How to calculate the accurate capacity of a battery?

[CmdrRoot]

I'm trying to figure out how to calculate how much energy is stored in a battery between certain voltages. I know capacity is traditionally calculated by multiplying amps drawn by nominal voltage by time, but this seems like an approximation because voltage decreases as the battery is discharged. Also, the current drawn can change.

So if I had a graph of voltage vs time and a graph of amperage vs time, how would I go about calculating capacity between two voltages?

If it is necessary we can assume that voltage and amps vs time can be expressed by continuous functions.

Thanks!

 

[Borek]

So if I had a graph of voltage vs time and a graph of amperage vs time, how would I go about calculating capacity between two voltages?

Just integrate - $\int_0^{t_{end}} i(t)V(t)dt$

 

[berkeman]

So if I had a graph of voltage vs time and a graph of amperage vs time, how would I go about calculating capacity between two voltages?

As @Borek says, you would integrate. But be sure to also take into account how the output current level changes the discharge curves. And the datasheet curves are for a fresh battery that has been charged well (assuming you are talking about rechargeable batteries). As batteries age, their capacity diminishes. You also may need to take temperature into account, since that can also alter the battery discharge characteristics...

Helpful PDF from MIT -- http://web.mit.edu/evt/summary_battery_specifications.pdf

Typical datasheet curves -- https://www.mathworks.com/help/physmod/sps/powersys/ref/batterydatasheetfit.gif

 

[CWatters]

As others have said, integration is the answer.

You can do this manually by sampling the voltage and current at fixed time intervals and putting the data into a spreadsheet. Calculate the product of V,I and the sample interval. Add up the result.

PS Fixed sample intervals should be ok in this case but in some cases variable sample intervals can improve accuracy or greatly reduce the number of samples needed.

 

[russ_watters]

If you already have the data in a spreadsheet, you may as well just numerically integrate it there.

 

[CmdrRoot]

If you already have the data in a spreadsheet, you may as well just numerically integrate it there.

This may be the wrong place to ask, but is there an easy way for an Excel noob like me to do that?

 

[CmdrRoot]

Just integrate - $\int_0^{t_{end}} i(t)V(t)dt$

Thank you, that makes a lot of sense.

 

[Windadct]

As for "is there an easy way for an Excel noob" - do you know the common definition or description of integration?

 

[CmdrRoot]

As for "is there an easy way for an Excel noob" - do you know the common definition or description of integration?

Yeah I'm taking calc 2 now. I could do it easily if I found curves to fit v(t) and I(t), but if I just had a spreadsheet of values is there an easy way to do an approximation? Like have Excel calculate and sum each rectangle.

 

[Borek]

If you are taking Calc 2 you do know integral is a limit of a sum for dx→0. For reasonably small dx just sum works quite good (there are tricks to make to even better, google numerical integration).

 

[CWatters]

Like have Excel calculate and sum each rectangle.

That's essentially what I was suggesting in #4.

 

[russ_watters]

This may be the wrong place to ask, but is there an easy way for an Excel noob like me to do that?

do you have two columns of data; volts and amps? multiply them together and multiply by your time interval in the next column, then take the sum of the whole column.