Estimating energy density

A couple of years ago I made an Excel spreadsheet to estimate what the gravimetric energy density (or, more accurately, *specific energy*) of a scaled-up lithium-sulfur (Li-S) cell would be based on various parameters and performance indicators from experimental tests. At the time, I was working in a project with a stated goal of producing a 400 Wh/kg cell at the end of the project (an ambitious target, and although the project was generally very successful and productive we were in the end quite a way off this target).

I’ve recently translated that spreadsheet into a Shiny app, and now it’s available here. I thought it would be interesting to pair this app with a page describing the various parameters, where the default values I’ve chosen come from, and what values seem realistic given current literature. I hope this app will be quite instructive, and maybe give some insight as to why it’s so hard to make such a high energy battery.

Open the app here

The app is fairly simple, and should look like the screenshot below. Just change the values however you like and see what happens.

Energy density is calculated very simply:

$$\text{energy density} = \frac{Q_d \cdot E_{\text{mean}}}{\sum m_x}$$

where \(Q_d\) is the “surface capacity” (or, areal discharge capacity) of the electrode in mAh/cm2, \(E_\text{mean}\) is the average discharge voltage, and \(\sum m_x\) is the sum of all the masses of all of the components, in g/cm2. The product of Q and E gives an energy, and divided by the sum of all of the masses gives an energy density for the whole cell stack.

The different parameters that can be changed are as follows:

Try changing the parameters within the ranges I’ve suggested above to start with. There are plenty of things to think about: How high will the energy density be with values in these ranges? How much of the cell is active mass (i.e., Li and sulfur?) What’s the biggest contribution to the mass? What more do we need to improve to get up to, say, 400 or 500 Wh/kg?

Note! Cell packaging is not (currently) included in these calculations! The energy density of the cell will of course depend on the mass of the packaging. This partly depends on the format (size, type etc) of the cell. I would guess a reasonable estimate for the cell packaging would be about 10% of the total cell mass, but this is just an educated guess.

Also note: The excess on the negative electrode is also given in the app – it’s important! If it is negative, it means the capacity on the lithium electrode is limiting, and the energy density of the cell will be reduced. This is factored into the calculations.

Worthwhile literature on the topic: Hagen et al (2015), Urbonaite et al (2015), Pope et al (2015), Mikhaylik et al (2010), Berg et al (2015).

I also wrote a separate post providing some context to this page. You can find that here.

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