# Homework Help: How to verify the Energy delivered by Lithium ion battery?

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1. Aug 14, 2015

### SIvakumaran

How to verify the Energy and Capacity delivered by the Lithium Ion battery?

I have a Lithium ion batter with below configuration:
Nominal Voltage 4.2 V
Nominal capacity 2250 mAh

I am calculating the energy and capacity every second for my experiments.

I use below formula to calculate the energy and capacity calculation:

consider initial V= 4v and constant current I= 5A
E = P * t --> E-energy,P-Power,t-time in hour
eg: E= 20 * (1/3600) = 0.005

C = (E * 1000)/V --> C-capacity, V-voltage
Eg: C = (0.005 *1000)/4 = 1.25 mAh

I have discharged the battery from 4.1V to 2.5V
I added the energy and capacity from every second.

Total accumulated Energy I got was around 7 wh and capacity is around 2500 mAh

Capacity which i got was more than the rated capacity.

I really dont know where i did the mistake or this was expected.

A small help,will be highly appreciated.

Thank you.

2. Aug 14, 2015

### CWatters

I haven't checked your sums but there are at least four possibilities..

1) 2250mAH is the nominal capacity not the maximum. Manufacturing tolerances mean you might have a good one.

2) Batteries degrade over time. A battery is typically considered to have reached the end of it's life when it's capacity falls to 80% of it's specified capacity. One way to achieve long life by that definition is to start with slightly more than the specified capacity.

3) The specified capacity might not be measured down to 2.5V. It's not really a good idea to go below 3V regularly or you can effect the life of the cell. The specification might assume a different end voltage than you used.

4) Capacity probably varies with temperature and current draw. The specified capacity will assume some worse case that might not match your experiment.

3. Aug 14, 2015

### CWatters

PS: I once had a discussion with a company that matched NiMH cells into racing packs for model cars. They said that according to their tests the capacity of some cheap cells varied by up to 30% batch to batch. I don't know if the same applies to li cells.

4. Aug 14, 2015

### SIvakumaran

Last edited: Aug 14, 2015
5. Aug 14, 2015

### CWatters

That seems a bit of a roundabout way to calculate the capacity in mAH. There is also an error because 5A for 1 second = 1.4mAH. Looks like a rounding error as 20 * (1/3600) = 0.0055555 recurring.

Since you are discharging at a constant current all you really need to do is measure how long it takes to discharge the battery in hours and multiply by 5000. No need to measure the voltage for that calculation. If you look at your sums you are multiplying by V and then dividing by V again.

If you also want the capacity in kWH then since the current is constant all you need do is add up all the voltage samples and multiply the result by 5 to give the answer in Joules. To convert the capacity in Joules to kWH divide by 1000 * 3600.

6. Aug 14, 2015

### CWatters

PS If the current and voltage are fluctuating then the best approach is to sample both and multiply together to give the energy in joules. Add them all up and then convert to kWH.

7. Aug 14, 2015

### Staff: Mentor

I was looking at lithium polymer cell ratings recently, where each had two associated mAhr figures. I assumed one to be a measure of the energy available without compromising the cell's life, and the other to indicate the absolute total energy held by the cell. My understanding is that you need to connect these cells to the charger before they drain to less than around 12% of full charge; total discharge being their ruination because it allows undesirable chemical products to form.