[Music] welcome to the stifle systems insights video series I'm Eric Staal president of Stoffels systems the topic of today's video is the state of charge of a battery pack as estimated by a BMS so what is the state of charge or SOC so it's very simple the state of charge is defined as the capacity remaining so that total capacity in amp hours or coulombs that you can discharge over the total capacity of the battery pack so let's give an example so if we had a battery pack that was say 100 amp hour battery pack total capacity and we had 70 amp hours left to discharge that would give us a state of charge of 70% so this would mean that if we fully charge the battery pack up to the 400 amp hours and then discharge 30 amp hours we would have 70 amp hours or 70 percent of the capacity remaining now it's very important to note that this is in units of amp hours not in units of energy and why is that important well if we look at the discharge curve for a lithium-ion battery cell or a battery pack for that matter with voltage here on the exit y-axis and on the x-axis we have amp hour discharged what does the curve typically look like so 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 falls off towards the end and so typically this is about 4.2 volts per cell and the end of discharge is 2.5 volts per cell this could be a little different for different chemistry's but the point is the same in general you have a varying downward facing slope for the voltage as you discharge capacity out of the pack so for example if I took the 50% point for the amp hours discharged so if we took the example above and said that this was a hundred amp hours or 100% and this was 50 amp hours this is zero then this would be the 50% state of charge point which means that we've discharged 50 amp hours out of a hundred amp hours and we have 50 amp hours left to go before the battery reads reaches its termination voltage so one thing to notice is that look at the areas under these relative curves one side is bigger than the other so for example there's a lot more energy on the left side of this line than on the right side of the line and why is that important because when you confuse state of charge with a fuel gage algorithm this happens which is typically if you want to get a fuel gage if you want to use a fuel gage for example from electric vehicle application or most applications you're more interested in the energy available as opposed to the capacity so for example if we were doing an electric vehicle design and we were trying to determine okay this is a 200 mile range at what state of charge would you have a hundred miles of range remaining well look at this the balance between this side and this side is clearly imbalanced because the voltage is higher in the lower than the higher states of charge and the voltage is lower in the lower state to charge so it's important to introduce the concept of soe II or SOC based on energy so we denote this as follows I use the black pen for this so SOC c4 capacity or SOC II for energy and these are different and this is actually what most applications are interested in because this is actually the more accurate fuel gauge algorithm that tells you how much expected runtime use distance range you ever made so let's look at look at this example again if we say okay where is the actual 50% SOC II point on 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 that would be somewhere more like here say that this corresponds to a point of 42% SOC see but this equals 50% SOC II so it's very important to understand the distinction between energy state to charge fuel gauge algorithms and capacity states of charge in a future video we'll discuss how the state of charge is actually calculated it typically has a number of more sophisticated elements but for the purposes of today I do want to discuss Coulomb counting which is the primary way that state of charge is calculated so as I mentioned earlier in this example we have a hundred amp hours and we discharged 30 amp hours to have 70 amp hours remaining which means we're at a c2 charge of 70% but how did we determine that we discharged 30 amp hours well from the first video we can remember that a BMS typically has a current sensor either a shunt or a Hall effect device that can monitor the current flowing in or out of the battery pack and what are you doing to determine amp hours since amp hours are in units of current times time we are actually performing an integration called Coulomb counting so this is your current and this is time so say that we have a curve that looks like this that is how much charge that's how much current at any given time is coming out of the pack the area under the curve corresponds to the actual capacity removed so this is in units of amp hours and this is what Coulomb counting does Coulomb counting is basically looking at every single slice in a time slice integration fashion multiplying the current times the time interval and summing that up to get an approximation of the integral of this function and what that does is that gives us an accurate estimate of amp hours which gives us a basis for SoC now one of the things to note about Coulomb counting and current sensing is that the current sensor has drift and integration error so you're not going to get perfect alignment of all your sensing with the actual current spikes itself so it's important to note that oftentimes you also need what's called a ocv or open cell voltage lookup to compare what you're integrating with your actual voltage so we'll look over here I'll draw on this plot voltage times I'm gonna introduce a new term called depth of discharge depth of discharge is the inverse of state of charge so for example at 70 percent SOC you would have a depth of discharge of 30% so for example 30% SOC right depth of discharge 60% depth of discharge and say this is a hundred percent your voltage is gonna go like this so when the PAC has been at rest for a considerable period of time what you do is the BMS will look up with 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 equate that or determine what the corresponding state of charge or depth of discharge is for that and then it will re cede the soc function so that you have a basis upon which to get an accurate understanding of where you need to start Coulomb counting again and this is very important because you don't want to have a fuel gauge algorithm that gets off so you can imagine how frustrating it would be if you had say you're driving along and all of a sudden you went from 30% to 0% state of charge immediately because there is an inaccurate estimation it would leave you stranded at least anxiety all sorts of problems like that so the benefit of having both open circuit voltage lookup and accurate Coulomb counting is that you can actually ensure a high degree of accuracy for the state of charge algorithm and the state of charge energy algorithm such that your results are expected in a reliable and predictable operation of your battery pack that's all for today thanks for watching see you next time [Music] you