 Hello and good afternoon. Welcome to SmartGrid seminar co-produced by civil engineering department Stanford Bits and Watts Initiative and Tomcat Initiative. My name is Naomi. I'm the Managing Director for Bits and Watts Initiative and I will be the host for today's webinar. This quarter our seminars are futuring and focusing on highlighting Stanford post-doc and the video scholars. They bring tremendous external research experience to Stanford and they're working with our faculty and the students on different topics. Today our presenter is Dr. Jason Pom and we'll discuss the power electronic-enabled smart grid. Now let's welcome Jason's mentor Professor Wang Rivas to introduce Jason. Hi, thank you, so I'm Professor Wang Rivas. I'm an associate faculty here in Stanford and I have the pleasure to introduce Jason. We've been working with him for a couple of years now and it's been a great experience. So Jason Poon is a postdoc in my lab here in Stanford and it's also an affiliate researcher at Lawrence Berkeley National Lab. He has worked extensively in power electronics and their application for a next-generation power and energy system including renewable energy integration, naturalized energy power and electrified transportation. He received his PhD from Berkeley in 2009 and it's been a pleasure to work with him. So like with that and for that you Jason, please take it over. Well thanks Wang a lot for the introduction and I'm very excited today to talk about the work that I've had the privilege to do over the past year and a half during my postdoc here at Stanford and it's really been an incredible opportunity and towards that end I just first wanted to acknowledge a number of people who not only contributed to the work that I'll be presenting today but also we're really instrumental in supporting it. So of course, Juan Rivas, my my advisor here and also Brian Johnson at UDUB, Syraj Doppel from the University of Minnesota, Mohit Sinha from Enphase Energy and my doctoral advisor from UC Berkeley, Seth Sanders. And the funding for this work came from the Solar Energy Technology's office and we're very fortunate for their support of this work. So I wanted to start the talk today with a brief discussion about the electric grid as it currently exists and talk about some of its its fundamental properties and also importantly discuss the ways that the grid is changing and evolving with respect to our need to decarbonize our energy use in the future. And indeed, many of these changes are happening very very rapidly, particularly within the last few years. So today the grid is really designed around very inherent and unique properties of synchronous generators. So synchronous generators are essentially big things that rotate. And today they're almost all driven by fossil fuels, such as coal and natural gas. And it turns out that over the past hundred or 150 years, we have designed our electric grid to leverage very specific properties of these types of generators. And I've listed some of these properties here. So first, asynchronous AC generators have or literally are large physical rotating masses. And it turns out that the inherent inertia that comes with this rotating mass is a very important property that we leverage to maintain the stability of the electric grid. Similarly, a large rotating generator provides a very natural means of doing frequency regulation in that if the grid is drawing too much power, the frequency of this rotation will slow from its its rated speed. So some multiple of 60 Hertz in the United States. And that slowing of the machine is a very natural signal to the operator of this generator that more power needs to be introduced to this synchronous generator. Secondly, these generators can handle large surge currents beyond their nameplate rating. So typically, most synchronous generators can provide currents for very brief amounts of time at about five to seven X what their nameplate rating is. And that's really important because when faults occur on the grid, so say a short circuit fault occurs somewhere on the grid, the synchronous generators can then provide this very large amount of surge current. And there are various protection mechanisms on the grid that are carefully looking for these surges in current to either trip a circuit breaker or to activate their protection mechanism. It's really the protection mechanisms of the grid are designed around around this property of synchronous generators. And finally, reactive power support is a very important control mechanism of the electric grid today. And that's something that's enabled very easily with synchronous generators simply by changing the excitation of the rotor. So this is this is just a glimpse of how the electric grid is designed today. But of course, of course, as we know, there are things that are changing. And what I list here are two societal skill mega trends that I believe are transforming the grid. And of course, there are there are many others. But two of the big ones today are this very large scale integration of renewable energy. So represented here as solar panels, but of course, there's many other types of renewable energy that's also being integrated with the grid. And also vehicle electrification. So the fact that in the very near future, we'll have to augment the capabilities of the grid to charge this completely new type of load that was historically provided by by gasoline by completely different form of energy now needs to be supplied, generated and transmitted through the electric grid. And of course, these these trends are in an effort to decarbonize our energy usage, and hopefully eliminate our dependence on these these synchronous generators that are driven by fossil fuels. So that's hopefully where we can get our grid to be one day, hopefully one day soon. But it also raises some potential issues in that, as I just mentioned, the electric grid as we designed it today was really tailored, you know, and optimized for these very unique properties of synchronous generators. And unlike unlike synchronous generators, these new types of energy sources and loads do not utilize rotating electromechanical systems to interface with the electric grid. But they now rely on power electronics. So these loads are typically, so I should mention that typically solar panels are assembled into arrays of about 600 to 1000 volts DC. So of course, we need a mechanism by which we can interface that DC voltage with the three phase AC grid. And similarly, electric vehicles are essentially big batteries that that are typically, I believe, like 400 to 800 volts, also DC. So of course, we need some other power conversion device that can interface it with the grid. So these power electronics are quite unique in and of themselves, because unlike synchronous generators, they do not have rotating mass. And they also cannot handle large, very large surge currents. So typically, power converter can only be pushed to about 2x of its rated current before something bad happens. And similarly, again, there's nothing rotating. So there's no concept of a rotor that can be excited to provide reactive power. So these are fundamentally different devices than synchronous generators. So in the recent years, and by recent, I mean, maybe in the past 10 or 20 years, many researchers have been posing this question. We've designed our grid around synchronous generators. How can we operate or transition to this future grid that is designed around power electronics? And a term that some people use or many people use to refer to this field of research is a so-called grid forming inverter. So the idea that the inverters themselves will now, so similar to how the synchronous generators formed the previous generation of the electric grid, these inverters will form the foundation of the future electric grid. And I'm showing here a very recent report from NREL and many other institutions came together to propose this research roadmap that brought up many of the exciting challenges and open questions and research opportunities in this space because it's a very important topic and also very timely. So towards that end, a first thought one may have in that how can we design grids around inverters will be design them or have them perfectly emulate what a synchronous generator would do. So power electronics are completely controllable by digital control. So why not just emulate exactly what the synchronous generator does? Since our grid is already designed to work with synchronous generators. And I personally believe that this may be a misguided perspective in that, as I mentioned, inverters are very fundamentally different from synchronous generators. So it may not make sense to ask the inverter to do something that was actually designed for that something else was actually better at doing. So from that perspective, it may be better to take advantage of the power electronics for what they're good at. And secondly, the electric grid, as I mentioned, was designed around these properties of synchronous generators. But there's nothing really inherent about why that is the case. So in fact, if we had the opportunity to design, you know, say new operation operating principles for grid designed around power electronics, it could potentially look completely different than how the grid conventionally worked when it was relying on synchronous generators. So a question that my research addresses and that many other researchers address as well, and in fact, many of these same questions were brought up in the research roadmap on grid forming inverters, is thinking about how can we go beyond simply emulating synchronous generators and what's come before, and perhaps what are some new functionalities that inverters or grid forming inverters specifically can uniquely provide that weren't possible with synchronous generators. And more importantly, how will the electric grid benefit and potentially change from these new functionalities that can be provided by grid forming inverters? And a second question that I think is very important and I think many other people think is important as well, is asking how we can practically implement these new functionalities in a way to enable mass adoption and impact. So we all really care about decarbonization and we hope that it will get here as fast as possible. So it's really important that whatever we develop has a really feasible means of being implemented on a wide scale. And for renewable energy systems broadly, that really often comes down to cost. So I think that's an important consideration that we should ask as well. So I've divided my presentation today to addressing both of these questions or at least presenting some of our work that has posed some small answers to both of these questions. And with that, so we'll start with thinking about at least one new functionality that grid forming inverters can provide that weren't possible with synchronous generators. And again, so this is just one example from our work, but and there's many other possible functionalities that could be provided. But at least in our work, one aspect of this problem that we thought could be interesting is looking at what are called harmonic or harmonic distortion. And the reason we thought this was interesting was that because when more and more inverters are introduced to a particular network, they can introduce these undesired harmonics that can detrimentally affect the operation of the electric grid. So conventionally, what I'm showing on the bottom are kind of the historical linear three phase loads that were mostly passive and were relatively easy to control. Whereas power electronics rely on high frequency, nonlinear switching, which can severely distort the voltage that you see on on the grid. So what I'm showing here is essentially highlighting all the power converters. And if we were to look at, say, the aggregate current from all of these devices, instead of seeing the perfectly sinusoidal 60 Hertz wave form that we want to see, we can see this red wave form that has these undesired artifacts on top of it. And there's a way that people quantify it with this metric called total harmonic distortion or THD. So when a waveform has zero percent THD, it's perfectly sinusoidal. It's just the fundamental that we want. But as this THD increases, then we start seeing some of these high frequency artifacts that are undesired and they're undesired for a couple of reasons. One reason is that these harmonics actually impact the efficiency of of the overall grid. So these harmonics impose losses in the wiring and transformers in the power electronics themselves. So there's an efficiency component to why we don't want harmonics. But also, more importantly, there's also research that has shown that high distortion in networks can directly cause grid instabilities and outages. So this is a relatively old paper from 2004 where some researchers were trying to characterize the impact of of higher amounts of THD in these very solar dominated types of systems. This one's particularly in the Netherlands. So on the bottom, you can see what happens as they slowly start to increase the THD. And even even at 3 percent, we see that the current that is being injected by all of these solar inverters and all of these other devices starts to have these undesired artifacts that we can see here. And at 8 percent THD, we actually totally lose track of the fundamental component. And essentially, at this point, the inverters tripped. So the network became unstable and there was possibly an outage. So there's very real consequences for higher amounts of THD. And towards that end, there are grid codes that dictate the maximum allowable distortion that that the utility will tolerate. And a commonly used specification these days is IEEE 519. So the latest revision was from 2014. And as you can see, for these low voltage networks, the below 1000 volts, the maximum allowable THD is 8 percent, which is already quite interesting in that we saw in the previous slide that 8 percent THD can already cause some of these stability issues that are greatly undesired. And at higher transmission level, voltages 161 kV and above, the allowable THD is even lower at 1.5 percent. So OK, let's look at a simulation that we've done to essentially characterize how the number of inverters on a typical network or on a candidate network influence the resulting THD that is measured. And what we can see here on the plot is quite something that we would expect. So as we increase the number of inverters on our network, the THD has this monotonically increasing value. So more and more inverters implies more distortion. And in fact, if we plot this line, this 8 percent limit that's established by IEEE 519, then in a certain point, so for this particular simulation, when we try to integrate 40 solar inverters, then we're no longer able to meet this limit. So it constrains the size of how big these networks can be. So how is this problem addressed today? So one thing that people do is utilize a device that's called an active power filter, and this device is essentially added in shunt to these large networks of harmonic producing devices. And as you can see here, what it does is it essentially looks at the difference between this squiggly red line, this undesired, this very noisy current that we're trying to get rid of, and it injects the perfect anti-harmonics that will eliminate those undesired components, such that when you add together this red line and the blue line, sorry, the red line and the purple line, you get the blue line, which is a perfectly sinusoidal 60 Hertz waveform without any distortion. So from the perspective of the grid, everything is perfectly fine. The issue with this is that active power filters are relatively costly. So I'm showing here an example of a low voltage harmonic filter, active power, active power filter from Schneider Electric. And we can see that the hardware cost of this device is already well over a hundred thousand dollars. And that's just the hardware cost. There's also the cost of installing this, the cost of maintaining it, and the fact that this introduces another reliability failure point in the system. So solutions like these aren't free. And I think this can have a particularly detrimental impact for renewable energy systems where cost is such an important consideration. However, it does work. So if we add in this active power filter to our simulation here. So the gray, the gray bars were with the previous simulation without the introduction of this active power filter. But now with the active power filter, we see in this red bars that the distortion has been reduced quite significantly. And in fact, it's reduced to the point where we don't cross this 8 percent limit until about 80 or so inverters. So we've effectively doubled the amount of solar that we can integrate into this example network with the introduction of this active power filter. OK, so where am I going with all of this? So a question that we asked, and again, we were asking about functionalities that grid forming inverters can provide that weren't possible with the conventional technologies. So we asked ourselves could. Inverters themselves somehow filter their own harmonic content without and eliminate the need for an active power filter. So and maybe not necessarily a single inverter, but in aggregate, if we could somehow collectively control all of these inverters in some intelligent way, could we eliminate the need for this very costly device? So in order to look at the solution that we came to, it's first important to understand where this distortion is coming from. So if we look at the output of a single inverter, we can see that it's essentially a composition of the 60 Hertz fundamental. So this is the precise way form that we want to get out of our inverter. And superimposed onto this 60 Hertz fundamental is what we can call a switching frequency ripple. So this is the undesired component that we're trying to get rid of. And it essentially comes from the switching dynamics or the mechanism that the power converter uses to control and condition the electricity that flows through it. So it's actually this switching frequency, high frequency ripple that we're trying to target and eliminate. So what happens when we put many of these inverters together is that all of this high frequency switching ripple sum up from multiple inverters and in the aggregate, they produce this high THD waveform that is then observed by the grid. So that's really the source of where this undesired distortion is coming from. So the idea that we had was to leverage or to look at what types of control mechanisms can we leverage with these inverters? And it turns out that inverters in generally, so not just grid forming inverters, offer us this control input where we can precisely control the phase shifts of these high frequency components with respect to one another. So typically this is a control input that is typically unused or it's not used in conventional systems, but we asked, is there a way that we could leverage this control of the phase shift to mitigate some of these high frequency harmonics? So our idea at this point is actually quite obvious. So we just have to pick the optimal phase shifting of these various waveforms in such a way that when we sum them all up over an entire period, it's as close to zero as possible. So that's what you can see in this cartoon here where now if we pick the phase shifts of these various waveforms in this particular way, we can actually dramatically reduce the magnitude of the distortion in the aggregate waveform. And there's a number of very interesting details that went into this work. So we formulate it as an optimization problem and there's different cost functions that we can explore. And importantly, it's one thing that I do want to mention and we'll get into a little bit later is the fact that we could formulate this as a decentralized optimization problem. And that's quite important and something that I'll touch on in a couple of slides. So going back to our picture, let's evaluate how would this technique compare to the conventional way of doing things? So again, here we're looking at the THD from our simulated network when we don't use the active power filter and also when we are using the active power filter. And when we use this algorithm to control the phase shift across these multiple inverters, we get what you can see here in blue. So we can really achieve a dramatic reduction in the distortion even compared to the case of using an active power filter. So to forex reduction in the THD and even higher when we compare to the case without the active power filter where the phase shift was not being controlled at all across these inverters. And what's very promising about this method is that even at very high numbers of inverters, we are still below this 8% limit that's set by IEEE 519. So by using this method, the size of our system will no longer be constrained by the harmonics. There'll be other constraints possibly, but at least we've checked off this one box, this one thing that we no longer have to worry about in the distortion. So to evaluate this method, we built a small-scale experimental setup that you can see here. That consists of three custom designed inverters. So on the right, you can see the stack of red board. So the red board is an inverter. And you can see that each inverter has its own controller. So each controller is doing this optimization problem to find this optimal phase shift. And what's very unique about this is that we're not relying on some type of centralized coordinator that would require communication or variables from all of these inverters. And then from a top down, send variables to each inverter. We're actually doing it from the bottom up, so to speak, where the inverters themselves only need to measure their local voltages and currents. And just from that information we can make the appropriate decision as to what the optimal phase shift should be. So here are some measurements from our experimental setup. And they match what our expectations are. So we're measuring here the grid voltage or the voltage at the point of common coupling. And we can see on the left that without this coordination, our THD is about 8.7%. And when we turn on our algorithm, that the THD is reduced substantially to now 2.2%. Secondly, the other important thing that we wanted to evaluate, and I alluded to this in the beginning where I talked about some of these instabilities that can emerge in these high harmonic content networks is evaluating whether this method could eliminate these instabilities that emerge from harmonics. So on the left, we were able to recreate these types of instabilities that occur when harmonics are higher. And so you can see that the current waveform is, or I grid, is very chaotic. And in fact, in a normal system, this probably would have tripped some type of protection mechanism in the system. Whereas on the right, what's happening is for the first half of this picture, our algorithm is off. And then we turn on the algorithm, it reduces the THD to 1.3%. And we see very quickly that the current comes back to a very stable and safe operating state. So to wrap up this section of the talk, this first part of the talk, what we showed was simply one example of a functionality that grid-forming inverters could possibly provide. And that functionality was this autonomous minimization of distortion. And in terms of how the electric grid will benefit, there's a number of ways. So firstly, there's lower system cost in that there's no longer a need for active power filters or these other mechanisms for filtering harmonics. And this can be done essentially for free by the inverters. Secondly, it improves the power quality. And we, as I mentioned, we have important consequences for the efficiency of the system, among other considerations. And finally, we showed that it can enhance the stability and resiliency of the network. So we show that by mitigating these instabilities that emerged from these high harmonic content systems. Okay, so that concludes the first part of my talk. I'll answer questions at the end. I see there's a few questions. I'll come back to the questions at the end. I see there's a few great questions. Okay. So for the second part of my talk, something that I feel is very important and could often or is often somewhat overlooked in research and different things that are presented is how we can practically implement some of these functionalities. And by functionalities in particular, I mean algorithms and optimization techniques similar or exactly like the functionality that I just presented and ensuring that we can implement these techniques in cost-effective and very practical ways. So where do I think an issue emerges? Well, there's what I can call... So there are hidden costs that are associated with increasing the complexity of these grid-forming inverters. And specifically when we talk about more complicated optimization techniques or algorithms that are going to be required to add this extra intelligence to the inverters, there's oftentimes an increased complexity associated with the underlying digital microcontroller or control platform that's used to implement this control technique. So what I'm showing here is a recent study from these researchers from UMass Amherst. And what they were showing was... or what they looked to evaluate in this particular work was looking at a number of different algorithms. So in this case, these are machine learning and AI type algorithms. And they wanted to quantify how much power is actually used in order to train and implement these types of techniques. And their results were actually quite astounding in that even the simplest algorithm they evaluate requires hundreds of watts to implement. And some of the most complicated ones can require tens of kilowatts. So this is the hidden cost that I'm talking about when people talk about implementing new algorithms based on ML and AI and optimization that there could potentially be this hidden cost that is very... or has a substantial impact. So say your solar inverter is only producing 10,000 watts of power, then it may not make sense to use an algorithm that requires 1,000 watts. In fact, it completely wouldn't make sense. So in order to look at that or in order to address this issue, we first looked at where is all of this energy being used? What's consuming all of this energy for these algorithms? And in essence, they're implemented in these digital control systems. And by digital control systems, I mean microcontrollers, CPUs, GPUs, so on and so forth. And the reason we use these platforms is because they're incredibly programmable and they're very accurate. But as I just alluded to, there's this fundamental trade-off that exists between how much energy this particular platform will consume and also how fast we can obtain an optimal solution. And this aspect of speed is actually really important for these real-time applications in that this is something that's running with a physical, say, solar inverter. So the need for online solutions is actually very important. So as was discussed, there's this fundamental limit between how much power will be consumed by this computing platform and how fast an optimal solution can be obtained. So of course, digital controllers weren't always the way that these types of problems were addressed. I mean, today they're almost universally the way that the problems are implemented, but computing actually started out by these so-called analog controllers or analog computers. So unlike digital systems that utilize processors to compute solutions, analog controllers rely on physical principles such as circuit laws or energy principles in order to compute solutions to mathematical problems. And as I mentioned, the earliest computers were actually analog. So what I'm showing here is a picture of Professor Vannevar Bush from MIT and his famous differential analyzer. It's essentially a big network of gears and pulleys and axels that he could configure in such a way that when you hit run, it will give you the answer to a differential equation. So the reason why analog controllers for these types of problems have fallen out of favor is because they're not very programmable in that if Professor Bush wants to change the differential equation he's solving, may take him a day or a week to reconfigure this entire machine that you see here. So compare that to what you can do on a digital computer today. And also analog controllers are not very accurate in that so even if we consider, say, an analog electronic computer, resistors and capacitors have tolerances and those tolerances will impact the solution that your analog computer will give you. However, it turns out that in terms of speed and energy consumption, there's been recent work that's shown that for a certain class of problems, these types of analog controllers can actually vastly outperform their digital counterparts. So we looked at this picture and we were really curious, we were wondering, can we do like a Goldilocks type thing, combine the best of both worlds and combine a little bit of digital, a little bit of analog and somehow get an overall solution that is programmable, accurate, high speed and also doesn't consume too much energy. So what we developed was what we call PAC or a programmable analog computer for grid forming inverters. And in the bottom left, you can see our prototype of this PAC computer and that's, so it's a US penny for scale there. So it's relatively small, not like Professor Bush's one that used an entire room. And in the right, you can see a system diagram of what the PAC is. So the details of what's here isn't really important. What is important is the fact that we've divided this computer into an analog stage and into a digital stage. So again, we're trying to leverage the best of both worlds and then ultimately trying to obtain something that can transcend this existing barrier that has somewhat constrained the existing implementations based on microcontrollers and come to a computing platform that is faster and more energy efficient than what exists. So in order to benchmark what we developed, we used this particular optimization algorithm. And again, this was just one example that we used to compare our computer to the existing techniques. So again, on this slide, the details of this particular optimization problem aren't important, but you can see on the left that there's a particular cost function that needs to be minimized. And then there's these variables, alpha one, alpha two, alpha three that are going to be determined by the optimization problem or will be determined by the minimization of this cost function. And on the right is just an example of what people have been able to do with conventional digital microcontrollers. So in the table, what we can see is that, okay, so what these people are doing is essentially taking this cost function and putting it into MATLAB and using essentially the solvers that MATLAB provides for these types of problems. And we see even with those types of computers, it takes up to 1,000 seconds just to reach or to obtain a solution to this optimization problem. So of course, if we want to run this in real time, it wouldn't be possible to run this type of algorithm in real time. So what they do is they compute them offline. Maybe they run their computer overnight. And then what they do is they just collect all of these optimal values for various conditions and then they put it into a lookup table and then that's actually what they refer to in real time. So in a way, it's a very static, it's not very responsive, it can't respond dynamically to changing conditions, so on and so forth. So we applied the PAC to the same problem and we obtained the results that you can see on this slide here. So on the top right, what we're looking at are voltages on this PAC circuit that represent the variables in this optimization problem. So you can see is on the left, we started all the variables start at zero volts and then we turn on this computer and then the voltages vary for a little bit and then after about five milliseconds, they reach this steady state value. And it turns out that these are actually the solutions to the optimization problem that's encoded on this platform. And in the bottom right, essentially, what we're doing is we're taking these optimal values that are computed by the PAC and then using that to generate or to control the solar inverter. So on the top in the time domain, you can see that this sinusoidal or approximately sinusoidal waveform that's being generated by the inverter. And then in the frequency domain, what we're doing is we're just evaluating whether or not the optimal values that were produced by the computer actually meet or satisfy what we were encoding in the optimization problem. And in fact, it is indeed doing that. So what we can say is that the PAC one demonstrates a very significant speed improvement compared to the existing works. So unlike the previous solutions that required a thousand seconds to obtain a solution, using MATLAB on a desktop computer, we can obtain the same solution in just five milliseconds. And similarly, there's a substantial reduction in the amount of energy that's required in that we're not using a desktop computer or actually only just expending energy during this transition period. And in fact, in steady state, the amount of energy that's consumed by the circuit is vanishingly smaller, in fact. So at least for this particular benchmark algorithm that we've shown, this is, to the best of our knowledge, the first time that something like this has been shown to be implemented in real time. And of course, we're allowed to do this in real time given that we're able to obtain solutions to these types of problems in the order of a few milliseconds. So okay, that was a very brief aspect of how we could practically implement some of these increasingly advanced algorithms and techniques that people are proposing. And specifically what I showed was a hybrid analog digital processor that substantially outperforms conventional digital control platforms in terms of both speed and energy efficiency. And we think this is very promising, particularly for very advanced grid-forming algorithms and controllers, specifically to run locally or at the edge of the grid. And we think this has important benefits compared to centralized scenarios where, say, you may need an inverter to sending data back to some cloud computer and having this cloud computer or server computing your optimization problem. But with this PAC architecture, we're able to practically implement these algorithms exactly where the inverter is in a cheap and low-cost way. And I think that has tremendous benefits with respect to cybersecurity, with respect to responsiveness and performance, and also cost in that we don't need to send data back to this centralized system in order to compute or to run these optimizations and algorithms. Okay, so that concludes. So that's actually all that I have. So in this talk, I tried to address at least some of the work that I've been involved with where we try to look at answers to these questions in terms of what are some of the new functionalities that grid-forming inverters can provide that weren't possible with synchronous generators. And I showed this somewhat complicated optimization routine that could enable inverters to autonomously minimize distortion within their networks. And then in the second part of my talk, I presented a platform that can implement and solve these types of complicated optimization routines and possibly ML and AI type algorithms in a way that's significantly faster and more energy efficient than what's possible with digital control platforms. So with that, I will conclude my talk and... Thank you, Jason. Appreciate it. I think we have about 10 minutes left. We already cured a lot of questions on the Q&A. So what I'm going to do is to combine these questions probably I will only have time to ask you about two technical questions. Then I also would really love to ask you one non-technical question. So let me start with a technical question, relatively simple one. So if you can go back to slide number 14 or 17, that shows the relationship between the THD and also the number of inverters. And the question is, what kind of PV inverters are we talking about? There's a great forming or great following inverters and why does the great voltage THD increase with the number of the solar inverter increase? Then also another audience want to understand a little bit more in terms of the simulation environment you do here. What type of network you generate is graphic and how large of the network because if we talk about large network, you may talk about high inertia, right? And also what percent have the load of the network that this inverter are serving? So that's the first set of questions, regarding your slide number 14 and 17. Okay, that's a fantastic set of questions. Okay, so at a high level, the purpose of the simulation was just to illustrate the idea that increasing the number of inverters has a monotonic impact or will monotonically increase the amount of distortion on the network. And in fact, whether or not the inverter is grid following or grid forming would not impact this plot at all in that as I mentioned in one of my slides, the phase angle conventionally is something that's not being controlled. So regardless of whether this thing is, regardless of whether it's utilizing a grid forming or grid following controller is irrelevant. But I think the important thing that I wanted to get away from this slide was does this monotonic approximately linear relationship between the number of inverters on a network and the amount of distortion. So a few more details about how it was implemented. So this wasn't implemented using any type of like IEEE network or that sort of thing. This was really purely looking at the impact of just the converters themselves. So it was in that sense a little bit idealized. So some of the topologies of certain grids were not considered. But that's certainly something that would be interesting to explore in terms of how different network configurations would influence what the shape of this curve would look like. Great. The second question is really about your synchronized algorithm you discussed here. So the question is, I think it's from one of your collaborators. Most of the grid connected converters don't have a synchronized switching functionality since they are independent of each other. They are switching cycle phases that generate random and the drifting around. How do randomness phase shifting compared to this optimized one? Basically what's the benefit of the optimized versus the randomness of the phase shifting? Sure, yes. So actually that randomness was encoded already into what you can see here in this plot. So that randomness was encoded as these bars in terms of a percentile probability that given a particular phase shifting angle across these multiple inverters, what would the resulting THD be? So in fact one of the slides that I showed, perhaps this slide may have been a little bit misleading in that so conventionally it is not the case that the inverter waveforms are locked on or at least the carrier waveforms are locked on to each other in this way such that they're perfectly in phase and of course that would maximize say the constructive interference among these multiple waveforms. So this is not illustrative of what was generally done in the previous simulation but more just to give intuition for this smaller example with just three waveforms. But that's a great point. So to follow on that, the question from another audience asked about do the grid of forming inverters need to be physically close to each other to allow the phase shifting optimization to work? I'm trying to think about that question. Basically let me ask another way. What kind of communication requirements to implement your algorithm, your phase shifting optimization algorithm? So again in terms of communication requirements at least what we've implemented so far does not require communication. So in terms of distance required for communication there would be no impact at least with respect to the need for communication. However the distance could actually very interestingly impact how the harmonics propagate through a particular network. So of course if inverters are farther apart there will be network impedances between multiple inverters. And that's actually a very interesting question because then at that point the question is really where are you trying to minimize the harmonics? So if I go to... Okay this may be a bit of a tangent but actually so for something like IEEE 519 the standard for distortion only applies at the point of common coupling. So IEEE 519 only cares about the THD where you're connecting to the grid. So anything you're doing internally at your network it doesn't care about. There may be other consequences in terms of what I showed with respect to stability and efficiency losses but at least with respect to meeting the standard you can still meet the standard without meeting it at every single node within your network. So that's an interesting question. I don't know if I answered it but I think looking at various network configurations various distances between inverters different network impedances these are all interesting questions that are not answered at this point. No worry I think there's still a lot of questions coming. I would say for folks a lot of questions we have not answered today but feel free to contact Jason and his information can be easily found at Stanford site and I'd like to ask a last question which is non-technical question basically I think when we introduced you mentioned that you are sponsored by solar office of Department of Energy but you're doing your PhD or you're doing your post-op program here how did that happen? How did you land at Stanford? That's a great question and so as I mentioned I'm very fortunate to be supported by the Solar Energy Technologies Office and the specific award that is funding my research is the EERE postdoctoral award so EERE is a department or as a agency within the Department of Energy and while I was in the final year of my PhD at Berkeley they had this EERE postdoctoral award essentially the idea is you propose a particular idea that you want to work on and you also propose an institution and a person at that institution that you want to work with so in addition to the so-called core research project you also ask you to develop a type of innovation project as well so a side project that's not related to your core research but can somehow extend your research beyond the lab whether that's some type of entrepreneurial activity or some type of teaching activity or something like that so I was very fortunate to be supported by this award and I think over the past year and a half coming up on two years now it's given me a tremendous amount of opportunity to look into these research questions that I find really interesting and I think it's a fantastic opportunity and again as I said I'm really grateful for their support and look forward to continuing this research direction going forward Thank you Jason, appreciate and thank you for all the audience online and appreciate for your attendance and just a quick reminder next week, next Thursday we will have another topic the role of reversible power to guess will be delivered by a Viennian scholar at Stanford campus we thank you all and good afternoon