# Battery (Charge-/Discharge) Efficiency Curve

I’m working on an university assignment at the moment and can't figure out how to do derive the efficiency curve of my battery. I have a fully functional battery model (on current/voltage level) on simulink and want to build an efficiency curve of my battery. My y-axis should be the efficiency and x-axis the power. I know that I need the output power compared to the input power. In my case I just have the input current and from the model the current voltage, based on the SOC and input current. How can I come up with the efficiency map? Does any know how I could proceed with my problem.

I was looking for something like this

• Document carefully for us your assignment. Commented Sep 17, 2023 at 16:03
• I will try to explain it as good as possible. My full assignment is based on a BMS, but to be able the derive the BMS, I first wanted to get some Information from the Battery. I would like to plot the Discharge and Charge Efficiency of my Battery based on the Output Power. For that purpose I have a Simulink Battery Model which takes the Current as Input and has several Outputs, like Battery Voltage, SOC, Power, SOE, etc. I tried a Staircase Input of the Current starting from 1A up to 150A with a sample size of 100s to avoid transient signals. But when I plot Output to Input Efficiency iswrong Commented Sep 17, 2023 at 16:10
• So you mean SOC-Charge - SOC_Discharge and Integrate the Difference? Should the Input Current be constant or Staircase Signal? Thanks for the Idea. Didn't though about integrating the SOC Difference Commented Sep 17, 2023 at 16:12
• Can you provide us with your fully functional battery model? It might help to see it so that a shorter and more directly useful answer can be provided. Commented Sep 18, 2023 at 4:36
• Unfortunately I am not allowed to share the model itself Commented Sep 18, 2023 at 7:10

First, you need a table of internal series DC resistance and Open Circuit Voltage vs State of Charge.

For simplicity, you can assume that they are constant (a single value for each) or that you want the efficiency at a single State of Charge level. In that case, the efficiency is simply:

Efficiency = 1 / (1 + Rs/Rl)

Where Rs is the internal resistance and Rl is the load resistance. Note that it's independent of voltage. It will look like this, with a peak when the load resistance is equal to the battery internal resistance.

{Source: I made this graph and published it in a book.}

Then you can convert that to power.

• I don't have the Information of my Model. It's like an Blackbox. I can just input Current and read the Outputs. Isn't that sufficient to derive the Efficiency curve? Commented Sep 17, 2023 at 16:45
• Davide Andrea - Hi, Please remember the site rule about adding a reference when including information from elsewhere. (I don't know if that image is from your book - if it is then the site rule still applies, as the image is copied from a published source). Thanks. Commented Sep 17, 2023 at 16:52
• "How to reference material written by others" Oh! I assumed that rule doesn't apply to my own work since it's not "made by others". I assumed that if I made it then I didn't have to credit myself. Thank you. I will abide. Commented Sep 17, 2023 at 18:47
• @DavideAndrea - Yes, yours is an unusual situation, as the author of a book. The way it was explained to me, if people put something onto this site which is an unpublished work of their own, then no attribution is needed (although frankly, saying that it's their own work in that case can be helpful, i.e. a self-attribution statement, to avoid people flagging that it's unattributed). However once something is published, as in your case, then even if you provided the original diagram to the publisher, a copy from the book (to which the publisher has rights) needs a proper citation. OK? Commented Sep 18, 2023 at 8:02

Here is how I would do it:

Produce a voltage versus SOC for both discharge and charge with the same start and stop points for a given power or current.

Here is one I blatantly stole from https://www.researchgate.net/figure/Charge-and-discharge-voltages-at-025-C-in-dependence-of-SOC-for-the-NMC1-battery_fig1_323154990

If you integrate both curves and subtract discharge from charge (or the area between the curves), and divide with discharge area, you get the efficiency. Repeat for various power/current levels. Plot your graph.