# Calculating the State of Charge of a Lithium Ion Battery System using a Battery Management System

Jun 07, 2021
Welcome to the video series on smother

### system

ideas. I'm Eric Staal, president of Stoffels Systems. The topic of today's video is the

of

## charge

of a

#### battery

pack as estimated by a BMS. So what is the

of

## charge

or SOC? It's very simple. The state of charge is defined as the remaining capacity, so the total capacity in ampere hours or coulombs that can be discharged over the total capacity of the

#### battery

pack, so let's give an example, if we had a battery pack, let's say a 100 amp hour battery pack. full capacity and we had 70 amp hours left to discharge, which would give us a state of charge of 70%, so this would mean that if we fully charged the battery to 400 amp hours and then discharged 30 amp hours we would have 70 amp hours. amp hours or 70 percent of the remaining capacity now, it is very important to note that this is in units of amp hours, not units of energy, and why is it so important if we look at the discharge curve of a cell of

#### lithium

ion battery or a battery pack with voltage here on the output y axis and on the x axis we have amp hours discharged, what does the curve normally look like?
For most

#### lithium

ion batteries, for example like an MMC or lco type chemistry, you would expect to see a curve like this and it drops off towards the end, so it's typically about 4.2 volts per cell and the end of the discharge is 2.5 volts per cell. This might be a little different for different chemistries, but the point is the same in general, you have a varying downward slope for the voltage as you discharge the pack capacity, for example if I take the 50% point for the discharged amp hours, if we take the previous example and say that it is one hundred amp hours. or 100% and this was 50 amp hours, this is zero, so this would be the 50% state of charge point, which means we have discharged 50 amp hours from one hundred amp hours and we have 50 amp hours left before the readings. of the battery reach their termination voltage, so one thing to keep in mind is that look at the areas under these relative curves, one side is larger than the other, so for example there is a lot more energy in the left side of this line than on the right side. line and why it is so important because when you confuse the state of charge with a fuel gauge algorithm, this happens, which usually happens if you want to get a fuel gauge, if you want to use a fuel gauge, for example, from electric vehicle application or most applications.

## calculating the state of charge of a lithium ion battery system using a battery management system...

We're more interested in available power than capacity, so for example, if we were doing the design of an electric vehicle and we were trying to determine, okay, this is a 200 mile range, in what state of charge would have a hundred miles of range left. Well, look at this, the balance between this side and this side is clearly unbalanced because the voltage is higher in the lower states of charge than in the higher ones and the voltage is lower in the lower state of charge, so it is important to introduce the concept of soe II. or energy-based SOC, so we denote it as follows.
I use the black pen for this so SOC c4 or SOC II capacity for power and these are different and this is actually what most applications are interested in because this is actually the most accurate fuel gauge. algorithm that tells you how much expected runtime wear range you achieved, so let's look at this example again if we say, "Okay, where is the actual 50% SOC II point in this well? That would be where we would have approximately 50% of the area under the curve on the left side of the line as on the right side would be somewhere more like here, let's say this corresponds to a point of 42% SOC, but this is equivalent to 50% SOC II , so it is very important to understand the distinction between power state to charge fuel metering algorithms and charge capacity states in a future video we will discuss how state of charge is actually calculated - it usually has a number of elements more sophisticated but for today's purposes I want to discuss Coulomb counting which is the main way the state of charge is calculated, as I mentioned earlier in this example we have one hundred amp hours and we discharge 30 amp hours to have 70 amp hours hour remaining, which means we are at a c2 charge of 70.%, but how do we determine that we have properly discharged 30 amp hours from the first video?
We can remember that a BMS usually has a current sensor, either a shunt or a Hall effect device that can monitor the current flowing into or out of the battery pack and what are you doing to determine the amp hours? Since amp hours are in units of current time, we're actually doing an integration called Coulomb counting, so this is your current and this is time, so let's say we have a curve that looks like this, this is it Like how much charge is the amount of current coming out of the package at any given time the area under the curve corresponds to the actual capacity removed so this is in units of ampere hours and this is what Coulomb counting does.
Coulomb counting basically consists of observing each of the slices in the form of time slice integration by multiplying the current by the time interval and adding that to obtain an approximation of the integral of this function and what that does is it gives us gives an accurate estimate of amp hours which gives us a basis for the SoC now One of the things to keep in mind about Coulomb counting and current sensing is that the current sensor has drift and integration error, so You won't get perfect alignment of all your sensing with the actual current peaks, so it's important to note that many times you'll also need what's called an open cell voltage or ocv lookup to compare what you're integrating with. your actual voltage, so we'll look here.
I will rely on this voltage timing graph. I'm going to introduce a new term called depth of discharge. Depth of discharge is the inverse of state of charge, so for example at 70% SOC you would have a depth of discharge of 30%; for example, 30% SOC, correct discharge depth, 60% discharge depth and let's say this is one hundred percent its The voltage will be like this, so when the PAC has been sitting for a considerable period of time, What you need to do is have the BMS look up a lookup table or something similar to see what the open circuit voltage of the cell is for a given temperature and then it will match that or determine what the corresponding state of charge or depth of discharge is for. that and then it will backtrack the soc function so that you have a base from which to get an accurate understanding of where you need to start.
Coulomb counts again and this is very important because you don't want to have a fuel metering algorithm that goes off, so you can imagine how frustrating it would be if you said you were driving and suddenly went from 30% to 0% state of charge immediately because there is an inaccurate estimate, it would leave you at least anxiously stranded on all sorts of problems like that, so the benefit of having open circuit voltage lookup and accurate Coulomb counting is that you can really guarantee a high state of charge. degree of accuracy for the state of charge algorithm and the state of charge power algorithm, so expected results in reliable and predictable operation of your battery pack.
That's all for today, thanks for watching, see you next time.