# How to Calculate the charge/discharge power of a battery?

I need to measure the discharge power of a battery in general.

At the end i want the maximum charge/discharge power as a function of the state of charge(SOC). So i need a curve that looks like the figure that is displayed here.

I already calculated the power as a function of the SOC but i am not sure if my method is correct.

Lets assume we are looking at a lithium ion battery. I found two ways to calculate the power.
The first one was simply using the voltage curve as a function of state of charge for different C- Rates. Then multiplying the Current with the voltage and getting my power. P(SOC) = U(SOC) * C-Rate.

The second method was using two graphs of a battery the voltage as a function of the SOC and the internal resistance as a function of a SOC and then P(SOC) = (U(SOC)^2)/R(SOC).

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## 1 Answer

The first method calculates the power delivered to the load, the second one calculates the power dissipated (wasted) in the battery itself. I suspect you want the first one.

Are you sure you are interested in power and not energy? Or in remaining battery capacity in ampere-hours?

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Yes exactly i want the first one. The thing is i am regarding a grid connected pv battery system. I get the pv output power in Watt. Battery output is also in Watt (Power). I am interested in the power(Watt) because the battery has to take part in the electricty market(spinning reserves etc.). Ofcourse i need to know the amount of energy the battery has, so i can determine the SOC and how much energy i still have. – user23970 May 16 '13 at 14:58
I also need to know "how fast and for how long" the battery can be charged or discharged with a certain amount of power. Lets say we have a Lithium ion battery with 100 kWh energy. The question is can this battery discharge the 100kWh in 1h. So this means the battery has a discharge power of 100 kW. I know for a fact that when you discharge the battery with a very high C-Rate/Power higher than the nominal you dont get the maximum availabe capacity. – user23970 May 16 '13 at 14:59
At the end i need to know, when the battery is fully charged SOC = 100%. It is able to give me until for example SOC = 80% constant 1 kW. And then it linearly drops with a specific factor, which depends on each battery type. – user23970 May 16 '13 at 14:59
@user23970 Keep in mind that utility companies sell units of energy (kWh), not units of power. The capacity of a battery is a function of the discharge rate and many other factors so even if you start with 100% SOC the amount of energy you get from the battery will be different if the discharge rate is different, if the temperature varies, and as the battery ages. – Joe Hass May 16 '13 at 21:07
Thanks for your reply Joe! I am aware that the amount of energy i get from the battery will be different if the discharge rate is differernt(and if the temp varies and ageing) Lets assume that we have an ideal battery so there is no ageing, the temp is held const and the AH is independent of the C Rate. So if you take a high current you get the max capacity available in the battery I just need to know the maximum discharge power of the battery in relation to the state of charge So if the battery has 50 % SOC It will be able to give me a certain amount of power – user23970 May 17 '13 at 8:47