Estimating the battery capacity using current power consumption and battery percentage

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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

Although this question is absolutely suited to this site, I suspect you might have more luck over at http://electronics.stackexchange.com

– CatsLoveJazz – 2016-02-09T10:45:58.477

@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 – 2016-04-12T20:44:32.710

Power consumption is measured in kW, nor kWh neither kW/h. Are you sure you get your physics right? – Diego – 2016-04-18T04:28:04.597

1@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 – 2016-04-18T07:35:21.657

@Drj: 1.) I do interpolate the two times series "state of charge" and "power consumption" in order to make them equidistant in the time domain (for direct comparison) but other than that, no. 2.) I am not sure what you mean here. (could you please explain yourself a bit more?) 3.) the data is tagged with a charging variable stating whether the cable is plugged to charge the battery or not.. however I only consider complete data samples where the cable is unplugged, so it might not be relevant. – R. Doe – 2016-04-18T07:42:40.413

@Drj: 4.) Link is in the main post. – R. Doe – 2016-04-18T08:35:36.560

It's been a while since I did my B.Eng (elec), but I have a recollection that discharge curves were different for different types of batteries Lead-Acid / NiCd and now NiMH. What type of battery are you using, or have I missed that? I'm pretty sure that the discharge curves of the last two are quite different to Lead-Acid and solid chemical battery. – Marcus D – 2016-05-09T07:53:04.653

@MarcusD according to the manufacturer, the battery is an ithium ion; Battery weight: 260kg; Capacity (kWh): 22kwh; Number of elements: 192 cells; Nominal voltage: 240 to 400; From 0 to 100%: 8h; From 0 to 50%: 3h30; From 50 to 100%: 4h30; From 20 to 80%: 4h30; Maximum Current drawn from 220V main: 3KW; Slow Charge (A): 16A – R. Doe – 2016-05-09T08:49:24.333

@MarcusD The discharging curve seems pretty linear to me (in the area of 40% to 90%). However, I do expect some non-linear progression beyond that, but I do not know how to take them into account since I have only very few data beyond 40% or above 90%. The discharging from 90% to 40% will take several hours of driving an electrical car. – R. Doe – 2016-05-09T08:54:36.907

Welcome to the site :) – Dawny33 – 2016-01-27T16:34:51.417