 Hi, everyone. Welcome to the Smart Grid Seminar. This is the last one for this quarter at the end of this presentation. We also talk about this seminar for the next quarter. So our speaker today is Professor Bolenso from Columbia University. Before we introduce him, I would like to go over some of the features that you can use during the presentation. So you can use the chat feature to communicate any technical difficulties to us. So for example, if you cannot hear the speaker, you can let us know. And you can use raise hand if you have a clarification question during the presentation. And if you have any in-depth questions, you should use the Q&A feature. And all the questions will be addressed and answered at the end of the presentation. Now, this is the list of speakers who have visited us online, at least this quarter. So I just want to remind everyone that the presentations were recorded. So if you miss any of the presentations, you can view the video. Professor Bolenso is an assistant professor of Earth and Environmental Engineering at Columbia University. He's also affiliated with the EE department and is a core member at the Electromechanical Energy Center. His research areas are on design and operation of sustainable energy systems, spending from battery modeling to your city market design. He received his PhD from the University of Washington, Seattle. And he was a post-doc at MIT before joining Columbia University. Yeah, let's welcome the speaker. Professor Sui can share your slides. Okay, sharing right now. Thanks, Ching Wu, for the introduction and thanks everyone for attending. I'm seeing my slide on my presentation, presenter Wu, I guess the slides, okay. Okay, cool. Yeah, yeah, good afternoon. I'm very glad to be here and talk about my research. And I really cover the work I started since my PhD to my postal and even some of my very recent work here at Columbia. I'm doing operation at lifetime valuation for battery, okay. Okay, so battery, battery, battery, right, battery is becoming a key topic at the start of the show for the future energy system, and it has many different applications, all right. The most popular one is battery powers electric vehicle, right. And now many region California and countries UK have declared our targeting date that then the sale of traditional fuel vehicles. Battery is also a key enabling technology to improve utilization to integrate renewable energy right by charging discharge it mitigates the fluctuation from wind and solar. Another interesting development with battery is it actually demonstrate a show proved to be a very reliable resource for improving the power system reliability and resilience and the industry this is called nonwire alternative, and especially in some rural areas of mountain or coastal areas, and battery showing to be more cost effective than building a new transmission line, and battery is also much more resilient to extreme weather like wildfire or or hurricane. So we will see a dramatic increase of behind the meter batteries and these batteries will, including electric vehicle, and this will provide vast opportunities to promote demand response program. And some of you, some of you may know there's a very recent development from FERC, a FERC order 2022, which encouraged the participation of demand aggregation electricity markets. Okay. So here let's take a quick overview of what benefit batteries bringing us sustainability. Okay, battery is making our system more sustainable by integrating renewable energy. Also reliability battery is making our grid more reliable. The third pillar here in power system design operation is economics, right, and I hear the key focus of my research and also this talk is how do we improve the economic utilization of battery resources in the grid. And this is essentially a problem of valuation dispatch and control. So let's take a step back and just a quick review of what is how would that economics mean in power system and the basic, the most basic concept here is economic dispatch. Okay, and many of you may be familiar with concept is basically we are figuring how to use multiple generators to meet the demand, and each of the generator has a cost curve and also has incremental cost. Right. And then we can formulate this into either a linear programming of mixing linear programming problem. The objective is minimize the total generation cost. And we have constraint supply, demand and balance, unique constraints, network security, and this is a traditional definition of a generator based economic dispatch. And now we'd like to see how do we include battery into this framework. Okay, and in a very high level, the solution is pretty intuitive, you add battery into the constraint, and you add a battery operating cost into the objective function. Right, but this is just a high level overview but in detail that this may not be so trivial has the same right. So let's start from the constraints first. Right, the battery of depending on various technology are very have very complicated later chemical process going inside the battery, but seeing from the power system perspective, battery are actually very simple devices model. Right. It doesn't have a complicated ramping or other, you know, governance dynamics, no mean up on time, no, no minimum generation limit right it's just a power rating. Right, the power rating or the power electronic device. And energy rating, right energy dynamics the changing the stored energy equals to the energy or charge or discharge, and also efficiency. Right, it can either be a constant, or it can even be a piece by sling your approximation. And here, this is a recent paper, just showing how the seemingly complicated battery charge and discharge efficiency dynamics can be represented use a piece by sling your approximation. So we can very easily formulate battery operation constraints into a linear programming framework and putting the dog dispatch. Okay. However, to characterize the cost of putting costs but battery is not so tribute. Okay, and here we are looking at two components. One is capacity opportunity cost. Right, battery has limited capacity and actually compared to most other resources in the power system it has a very, very limited capacity usually one, one to four hours. Right. And that means to operate the battery we must plan ahead and determine what need what we need to do now based on the future expectation of the price. And here are two examples. In the upper price here, we have relatively high somewhere around $100 but pretty flat price profile. Okay, so this will be a good day for a generator because for for conventional generator if the price is higher than the generator fuel cost. I just generate but for battery. There's not so much profitable opportunity but battery profit, not by generating energy but for up a charging price differences. Okay. On the lower plot here, we have much lower average price somewhere lower than 50% $50 per megawatt hour, but this will be a pretty nice day for battery because well, that's high fluctuation right, especially here during this a few price valleys and the battery would would be it would be very good opportunity for battery to charge and later it has the opportunity to sell this energy charge here as somewhere around $50 per megawatt hour. Right. So this is what we mean by capacity opportunity. Right. So it's a trade off to save your capacity now now or use it and sell your energy later. Right. So this is the best opportunity. On the other hand, we have degradation. Right. And some of you may have heard of this term before that this basically means for battery is an electrochemical device. The useful energy capacity decreases slowly with time and recycling meaning charge and discharge. Okay, so I guess we all have a phone on iPhone or any other phone and we all know how the battery looks after two or three years of use right even now. And now iPhone even has a has the function to estimate the remaining lifetime of your battery in your phone. Okay. But here I have an example of battery warranty and it's very similar to the ones I saw in the industry is well the warranty will specify that your battery has a 10 year calendar life. Okay, if you do not use a battery at all it lasts for 10 years, or if you use the battery cycle one cycle per day it lasts for five years and at the end of the warranty, it guarantees you'd have 80% remaining capacity. Right. And there is even a fancier way to define this but you get 10 calendar at 10 years of warranty days for a battery. And then every cycle you perform reduce the warranty time by one day. Okay. So how do we, how does the relation impact our economic decisions. Okay. And here, it's again, an opportunity, right, but it's not no longer opportunity of capacity is a community of your lifetime. You know, if you, if I cycle my battery now, I got my money now, or any other benefit but the drawback here is I have less capacity to use in the future and I shortest my battery life. And here is a bigger from a battery testing data from one of our earlier publications that really shows the remaining battery capacity is crucially dependent on how you use the battery, how the batteries are charged discharge so it's very correlated highly correlated with the battery operation. Okay. And so here's the problem we have capacity opportunity cause we have lifetime opportunity cause how they are, and they are correlated and how do we get the value of both of them. Right. I'm here. I'm just do a quick summary and a bottom up introduction on this problem. We start right with a daily operation. They're short term capacity opportunity cost model right, which we had the pricing for the day we put it in, and it generates the revenue and the control of it. Right. So this is for one day. And also, we can go one day prior right this is from widely prior, and also these two days are weekly coupled energy you left from yesterday is energy of service from today, right. And also, the day before yesterday and going on and on right and this is a coupled sequential operation problem. And it's also similar it's a very similar problem to inventory management, or even our hydro storage planning. Okay, comp hydro storage, but it was unique about battery is a degradation model, right. So, all this operation we perform will cause incremental degradation, right in the battery. And also, the remaining capacity of the battery will be impacted. And that will also impact how you operate the battery here and here and here. And this is another layer of coupling. And this is unique in electrochemical batteries and this and our long term by long term life opportunity cost, we are trying to capture all of these interactions, like to capture an opportunity value of the battery degradation. Okay. Right, and here is a summary of the three blocks we considered here I think this really is a good summary of the work of the research, a main focus of my research since my PhD, especially my PhD I've worked a lot on degradation modeling. And then during my postdoc at MIT, I spent a lot of time doing the short term battery operation. And here, during my recent time at Columbia, Columbia, mostly during the COVID lockdown, also got some very interesting results on long term lifetime opportunity costs. But let's just start step by step, and from the very basic degradation model here, right, and degradation model basically takes in the lifetime opportunity cost and has an input and translate that into an operating cost for the short term capacity evaluation. Okay. However, we have to start somewhere right we don't know the lifetime opportunity cost yet but remember, this is the model for technically, it can work with any, any number, right, any number opportunity cost. And here, a preliminary approach we take is to use the cost to pour it the battery replacement cost has the value of lifetime right and this is actually a very common approach in the industry and also used by many other publications. And a quick example here we have the battery degradation curve. This is the incremental battery life loss. And this is a long linear function with respect to how deep you cycle the battery. This is from the degradation from single cycle. Right, which we have the life loss here, and we have a cell replacement replacement cost here, we multiply them together we get the cost of degradation. Right. So that is, and following this, this assumption, right, and we'll revisit this topic later. And we, we did a modeling on the piece by senior approximation to a long linear degradation model, doing to model better degradation in optimization and this is a joint work with folks at I so in England. And a piece by linear approximation. Okay, and eventually we convert the long linear cycle battery cycle degradation model into a linear programming that can be using any of my different problems and we use, we test this you see a very simple arbitrage example, which we have where we have the price data here. Here is the seed of charge response the resulting seed of charge from the arbitrage using different resolutions. Okay, using different approximate level approximation. And you wish we can see with a higher number of segments. Okay. So the long linear variation start to be more responsive to the small price variation where you have big cycle with big price change. Well, you also from on top of they also have small cycle responding to small price variation because of the long linear here. And our model achieves a diminution arrow compared to the benchmark nonlinear model with more number of approximation blocks. So the work I'd like to briefly talk about is a work with actually with Wilson, some, some of you may know him, and on calculating battery degradation into control and specifically specifically tracking control, right, and this for frequency regulation, in which you better think to regulate a stochastic signal. But the arrow, right, the arrow in the response will be charged for a penalty. And we show that the optimal response is really a threshold policy on the seed of charge you just follow the signal until you reach an upper lower bound. Okay. And then we show that this dress code can actually be analytically calculated. Using the market tariff and the degradation mechanism and intuition is really when you follow the single or you have degradation cause if you don't follow the single or you have penalty and that's a trade off there, again, due to the nonlinearity, the degradation. Okay. And we squeeze out to actually to publication out of this one focus on frequency participation to fix the regulation market, and the other is on control policy itself, which although it's pretty elegant here is actually take a quite, quite, quite amount of effort to to prove to do the proof. So that's from the degradation model and the less moving on to the next component, which is a short term capacity opportunity cost model. Okay, so what is the value of the short of the capacity of storage of the energy stored in the battery. And there's definitely many different framework the way we can show this but I just want to today, talk about a pretty interesting work I did when I was at MIT it's using a stock testing dynamic programming framework to do this. So if you were familiar with dynamic programming, you will know the dynamic programming itself is evaluation framework because we need to get a value function of the state and state here is the battery state of charge. So we automate by doing a dynamic programming way automatically get the value function for storage. And here just a quick summary about the formulation and this is the single stage of my objective function separate power in a state of charge limits. We have a single stage profit, the arbitrage profit, and also the cost of regulation, and also the value to go function life from from from the future. Okay, and for stochastic dynamic programming is really the optimized value here goes into the expectation function right and then our value depends on the expectation for the future profit. And here the stochastic rival is the price lambda, which is the real time market price. And this is basically the stochastic dynamic programming framework here. So just a quick over insurance stochastic dynamic programming and for folks who worked with stochastic dynamic program before. I think we all know this not a very pleasant experience, and simply because inherent complexity, right, and the combination of uncertainty and a state just just just blow up exponentially right especially for real time price arbitrage. So five minute market clearance of 288 uncertainty stages per day. Right. And here just a quick overview review about some prior method of showing solving spochastic dynamic programming. One is Markov decision process, right, value, a very map your action as a based on your states. And also following that Markov dishes and process we also have reinforcement learning. Okay, also use Markov decision process and also approximate dynamic program. Okay, but, but here, a big limitation from MVP based approach is it's very accurate to model efficiency, because the battery has no idea efficiency, you know, 92%, 93%, 94%. And it's really difficult to be captured by transition of discretized states. Okay. Or you can do a very fine when you let it be of state but that will increase your computation expense by quite a lot. Okay. And on the other hand, there's another algorithm called stochastic do dynamic programming and this is actually the classic algorithm for scheduling hydro storage. Okay, pump hydro storage, which, which actually a more complicated problem than battery because for hydro storage scheduling was a many environmental temperature factors, right. The inflow or even the flow of the salmon the migrate of salmon if you live in Washington state. Okay. And MVP is in many cases computationally expensive. Okay. It just need to do it still do a lot of iteration back and forth. Okay, and here are some of the prior literatures as it tackled on this problem. Okay. But for the algorithm here, a proposed organism is this study is we develop a analytical organism tailored to storage price of a trash. And we use a piecewise linear approximation to the value function. And as a result, we don't need to discretize anything no discretization of states control or distribution of the of the uncertainty. Okay. So here, this is a quick summary of the technical approach we do with this. And the main theory we use is, it's the same theory foundation to stochastic do dynamic program is which do decomposition, which we decompose to do with respect to the state of charge evolution constraint, right. And then we use a relationship between these two sub problem to derive to derive the analytical representation of the distribution of small q, which is the derivative of your profit of your profit. And what you hear is the maximize the profit, your stage wise maximize profit and here this is the derivative of it, and we are able to show it is a closed form on distribution function directly based on the distribution of the price. Okay. And just know that here we have a gradient update rule and I'm just want to clarify that we use this for the proof, not for design the algorithm itself right and we use this as a way to prove this room. Okay. And as a result, our. So we have the distribution and then by taking the expectation we can analytically cutter eyes, the derivative of the value function, it's a small thing, right. It has a function of the value function derivative from the next time period, right, because in dynamic for me work backwards so this is a function, this is the result from our prior step. Okay. And also a function of the price distribution function right CDF PDF and this is this integral here is basically the conditional expectation. Okay. So storage for a coefficient cost efficiency power limit. Okay. And although this function looks pretty pretty ugly pretty complicated it's actually very simple to calculate. You know, if this is, this is basically can be can be finished, but can be calculated on the most software or hardware platform. So here is, we don't need to criticize anything. The pro that assume, especially no discretization of distribution right we can deal with distribution function directly is analytical form, or you can use samples, right, that you have discretize you have this great distribution function. It has extremely fast computation speed with one backwards trip you just start from the last time period go backwards to solve the problem for. It's a simple hardware or software, but as long as you can finish this computation, you're good to go. You can implement anywhere. And also we have a current limitation is we still assume statewide independent distribution for the price which is not realistic but you know, but based on our preliminary computation performance we're pretty confident that this can be easily adopted into more complicated and less dependent distribution. And here this is a comparison with the benchmark as DTP solution in solving average watch, which 24 uncertainty stages. And here we use 24 no 288 is at least this as DTP cannot solve 288 stages on my computer, right. I have to do 24. So here we see, we consider different number of state price, price note or different number of uncertainty notes per stage. Okay, and the solution time for STP goes up to nearly an hour, right, but with our method. So everything is solved somewhere around a below 25 milliseconds, which is a huge improvement. And also the two methods achieve identical performance in exposed Monte Carlo simulations based on the derived the value function. Okay. And here this is the case study of the battery, the value of the battery capacity on the under different price divisions. Okay. And here we have, we have price series that they had quite also different. We model real time price has a normal distribution around it with different standard divisions, which give us different value of the energy storing the battery. And just to note here, this is the value and just stored in the battery not the battery profit right if you if you should the battery profit, higher price duration will give you much higher profit, but here, this is how much is the energy stored in my bag. And it also shows interesting that with higher price division, the energy stored in the battery, versus more. It's kind of interesting because the US because because the expectation of all these prices are the same. If you only think about the one stage where you store, you have energy storing the battery, and you want to sell them in the next time period. Your profit should be your expected profits to be inspected price times your energy. But here, if we consider multi stage uncertainty, it does show a difference here that battery values more with higher uncertainty. And another advantage here is this curve can be directly used has to be done bidding curve into the into the electricity market for battery. Okay. Which is pretty difficult to achieve which is with Markov decision process based methods. Okay. So we have degradation model we have short term creation model and let's go back to where we started the long term life opportunity cost model right and just bring everybody back by long term life opportunity. It's a trade off between use your battery now and shorten this lifetime, or save your battery to use it now and you get a little bit longer lifetime right it's again a trade off problem. And it turned out this problem has not be very commonly studied. In fact, the first and only publication command knowledge is written by actually a very good friend of mine. And we both worked at MIT. Dr one and her, he's still at MIT now, and he publishes paper in major energy that tackle this problem. But there's a theory because we are targeting a very long term operation here. There's some inherent computation difficulties, and he has to meet and made an assumption here that the marginal cost of battery degradation also incremental cost of battery degradation. It's a time invariant life state independent term. Okay. But here. If we introduce a dynamic is supposedly more accurate dynamic programming framework into this we do show that this number this degradation but it's highly time. Okay, and life dependent. Okay, so it's still, it's still dynamic programming. It's just another, another version of dynamic programming here to do the valuation of lifetime. And here we started with the daily operating problem. And now the our value function is longer the value of the stored energy, but the value of remaining battery lifetime. Okay, all the remaining battery capacity. So we have the battery, the battery revenue from operating day. Okay. And here we're still targeting arbitrage application but essentially, it can be any battery operations that can, as long as it can be formulated as a complex problem. It can be anything but here we just focus still for simplicity we use arbitrage. Okay. And, and we have, we get revenue. Okay, from from today, right from today, they end by operating battery and the battery operation passing through a cycle degradation model generates tells us what's the incremental degradation of the capacity. And this will change in my lifetime in the in the remaining capacity of the battery, and this goes into the future battery value. Okay, and then we do a trade off between our profit now, today, and the remaining value of the battery. The daily operating problem. And also we have a alter loop, or the intraday value function update model because the optimized value here. Okay. It is essentially the optimized battery value from today. Okay, to the project that line. We assume there's a deadline of the battery project that after that, the battery project has to be terminated. Okay. And then we can even add some complicating factors into this right like calendar degradation, your battery, there's a calendar degradation component in battery degradation that even you don't use your battery, it still lost a little bit of lifetime every day. And if we can add daily discount ratio, right, the money tomorrow versus a little bit less seen from today, we can also include a benchmark resale value right off the battery, which means, well, we are targeting the battery arbitrage application right now, but I can still sell my battery source to to say backup power supply or two electric buses right but we still worth a little bit of money there so we can even consider a benchmark resale. I'll show you that later. And that will get included into our future value function. And here is the formulation again, and our daily objective is maximize arbitrage income and the remaining value of the battery right and here. This is the value function from today, but optimize the value here is the value from from today to the future right and and and this will be the value from tomorrow to the future. So we add, we can add discount factor to it, right, daily discount factor, and also if our resale value benchmark resale value turned out to be higher than this. This term, we used to benchmark resale value and the physical and practically this basically mean we should just sell our battery and terminate the project. And so we have power rating system chart evolution rating this is pretty standard way to write this. And a special constraint here is the battery lifetime evolution. Okay, then I'm where my maximum energy capacity, okay, my battery energy capacity depends on the battery energy capacity from yesterday, minus cycle degradation the function of my power. Okay, of my power, and also my calendar degradation this model has a constant value my battery lost a fixed amount of life of capacity everything. Right. And this term defined limits how much energy we can charge this chart and also this term goes into the value function. For tomorrow. And, and here. This will be our initial state. Okay, which is the energy remain the capacity of the battery from yesterday. Okay. This, this dynamic programming problem is actually solve using a very similar approach to the previous one and using piecewise linear approximation, right, it looks like I'm really a lover of piecewise linear approximation. But it does show that it's in many cases a very good trick to so many, many nonlinear problems. Okay, and I'd like to jump to the results directly. Okay. Very similar to the previous one here in the simulation setup is we got we use real time Christ data from line of New York from 2010 to 2019. Okay, and we do the simulation backwards. And using a determinist framework, we assume the battery one meg about two meg bar battery and this is a popular setting for a grisco battery now one to one to our battery 85% long trip efficiency. And here, this is our valuation result, right, and the 3d plot during the value of battery depends on the remaining capacity, right, of the battery, and also we assume the battery last for 10 years. So, so, so the value is also dependent on how many remaining project years we have. Okay. And, sorry. And at the end of the project with what we left is a resell value. And here we assume the resell value to be assume we have a battery warranty until reaching 80% degradation. So that means a battery with valid warranty with still some warranty that has some priority to resell value. And once the word expired the battery can still usable until 60% remaining lifetime, but it has no sale value because it's no longer have a warranty, but this is considered to be a second life battery. Okay. So here, we show the second life battery, you know, the result is zero but if you do that, do the valuation issues, it actually show that second life battery do worse. Quite a lot has with more project duration remain. Okay. Another interesting angle to look at is the surplus bed, which is we minus the resell value, what do we minus the resell value from the total value which we get the difference, right, which means additional value we can get from this battery from this resell right, which we can assume that we can buy any kind of battery at its resell value, right. And here does show that once we consider that 80% lifetime which is the, you know, the newest end of the life battery, the battery that just had a expired warranty. Give us the most value here, right, in all scenarios. Okay. And of course, you see here by approaching the battery deadline and with a newer battery, it has zero surplus value, which means he has a value is basically dependent on the resell value. So another good angle to look at this is take this look at an incremental degradation cost or the marginal cost, basically you take the derivative, we take the derivative of this plot, right. And this is the actual this should be the actual term the marginal cost of dignity, this will be the extra term to be plugged in into market optimization. Right. And does show here that's a very strong dependency of the marginal cost, with respect to the remaining battery capacity right a new battery has somewhere around zero to $20 marginal cost, but once the battery approaches end of life, the marginal cost to even five foot or even ten foot. Okay, to even to up to $100, somewhere over $100 per megawatt hour, right. And this, and it also get more sensitive to the price dynamics. But here I'm showing the, the Saturday moving average price deviation in Lyle, right. And this is 2010 to 2020. And I can say it's very similar to the shape here so it's highly coupled become highly sensitive. And that's a very interesting takeaway from this is the battery. So we, with, with aged battery we should use it much more conservatively with a much higher marginal cost. And this actually very much in line with the car with, with using second line batteries because the second line battery has high impedance, and also less stable internal performance. So we as we so physically, we should use it more conservatively and we also show that economically, we also should use it more conservatively so it's actually a pretty positive result here. It shows that second line battery is really a viable concept here. And then Lyle and next thing we just want to compare the battery performance in different price phones. And here we consider four different prices of New York. And here it shows you have very different dynamics in terms of average price and the price deviation because they have very different price portfolio, New York State has very strong congestion, south to west, south, sorry, east to west, and north to south. And that costs a price to be very different before in the four zones. Okay. And here is the comparison of the value of a second line battery versus new battery and here, again, just remind, second line battery is the battery with 80% capacity, we, which we assume that no longer has a ready warranty. And to continue the uncertainty of better end of life right in reality we are not sure what is the true end of life of battery without a warranty. We assume it can be, it can be distributed uniformly anywhere between 75% 50% so we assume here end of life is uncertain, and that really shows as a, a shaded range here. This is blue in the second line battery, new is, it's, it's, it's, it's for a new batch and we also here for new battery, we assume, we can still use the new battery after the run takes by the new battery covers included the second line battery here. And also just to be fair, we do not consider resale that anymore. So the key takeaway here is, you see the battery value is very much dependent on the price realization the frozen. But the ratio between these two guys, like between us like every, it's pretty stable in all these four zones despite they are very different price dynamics. It also said that the value, the ratio between second life to new batteries go somewhere around 50, 50, 57%, right, all the way to around nearly 100%. And when you are approaching battery life at that point, and this is a pretty encouraging result considering first, second life battery doesn't have any, I'm not supposed to have any resale value compared to new battery. And even you compare the energy, lifetime energy throughput, right, every second life, second life battery can only provide less than 40% lifetime energy throughput compared to new bed. Okay, and here, remember, for new batteries, we assume new batteries include a second life portion right. And so this is a very preliminary work I just uploaded to archive this this Wednesday I believe. I think this is also pretty promising and currently result, especially we have a very new study from from the Kenzie scene by 2030. Our work will have 200 gigabytes of of second life that was pretty. Okay. Now let's go back to where we started we want to include battery into economic dispatch right. We have a valuation framework we can run the valuation from framework on some red with low dimension data right price, or demand forecast regulation signal right. And we have our economic dispatch, which we optimize will be meaning my generation costs, separate the country. And then we have the value and it's pretty simple here how that way, how do we include a result into the economy dispatch is basically the value function. So the cost function is a negative to a very fun right. And if we hear we have storage cost, and it's a function, a battery state of charge and battery lifetime. And also the degradation model will go both into constraint and also objective function. So here we can optimize battery operation using single period route single period real time dispatch. Which is basically existing route and dispatch framework in most system operations. And we can directly incorporate this cost function into economic dispatch or dysfunction can be used to design bidding curves, and with supporting market model. And now we're talking about market design. Okay, that's why many people now talking about marketing. Okay, just a little bit of outlook here. I think we talked about a lot about battery valuation, right. And one of my visions, I hope my on my future goal is to develop open source control and evaluation framework for battery storage by including modeling right we have all model we need operation tracking problems, more than predicting control stochastic programming and also valuation planning right we have the market signal here. Right. And this really to us, the social wide utilization of battery, right both distributed or even electric vehicle as a residential right. The key technical in me below here is we should be we are we are able to solve this using open source organism, right. And with minimal requirement on the software and hardware, right we can do this anywhere in home management devices on electric vehicles, right. And then we can, and this is the main engine of this valuation and then we can integrate everything to a holistic open source software platform, which for the utilization of industry in every social industry, I will say. Yeah, this will be the end of my talk, you for your intention and I really want to acknowledge many of my collaborators along the way, and also the companies that we work with. And yeah, this will be all for for today. Okay, and I'm glad to answer any questions. If you have any questions you can use the Q&A feature to type your questions, and you can also unmute yourself if you want to ask the question directly. I see there is one question. Yeah, about the resell value of first life batteries determined. Yeah. And here it is assumptions I made, but also I think there are some supportive literature of this is a new battery versus $200 per kilowatt hour. Okay. And then based on the remaining duration of the warranty. The resell value is prorated right here you have we have 50 we have half of the warranty left the battery versus $100 per megawatt hour, right. And then once your battery. It's the warranty expired, we have no more resell value. But on the other hand, I will say this just the framework is able to take into consideration of any possible. Assumption on second life, trading back, sorry, resell. There's a second question. Can you talk about the intuition why second life batteries are less economical than new ones. Yeah, so do me is. Yes, you mean the battery of second life battery. Well, let me go. This is here. Second life battery versus less than your battery as well, because we have less lifetime and less capacity right for new battery in this framework. For example, I can my battery can I can use my bed for 100% capacity to anywhere between 75 to 50% capacity, right. And for the battery of a second life battery, I'm starting at 80%. I'm starting at 80%. Right. So, I can, I can arrive. So I have much smaller battery in terms of capacity and in terms of available lifetime. All right. So here's the intuition for the second life batteries really aiming about any at batteries that retired from electric vehicles. They probably are are are degraded is not enough to beat a many, many, many mileage requirement or performance requirement, but the system can have hope can can can charge and discharge. Not good enough for electric vehicle, but still good enough for electric for electric power system applications. Okay, let me. Does the model characterize the value from recycling the battery. Very good point. Yeah. Yeah. Yeah. Yeah. This is a very good point is this actually part of our ongoing effort. So the recycling is another. Big topic, right. And actually I just talked with some battery people working on recycling. So it turns out the battery state of life, right, whether your battery is at, you know, 90% 80% 70% 60% the procedure and the quality of the recycling is exactly the same. Right. So really is think about to to drink the full potential out of the battery before recycling. It's a big, it's a big thing here, right, because because it makes no difference recycling. And on the other hand, we are trying to look into the problem further. In terms of recycling, as well as, as well as production is a mine. We have many different battery technology, and they have many different requirement on the material. I think I would. And you may know that cobalt is critical is the critical material for for AMC on many car batteries to stick to prolonged the left time and stabilizes the battery performance, but cobalt has its head is a very limited. Mineral right and definitely may not be sufficient to power up power system electrification for power sustainable power system the future right so and so really I think one of the future that we are looking into this is how do we incorporate life cycle right recycle production or even logistics into this framework so we can profile different types of battery technology and identify like like the best technology for for for grid. There's one more question. Yeah, this is interesting. Do you model second life batteries from primary usage differently from second life batteries from grid storage primary usage. Oh, good question. No, in this framework. No, okay, in this framework, we both new second life battery be assumed to be operating for grid arbitrage. Okay, so so so so so it's always great. But as I mentioned, cobalt is general. Okay, so so so here is a day and revenue but we can insert a different application right into this we can. add the utilization of our benefit of electric vehicle into this. And so that's I think that's the economic perspective and then back to your point. I see another perspective here is a battery retired from electric vehicle may be different right from battery, battery that has been on the grid is operating very different conditions right and and also an electric vehicle, supposedly, lives in a much more dynamic, less stable environment, so the battery can be different and right and you have the battery collected from different cars, they may be different right. So I think this goes into another very important topic here is for utilizing second life battery is to develop a dynamic adaptive battery management system right and right now I believe most battery management system are still based on are still basically based on the manufacturer said right. So I think that is a critical topic that batteries second life battery special from electric vehicles they are very diverse very different. Okay, but go back to the one of the results here is a good side of partly good news is we show that these batteries are second life batteries should be used very conservatively. Right. So if you consider, like here, the battery may have a marginal production costs of somewhere around 50 to $60. And this is the definition cost. This is, we have the counting opportunity, the capacity opportunity cost. Yeah, right. So if you can't do that we will expect the actual cost right actual operating cost discharge second life battery on this from framework, maybe it's likely $80 to $100. So that means the battery are operated very, very conservatively only get this chart a few times in the day or even week. And then this actually a good news to utilize a second life battery that means that the operation that we put, okay, on the second life battery is much more simple, simpler, right, much more conservative than new batteries, which means the second we can deal this presumably using a sloppier BMS right. Yeah, so this is the multi factor problem. And I haven't going to the standard right I think there are a lot of people discussing we should make more standard about how to diagnose second life. So, but this is a, again, I think this is also very important topic. So, are there any more questions. Okay, so, thank you for giving such an interesting presentation. Yeah, we look forward to another opportunity when you can visit us in person. Yeah, yeah, thank you for the invitation. And yeah, really, really looking forward to come to come to the campus and see, see all right. I think Dr. Liang Ming has an announcement. Are you sharing your screen right now, Professor Su. Yeah, okay. Before I do that, I'd like to thank a bullet again for the excellent presentation. So I think next quarter I'd like to connect you with some of the researchers we hear doing research in the degradation model. You know today is the last seminar for this quarter. I'd like to give a special thanks to Dr. Chin Wu Tan and Wahilla Wilkie for coordinating and organizing the seminar series for this quarter really appreciate. And I'd like to quickly announce what we're going to have in the next quarter. So next quarter we're going to highlight the Stanford postdoc program. So we will have a five postdocs. They are doing research with different professors at Stanford on different topics and power electronic, e-com policy, climate change, and power market, etc. And each of them will bring different perspective from their previous organization universities or even from different countries. So we'll be very exciting seminar series for the next quarter. And we will still deliver the smart grid seminar series next quarter through the zoom through online. And with that, I'd like to wish all the students good luck with your exam and the final report and for all the attendees and happy holidays. Thank you.