 Hello and welcome to SmartGrid seminar produced by Stanford, Bits and Watts, and many other co-sponsors. For Bits and Watts, our mission is to engage research, education, and industry to develop innovation for the 21st century electrical power grid. My name is Liang Mi, the managing director of Bits and Watts. It's my honor to be the host for today's webinar. This quarter, our webinars will be highlighting Stanford Postal and their research work. In the last several years, we always invite external researchers, scientists, and engineers to give the lectures here. And we saw that Postal also bring tremendous experience outside of Stanford, and also now is working with Stanford professor on different topics. So this quarter will be highlighting their work. Today, our presenter is Dr. Omar Karadouman. I'd like to hand this over to one of Omar's mentors, Professor Charlie Costa and also the co-director of Bits and Watts to introduce today's speaker. Thank you very much. It's my pleasure to be here today and also to introduce Omar Karadouman, who's joining us from just down the street. And Omar is a new postdoc here. He started in the summertime last summer, which seems like such a long time ago now. He has received his bachelor's degree from Bill Kent University in Turkey and his PhD just last year from MIT in Cambridge, of course. And he works in the area of market design, which you'll see is highly relevant to today's talk. And Omar is here for a two-year postdoc and we are absolutely delighted to have him here and we're anxious to see him in person when this unpleasantness of COVID has passed us by. His talk today is entitled, Impact of Storage on Electricity Wholesale Markets. Thank you, Liang and thank you, Charlie, for a lovely introduction. So today I will talk about economics of great scale energy storage and the plan is, so we'll first try to make a case for energy storage and why we need energy storage. And I will introduce a model that can incorporate energy storage impact in the whole selectors market. This model is going to be sort of the energy storage that I'm going to use in this model is going to be economical. So any type of energy storage that you have in mind in a technology can be incorporated as model with some caveats, of course, that we'll also mention about those. And then I will apply this framework to South of Australia and I will talk about some results and why South of Australia is a good example for energy storage. Then if I have time, I will share some thoughts about energy storage need in here, California, Kaiser as well. So producing cleaning electricity, as you know, it's very important for decarbonization. Is it accounts for one third of overall COT emissions? But not only for that, but also as a foothold for other industries in this transition as well, such as transportation and heating, producing clean electricity is very important. And the way that we basically try to make our grid more green and clean is with renewables. But renewables come, they come with a caveat that they're intermittent, they're not dispatchable, so their production changes with some exogenous factors. If the wind doesn't blow, you don't have production from wind power plant or if the sun is not up, you can produce from your solar PV. And that's causing balance. And in the absence of energy storage, we use inefficient and high carbon unit to maintain this balance. And I'm sure many of you are familiar with the dot curve that we have in California. So in the green line here, you can see this is a demand of electricity in Kaiso yesterday. And this green line is demand. And this blue line is net demand, which is the difference between demand and renewable generation from wind and solar. So you can see this ramp, which is caused by basically the sun. So you can see this when sun is down, solar PVs cannot produce. And because of that, the renewable generation decreases and you need to ramp up some fossil fuel power generation generators. And you basically waste some energy and increase the carbon emission a lot by ramping up this net demand. And this problem is going to, this problem will deepen more as we have more renewables because this curve is going to go even down and more down. And we will probably have a point where the overall renewable generation is probably going to be higher than the demand. And then we need to curtail, et cetera. So energy storage is basically a technology that capture energy produced at one time to use at a later time. So it makes electricity more durable. And in the electricity market, such technologies provide different services. And certainly services, it can contribute to reliability at the distribution level, also transmission level, it can provide some transmission relief, can be used as a transmission asset, can deal with curtailments, and it can engage in price arbitrage in time. What I mean by that is energy storage can buy electricity when the price is low and sell back to the grid when the price is high and make revenue out of this arbitrage opportunity. So the thing that makes energy storage a little bit different than conventional power plants is the opportunity cost of producing electricity is basically the price of electricity at the time of charging. So with the conventional power plants, the cost is the fuel cost, but here the cost is also a dynamic part of this market. So that makes energy storage problem a little bit different than most of the conventional power plants that we have. So there are different levels of markets for energy storage. There's a household level, such as the home energy storage systems, EVs, which can help by decreasing rooftop solar PV waste or can provide some resilience or help with the congestion and line losses at distribution. Also community level energy storage can help with that as well, that help with the congestion and line losses can also provide some extra resources for virtual power plants or distributed energy resource aggregators. But in the grid scale, it can provide lots of other things as well. And today's focus is going to be about grid scale one. So why energy storage is now such a hot topic or like why you're more interested in energy storage nowadays is mostly because the costs are decreasing. So as you can see here, there are most of the different battery technologies, also some of the old ones like pump hydro. The one thing that is interesting about energy storage is there is no silver bullet. So there is no one technology that has all the attributes that we want. Some of them are good in terms of the cost structure. Some of them are more efficient. Some of them are vastly available. Some of them are geographically not available. So we probably need to use some combination of different technologies in the future or even now. But it's nice that every one of these technologies seem to have a decreasing cost. And today, even though my model is canonical, I will focus on lithium ion batteries for a couple of reasons. First is that's the most popular one now for the grid scale implications. There's a huge decreasing cost or 70% in the last decade. It's very good with dealing with determinacy, intermittencies because it provides very fast adjustments and there's no locational dependence. You can put lithium ion batteries pretty much anywhere on the grid and it doesn't require a lot of grid expansion. So there are lots of intensive programs all over the world including California. And there's a discussion about the ownership like there's a recent work order, 841, also 2222. In California, there is a mandate for utilities to have an energy storage. But in our call, for instance, utilities cannot have an energy storage. So energy storage makes money, as I said, by using price differences. And if there's a variance in prices, it creates revenue. But while doing that, it also changed social returns. First of all, there is a price impact. So if the energy storage is large enough, it's going to have a price impact. And that will induce a transfer between consumer and producer surplus. Also due to this price change, there could be a change in market power in common firms. In California, we're all familiar with the 2001 energy crisis and market power. So energy storage can also help mitigate this market power by smoothing the prices. And it can also provide some efficiency, increase in efficiency of production by basically changing the marginal units when it's buying, when it's selling. So when energy storage is buying, electricity is probably cheaper. So that means the cost of electricity production is lower. So energy storage can buy that electricity and switch that up with the time where the electricity cost is higher, so that it can introduce more efficient electricity production. In the same spirit, it can change the CO2 emissions, also can help to decrease renewable current. And as I said, these are particularly significant when storage is large. So my question is, are incentives for investing and operating such technologies in a whole-selectors market socially efficient or not? So related questions with that, should we subsidize energy storage? Is it welfare improving? Does the market work? Does the prices or incentives in the market create socially efficient outcomes? And how about the CO2 emission impact of energy storage and how energy storage and renewables are interacting? And also policy-relevant question, who should own an energy storage? Because different ownership can result in the different outcomes of operation of an energy storage. So to answer that, I build a dynamic equilibrium framework to quantify hypothetical energy storage impact in a whole-selectors market in which I allow for storage and uncertainty about future prices. Excuse me, I allow for incumbent firms, fossil fuel generators, to respond to such entry, and then I endogenize storage's price impact by finding new equilibrium prices. So there are two technical challenges to do that. First of all, as I said at the beginning, energy storage's problem is dynamic. So how much you can sell depends on how much you can have in your battery or how much you can buy depends on how much you have. So that's basically an inherently dynamic problem. Also another problem is calculating these new equilibrium prices. So in many whole-selectors markets, firms are required to submit their renewables to produce supply functions. So the equilibrium concept that we use here to find equilibrium prices is supply function equilibrium. And it's hard to compute the supply function equilibrium. Sometimes it's not unique, sometimes it doesn't exist. So I basically circumvent that problem in this paper by using estimated best response to observed variation in demand volatility. So I will talk about this, but you can think that this is a model energy storage production as a shock to renewables or the demand. And then I simulate this grid-scale energy storage in the South Australian market. So as an example of what energy storage does in real life, we have a hostile poverty reserve in South Australia, which was the biggest lithium-ion battery that was online until I think last year. So here you can see in these two graphs, the blue line represents energy storage production. So above zero means that energy storage is producing and giving back to the grid. Below zero means that energy storage is buying from the grid. And the red line represents the price path for a whole day. So on the left hand side, you can see a stable price day where the price doesn't change much. So energy storage doesn't actually produce much. But on the right hand side, you can see a volatile price day, which energy storage production basically follows this price path pretty closely. So energy storage, as you see, responds to electric prices, and it tries to take advantage of this price variation. As a very canonical model, I will just try to show you how energy storage changes the social returns. Here we have two periods, a very simple model. There are two periods. In the first period, demand is D1. In the second period is demand D2. So second period, the demand is higher. So PCQ here is basically aggregated cost curve of conventional power plants in the system. And PMQ is their aggregated bit. So you can notice here that PMQ is higher than PCQ at all queues. So that's because we were assuming that there will be a market power and there is a market power in the system, meaning that firms usually submit their willingness to produce higher than their cost. So what energy storage does in this case basically buys in first period and sells back to the grid in the second period and it affects prices. So the price difference is the part where energy storage makes its profit. And this difference here is basically the change in production efficiency in the overall system in two periods. So in first period prices increase, but in second period price decrease more than it increase in the first period. The reason is because in electricity markets, we usually see that the aggregated bits here and mostly aggregated cost curve as well they're usually convex. Therefore, energy storage price impact in the later period is higher than effect in the first period. Therefore, consumers pay less when we introduce energy storage. Another thing you may notice here is that consumer welfare is the overall change in production efficiency doesn't really depend on the prices. It depends on how much we go down in this aggregated cost curve. So the profit of energy storage might not be indicative for the overall change in welfare. And I will argue that the overall profit of energy storage is going to be mostly higher than the overall change in production efficiency. Therefore, if you only think about the arbitrage of energy storage, at least in this simple case that we don't have an incentive to subsidize energy storage because it will make profit that is probably going to be higher than the welfare change. Anyways, okay. So next, I will introduce my model. I will talk about the electricity demand from strategies equilibrium and then a simple algorithm to find an equilibrium in this model. So in the electricity market, usually we have they had small units price, small units uniform price auction. We have age periods for the following day. And here I'm assuming that in each period, DDH, which is the electricity demand for DDH is perfectly inelastic. There's a public signal XT that everyone sees before the auction. You can think this as a weather forecast or like demand forecast. And then the actual vector of demand vector DD distributes the condition on this public signal. So everyone sees the signal and everyone has a distribution in mind about the demand vector. And there's a market process for this signal between days. So each firm K submits a supply function, SPSKB, for each of the periods. So let's say we have 24 periods. That means each firm at the beginning of the day submits 24 different supply curves for 24 different hours. And market and market clears where demand equals to supply at all periods. So there are three types of firms in this model, thermal storage and renewable. And I'm assuming that renewable generator is not strategic in its production is exogenous. So I'm basically defining this net demand is the demand that combustion power plants are computing to meet. So I'm basically here giving a priority to renewables to meet the demand. So from now on, when I say demand, you can think this is a net demand, which is basically the difference between demand and renewables. So thermal generators here, they receive an independent private signal Epsilon JD, which is conditional on XT. And the main assumption here that I'm assuming thermal generators are myopic. So they submit their bits to maximize their data profit. So when you think about different technologies, like nuclear power plant, nuclear power plants usually they don't change their production because they don't have the capacity to ramp up and ramp down right away. So they think about their future periods as well. But most of the GHS, like in California, gas for plants, they have the capacity to ramp up and ramp down very fast. So this assumption of maximizing expected daily profit is usually well adjusted and can be argued well fit into the model. So firms basically submit their bits to maximize their expected daily profit, given the signal that they see and their expectation of other firm's bits. So on that other hand, it solves an infinite horizon problem. And why this is an inferential horizon problem? It's because the energy level of energy storage is linked between days. So if you expecting high prices next day at the beginning of the day, you would want to probably charge up a lot to make sure that next day you have enough electricity in your battery or in your storage. So because of that energy storage problem is linked and here energy storage picks set of charge levels for the whole day to maximize its net present value. So this flow payoff is the revenue that energy storage makes during that day. And this continuation value depends on how much electricity that energy storage has at the end of this day and the signal of the next day. So it's with the assumption here that I'm making that energy storage's charge level at the beginning of the day is private information. Firms do not know energy storage's charge level at the beginning of the day. So given that the strategy profile signal star is the market perfect equilibrium, if thermal units is maximized in the profit, storage maximizes net present value of revenue and market clears where demand equals to supply. So solving this first part is usually a tough task because it includes supply function equilibrium which is computationally tractable and usually not unique. So to solve that, I introduce an algorithm which I'm going to represent in the picture here. So let's say we are observing this is let's say we see a signal xk which is what demand forecast or like weather forecast which gives a distribution about net demand for the whole day. Okay. After seeing this distribution, let's say energy storage, we introduce an energy storage with the strategy of sigma i. So what energy storage does, it's basically buys when the, excuse me, when price is low. So it increases demand when the price is low and decreases demand when the price is high. So since price and demand is usually highly correlated in electric markets, by smoothing price pad, it also smooths demand. So in a sense, energy storage sort of shrinks the distribution of net demand conditional on the signal xk. So the idea here is that if I find a similar net demand distribution in the data, I can use firm strategies in this case as a best response to energy storage in the previous case. Okay. So this assumption relies heavily on the variation in the net demand, which is usually, you need to have a rich data in terms of net demand distribution, which is usually the case in the markets where you have lots of renewables because renewable generation usually varies a lot and that creates lots of different net demand distributions. So next, I will talk briefly about southern Australia, which is a great market for such applications because wind generators make up almost 40% of the generation. And solar PV also introduced some variation, but wind generators are much more volatile within days, between days, between seasons. So that introduced a very high price volatility in southern Australia, which is great for energy storage applications. And there are also three firms, conventional power plants, that makes up almost 95% of the generation in this market, which is a good setting for market power examination. And also, as I said in the beginning, the largest lithium ion battery came online here in 2018, which is the horse tail power reserve that I mentioned at the beginning. So I use data on forecast and realize demand and prices, which is the case how I, this is how I constructed those signals and realize demand and prices. This is how I construct those distributions of demand. I use unit level half hourly bits. This is how I construct the empirical distribution of bidding strategies of firms conditioned on this demand distributions. And I use forecast and realizing able generation, also industry costs and emission estimates to understand the energy storage impact in terms of the overall cost and emissions in this market. So in terms of results, I have several of them. So I will first talk about the price impact of energy storage. And I will mention about how the ownership can change this impact and overall welfare impact of energy storage as well. Later, if I have time, I will talk about how energy storage changes the incumbents revenues. And then I will talk about how energy storage and renewables are interacting. So throughout this exercise, I will focus on one particular energy storage, which is the Hornsdale and the power reserve that I mentioned, which is a totally independent monopoly energy storage with 120 megawatt hour capacity, energy capacity and 30 megawatt power capacity, with an 85 run to the efficiency, which is accounted for to the 10% of net demand in south of Australia. So this is big enough to change prices and it will change prices. So to distangle energy storage price impact, I compared three different cases. And first, I follow a no price effect case where energy storage basically takes the price path and maximizes profit. And then I will introduce energy storage price impact, but I do not allow firms to pass response. Then in the last one, I basically computed Nivea equilibrium prices in which I allow for these firms respond to energy storage and fee. So here in this figure, you can see different price paths under different modeling assumptions. So this blue line is the energy level of energy storage. And the black line is the original price level before the entry of energy storage. So once energy storage enters and firms do not respond, the price path smooths out. This is the red line here. As you can see, it decreases when the high price period and increases in the low price periods. This is expected as we're expecting energy storage to smooth the price path. And firms response to energy storage basically furthers this smoothing. It's mostly because when you have energy storage as a market power mitigating factor, firms submit their bid more competitively, meaning that they submit their bids closer to their cost. Therefore, it further amplifies the price impact of energy storage. So here, I'm comparing different models in terms of the profit of energy storage and the revenue of energy storage. So here, the cost part is basically the assumption over this technology, this particular technology of Hornsdale Power Reserve. Given the assumption of this is going to last for 20 years. And this cost section here basically just division of such costs into a 20 years period. So you can play around with this, but the part that the model gives me is the revenue part. So if you're expecting prices to go down for energy storage, you can play around with this part and see how energy storage is making money or not. So in the first column, you can see energy storage takes prices as given and with no price impact and no uncertainty. In this case, energy storage makes revenue, makes profit. But then energy, when you introduce uncertainty to price uncertainty, energy storage all of a sudden lost all of its profits. So this minus means that this is conditional normal energy storage introduced to the market disregarding the cost of energy storage. So this is basically, this energy storage wouldn't enter the market. But if it enters, it will lose money. So that's what this minus 1.96 is showing. But the interesting thing is once you introduce price impact of energy storage, it loses even more, it loses much more of its revenue. It loses 50% of its revenue. So that means that for this kind of energy storage at this size, this price impact is non-trivial. And once you introduce the firm's best response to energy storage, that furthers, it decreases the revenue because the price bet is now smoother. So there is less opportunity for energy storage to make revenue. And while energy storage is making this set of revenues, it also changes consumers' welfare. And one thing that I want to show you here that consumer surplus impact of energy storage is actually higher than its cost. Meaning that energy storage smooths prices so much that the consumers are now paying less for electricity than the cost of energy storage itself. So that sort of argues that maybe consumers might want to have an energy storage in the market. So in a sense, it's sort of a utility saving energy storage in the market or different local authorities might want to have an energy storage in the setting. So in terms of ownership, I will go deeper into this question. I basically compare monopoly energy storage, low-down energy storage, which we can think about the demand side, and then perfectly competitive energy storage market, which you can think of as a mini small energy storage that operates at the same time. So here in this figure, I'm trying to show you that how different energy storage on the different ownership structures work. So the blue line here shows the monopoly energy storage, which is the energy storage that I introduced in the first part of these results. And then I changed that ownership into the low-down one, which is to say that energy storage is trying to this low-down energy storage rather than maximizing its own profit. It's trying to minimize the cost of electricity acquisition from the consumer side. So it's basically trying to decrease prices as much as it can, so that consumers pay less for the overall electricity. And the green one is the competitive one, meaning that monopoly energy storage has an incentive to underproduce because it accounts for its price impact in the electricity market. So it basically has a market power, but competitive energy storage ignores that effect. So as I said, you can think this is a mini energy storage working at the same time, arbitrage, and since they're small, they don't have market power, so they do not account for their price impact in the whole electricity market. So you can see here that monopoly energy storage blue line underproduces relative to competitive energy storage, which is expected. And low-down energy storage operates differently. It looks for high price impact periods. So it's one of smooths price as much as it can, unlike the monopoly energy storage, which want to maintain some sort of a price difference to have at least a good amount of revenue. So here in this table, I'm comparing profit of these such technologies under different partnerships and the consumer welfare impact. So monopoly energy storage is, as I said, this is the first slide. It increases consumer surplus more than its cost. But this is not designed to maximize consumer surplus. The one that designed to maximize consumer surplus, low-down one, increases consumer surplus 50% more than the monopoly one. And that difference cannot be just the market power of energy storage that underproduction incentive on energy storage, because the competitive one, as you can see here, its consumer surplus impact is closer to monopoly one. So this increasing 50%, only 10% is accounted for the market power of energy storage. So the reason why we have such underutilization of energy storage, if you're thinking about the consumer's perspective, that we have two distortion and prices, market power of monopoly energy storage, which accounts for 10% of that increase. But the other distribution, such as market power of incumbent firms, which accounts for here, or like other type of distortion in the prices, accounts for 40%, which is more than the market power concerns here. So we have an underinvestment and underutilization if you're thinking about the consumer's surplus one. But in terms of the cost one, which is, if you can think this is an overall welfare change, the cost of the overall welfare doesn't actually improve too much in all three cases. So in terms of CO2 impact, I found that energy storage actually decreases CO2 emissions for the monopoly case. It's mostly because, so there are two factors here. So two drivers. First is run through efficiency. So if energy storage when buys and sells, it loses some of the energy that it's producing. So that is basically a waste. So that increases CO2 emissions because someone needs to produce that extra amount that is going to be wasted. So that is an increase in CO2 emissions. But the other driver is the efficiency differences between marginal units. As I said, when energy storage buys, there's going to be a new generation that produces that amount. And when energy storage sells, it's going to replace some generation when the price is high. So overall, I found that CO2 emissions, CO2 emission efficiency difference between marginal units are higher here. So that energy storage actually decreases CO2 emissions. But here, none of these calculations account for the price of carbon. So if you introduce a price of carbon, that also wouldn't change things if you can go up to like $1,000 per megawatt hour. So any amount of like any reasonable, politically reasonable cost of carbon dioxide won't change the results much. But the reason why here the low-down one increases emissions is because it works more. It produces more so that it wastes more so that the CO2 emission impact of low-down energy storage is actually negative. So it increases CO2 emissions. So in the interest of time, I will skip this, but just to say that energy storage increases gas generators' production because it's going to waste energy while producing it. So someone needs to produce it. Here, natural gas generators produces it. And diesel oil generators, which are usually used to ramp up and ramp down in this setting, in this market, they lose more. But while gas generators increases their production, they actually lose revenue, mostly because the price impact of energy storage and the low-down energy has the highest revenue, the largest revenue impact on gas generators, mostly because it has the highest price impact. So lastly, I will talk about renewables and energy storage and how they impact. So in this exercise, what I did is I doubled the wind generation and doubled the solar generation in this market and introduced an energy storage afterwards to see how energy storage's impact changes, how its profit changes and how it changes the revenue of these renewable generations in the market. So in the baseline, as you can see, wind generators actually lose money and also solar PV generation lose money. It's mostly because they can't really adjust their production. So they basically, given this price smoothing behavior of energy storage, they might lose money. And there are two drivers for this impact. One is, as I said, the average price changes because once energy storage smooths prices, it actually decreases average prices. So the renewables lose money. But also, it depends on the correlation of renewable generation and prices. If renewables are highly correlated with prices, they will lose more money because energy storage basically sells when the price is high. So price is going to go down. And if your renewables production is highly correlated to the prices, you're going to lose money. And if you're negatively correlated with prices, energy storage actually will increase your revenue. And here in this case, in the baseline, we have no curtailment. But when you double the wind generation here in this market, there is a significant amount of curtailment. And energy storage actually, in that case, increases with generators revenue by decreasing that curtailment. Also, energy storage profits actually increases. It's still negative, but it increases a lot. Also, the consumer surplus impact of energy storage increases by a lot, but mostly due to this decreasing curtailment impact. Also, you can see that CO2 emissions are decreasing in more rates. And I probably forget to mention, but in all of these cases, the energy storage technology that I'm using is the same technology that I talked about at the beginning of the results section. So it's the same energy storage that has more impact or less impact given the different combination of renewable generation here. And in terms of solar, the solar penetration in the south of Australia is not much. So that the impact doesn't change much. But one thing that to mention here, solar PV generation is just correlation with prices. It's usually higher. So when solar is there, the price is usually higher compared to the wind. So that's why actually solar PV loses more money when you double solar generation in the south of the Australian market. Okay, so I want to summarize here and talk a few minutes about KAISO. So in this paper, I tried to introduce a model to quantify hypothetical energy storage impact in a whole selectors market by endogenizing the price impact. I find two market failures or like welfare improving policies from the perspective of consumers. So energy storage is basically not profitable in south of Australia. And this is one of the markets that has the highest price variation. So if energy storage is not profitable here, it's probably it's not profitable in most of the parts of the world. But it's consumer welfare improving if you have, if you want to subsidize energy storage. And there's an underutilization for energy storage. So prices are not the right incentives for efficiency. So that leads up to an ownership discussion. And I find that in independent energy storage does not really support renewables when there is no curtailment. But when there's curtailment, it supports renewables revenue and it makes more revenue itself as well. So if I have time, I want to give a couple of minutes about commands on overall energy storage and talk a little bit about a very simple exercise in KAISO. So in today's world, ancillary services seem to be the one of the main revenue stream for energy storage. So it's a good source of income. But it will evaporate rather quickly with a large storage investment because it's a smaller market compared to the energy market. So I believe that we need to have a better sense about the energy storage's revenue in the energy market by disarbitrage, unfortunately, rather than the ancillary services. And overall average cost for this type of technologies does not decrease much with the size of 5 to 10 megawatt hour. So there's not much of a decreasing cost and increasing returns to scale. But there's a still lumpiness. There might be a lumpiness problem in investments similar to the transmission expansion due to this decreasing returns and decreasing revenues in the whole selectors market. So that's the one thing also to think about. Energy storage can also provide some other products because of this replacement of fossil fuels. So like spinning reserves, which we usually take for a given, because this is a sort of a side effect of fossil fuel generators that we have in the market. So energy storage can provide some of these products as well, can be introduced to capacity to markets, which is the case in PJM, I believe. But we need to have more rules to sustain that. So if I have time, I want to just quickly go over one particular very simple exercise that I did with the Kaizo. So here in Kaizo, we have four gigabytes of pump hydro in 2020. And we have a contract that announced 2.3 gigawatt hour coming in the next couple of years. In terms of batteries, we have 250 megawatt. We hope to have close to 1 gigawatts by now, but it's due to some problems postponed. So we are hoping to have 1.5 gigawatt at least in the next couple of years. And we expect an incoming large investment in solar PV in Kaizo. Rather than wind. So, but this is sort of a concerning because we already have a large of large curtailments, wind and solar curtailments. And these are not due to supply is larger than demand. These are mostly due to transmission constraints, local distribution problems. And once we have more renewables, these numbers are going to go up and up. And without energy storage, we can't have a lot of waste renewables in the system. So here what I did is I tried to think about how much energy storage we might need if you want to sustain 100% renewables relying only on wind and solar. So I took 2020 renewable generation profiles in Kaizo, wind and solar. Here you can see in this graph the capacity factors, meaning that how much wind generators and solar generators can produce within a day given their capacity. So you can see that which generators sometimes produce less than 5% of their capacity in a whole day. So basically try to invest 10, sorry, try to invest 100 gigawatt capacity in each of these wind and solar generations, where the peak system demand in Kaizo is roughly 50 gigawatts. It could be higher with more EVs, but it's roughly 50 now. So the problem is there are some days in most of the power systems with almost no wind and solar in the whole system. So that means you're going to need a short run energy storage capacity that enough for this whole day. So in Kaizo, that is around 200 or 300 gigawatt hour storage capacity to maintain this short run balance. Without nuclear or without any type of base load generators that we might want to have with only solar and wind, we can't really maintain this without this much better storage. And on top of that, there is also differences in terms of production and capacity factors between seasons. So, unlikely in California, wind generator, wind generation and solar generation capacity factors are highly correlated. That means during the summer, we have lots of generation from both of these resources, but less in both of those generations in winter. So if you don't want to over invest, we need to have a cheap source of energy source to shift this renewable generation from this high production seasons to low production seasons. And for this, we need probably one, two, three, tell what hour of capacity of cheap energy storage could be very low efficiency. With that, thank you very much. Terrific. Oma, thank you for your presentation. Now, I would like to remind everyone that you can submit your questions through the Q&A, which is down below your screen. And I think we have a very quiet audience today. So I would encourage you to submit your questions. So let me ask kind of a non-technical question to help you to warm up the conversation. So you know, you are a PhD student at MIT, now you're a post-doc here. So what's the difference of your PhD life versus post-doc life? Of course, COVID-19 changed everything. But January, what's the difference between PhD students versus post-docs? So yeah, that's a great question that I sometimes ask myself, what's the difference, how I evolved in the last year? I think the main difference is like now, even during the PhD, you can think yourself as an independent researcher. But this is the time when you need to become an independent researcher. I think that's sort of a main part of the transition. So even though I now have Charlie, John and Erica to still talk to you, but I need to sort of keep up my research agenda myself. I need to try to... So the transition with the post-doc, it's kind of a different environment. But it's a better environment in the sense that it increases the sort of an individual... It gives you individual challenges to deal with. And I think this is helpful in the long run to become an independent researcher and produce interesting results that people can enjoy. Great, great. Now let's go to the technical side. So in one graphic you show very interesting in the end is the wind and the solar production in the state of California over the whole year. And we realize that when wind is low, solar is low. And so the question around that, how extendable of your model to long-duration like seasonal storage, because the case you presented is more on the battery, which on the sweet spot about four or six hours, like charging or discharging, that's perfect, sweet spot. But for the long-duration seasonal storage, is your model also applicable to that? What's the change? So the thing that changes in my model is basically I have an assumption of market process between days. So in a sense that energy storage needs to make decisions based on how much energy, how much the price path that I'm expecting tomorrow. So if you introduce a larger sort of a mark of chains into this model, you can achieve larger sets of decisions that it comes for like six months, three months. But I think that would be sort of a overkill in a sense that for technologies that can give you a six months or like eight months of charging time, they're probably not interested in short-run the price differences. They're probably more interested in price difference, seasonal price differences. In that sense, I think the sort of a strategic competition between the such energy storage technologies and incumbent firms are going to be more simple in the sense that such technology would probably don't have enough strategic incentives to respond very fast. So I think that my model would be sort of an overkill for that type of technologies. Great. I think some audience also like my question and they have a kind of follow-on question. I want to get some thoughts from you regarding how my market mechanism need to change to encourage long-duration energy storage to take advantage of the seasonal variations like you're presenting in the end. Yeah, that's a great question. I think that is, I mean, you can do this in different ways. Like if you have sustained price differences in seasons, you can, free market can help with that. But I think that the thing that we need most for especially for long-duration energy storage is the sense of different capacity markets or different sets of reliability payments for such technologies. Because I think we don't have, we have pump hydro. So we can take some lessons from pump hydro technologies as well. But for long-duration energy storage, I think we need to introduce more, as I said, like long-duration reliability payment type of structures, which is like the capacity systems that we have in different markets that seem to work in that way. But to define what energy storage can do in such markets, which is sort of that they have different sets of expectations for like fossil fuel generators, that is sort of a challenging part. I have actually, so I'm working on a different project not about long-run duration of energy storage, but different revenue streams for energy storage in TJM. And I'm hoping to find some answers in terms of policy implications of not just price arbitrage, but also different sets of incomes, like capacity markets, which can also help to introduce more long-run duration energy storage. Okay, we have another question coming here is regarding the, you know, how much do you think finding of the entry and the non-engine points of storage in Australia with a change, if you consider the answer to the service? Let's give you an example. Yeah, go ahead. It's right on point. Yeah, it was the main reason. It was the main reason for the Horsial Electric Power Reserve in South Australia to enter the market. So it actually supported by the local government. There was a fixed payment for that energy storage and that energy storage actually killed the FKS market, like the frequency response market, killed in the sense that it decreased the cost by 50%. So that was the part that I tried to mention about the exterior services. So energy storage introduced, especially in lithium ion batteries, they'd have a very unique feature that is different than most of the generators that actually produces this product, this frequency response product to the market. They can adjust very fast. So that makes them very competitive in such markets. And in many parts of the world, like in PGI, for instance, as well in different parts of California, most of the small-scale energy storage are used in this frequency response market. So that is the main motivation right now for such technologies entry. But as I said, in the long run, these markets are going to evaporate very fast. And then these technology will need to rely on a price arbitration energy market. Great. Let me ask the last question kind of concluded to this conversation. And you mentioned the first A41s and 2222, right? And if we look at the products at different markets, like Kaiso, you touched on that and PGM, we have a demand response products. We have a energy storage product is called differently, like California, we call the NGR, non-general provider. And how your model is applicable or extendable to handle the DER, which is different. There should be any resources, which is different, but also has a similarity to the storage. So in DER, I think it's simpler in the sense that we are expecting DER to not to be especially like the one that is in firm order 2222, we're expecting such players to be not big enough to change prices. So in a sense that it's kind of a simpler because you can play with that price. Since the price impact is not large enough, you can't really, you don't really have to think about the strategic interaction. But I think in DER, the more challenging part is how utilities are interacting and the whole selectors market and who's the owner of the DER and how the households of like maybe DER is sort of a own couple of generators from households or like the local communities, how sort of an interaction in that market is I think more challenging to model. And like my paper is mostly about the wholesale level and I can, my model can help to take some DER strategies given and then try to understand the impact of that in the whole selectors market. And in a sense that my ownership model, which I assume that perfectly competitive energy storage market can help with the understanding of how, like if you have lots of DER, how much revenue that they can make. Terrific. Thank you, Oma. Appreciate. Okay, let's conclude your presentation and the Q&A. In the end, I'd like to remind everyone that we will have the next presentation and the seminar from Katherine Wagner. As I mentioned beginning, this quarter we're going to highlight different postdoc program and the postdoc and their research work at Stanford. And the previous, today's speaker Oma and the previous speaker Nicholas are both funded by Bits and What's program. So next week, we're going to highlight a different program and a very interesting work, which is slightly different as you heard today and last week, we will discuss the models that Katherine developed to help come up with a strategy for the insurance of natural disaster. That will be very interesting, especially under the situation what happened in California and Pacific Gas Electric. With that, thank you everyone for attending today's webinar and its webinar is recorded. We'll post that to the Stanford Bits and What's website, which is energy.stanford.edu Bits and What's. Thank you. Have a good afternoon.