Hi guys, happy Wednesday. I hope your day so far is coming along well. Asu in studio, our day is fantastic and we are back again with another video. My name is Ndanya, the gracious host. And I'm the media girl, this Jackson. And today, a few things have been happening, right? We start with Jabidi. Jabidi is a gospel artist mone. Amang the few gospel artists mone wali, nzakita mone bado mkwa mkwa gospel industry. Many of them wali rukuko kwa secular. And yesterday, I was covering a gospel event and I asked him, why do you think most gospel artists wali rukayo say they are secular? And then, monejua, speaking of years to rea wa sewa wali sewanyel to kapia gospel. One thing mone wali mkwa mkwa, gospel nni talent. The only reason wali rukayo to kapia gospel. First of all, sejuia tia pesa manini. Wali to kapia gospel kwa zawazi meintenio creativity na ita jika kuskuma yo gospel. And then secular pia secular wali kuja, like one isa imba anything. So akuna talent pale, but one isa imba anything. Natukaba kitu na glorify yo. Matili tia imbenu lukwansiki, gospel nni gospel luki tiki from attack. For example, tumasi mmasika. Unasiki yanga vocals, zaki wana jwa mazezi. Unimsa nitu na mwaika, wuko inchena to represent. And he said, for you to become a gospel artist, to keep your momentum ya gospel artist, you have to be very creative. Kus apparently secular music, you can just sing anything. Tu nonga, utu hanga pwa na mkwana ni sing. Ka zawze, ka zawze. Pani moja nika bebe, ka zawze. Uni bebe atambe rea kirindi. Miya mafanu fukambe rea kirindi. Ya tu si so many people just wake up and sing nonsense, but for you to become a gospel artist, people you have to be creative. Ya, like her vocals, how she puts her music. Jabidis daon who sings in Chinese. What are you saying? What are you saying? Kufu, kufu, kufu, kufu. Hei ni creative, nika na kamesi. Chara, nika mo skiza ni na jabidi kwa ni. Ya, sija saiba ibo, but nili ketichi ni nika skiza yo goma ya Chinese. Mi na fano jabidi by the way. Na kumkakwanza bili ya li toa, goma ya kia kwanza ya kanot remember, ali kwa nga na shufu na ni na so easy to li kwa na fanya. I was so obsessed with jabidi. Anafu aka leta odi dance, wa kiwa na timeless. Eh, tukasu. Tukasu mua. So I feel jabidi ya bidi ya mkwa consistent, na ni na make sense. I feel if you're really not passionate about gospel music kawizi toboa kusapo, you need to put your thoughts, you need to put your creativity into mind, kus you can not just sing nonsense. Our boy is a harambestaz, beat katar last week en jana kule kwa na match, ya south Sudan and harambestaz. And to ligongwa, we were really hit. And Kenyans were disappointed, doa toa li kwa gloomy, na kumu sandra, mutu toa so kwanza ito, sandra. Ya, she was very down kwa she was rooting for the Kenyan team. Poizori? Ya, it was fun. Ya, but I'm disappointed. Like guys, you could do better next time, like you know, but I mean practice makes it perfect, right? Yes. I feel, labda jyu tulishinda jyu a katar, kule kwa na yo kiburi. Ara mimi kwa na kiburi, I was like to na cha pa o south Sudan. But coach anasema, the Kenyan team mimi kwa ikifes a lot of challenges, that's harambestaz. There's always delays, kama ni visas are players. So ya na feel, if the nation ingekwe na support harambestaz more, wange kwa so motivated, na wange kwa wame up their game. So these things are not so simple, how everybody see it. Or let's go on with Kasarian annex. You know what is going on every time we've made a national team. There is a so interesting system. The ministry is paying these people in annex, so the government is paying the government, so that we can train. Sayi. Well, okule, I agree, but I also feel like kwa kila mabaya kuna wuzuri kidogo. Ya. I feel like what I loved most about yesterday's game is how Kenyans went support harambestaz. Ya ni. Ta kama ni sawa alifaja mabaya wapo, we were not happy, but still. Ya. This is always next time. Ya, you also so root o alifanya video kuwachi. Ya, I think that was really good. Like the spirit of Kenyans and coming like together, ok, football brings Kenyans together, but most of the time na kwa nga sort of tribal. Uta pata harambestaz, iya blue netwa sofa paka. Ya. Ya. Ina kwa nga like kuko western like the really rally about football, but na feel it's time sisi wakenya water like to wange united. Ok, we are united by athletes na wakin busy. What? Na wakin busy. What are you saying? What is he saying? Marathonas, it's also time for us to give space to other sports. Ya. I agree. Kama wana joti miaboli bolia kenya. Exactly. So I feel we need to be like that in all the games. I agree. On to other news, iPhone 15 in the talk. Ya wangi. Sisi wangi, tu badawa tata jefika 14, 15 pressure. Do you think it's necessary or pressure? Personally, I really don't know the difference between iPhone 13, 14 and 15. The only thing I know about iPhone 15 is that now you can charge it with that type C. With that type C. Ya, but I feel, ok, ni miwa na kualiti ya video ya hi, na mine is at 12, na 14, 14 is way much later. Oh, ya, for sure. But now I want to know what's the difference between 14 and 15 apart from the charging port? Ebu, tell us in the comment section. Ya. And someone told me zita kwa wuku by October and we show October November zita kwa zimefika kenya. So hopefully, tokwa na tunes, tununu ya lafutu wa perreview. Ya. Tosa ebu lemi ask. Tona utapa 15 uskera 15. Tell us things. Minda mai 20 ki tokwa. For now, Oh Lord. So on to the next story. Andrew Kibbe who is a Kenyan U.S. based content creator lost his channel. It was terminated on YouTube and there are some content creators who are celebrating and he is very controversial and he talks about controversial things. But also his supporters who are rallying him up or can go and address the nation, which he did address the nation live. He created another channel and he also, he is normally live on YouTube, Facebook and Instagram. Ya. Aka se ma, he feels like his channel was terminated because of some of the Kenyans because most people who consume his content ataka ma kwa U.S. ni Kenyans. Ya. So he was saying that Kenyans wa lemi report ika kwa terminated. But now he has also formed his own platform in Atuaia, Africa, which basically to him means it is his app where he can set the rules and no one has to put regulations on his opinion and what he has to say. Na kuna wasani wali anza kum no ni ni. No kumuka no ni ni and I show U.S. So far so good what Tim Kibbe wa me sign up wa me sign up wa me sign up. But for me, I feel easy apps is here too. Muslim is our Zungu and of course sometimes you just have to bow down to come at TikTok ni ya it's not an American it's a Niger tweets from country from Asia. Most of the time we tapata like CC Africans when we are using this app kuna viletu. Kidogo we are slightly disadvantaged but now that does not mean he goes on his platform and he talks the way he wants but what's your view general view on that? Ya You know what Kibbe unongi ya na kutani wa ni uko maybe I wish I wish him well in his career Sina man eno mingi ya Kibbe Whatever works for you bro you do it. Now guys Akiko Stoxic relationships now this 20-year-old who apparently had a disagreement na the boyfriend and the boyfriend decided 20-year-old Ako hosisai Ako nama dance everywhere now the story is this guy is from this boy is from our family so he is telling me kwa kut now he is telling the girl to withdraw the case from kut so that can help him can help her pay the bill does it make sense? He wunim tume kwanza e kuchoma na wali explain wili wali wali kwa melalakam pa no they said apparently wali kwa lianda tukuburugana kwa nyuomba and then a kuchoma jima o to end kai a kumchoma okay now kwanza 20-years no auto-elebrant boyfriend a kwa kwanza 20-years and then the amount of dame jima fanya kwa usuia kwa ujui kama kuna structures dita badili kama forever to yama I can imagine my little brother lichoma kwa mugu nana kwa nga na yoma kno ebu picture usuia imagine usuia usuia maybe she is her her modeling career her modeling career maybe she was meant to join media maybe any usuia wechome kwa kaban pure self esteem pure self esteem like it's so wrong in so many ways me keep telling people you see that first red flag ignore that second one it will cost you what if red is my favorite color? make me think of your favorite color I can be cool it's not worth it it's not worth it we wish her quick recovery and I hope the boy and the boy's family because obviously I feel like for him to say that there may be orders from above labla parents wake wali mwambia okay this is the ultimate and if you want us to help ya ya ya ya definitely so I feel for the party especially the male ones kindly kindly kindly it's only human if you assist her without kumpatia altimedia on to our last story so muheshimiwa Jalango was actually in the papers which newspaper was it? was it Citizen Daily? ya Citizen Daily ya attaching him to a scandal iluka scandal ya ya fraud ya ya fraud and he called out citizen akasema that was bad that it is not good to actually taint his image and today in the morning I may address the issue akisema how wrong it was for them especially for someone who is in politics any article written about you will definitely affect you suika ma, unha kumbuka nini kuli kwan kanda scandal ingi ne kAST ni misa siangululi kumbukili ko iிn etoadze like any political person unha menyana patikana kwa scandal unha jokun onto ka fanyangi research unha jokun onto say and I believe ya ya ya ya ya ya ukue unha jokun onto waki skaitukitu anami no anami Ya. They don't care how much bloggers especially. Ya. Kusili ya. Example. Ja kama inventi wa kwa ni fumakimu yun. Kwa buni kata mahi mahi kaka kuna kuma mhmati. Ya. Asa amini. Ya. So I feel like you out there, if you're in a position like CC, where media personality is, if you are a writer, presenter, newscaster, nini, please, please, please, before you write an article about someone or before you make a statement about someone, just verify it and make sure at least it is true, because you do not know the amount of damage unafanyamse si poa. True, I agree, I agree. You wanna close the show? Alright, so guys, that was it from me, media girl Liz Jackson and my name is Ndanya, the gracious host. So we're gonna see you guys on Friday, we'll review nini tako ime hapen, in between the week, so keep your SPM bads.


And just like that the Baltimore Ravens have officially started their 2024 season because this is I believe they're very first signing right? This the first guy that they are bringing in or in this case bringing back that being Nelson Aguilore big news out of Baltimore, buddy The Ravens have signed Nelson Aguilore to a one-year contract extension Nelson Aguilore among with a few others It was Nelson Aguilore Gus Edwards Kevin Zeitler and there's a couple other people whose contracts they have these specially designed contracts that are set to expire Tomorrow at 4 p.m. Eastern time and if they had not been re-signed Extended whatever you want to call it then they would be free agents So Nelson Aguilore avoids being a free agent because now he's back with the Baltimore Ravens And I know there's not many things that all Baltimore Ravens fans agree on and I know this is not gonna be one of them But I'm pretty sure that the majority of Ravens fans can all agree the majority not everybody But the majority can all agree that this is a good move for the Baltimore Ravens And I'm gonna talk about why and just a little bit before we get into it Make sure you subscribe to the YouTube channel turn your notifications on team. Keep it clean We are at seventy three thousand five hundred seventy two subscribers. So we are 428 away from 74,000 so getting closer and closer to it But we'll get there when we get there ain't no rush but make sure you subscribe to the channel turn your notifications on because It's gonna start getting busy as y'all know. I mean stuff is always busy But now with the new league year right around the corner Ravens got some moves to make there could be some moves possibly tomorrow as well We'll see but so you can stay up to date with everything subscribe to the channel turn your notifications on and leave a like on The video because it helps out the channel a lot and y'all help out just by being here just by coming through just by showing support So I appreciate y'all now somebody else who we appreciate is Nelson Aguilera We think about Nelson Aguilera. I remember last year Last year when we first signed Nelson Aguilera because he I think he was the first signing for the Baltimore Ravens last office He's in two. So that's Aguilera said it's so nice. I'm gonna do it twice But Nelson Aguilera when the Ravens first signed him last year.  It was Nelson Nelson Aguilera But I was thinking is this gonna be it a lot of us were thinking is this gonna be it because that's normally how the Ravens would operate But he wasn't it but he proved to be worth it now When you look at his numbers you look at the nut 35 catches 381 yards average 10.9 yards a catch had four touchdowns You'd look at that and like Okay, that that production can easily be replaced you could find that somewhere else But with Nelson Aguilera goes beyond that because you got to have you got to put that into context Nelson Aguilera was not the number one receiver was not the number one target He was not the number two receiver was not the number two target It was not the number three receiver was not the number three target Nelson Aguilera was like say like three four Because you had as far as targets and receivers just mix it all in there. You got say flowers You had Mark Andrews for a little bit You had Isaiah likely in the second half of the season. He's just going crazy with it Bateman was in there a bit. Oh, they'll beckham junior when he would be healthy. He'll be in there a bit but um Nelson Aguilera was behind a lot of people but When he did get his opportunities for the most part, uh, he did his thing He was somebody for the most part who um, he made the catches he made the plays And he's just somebody that is extremely unselfish You would think somebody that first round draft pick First round draft pick they first round pick Odell first round pick Bateman first round pick Nelly a first round all these first round picks we had at the receiver position But you could easily think that a first round pick that they would be selfish Because I mean hey, I was drafted in the first round. I belong here. I deserve this and they do of course But you could think that that Attitude would be displayed on the field and especially at the wide receiver position because their job is to catch passes Like why wouldn't it be displayed? It's not necessarily a bad thing that they it's not a bad thing at all that they want to vote But with Nelson Aguilera, you never heard Oh, I was saying here and heard at the same time, but you never heard or hear of him complaining at all You never hear of him being a bad teammate You never see him grumpy on the sidelines anything like that You you you would never see anything like that from a Nelson Aguilera And one of my favorite moments from this season When Nelson Aguilera, it came uh in the game against the Rams Are they playing the Rams and that game of course was it was insane? But Baltimore Ravens, they needed a touchdown to get back in the game very into the game very into regulation I mean needed a touchdown and Nelson Aguilera, he saw talked to Lamar He saw play while it was happening because I mean he's out there on the field Uh, and he came back to Lamar.   Y'all already know But um Stuff like that and I'm sure there was more stuff like that that happened that we don't know about Um, but stuff like that it stands out to me a lot because it just shows Unselfish play it shows that Nelson Aguilera was like look I I want my catches. I want my pass of course because they didn't receive a wood But I want to win. I do. I want to do what's best for the team Um, but then when his number is called he still will make some stuff happen as well So this is a real nice move for the Baltimore Ravens Now I have seen a lot of discourse from Ravens fans And I've seen a lot of Ravens fans saying that they feel like this means that odell beckham junior is out of there and I Disagree to an extent and never to explain that what I mean when I say that is that I do think odell beckham junior could be out of there But not because of this This move this extension with nelson aguilera. This is not going to break the bank This is not going to demand so much money from the Baltimore Ravens and so much cap from the Baltimore Ravens that they just can't do anything else Even at the wide receiver position. No nelson aguilera is a solid receiver He could come in and contribute and come do his thing He could help out here and then in some different ways But nelson aguilera. This signing is not going to stop you from doing anything Now it's a lot of pending stuff right now with the Baltimore Ravens and the receiver position because Gotta figure out the whole thing with ze flowers We'll see what happens with that still waiting on more news with that And I'm sure in the coming weeks. We'll continue to hear more and more. So we'll see Devin Duvenay believe he is getting ready to be a free agent. See what happens with that Rashal Bateman while he's under contract for at least another year Ravens got to make the decision if they're going to pick up his fifth year option or not So we'll see what happens with that and then of course for odell beckham junior. They um Yeah, we'll see what what goes down with him whether they decide because they did sign him to that contract They redid his contract. That's what it was. They reworked his contract. So They will either sign him to an extension or they will cut him and then just split up the dead money. However But yeah, so ravens got some different question marks at the wide receiver position right now But this is the answer to one of those questions with nelson aguilera Um, so yeah, we'll see we we will see because there's a lot there right now We just really don't know about but assuming that Going into next year. It will be ze flowers. It will be rasha bateman It will be nelson aguilera and it will be tylin wallace um At the top that's a I feel like it's a top heavy Uh receiver unit, uh, but they could still use a little more a little more. Um, just like one more guy And of course, you still got a ze likely you still got mark andrews You can't forget about those guys, but they could still use just a bit more. They ain't got to be nothing crazy I mean if they want to do something crazy, you know problem, but already, you know, we don't mind but They could use a bit more, but um Yeah, man, this is a a good move for the baltimore ravens because nelson aguilera, he brings Consistency, I know a big thing with a lot of people with all the drops to drops to drops He was known for the drops and yeah, he was known for the drops and he did have some drops with the baltimore ravens He certainly did But not that this excuses or anything, but every single receiver that the baltimore ravens got had drops All of them. Yeah, this Ze flowers, he had plenty drops, but he he got the most opportunities out of all of them He was touching that ball all the time um Odell Beckham jr. Well, he had a few I think he had maybe one actually Yeah, I think he only had one He really dropped the ball I mean he really made that many catches because he wasn't really healthy all year But and and then you think about that just to speak about Odell Beckham jr. Real quick because again I know a lot of people are saying that they think that this means that Odell Beckham jr. Is going to be going I just To me, I don't see the correlation Even if they didn't resign nelson aguilera whether they did or they didn't I just don't think it has anything to do with Odell Beckham jr. I think if Odell Beckham jr.  But 15 mil base for I I just don't think the the salary matched and I know leadership and I and I get that I really do um But and and he had some moments, but with Odell He was just hurt man He was hurt and but my concern though with Odell I really like Odell Beckham jr. But my concern with him moving forward my concern is same concern It was last year too, but my concern moving forward will be all right Odell Beckham jr. Was never healthy this season. He was never healthy Is he ever going to be healthy? Because the reason to me that that's such a biggest concern is because from his rookie year He missed a significant amount of time still broke all them records, but he missed a significant amount of time And like I think like every just about every season. He's been he's dealt with a he's dealt with injuries Throughout the entirety of his professional career He has dealt with injuries the whole time So as an older receiver now as somebody who was literally hurt the entire year last year He still came in and did this thing here and there but as somebody who was hurt the entire year last year What should we expect from him moving forward? So but if the Baltimore Ravens are gonna keep Odell Beckham jr. All right cool But I think it will be wise for them to keep him at a much lower Rate and much lower price tag Um, or if they're gonna move on and be like, you know what we're gonna go in a different direction I I wouldn't be mad at that either with Odell Beckham jr. I'm like at a at a weird point because again if they keep him All right cool lower price if they let him go. Okay. I I understand either a decision that they make Either decision that they make because I know what he brings to the team what he brings to the city really Um, so if Odell Beckham jr. Gonna stay all right cool But I know you're definitely gonna want to get more production out of him than you got this year Um, and and not even just about the numbers just really about just being out there too Because he missed like when he would he would be in the game. He'll make a catch and then two minutes later Boom, he's going for the rest of the game You do it again his next game. Oh, he made a play. He made a couple plays. Oh, boom. He's out for the rest of the game We don't see him no more So again, it just I don't know man, so we'll see But we're not snagging lower Good stuff good stuff the receiver. He's healthy. He's healthy. He ain't got no health concerns or anything like that Um, got some good speed the hands are decent too. So, uh Yeah, man, and he obviously got a connection with this team and I guess he he believed in them enough He's like, hey, we got right there Let me stay with this team to see if I can help them get over the hump


What's up everybody, Jason here for jazbyzcasebridge.com. This sells out the break guys, we're giving away the last nine spots in Opulence Vastball Random Teams number 30 in this 2020-21. Panini, Donner's, Vastball Hobby, one-pack break number 12 random teams and the way this works guys is first we do the break, randomize customer names and teams distribute the hits out and at the end of the break we'll randomize only the customer names that bought in and the nine out of the 30 almost won their chance to get a spot in the break top nine get in so here you go guys let's do the break let's roll we've got ourselves a four and a two six times good luck one two three four five and six William down to Eric four two six six one two three four five and six Golden State Wars out of the Boston Celtics All right again stick to what you got guys Just right back That's a quick glance at your teams The second to not, you might have been able to read that combo and just take that extra base but this is why you're down by one. You don't want to force anything to this yet. Justin Turner has sent Wichuan strikes out against Kendall Graven alright stick to what you got guys Lulu strikes him out Tyler hero to 49 Obi-Toppin we all marvels. Oh, we're gonna have a press-proof marvels And it's Anthony Davis very nice press-proof marvels for the Lakers Who has the Lakers? Robert Ronkel. Wow what a pack of rookies You know wise men Coral Halliburton Cole Anthony Precious All right, there you go And the switch scenes in your way the last nine spots guys top nine get in roll the dice three and a six nine times top nine get in one two three four five six seven eight and Ninth and final time So Donnie you're in twice Robert Ronkel seven Allen six Robert five Matt four Allen two Robert two and Robert one There you go top nine are in Congratulations guys coming up next is the break itself


Hello friends welcome again to session on lines and angles and in this session We are going to discuss an interesting topic that is types of angles So I'm assuming you are you know sitting on the study table and there are lots of objects around you Okay, so if you are using our notebook to write the notes Then if you observe the two edges Adjacent edges of your notebook. They are meeting at a point and making an angle is it So look at the ceiling and the point where ceiling and a wall vertical wall is meeting again You can imagine or you can see there is an angle being made isn't it? So if you you know, basically the point is there are lots of You know angles around you which you observe on a daily basis But there are different varieties of angles as well So today in this session we are going to categorize those angles and hence the topic types of angles So this is how we categorize angles to start with so there is something called acute angle And how do we classify these angles on what basis and the basis is nothing but the angle measure So we measure the angle and if the angle is between 0 to 90 degrees we say the angle is acute angle We'll show you some examples with some pictures and all but right now Let's first go through the all the types and then we can see different examples, right now Right angle right angle is nothing but an angle which makes 90 degree So the angle between the two arms is 90 degrees called a right angle Okay, then there's something called obtuse angle guys obtuse means Something which is between 90 and 180 none of these two angles are included That is the angle must not be 90 and the angle must not be 180 degrees So anything between obtuse angle, sorry 90 and 180 is obtuse example 120 degrees 155 degrees and so on and so forth What is a straight angle straight angle is nothing but two arms if They are making 180 degrees, right? So hence this is the example of a straight angle So there's a point. This is point a b and c. So if you see this angle is 180 degree, right? It's called straight angle Then there's something called a flex angle again So if you see if you make an angle like that more than 180, but less than 360 is Reflex angle. Okay, and the last is complete angle that means the the two arm Coincide each other and hence this angle is called two six Complete angle and the measure is 360 degrees. I've also given the measures in radian for your understanding because later on we are going to use Radians a lot more than let's say degree So hence if you see a cute angle is nothing but between 0 to pi by 2 radian You must be remembering that 2 pi radian is equivalent to 360 degrees, isn't it? So 90 degree clearly will be pi by 2 radian. So 0 to pi by 2 radian is acute pi by 2 radian is right angle Pi by 2 till pi. So pi is equivalent to 180 degrees these radians So pi by 2 and pi are the limits for obtuse angle So the theta must be between pi by 2 and pi then straight angle, which is nothing but pi radian 180 degrees is pi radian and Reflex now, you know pi less than theta less than 2 pi radian is reflex because 2 pi is 360 And finally complete angle is 2 pi radians, right? So this is what is that different categories or different types of angles. Please keep these information in your mind Now, let us see some examples of these angles in our day-to-day life So here are few examples of acute angle if you see the edge of the knife, you know So it's very very small this angle this angle made at the edge is around 30 degrees. We see in this figure so this is an Example of acute angle Similarly the rockets if you see if I draw the you know the lines like that This angle has to be acute, isn't it? Similarly here also. These are all Angles acute angle. These are the you know practical application of acute angle So you're a rocket cannot have an obtuse angle like that You cannot have this the rocket will never have a shape like that. Why? because then the aerodynamics for the rocket, you know becomes You know poor and and and let's say it will it will face a lot of resistance from air while it is going up So basically whether it is a bullet or whether it is an arrow if you see we always have acute angles Because acute angles in such cases helps in you know Achieving the objective right so hence you see acute angles In such cases so here again another example is this cactus thorn if you see the thorn The angles are pretty Small isn't it? I'm not able to you know draw it so properly, but this is the case of acute angle Correct. So these are some practical applications or some examples where you see Acute angle now. Let us see some examples of other angles as well now here is an example of Or a picture of how about a bridge very famous how about a bridge in India? Okay, it's on the River Hoogley in you know and it it joins Kolkata to Havra. Yep. So hence this is River Hoogley Okay, so this is River Hoogley a distributory of Ganges Okay, so here is This bridge now here a lot of examples on different types of angles can be observed So let us first find out acute angles. So if you see very easily there are lots of acute angles guys This is one this is one like that, right? These are all acute angles. Can we get some 90 degrees or right angles? Yes, we have this is 190 degree. This is again another This one another this one another. So these are all perpendicular, right? So 90 degrees Similarly, if you see underneath also, there are lots of 90 degrees. Isn't it? These are right angles What about let's say The obtuse angle again. Yes, there are lots of obtuse angle as well How so if you take this arm and this arm so here there's an obtuse angle, isn't it? Similarly take this and this so this is obtuse Do we have some? Straight angles. Yes. So if you see this is the point. So this becomes the straight angle, right? So this is 180 degrees Two links are there like that 180 degrees straight angle. Okay, fair enough. Now. What about Reflex angle perfect. So we have reflex angles as well. So let's say this is one arm here and This is another arm here. So if you see this angle happens to be Reflex, isn't it? So if this is reflex automatically the other one is either obtuse or acute Okay, so this is a reflex angle now another example of reflex action Sorry, reflex angle would be so if you take let's say this arm and This arm so this angle is a reflex angle more than 180 degrees, but less than 360 and there are lots of examples of Complete angle. So let's say this is the point and hence You know, there are two or let me just give you this example Let's say this is one link one link is denoted by let's say this color. This is one link okay from here to here and Other link is nothing but from here only to this part So the angle between them is nothing but complete angle 360 degrees or Which is equal to zero degree as well Okay. So hence in one example in one bridge, you can see lots of different types of angles are visible Hope you understood the different types of angles guys Now does this mean that angles can be only till 360 degree? No, you can actually have 400 degree 400 degrees 560 degrees even 1 lakh degrees all is possible.  But what does it mean? So for example, let's say this 400 degree 400 degrees nothing but imagine a line or ray Let's say this is point O and this is point P. Okay Now it starts rotating right it starts rotating anticlockwise and goes and goes and goes and comes back after some time back to the same position So hence we say it has covered a full circle or it has covered 360 degrees or two pi radians Okay, now if it moves ahead and let's say after crossing the initial point It is now somewhere here so that now it is making an extra 40 degrees angle So is the total angle if you see the total angle made by the line ray is nothing but 360 degrees plus 40 degrees which is equal to 400 degrees This is what is meant by an An angle which is having you know more than 360 degree value correct, so now you can see every 360 degree the The point or the ray will complete one cycle or one revolution Right one revolution one revolution so In 720 degrees it will cover to revolution It's like a you know a race which is happening and every 360 degrees one lap Okay, so hence. Yeah, so hence what will be one zero eight zero degrees. It is nothing but three revolution completed Okay, so hence now you can calculate what is one lakh degree as well and Any other value for that matter so hence degrees can also take values which are more than 360 Okay, so don't get confused when you see let's say tomorrow. They can say 520 degrees. So you now know 520 degrees means one full circle 360 and then another 160 degrees Is it so hence it is nothing but somewhere Here so hence it has the point has moved one full circle and in the second part It has gone to 160 degrees. Right. This is 160 degrees, right? So 360 plus 160 is 520 degrees. So then that is how you have to find out The meaning of all these numbers Okay, so we'll see you in the next class


Γεια σας, είναι Vicky, εδώ και καλώς ήρθατε σε ένα άλλο βίντεο καταλαβαίνω. Σήμερα θα παίρνω με νέα πρόταξη από Σάμμουσα's Tump. Αυτό είναι έναν νέο ρελείο και αυτό το βίντεο είναι αξιότητα από ένα βίντεο, εύκολο υπάρχει πολλές δεξιότητες, οπότε παίρνω να παίρνω το βίντεο μου. Σήμερα θα εξογηθήσω αυτό το στάμψε, το οποίο είναι called Fairy Tale Spinners, όπως και το ίδιο Λαβλί Τι, που αγαπηλαίω και θα σας δείξω δυο πρόταξες για πώς μπορείτε να χρησιμοποιώ. Πολλογηθώ το πιο ότι δίνει ένα λίγο πόνο, όπου μπορείς να σκοτήσεις το στιγμό σας. Πολλογηθώ αυτό το στάμψε από το Ματ-Μινά, και είχα εύκολο πρόβλημα, αν βρήκεις ότι αυτό είναι πολύ εντυγημένο για τη στάμψε, μπορείς να χρησιμοποιώ ένα στάμψε μεταλό, και θα το χρησιμοποιώ και καλό. Τώρα, αυτό το στάμψε έχει ένα καλό στιγμό σε όλο που λειτουργεί ως ένα στιγμό περφορές, ώστε να μπορείς να το χρησιμοποιώ εύκολο από το στάμψε, το οποίο είναι ακόμα αυτό που είχα εδώ, και έχω δύο διαφορετές. Πολλογηθώ another way to do that is to just run your scissors along the line. So I add the back, I'm using some double-sided tape, and I'm also using my scissors to cut off any excess. This way, all the little openings at the front are sticky, and I can add on top some glitter. This is very fine glitter, it's going to stick inside on all those openings. I'm going to push it down with my fingers. Very fine glitter sticks nicely and it doesn't fall off, but if you want to avoid the mess with glitter, you can just stick at the back any glitter cardstock. And of course you can work on a piece of paper so you can put back in the jar all the excess glitter. Now as a focal point, I'm going to stamp this little flower. This comes from the fairy tale spinners, it's one of the flowers that is included. I am going to stamp it with an alcohol-friendly ink and then I'm going to color it. I am using my three blends, these are alcohol markers by Spectrum Noir, and I like that they come with three colors in a barrel, so I don't have to go through my stars to find which colors match and blend nicely. So I'm going to do some quick coloring here, green for the stems and yellows and oranges for the petals. The quickest way to go through the petals is to start from the darker cow color and walk my way through to the lighter one. I'm using two shades from the orange marker and the lightest one from my yellow marker. So once I have the flower colored, I'm going to use my scissors and cut it out. Just like always I'm going to leave a white border, this makes a cutting super easy. There are matching dies for this stamp set. If you want to grab those, I don't have them, so I'm just fuzzy cutting every image that I'm going to use.  For this card I went with a sentiment that says sparkly birthday wishes. I'm going to play a little bit with the positioning, I'm going to bring in the flower and see what works best. So you see, since I have this angle on the flower, I'm going to shift the sentiment on the other side and then I'm going to stamp that on top with black ink and put my card together. For that I'm using a foam tape at the back of all those pieces just because I like dimension and just because these two pieces from the die cut are separate completely, I can have a bigger area to stamp the sentiment in between. I'm adding just a dot of glue at the base of my stamp just to make sure that this is not going to move and I'm going to call this card done really sparkly and with lots of dimension and I love the clean and simple look. And that's the first card for today using this die where I completely separated the design and added lots of glitter.  I am going to work directly on my card base and I'm going to blend some ink, this is the stress oxide ink, it doesn't have to be perfect blending here, you won't be able to see the whole thing, just a few bits and pieces are going to show through the openings. So I'm going mainly with a lighter color at the top and at the base I'm going darker just for an ombre look. Now I want to stamp the sentiment on the in between space that I have. That's why I'm bringing in my misty and this is where I made the booboo. My hands were dirty from inking before and if you see at the top of my panel I have some inking there. I'm just going to use a baby white to try and remove some of it just because the stress oxide ink reacts with water. The paper that I'm working on is not watercolor paper so it's not going to lift it completely.  Again I'm using this piece and I'm going to show you that there is always a way to cover up little mistakes like this. So I'm just going to continue as nothing happened there. I'm going to stamp the sentiment with black ink and for this card I went with don't stop believing since I'm planning to use one of the fairies. Again for the ferry I stamped it with alcohol friendly ink. I colored it with my tree blends and now I'm using my scissors to cut it out. Again there are matching ties for this stamp set so you can use that if you don't like fuzzy cutting. I have a foam tape at the back of this panel I'm going to place it on top of my card base so you can easily see through those holes the blending that I did. I'm going to pop my ferry on top and I went with colors that were inspired by Tinkerbell although mine isn't blonde. And now the only way to cover up this booboo at this stage is to stick on top some gems. I have smaller and bigger pink gems which I think are perfect and no one will ever know. So here are some close-up photos on the two cards that I made for today showcasing products from the latest release by Simon Says Stamp. Don't forget to visit my blog and enter the giveaway. I hope you had fun today that you got inspired. Thank you all so much for watching and I'll see you all next time.


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