[Music] welcome to the stopple systems insights video series I'm Eric Topol president of Stoffels systems the topic of today's video his state of health as it's calculated by a battery management system so what is the state of health of the battery well state of health or Soh is most commonly defined as the total capacity of the battery pack today over the total beginning of life capacity or what's called Bol capacity and these are given in units of amp hours or units of charge so for example the state of health describes the effect that you may have experienced when you have a cellphone that you purchased recently that seems to last all day and has excellent battery life but after about a year or two you'll notice that the amount of time that you can use your cell phone on a given battery charge is decreasing over time so that would be explained by the state of health so for example when you initially purchase your cellular telephone with your your battery it would have a state of health of a hundred percent because you just got it and its total capacity is basically equal to the beginning of life capacity but after say 300 or 600 charge/discharge cycles after about a year or two you would see that perhaps it's gone down to 70 maybe even 60% state of health and so it's very important to understand what this means because it gives you an understanding of how much time or how much energy you can discharge out of the system over time of the battery pack so let's look at how this actually works in practice so over here on the y axis I'm gonna describe capacity again in units of amp hours and then in the x-axis we're gonna use psycho life or just battery cycles rather so for example say this is 100 cycles charge/discharge cycles this is 200 etcetera etc maybe up to 600 cycles in this particular system some battery packs have longer cycle life other battery packs have less cycle life but what do we mean by cycle life well over time as you charge discharge of battery generally speaking the capacity of that battery pack will decrease over time so for example when you initially purchased that battery pack and it had zero charge discharge cycles this would have a capacity say of 50 amp hours after maybe 200 charge/discharge cycles now maybe you see a capacity of 47 camp hours and then maybe once you get to 600 cycles you see a capacity of say 44 amp hours so this forms a curve a decreasing curve of the total amount of capacity that you can store in that battery pack on each cycle as you age the pack and so that is the primary definition of state of health however there are a few other definitions or flavors of state of health that are very important to understand as well so from now on I'm going to refer to this state of health what we just talked about of state of health capacity so this is the effect of capacity fade over time but there's also another effect that can be calculated in an algorithm in a BMS that's very helpful as well and I'm gonna refer to that as state of health impedance so what is impedance meet impedance is just a fancy way of saying resistance so any sort of lithium-ion battery cell or any cell in general can be modeled as a 2/2 device model basically here's your ideal lithium-ion cell and then here's what's called ESR the equivalent series resistance and so typically for a cell this might be say 20 milli ohms at the beginning of life at a certain temperature so for example I'll say that this is 20 milliamps now over time as you charge and discharge that battery you will expect that this ESR or equivalent series resistance will increase over time so I'm gonna switch to a different color here to red and now in red the y-axis is going to refer to impedance and this is given in units of ohms or milli ohms depending on the scale so what you would expect to see is you would start with a relatively low impedance at the beginning of life but as you charge and discharge the cell you're impedance will start to grow and this is called impedance growth so as you age the cell and use it your impedance increases so we'll call that impedance growth [Music] so these two factors are very important to monitor within a BMS because it gives you an estimated understanding of how much capacity you have left to discharge at any given cycle in the cycle life of the system as well as as you discharge it are you going to have more voltage drop than before are you gonna have more temperature rise than before because as you can imagine as you charge or discharge the battery over an increasing resistance over time you're going to have more thermal output for that specific battery system so the battery in general will bill will run coolest at the beginning and over time it will start to be more resistive and thus less efficient and generate more heat over discharges so it's very important in the BMS modeling algorithms to be able to understand what this looks like as the battery pack ages so going back to an important concept to think about when you're talking about Soh so just in summary this is Soh impedance and this is Soh capacity so as you can imagine if you're trying to come up with an estimated range remaining algorithm for example for an electric vehicle and you want to say so I'm gonna say estimated range remaining okay so how do we actually calculate that well in a previous video we discussed state of charge so say for a simple approximation we want to say the state of charge of this system is 70% and the state of health capacity of the system is 80% and when the vehicle was initially purchased when the battery was brand-new we had a total Bol range of say 200 miles so what is the total range of the vehicle now that it's aged due to the capacity fade effect well if the soh capacity is now 80% then you have your current max range of the vehicle is now 160 miles so not an insignificant difference it's 40 miles reduction so very important to know that and then if you wanted to know range remaining then you would need to take 70% multiplied by 160 and that gives you your range remaining I'll do the math later so it's very important to understand that if you didn't model your state of health capacity correctly and you assumed that just your state of charge was going to give you an accurate range estimation you would be off by potentially up to 40 miles of range Delta so it's very important to understand this this feature and then going to Soh and pedis why is that so important well if you can imagine that the cooling performance of your vehicle is a limiting factor for example say that you have a race electric vehicle it's high-performance and the battery thermals are one of the limiting factors that prevents you from going to the end of the race with the maximum speed well now you might have thermal say that the beginning of life you had thermal limiting that occurred say that happened say 10 minutes into into a race that would be at the beginning of life now assuming that you've gone through a few races maybe you've have 50 to 100 cycles under your belt they were pretty high-intensity cycles which means that the battery degradation was worse than expected so therefore your impedance growth say was about 50 percent then you potentially would have a situation where now your thermal limiting instead of 10 minutes is now after 5 minutes so a pretty significant decrease in performance so it's very important to understand and quantify these values so that when you are making estimations about the ability of your battery pack to perform over time you're able to always give accurate estimations so that's all for today's video we'll see you next time thank you [Music] you