What do cell ratings actually tell us? Part 3: Watt-hour (Wh)

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Mooch

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In the previous post for this series I discussed the Capacity rating and how it can’t be used to judge the running time of a cell if it’s being discharged at above 1A or so. This is due to the voltage sag in the cell caused by its internal resistance. It forces the voltage lower during the discharge so you hit your low voltage cutoff point sooner.

Capacity doesn’t take the voltage of the cell into account. It doesn’t tell us how efficiently the cell runs or how well it performs when run at above 1A or so.

The Watt-hour (Wh) spec tells us more. It not only says how long the cell can run (hours) at a certain discharge rate (milliamperes), like capacity, but includes the voltage of the cell too. It’s a measure of how much energy is in the cell, not just how much “gas” is in the “gas tank” like what the capacity rating does. The Wh rating tells us how much gas the cell has and how efficiently the cell uses that “gas”

So what is a Wh?

A watt is (voltage * current).
A watt-hour (Wh) is then (voltage * current)-hours, or volt-milliampere-hours.

See something familiar? The Wh spec has the capacity of the cell, the milliampere-hour, spec as part of it. We can say Wh = volt * capacity and this is why the Wh the cell can deliver is so important. It includes how well the cell performs, i.e., how well it can hold up its voltage, for the amount of current and time that the rating indicates.

The Wh rating given to us by the manufacturer or pack assembler is as useless as the Capacity rating though. This is because it’s the “nominal” Wh rating. It doesn’t use the actual voltage of the cell when being discharged. It uses the “nominal voltage” spec of the cell, typically 3.6V or 3.7V for a standard Li-Ion cell.

Like the Capacity spec this is okay if we are discharging the cell at 1A or less. The “nominal voltage” is approximately the average voltage for a cell running at that low a power level. But a cell being run harder than that will not have an average voltage of 3.6V/3.7V, it will be lower due to the voltage sag.

For example…
A Molicel P42A has a nominal voltage rating of 3.6V and a capacity rating of 4000mAh. Its nominal Wh rating is then nominal voltage * capacity = 3.6V * 4000mAh = 14,400 milliwatt-hours, or 14.4Wh.

But when discharged at 20A the cell only delivers about 10.7Wh and at 30A it delivers only about 8.7Wh. This is because of the voltage sag. The average voltage is lower and that lowers the Wh number.

The capacity a cell delivers at current levels higher than about 1A is also lower due to the voltage sag. This also lowers the Wh rating since both the average voltage and actual delivered capacity are part of it.

The Wh rating that can be so useful for us is the one that is measured at the power level we will run our cells at. If we run our cells at, lets say, 10A then we need to measure the average voltage and actual delivered capacity of the cell when being discharged at 10A.

Unfortunately this is very difficult to do unless you have certain test equipment. I’ve measured the delivered Wh for many of the cells we use though and these numbers are what I use for my Energy Scores (E-Scores). Check these tables for the E-Scores of some cells I have tested:

18650: 18650 Battery Ratings Table | E-Cigarette Forum

20700/21700: 20700/21700 Battery Ratings | E-Cigarette Forum

This delivered Wh rating allows us to directly compare any number of cells without any concern for capacity, size, voltage, chemistry. None of those numbers matter because this Wh rating basically already takes all that into account.

A cell that delivers 10Wh at 10A will outperform any other size or chemistry cell that delivers less than 10Wh at 10A…when run at 10A.

We still want to stay under the cell’s continuous current rating though, and we still need to consider the charging voltage and how well the cell(s) fit, but how well each performs can be determined by just comparing the Wh of energy the cell delivered at the current/power level we’re interested in.

Not all cells that are best at one power level will be best at all power levels! An ultra-high capacity “energy” cell will be easily outperformed by a high-performance “power” cell at high power levels. But at low power levels the higher capacity of the “energy” cell means it will run for longer.

You would see this in the Wh numbers for the different power levels. The energy cell would have a higher Wh rating at low power levels and the power cell would have a higher Wh rating at high power levels.

Many battery packs have a Wh rating but that is the “nominal” rating. It is almost useless to determine how long the pack will run or how well it will perform if you are running at moderate to higher power levels. You can certainly use it to compare pack size though and, very roughly, how well it might perform if not being run hard.

So while the Wh spec given by the manufacturer and pack assemblers can be used to size a pack, or work out what cells might be in the pack, the Wh rating shouldn’t be used to determine performance unless it’s measured at the power level you will run at.

Then you can directly compare those cells and along with weight, size, and cost, determine which cells best fit your application. Use the tables I link to above to compare some of the cells I have tested.
 
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