Welcome to the final honors week of the specialization. I'm really pleased that you have chosen to study the topics of this week because I think that these topics point towards an important direction of future battery management system algorithms. At this point we have approached the final frontier of knowledge in battery management systems and algorithms. The electronics aspects of battery management system design are, of course, really important. But in some ways, the design of these electronics is also fairly routine. The state of charge of a battery cell is very well-defined, and the established methods using the circuit-based models that you've learned about really give very good state of charge estimates. You have also learned some good methods to estimate equivalent series reasons to understand the total capacity of battery cells, and that gives a good indication of the state of health of the battery pack as well. You have learned that calculating cell energy is straightforward once we know the capacities and states of charges of all the different cells and the open circuit voltage relationships of those cells as well. And you now know how to implement cell balancing methods for cells and these methods might have different complexities and speed. It is possible to improve any of these methods but honestly, the present state of the art is adequate for probably most applications. So there are still a couple of questions remaining. One of them has to do with how well these algorithms will work over the long term on aged battery packs. Simply because there are not very many old battery packs presently in service. The first Tesla Roadster was the first fairly high volume electric vehicle in the modern age based on lithium ion battery cells. And if I remember correctly, it was introduced in 2008 and I'm recording this in 2018. So, it's only been about ten years that we've had large battery packs in vehicles on the road and we expect that most lithium ion battery packs will last at least 10 years, probably in many cases 15 years or more. So there aren't that many old battery packs and service that we can learn from. And so that is why there is some question regarding how well these algorithms will work because we may not really know at this point how the battery cells will change in their behaviors as they age. But there is a good reason to expect that the present methods will work quite well aged battery packs as long as is possible to adjust the parameter values of the circuit model such that they can describe the battery cells reasonably accurately at every stage of life. My main concern with present battery management system algorithms is how they compute available power, and that is going to be the main topic of this week, and this fits right in to the last two weeks that you studied on different power limits estimation methods. So we're going to go into that. I'm going to pause on that right now and give you the summary statement. One of the pioneers and battery management systems, Davide Andrea said, Using custom electronics or current electronics and knowledge, it takes about two years and $250,000 to build a custom battery management system. And this is not a trivial task, but it's certainly within the realm of something that's very possible to do, and has been done by any number of companies. So again, my concern my main concern with the present state of the art of battery management system algorithm is how they compute power limits for the battery pack by now you've learned that I do not prefer the HPPC method because it uses an overly simplified battery cell model and assumes that the cell is always in an equilibrium condition when it computes the future power-limits. You have also learned that I do prefer the bi-section method over the HPPC method because it uses a better cell model and it does not assume equilibrium conditions. But I still have some concerns about the way the bisection method is applied to compute power limits, it has to do with the assumptions built into that. And all present methods for computing power limit assume that it is critically important to put limits on cell terminal voltage that is we never want the cell terminal voltage to exceed some maximum value, or dip below some minimum value. But why? Why is it important to put constraints or limits on cell voltages? The real issue is, we're trying to control how quickly a battery cell ages. The issue is how quickly does the battery cell degrade. The limits are imposed on battery cell voltages, because they assume that if a voltage limit is violated then the cell is going to age rapidly. It's going to deteriorate rapidly but if we always keep the cell voltage inside of some limits, then the cell is going to have a long and productive service life. So the present methods use voltage limits as an attempt to make the battery pack have a long service life. However, it turns out that voltage limits can be violated briefly, in some cases, without causing any kind of noticeable aging. And it also turns out that even if a cell maintains its voltage inside of limits, inside of a standard operational range, sometimes we can even cause accelerated aging especially as the battery pack is already getting older and some of its dynamics are changing. So, the real issue that we're trying to solve has to do with maintaining or extending the service life of the battery pack as long as possible. And we are using voltage limits in an attempt to do that, but the voltage limits are really not the direct issue. So since we're trying to control aging does it make sense to use an indirect measure of aging to maintain this battery pack health? Or is there a way that can more directly predict aging under some hypothesized future time horizon some power event, is there a way to predict aging more directly? And if we can predict aging more directly maybe we can control aging more directly. So my opinion is that we need to reexamine the voltage limits really carefully and probably replace them with something else that is a more direct indicator of the aging that a battery pack would experience at different power levels. And I believe it's the growing opinion and consensus that, of more and more of the industry that we really need to compute cell power limits based on a direct trade off or optimization between performance and aging rather than simply maintaining artificially derived voltage limits on the battery cell. So how might we do this? How might we compute power limits that optimize a trade off between performance and aging directly. So first, we need to be able to create a mathematical models of how the cell degrades. Because that's what we want to minimize. Second, we need to be able to create optimized controls that use these models to calculate what is the best trade-off and then enforce that best trade-off. And there's been some preliminary research done by our research team at the University of Colorado, Colorado Springs, and by other research teams around the planet that have reported in the literature some benefits that we can expect. So if we can perfectly create the optimal trade-off between performance and aging, then in many cases we can authorize more power for the same battery pack at different points in time because the present controls based on voltage limits are very conservative most of the time. So we can either optimize more power without really accelerating aging in any noticeable way, or we could instead, for the same design requirement of power, use a smaller battery pack to begin with that is optimized maybe more for energy storage than for power delivery. And that would allow us to use a smaller, less expensive battery pack to achieve the same overall design requirements. So, we could authorize more power, or we could use a smaller battery pack, or we could extend life compared with the present methods. And there's one publication by Kandler Smith and colleagues that said that for pulse power operation we may be about to get an extension of the available energy by as much as 200% or more in some cases using some of the basic ideas that I'll be sharing with you this week compared with present ideas. We can even achieve more available energy and HEV-type applications without changing the battery pack. Or we could use smaller battery packs with cells that are optimized for power than they are for energy, using the approaches I'm going to share with you, instead of the approaches you've learned so far. Or we could extend life, and so we can enhance the value of a battery pack for what we call the first life or the original application. Or we could make the battery pack more useful for a second life application. And so the resell value of the battery pack, once it has completed its first mission could be enhanced. A lot of different possibilities and none of them are really certain yet, but they look very promising. And so I think that these three different possible benefits give a lot of incentive to make a very strong attempt to be able to model degradation and devise controls using those models in the way that you'll hear about. So, how do we model degradation? It turns out that there is really an enormous volume of literature that describes battery cell degradation qualitatively. We can say, if I do this to the battery cell observed that has a worse state of health, than if I do something else, that's what I mean by qualitative. There's no equations, no numbers, but just kind of experiments that show what seems to cause more damage to a cell than some other things. But we need to devise, optimize controls that come up with hard crisp numeric values on how much power the user is permitted to use right now. So we must know how to model cell degradation quantitatively. We need equations, mathematical models, we need parameter values in those equations to make it specific to a particular cell, and this is a different problem entirely. So quantitative modeling of degradation is much more difficult than qualitative. And how much is known about this? So at this point in history, many of the mechanisms that cause aging are not well understood, at least quantitatively. And the interactions between the different mechanisms are fairly complicated and also not well understood. So there's a lot of unknown and a lot of uncertainty regarding how well we might be able to make models to describe degradation. But you have to understand, this is the nature of research and we're entering in this honors week of the specialization, the area of research of what is possible or what might be possible. And if it is possible, what are the advantages that we might gain? And so we're looking for maybe high risk, high payoff kind of scenarios, and that's what this is. So we make a hypothesis that we can model degradation. And we proceed to investigate that hypothesis and investigate the benefits that might be derived from that hypothesis being true. Now, we do have at least one thing that works in our favor, and that is we don't need to model every single degradation mechanism perfectly to have a useful result. For example, we're interested in battery control. So we don't need to create models of any degradation mechanism that is not influenced by some variable that we control. We are able to control battery current, and temperature, and maybe the state of charge range that's used, but we cannot control every possible factor experienced by a battery cell. So if some degradation mechanism is influenced only by factors outside of our control, then there's no point in modeling it because that model will have no impact on our control decisions. So then that narrows the list down to models that have some controllable inputs to them. Do we need to model these all? Do we need to model them all perfectly? And really, even if we model only the most severe of the degradation mechanisms reasonably well, not perfectly, but reasonably well, then we have a chance of designing controls that will make a difference in extending life or increasing the amount of power that is authorized. So we do not need to have perfect models and perfect controls in order to make a difference. Even imperfect models and imperfect controls are a good starting point and these can be refined overtime as the industry develops and we learn more by performing research and getting data back from packs that have been out in the field for a long period of time. So how might we model degradation? It turns out that none of the cell degradation mechanisms that you've already learned about in the fourth course of this specialization are tied directly to cell terminal voltage. But instead they're tied directly to internal stress factors to stress factors that are happening somewhere inside of the battery cell itself. So, for example, if we have knowledge of local concentrations of lithium in the electrolyte at some spacial locations internal to the cell. If we know the concentrations of lithium on the electrode surfaces at different places in the battery cell, then it turns out we can predict imminent collapse of power. And so we can guide the user away from that, guide the load away from that by restricting power, so that the power isn't constant for a while and then just gone. So we can do that if we know those concentrations. Or, if we have knowledge of local potentials internal to the electoral electrolyte region inside the battery cell. That helps us to predict the onset of side reactions like SEI growth, cell electrolyte interphase growth or lithium plating which if also seen introduced briefly in the fourth course, and we're going to talk more about it this week. And if we have knowledge of the mechanical stresses at different points of the cell, we can predict electrode-particle or composite-electrode fractures So none of this knowledge is available from equivalent series models, equivalent circuit models. None of this is available from the kind of model that we studied in the second course. If we're going to develop aging models, it turns out we need to develop physics-based models of looking at my own battery cells. They can predict these concentrations inside the cell, it can predict the stresses and strains, it can predict the potentials and so forth. If we can do that in some kind of a computationally and mathematically reasonable way, then we might be able to predict aging directly and then device controls to control aging. Suppose for now that we can make models of degradation? How are we going to use those models? There are at least three different controls problems that we could consider and probably more that I have not thought about. So for applications like electric vehicles where we can charge the battery pack from some external source, we might ask, what is the optimal charge profile of charging rate versus time. Maybe I want to fast charge, maybe I have some other objective. What is the bet way to charge my battery pack? There are other applications like electric vehicles are included or hybrid electric vehicles or other things. While the vehicles driving, we might try to determine and what are the discharge and charge power limit over some future time horizon that maximizes performance but minimize ageing. This is exactly the problem we've looked at for the last two weeks but we might be able to do it in a way that directly minimize ageing instead of simply maintain voltage. For applications that consider electric vehicles to be storage units on a smart grid where the smart grid can lease energy or borrow energy maybe from a vehicle to support the grid when there's high demand on the grid. And we can attempt to optimize when it makes sense for the vehicle to either give or lend or rent energy back to the storage grid. And if it's rental, what should be the rental fee for allowing this energy to be borrowed from the battery pack? So this week we're going to quickly overview the first two of these control problems, but the third one is beyond the scope of what we have time to examine. You'll see that there are different kinds of optimized controls that might be better for each of these different application problems than others. And indeed this remains a topic of research that is going to inspire a lot of researchers to do a lot of incredible work over the next years. So to summarize this introductory lesson, I have shared with you that present battery management system algorithms actually do work very well, but there's still room for improvement. Of all of the algorithms we've studied in this specialization, I think that the power limit calculations show the most promise for making large improvements in the future. And the premise behind this statement is if we can model the dominant degradation mechanisms that occur in lithium ion battery cells. And if these models happen to have controllable inputs, then we should be able to devise controls to minimize the degradation and maximize the self-service life simultaneously. You have learned that if we are to do this, we are going to need physics-based models of battery cells and physics based models of battery cell degradation. This is actually an enormous topic. It will take at least a specialization as long as this one that you are just finishing in order to cover what is already known about these research areas fully. But this week, you can get a really helpful overview that will prepare you to study these topics in the future if you choose to do so. First, you are going to learn about lithium-ion physics-based cell models. These models are based on partial differential equations and that kind of equation is too complicated computationally to be implemented directly in a battery management system. So you are also going to learn about a method that takes the partial differential equations and automatically reduces the computational complexity of these models. While at the same time retaining their predictive capabilities for a practical implementation. You'll also learn some details of a couple of degradation models and some details of how we might use these physics-based models inside of optimal controls. So without delay, let's proceed to the next lesson and begin looking at these topics.
