating electrical power (again in watts): P = I 2 R = V 2 /R = V ( V/R ) Finally, these formulas can be reversed to calculate current (I) and voltage (V) in the same manner: I = P/V V = ( P * R ) In any of these cases you need to have the measurements for voltage, current, resistance, or power or a combination of them in order to make these calculations.
An alternative method that may be a bit simpler to use, but not necessarily more accurate, is to quickly estimate the power in kW of a pack by multiplying the total number of cells times the power in watts (W) of each cell, for example: 96 cells Ч 648 W = 62 , 208 W or 62 . 2 kW In this case the cell power is usually available from the cell manufacturer on their published data sheet. If not available on the data sheet, the cell manufacturer should be able to supply this information to you. In addition to calculating the nominal power capabilities of your battery system, you should also be able to calculate the “peak power” that the system can provide.
This is usually a 10-s, 5-s, 2-s or 1-s calculation. But the general formula is a two-part calculation. First the system resistance must be calculated. This is typically done by running a hybrid power pulse characterization (HPPC) test on the cell and measuring the change in voltage and in current and then dividing the two: Resistance DC = Δ V/ Δ I Once you have the resistance you can use it in the following formula to calculate the peak power potential of the system: Peak Power ( in kW ) = V 2 Open Circuit /4R In this formula you are dividing the square of the maximum open circuit voltage by four times the resistance to find the peak power.