This value is then just divided by the volume of the cell to calculate volumetric energy density or divided by the mass of the cell to calculated the gravimetric energy density. Perhaps the simplest of the battery metrics as the capacity of the cell is fairly easy to measure and the mass is just a set of scales.
The calculations are quite simple as the energy content of the cell [Wh] = V nom x Ah nom. This value is then just divided by the volume of the cell to calculate volumetric energy density or divided by the mass of the cell to calculated the gravimetric energy density. There are some cautionary points though.
The Faraday Institution has developed a cell calculator called CAMS capable of modelling the energy density experimental cell designs. CAMS was designed to rapidly assess the potential energy density of different cell chemistries and cell formats. Battery pack mass estimation is a key parameter required early in the conceptual design.
When we say cell energy density we need to consider if this is gravimetric (Wh/kg) or volumetric (Wh/litre). The energy content of the cell will be determined by the discharge rate, temperature and other parameters. Discharge rate capability of a new SAFT MP 176065 xtd battery.
The energy content of a string E bs [Wh] is equal with the product between the number of battery cells connected in series N cs [-] and the energy of a battery cell E bc [Wh]. The total number of strings of the battery pack N sb [-] is calculated by dividing the battery pack total energy E bp [Wh] to the energy content of a string E bs [Wh].
The key relationship we have is between cell and pack gravimetric energy density. This graph has been pulled together by scouring the internet for cell and battery data. The ratio of cell density to pack density is 0.6235 and this is very close to the total cell to pack mass relationship of 1.6034