# Cell Capacity and Pack Size

Obviously Cell Capacity and Pack Size are linked. The total energy content in a battery pack in it’s simplest terms is:

Energy (Wh) = S x P x Ah x Vnom

Hence the simple diagram showing cells connected together in series and parallel.

### What about flexibility in pack size?

There are very good reasons for selecting a battery cell and using it for multiple applications, thus leveraging the maximum buying opportunity for one cell rather than splitting this across 2 or 3 different cells.

This means that the specifications of the cell will be fixed. Let us suppose we select a 50Ah cell with a nominal cell voltage of 3.6V

A 400V pack would be arranged with 96 cells in series, 2 cells in parallel would create pack with a total energy of 34.6kWh

Changing the number of cells in series by 1 gives a change in total energy of 3.6V x 2 x 50Ah = 360Wh.

Increasing or decreasing the number of cells in parallel changes the total energy by 96 x 3.6V x 50Ah = 17,280Wh.

This means we can use this cell to design multiple 400V packs, but the energy content will be multiples of 17.28kWh with some small variations possible if we change the system voltage.

If we select a very different cell, say a 5Ah cell, again with a nominal voltage of 3.6V we get a very different step size.

Changing to a 5Ah cell you now need 20 of these connected in parallel to equal the capacity of two of the 50Ah cells connected in paralel.

Hence, as shown a 96s30p pack configuration gives a total pack energy of 34.6kWh

However, now we see that the step down to 19p or up to 21p changes the total energy of the pack by 96 x 3.6V x 5Ah = 1.728kWh

However, the direction from the cell manufacturers is to make larger cells, in a drive to reduce the cost per kWh.

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Repeating this calculation with a 200Ah cell and the same ~400V pack requirements shows that the smallest total energy for the pack is 69kWh. Also, the increments are 69kWh for each increase in the number of cells in parallel.

This could be a very cost driven pack design, but is not so flexible in total capacity.

Also, with a 200Ah cell it is not possible to make a pack with a total energy between 75 and 125kWh.

This is perhaps easier to visualise graphically if we plot the total energy of the pack versus the parallel string capacity in Ah.

The steps for the small 5Ah cell are very small, the disadvantage is the number of electrical connections and ensuring those are all equivalent.

### How flexible is this with pack voltage?

The following table shows cell capacities grouped in columns, the top half of the table then shows ~800V packs with 192 cells in parallel and the bottom half shows the ~400V packs.

You can immediately see that the high capacity 200Ah cell produces a minimum pack capacity ~138kWh at ~800V. The increments in pack capacity are also 138kWh.

The small 5Ah cell allows a more granular approach to pack sizes, the downside is the number of cells that are used and hence the complexity of items such as the busbars.

In simple terms the total energy in the pack is just the total nominal voltage x total nominal capacity. Hence, you could have got to this point perhaps much faster, but I feel this is a good way of just working it through.

Hopefully this gives you just a different view of the options and flexibility of different cell choices.

The Pack Energy Calculator is one of our many online calculators that are completely free to use.

The usable energy (kWh) of the pack is fundamentally determined by:

• Number of cells in series (S count)
• Number of cells in parallel (P count)
• Capacity of a single cell (Ah)
• Nominal voltage of a single cell (Vnom)
• Usable SoC window (%)

Energy (kWh) = S x P x Ah x Vnom x SoCusable / 1000

Note: this is an approximation as the nominal voltage is dependent on the usable window. Also, the variation in cell capacity will be needed to be understood to establish accurate pack capacity values in production. However, all of this takes time and hence please use this as a first approximation.
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