# Estimating the battery capacity using current power consumption and battery percentage

I want to estimate the current maximum capacity (in kWh) having the current power consumption (in kWh) and the state of charge of the battery (in %) available in a time series.

I do not have a full battery charge circle recorded but only a snippet with the state of charge going from ~95% to ~35% in a 1 second data recording interval.

At first, i cumulated the current power consumption and noticed that the progression between cumulated power consumption and state of charge was almost the same (see figure 1 and 2).

progression of state of charge vs. cumulated power consumption So i tried to use a linear regression model to predict two values of cumulated power consumption at 0% and 100% state of charge. In my assumption the delta of these two leaves me with the current maximum capacity of the battery.

Ideally i want to monitor the capacity during the data recording. Which means i only have data of a few percent of state of charge. In figure 3 and 4 you can see my attempt of trying to create a linear regression model for every 2% state of charge. As you can see in the right plot, the estimated capacity has a very high variance.

LEFT: regression lines (green) of every 2% state of charge; RIGHT: estimated capacity of every 2% state of charge Since i am not an expert in neither the matter of regression nor batteries/physics, my questions are:

• Is there a much simple or more exact way (or both) to estimate the current maximum capacity of the battery?

• If yes, is there a good way to estimate an sufficiently exact capacity with an even smaller snippet in an ongoing process, lets say every 2% state of charge? (maybe using a characteristic curve of the discharge process)

Here is a sample of my data: sample file

• Welcome to the site :) – Dawny33 Jan 27 '16 at 16:34
• Although this question is absolutely suited to this site, I suspect you might have more luck over at electronics.stackexchange.com – CatsLoveJazz Feb 9 '16 at 10:45
• @r-doe. I have a few questions and some of these may or may not apply to your case depending on what the data looks like. 1. Are you imputing any values? 2. Is there a pattern to the state of charge % like a least count increment. 3. Is the data tagged with any other categorical variables? 4. Is the graph of state of charge (x) vs non cumulated consumption (y) a flat line? (Should be) 4. Any sample data? – Drj Apr 12 '16 at 20:44
• Power consumption is measured in kW, nor kWh neither kW/h. Are you sure you get your physics right? – Diego Apr 18 '16 at 4:28
• @Diego Battery Capacity is most of the times given in kWh. Because of that I integrated the consumption over time to get the time component in there. – R. Doe Apr 18 '16 at 7:35