Good evening aspirants. Welcome to the news analysis discussion session by Shankar A.S. Academy for the date 3rd of June 2022. These are the list of articles we will be discussing today. Without wasting much time, now let us get into the discussion. Look at this news article. The news article mentions that the International Liquid Mirror Telescope saw the first light recently. That is, telescope has been commissioned. It will start scientific observations in October this year. So, let us see few relevant facts about this telescope. See as the name suggests, this telescope has a liquid mirror. So, what is it? A liquid mirror is the one that uses a liquid material as a reflecting surface when it is spun. This is based on the principle that when a liquid is steadily rotated, its surface would take up a paraboloid shape. A perfect paraboloid directs and concentrates light to a focal point of a telescope. This happens due to the influence of gravity and centrifugal acceleration. Here, gravity pulls the liquid down and the inertia of the centrifugal force pulls it radially sideways. This principle was first realized by Sir Isaac Newton. Now, what liquid is used in these types of telescopes? Since the liquid needs to be a mirror, it should reflect light. So, liquids like mercury, gallium, gallium-indium alloy or oil infused with reflecting particles are commonly used. Now, when this liquid mirror is used in telescopes, it is called the liquid mirror telescope. Majorly, mercury is used as the reflecting liquid. This mercury is kept in a bowl container which is also called as a bath. The bath is a lightweight structure whose surface is parabolic and only a thin layer of mercury is needed to produce the accurate mirror shape. This ensures that the mirror overall remains lightweight even though mercury has high density. Then a camera is put at the focal point of the paraboloid. So, what happens is the bath is rotated smoothly around a accurately vertical axis at a constant angular velocity. The rim of a typical 4 meter mercury telescope spins about 3 miles per hour and the images are captured in the camera. Now, let us see certain factors that are ensured in the liquid mirror telescope. First, the liquid mirror acts as a primary mirror. That is, it is the mirror that collects and focuses the incoming light in a reflecting telescope. Second, the mirror has a fixed position. Third, the mirror has to remain accurately horizontal and cannot be tilted. Why is that? This ensures that the liquid does not pour out and it always points towards the zenith. That is, directly overhead. Because of this, the liquid mirror telescopes are also called as zenithal pointing telescope. Next, the mercury is covered with a thin layer of transparent mylar which is kept few centimeters above the mercury surface. This helps in eliminating the ripples formed due to the spinning and mylar also acts as a protection from the wind disturbance. Next, due to the toxic nature of the mercury, suitable protections are taken to protect the operators of the telescope. Now, the major advantage of the liquid mirror telescope over a conventional telescope is that it is very cheap. This is due to the low capital and operating cost. Liquid mirror telescope costs only 1-2% of a conventional glass telescope mirror of same size. And a conventional glass telescope mirror needs to be cleaned, adjusted, polished and aluminized. What does aluminized mean? Aluminized mean, an aluminum film is deposited on the glass. But these are absent in the case of liquid mirror telescope. So, a liquid mirror telescope is also cheaper to maintain. This low cost advantage of liquid mirror telescope also allows it to be dedicated to a narrowly defined project which is unpractical with conventional telescope as they are expensive. Apart from these advantages, liquid mirror telescope has a major drawback which is liquid mirror telescope always have to look straight up at the zenith that is overhead and cannot point at any directions or at different objects. See, this limits the telescope's field of view. But this drawback is also minimized because of Earth's rotation which makes a zenith to move continuously. So, these are the basics about the liquid mirror telescope. Now, the news article talks about an liquid mirror telescope called as the International Liquid Mirror Telescope. It is built with collaboration among India, Belgium, Poland and Canada. It is the first liquid mirror telescope in the country and the largest in Asia. There are three main components of the International Liquid Mirror Telescope. First is the primary rotating mirror. It is a 4 meter liquid mirror and uses mercury as a reflecting liquid. Second is the focal structure. The third is the upper end. The upper end is composed of a charged coupled device camera and a optical corrector. International liquid mirror telescope is kept at the Aryabata Research Institute of Observational Sciences site in Davasthal in the state of Uttarakhand. The site is located at Davasthal P in the central Himalayan range in India. This site is chosen due to its ideal condition like it has approximately 210 clear nights in a year which will help in capturing the image clearly. Know that International Liquid Mirror Telescope is the first liquid mirror telescope designed exclusively for astronomical observations. So, it will be used to carry out deep survey and hide photometric and astrometric observations of solar system, galactic and extragalactic objects within a narrow strip of sky. It is expected to detect and regularly monitor quasars, supernovas, asteroids as well as space debris. That's all regarding this discussion. In this discussion, we saw the basics and the components of a liquid mirror telescope. Also, we saw about the recently commissioned International Liquid Mirror Telescope in Uttarakhand. With this, let us conclude this discussion and take up the next news article. See this article here. It says that India's merchandise trade deficit widened to a record 23.33 billion in May month. This is because exports grew by 15.5% that is 37.3 billion dollars while imports jumped to 56.1% that is 60.62 billion dollars. And this preliminary data is from the Commerce and Industry Ministry. The article also says that goods exports shrank 7.2% from April's 40.19 billion dollars and this results in the trade deficit for the first two months of 2022-23 period. And that is all about the news article given here. In this context, we will brush up some basic facts for prelims perspective. See, every day Indians and Indian entities such as firms and governments import foreign goods and services and they also export domestic goods and services. And apart from these, they receive investments from abroad and make investments in other countries also. Know that each of these transactions involve a demand for a foreign currency or a demand for Indian currency. For example, we need dollars to import something from the United States or to invest in one of United States stock exchanges. By the same logic, other countries need Indian currency to buy goods from India or to invest in Indian stock exchanges. The interplay of these transactions decide the exchange rate of the rupee vis-à-vis the foreign currency. And recording of these transactions is called balance of payments or BOP. Know that the BOP has two parts. One is the capital account. This includes all the types of trading in capital. In other words, all investments inside and outside of the country are recorded here. For example, if an Indian firm invests money in the United States to build a new company there or if an Indian buys stocks in an American exchange. The second part of the BOP is the current account. See all the trade in goods and services noted here. For example, if an Indian imports an American gadget or software made by an American company or if an American entity imports Indian steel or engages an Indian IT company to create a software. See the current account has two specific subparts. First one is the important export of goods. This is called the trade account. The second one is the important export of services. This is called the invisibles account. Now with this basics, let us see the deficit. First of all, what is trade deficit? See, it is a broad term. To be more specific, it is a generic term. It is possible that a country, say India, imports more than it exports. In such a case, it would have a deficit on its trade account. In other words, more money is going out of the country than coming in. See this is called trade deficit. Now coming to current account deficit. It is the shortfall between the money received by selling products to other countries and the money spent to buy goods and services from other nations. If the value of goods and services we import exceeds the value of those we export, the country is said to be in a deficit. And the difference between the two values is called current account deficit. Now that current account deficit includes net income including interest and dividends and transfers like foreign aid. Also note that the current account deficit also includes the remittances transferred. See India's current account position is largely on the negative side because of our country's excessive dependence on imported oil. Now moving on to capital account deficit. As we saw earlier, the current account consists of visible trade that is export and import of goods and invisible trade that is export and imports of services. It also includes unilateral transfers and investment income that is income from factors such as land or foreign shares. But the capital account is a record of inflows and outflows of capital that directly affects the nations foreign assets and liabilities. The components of the capital account include foreign investment and loans, banking and other forms of capital as well as monetary movements or changes in the foreign exchange reserves. So a capital account deficit occurs when the equity turns negative. This means the total amount of liabilities exceeds the total amount of assets. Here a point to notice that NRA depositing money in an NRA account comes under the capital account whereas someone sending money via remittance comes under current account. Note this difference. Now moving on to balance of payment deficit. See like trade deficit, the balance of payment deficit is also a broad term. A balance of payment deficit means a nation imports more commodities, more capital and more services than it exports. This is about balance of payment deficit. That's all regarding this discussion. See in this discussion we saw some basic terms for our PLIMS examination in that we saw about current account deficit, capital account deficit, trade deficit and balance of payments deficit. With this let us conclude this discussion and take up the next news article. Look at this news article. This news article talks about the state formation day celebration in Telangana. See the Telangana chief minister mentioned in his speech that people in the country need employment, projects, power and water. This is the crux of the news article given here. In this context let us discuss about article 2, 3 and 4 of the Indian constitution which is talking about the formation of states, renaming of states etc. Now let us start our discussion. First let us start with article 2. See this article that is article 2 talks mainly about the admission or establishment of new states. Article 2 states that the parliament may by law admit into the union or establish new states. Now moving on to article 3. Article 3 talks about firstly the formation of new states. Secondly it talks about the alteration of areas, boundaries or names of existing states. Now comes the question. How can it be done? See this can be done by parliamentary laws. Firstly parliament may by law can form new states. This can be done by separation of territory from any state or by uniting two or more states or parts of states or by uniting a union territory to a part of any state. Secondly parliament may by law can increase the area of any state. Not only this parliament may by law can also diminish the area of any state. Fourthly parliament may by law can alter the boundaries of any state. Lastly parliament may by law can alter the name of any state also. Note that in these five classes that is from article 3a to 3e the word state includes a union territory also. Here when we talk about article 3 there are two important conditions that you have to remember. One is the bills for the purpose mentioned in article 3 can be introduced in either house of the parliament but only on the recommendation of the president. Secondly the bill that affects the area, boundaries or name of any states should be referred by the president to the state legislature and the state legislature can express its views within such period as the president may allow. This is about article 3. Now moving on to article 4. See article 4 talks about this. It says that loss made under article 2 and article 3 provides for the amendment of the first and the fourth schedules. Now do you remember what is spoken in the first and fourth schedule? See the first schedule talks about the names of the states and the union territories. It also includes the territorial jurisdiction of the states. Now moving on to fourth schedule. See fourth schedule talks about the provision in relation to the allocation of seats for states and union territories in Rajeshaba. Then article 4 also mentions that no such law as mentioned in article 2 and article 3 shall be deemed to be an amendment of the constitution for the purpose of article 368. That's all regarding this discussion. In this discussion we saw about article 2, article 3 and article 4 of the Indian constitution. With this let us conclude this discussion and take up the next news article. Look at this data point article. It talks about India's domestic crude production. See the domestic crude production in India has been on a constant decline. In the financial year 2022 it slipped to 28.4 million metric tons. This is the lowest in over two decades. See India has the third largest consumer of oil. But for 85% of its needs, our country depends on imports. This is the crux of the data point given here. In this context let us analyze the data point and extract some important points which will be useful for your main sensor rating. Before that we will see about the distribution of petroleum or mineral oil in India which is important for your plumes. See petroleum and mineral oil products are functional fluids derived from petroleum. To form fuel or non-fuel products we have to refine petroleum. This can be done using midstream oil and gas processes. The fuel produced include gases, petrol, kerosene, diesel and fuel oil. While the non-fuel products include petrochemical feedstock, base oils, mineral oils, intermediaries and base polymers. See the term petroleum is derived from the Latin prefix petra meaning rock and olium meaning oil. So petroleum essentially means rock oil. This term is correct because petroleum are actually extracted from sedimentary rocks. See the term can be used to describe any mixture of gaseous, liquid or solid hydrocarbons found beneath the earth's surface. It is a naturally occurring hydrocarbon based fuel with various molecular weights. Just have a look at this table to know about the well defined elemental composition of petroleum. See petroleum or mineral oil is obtained from sedimentary rocks of the earth. Now just have a look at this image to know how petroleum or mineral oil is being formed. See firstly dead tiny sea plants and animals got buried on the ocean floor. Then over the time they were covered by layers of sediments and rocks. Since these are all buried deeper and deeper they will be under enormous heat and pressure. As a result of this they are turned into oil and gas. This is what we extract during drilling today.  So they are a better fuel than coal. Now let us see about the distribution of petroleum and mineral oil in India. See the process of formation of petroleum or mineral oil started in the tertiary period that is 3 million years ago. So most of the oil reserves in India are associated with anticlines and fault traps in the sedimentary rocks. Just have a look at this image to see how oil is trapped in anticlines and fault traps in the sedimentary rocks. See when we talk about the distribution of petroleum or mineral oil we should know about the petroleum and natural gas basins in India. See the petroleum and natural gas basins in India are the Upper Assam Basin, the West Bengal Basin, the Western Himalayan Basin, the Rajasthan-Saurashtra and Kutch Basin, the Northern Gujarat Basin and finally the Ganga Valley Basin. Note that Mumbai High, the Kambat Gulf and Assam are the most productive area in case of petroleum or mineral oil. Now let us start the second part of a discussion. See here we are going to see about the analysis of the data point which will be useful for your mains examination to make your answers look unique. Now look at this graph. This graph shows the import dependence of India on crude oil. As I mentioned earlier, India is the third largest consumer of oil but the country failed to increase its domestic production. Because of this when the crude oil prices in the international markets increased, India's import bill grew in large numbers. So India's import bill for crude oil stood at $120.4 billion in the financial year 2022. Okay? Now comes the question why is India unable to reduce its import bill by increasing its domestic production? For this there are two main reasons. Firstly it is due to its ageing oil wells. Just have a look at this graph. This graph shows that the dry oil wells are increasing. This is happening due to the increasing demand in our country. The aged oil wells are the ones which had become less productive over time or in simple words it is becoming dry. And you can also see the new oil wells are not enough to meet the country's demands. Because of this the crude oil production in India is decreasing. Just have a look at this graph to know how the domestic crude oil production in our country is declining. See secondly there are less exploration or discoveries. See to understand this look at this graph you can very well understand that whether it is development of wells or exploring wells both has declined. See here development of well means maximizing the known resource and exploring wells means locating new resource of oil. Okay? That's all regarding this discussion. In this discussion we saw the basics about the formation of petroleum or mineral oil. Then we saw about the basins where petroleum or mineral oil or natural gas is found in India. Finally we saw some points from the data given in the data point. Okay? That's all regarding the news article discussion session. Now let us take up the practice prelims questions. We have four prelims questions today. Let us see them one by one. Let us take up the first question. See this question is about the International Liquid Mirror Telescope. Two statements are given. We have to find the correct statement. Let us take up the first statement. It uses a 4 meter diameter rotating mirror made up of liquid mercury to collect and focus light. See from our discussion we know that this statement is correct. Now let us take up the second statement. It is kept near Moons North Pole. See this statement is incorrect. First, because International Liquid Mirror Telescope is on Earth and it is kept at air site in India which is in Davastal Peak in the Central Himalayan Range in Uttarakhand. Second, it is incorrect because in Moon we cannot use liquid mercury as it will freeze. Instead in case of Moon, low temperature ionic liquid that do not evaporate are employed. The liquid would have to be made reflective by depositing a metallic film on its surface while the mirror is spinning. So statement one is correct, statement two is incorrect. So the correct answer here is option A one only. Now let us take up the second question. This is also a two statement question. Two statements are given. We have to find the correct statements. Let us take up the first statement. Current account includes only the visibles. See this statement is incorrect because as we saw in our discussion current account involves both visibles and invisibles. Visibles here mean goods and invisibles means services. Now let us take up the second statement. Currency depreciation makes the imports cheaper. See this statement is also incorrect. See depreciation happens when the demand for a currency goes down. Let us take the Indian currency for example. Let us say it is 60 rupees against 1 dollar. Now it has changed to 75 rupees against 1 dollar. Here the value of Indian rupee has actually declined. Think about it.  But after the depreciation you must pay 75 rupees. So rupee depreciation has made the import costlier and not cheaper. So since statement one is incorrect and statement two is also incorrect and they are asking for the correct statement. The correct answer here is option D neither one nor two. Now let us take up the third question. This is also a two statement question. Two statements are given. We have to find the correct statements. Let us take up the first statement. Diminishing the area of the state amends the fourth schedule of the Indian constitution. See this statement is correct because diminishing the area of a state comes under article 3. So we saw in our discussion that any changes made through article 3 requires amendment of both first and the fourth schedule of the Indian constitution. So statement one is correct. Now let us take up the second statement. Alteration of the name of the states can be done by the state laws only. See this statement is incorrect. Because alteration of the name of the states can be done by parliamentary laws only and not state laws. This is mentioned in article 3. See the states can initiate a process to alter the name but it cannot wholly do it by its own law. So statement one is correct and statement two is incorrect. So the correct answer here is option A only. Now let us take up the last question. See two statements about petroleum or mineral oil is given. We have to find the correct statements. Let us take up the first statement. All sedimentary rocks contains mineral oils. See this is wrong. Not all sedimentary rocks contain mineral oil. Okay. Now let us take up the second statement. All products produced by refining petroleum are all fuel products. See this statement is also incorrect. Not all products produced by refining petroleum will be fuel products. There will also be non-fuel products like petrochemical feedstock, base oil, mineral oil, intermediaries and base polymers. So since both the statements are incorrect, the correct answer here is option D neither one nor two. If you like today's discussion, like, comment and share it with your friends. For more updates regarding UPC preparation, subscribe to Shankara IS Academy YouTube channel.


I gotta look at her old video. Oh, yeah. Look, I'm like, why did he break him up? That's crazy. No, because I've seen you with him. Kevin Gates cool. Oh, what, y'all? Kevin Gates been sweet on my ain't here long time. For real? Don't boss talk one-on-one, one-on-one. Yeah, we gon' talk. I think I seen you on a picture where you was at Peaches. I think he was at Peaches. It might not have been, but Kevin Gates, you see, I seen you talking to Kevin Gates or something. Yeah, I think it was at Peaches. Yeah, at Peaches. He had a meet and greet at Peaches. I just seen, seen like y'all, you like, what's up? You know, I was like, that's hard right there. I just love, I love to see the real, you know what I'm saying? You gotta look at her old video. Oh, yeah. Look, I'm like, why did he break him up? That's crazy. No, because I've seen you with him. Kevin Gates cool. Oh, what, y'all? Kevin Gates been sweet on my ain't here long time. For real? Wow, I didn't even know that. Look, I'm gonna wave him up.   He got real, that's Louisiana. So when you're from Texas and you come to Louisiana, you think about the Louisiana stuff that was happening. So that was on your page. Yeah. And I watch you, cause me and you follow each other now. So I'm like, damn, what is Kevin doing down there? You're acting, you're acting all funny.  So how do you know Kevin since you go take him? I just know Kevin like everybody else. Through music and through, you know, the industry. Oh really, man? Through the industry.  What? You would have ate this alive. What? I said Kevin Gates, I seen you Kevin Gates, they went to tripping. I don't know what was going on with that. We went to tripping?  I'm like, Kevin cool. I'm like, what's going on, man? She start laughing like crazy. Yeah, cause you saw that picture of pictures, right? See what I'm saying? We seen that. What's going on with Kevin? How is he? I don't know. See how he did that. He said, how is he? Yeah, like is he a dope person? Cool, down to earth. I looked at what I'm probably like a month ago. And then he gave me his new number. I'm like, yeah, get at me. Gave me a hug, real embracement. You know, it's always been like that. He's very genuine. Yeah. Well, my first time meeting Kevin Gates, he ain't greet me like that. He wasn't even looking at me. He was worried about her. Oh. Oh. Ooh. No. Wow, but that's growing up, you know, probably because of, you know, you know what I'm saying? You're beautiful. I'm about to say it's beautiful. I'm about to say it's beautiful. Yeah. Yeah, she is.  You like what? You're getting from every corner. Man. I don't know. I'm just, you're just being herself. This me. Wow. So when you just, when you think about the music and stuff though that comes out of these areas, man, you guys got the most phenomenal sound, the bounce music or whether it be, you know, what's that other one that they do, the one, it's a music in that Bourbon Street is known. Oh, brass. Yeah. Brass and jazz music. Yeah, like so, like, when are you gonna, do you have that song? Do you think you have it? It was a staple song. I'm talking about her, because I'll get to you in a minute. Not just yet, but I think I'm in the mixes of matches of putting sounds together to possibly have that by, you know, the middle of this year by the summer. So I just think the new music that I'm pushing out is me, you know what I'm saying? I don't care to cater to any crowd of people. It's just what I want here. Yeah. And if you like me, then you gonna like it. You know, because I like it, I play it in a car. I might play it three times back to back. So that's how I know it's cool, cool. So if you like me and you like good music and I know a song when it's a hit song, so, you know, they gonna like it. You know when it's a hit? I know it. Like I tell people in the next thing, you know that's the song that the artist picked to play on the radio all the time. Yeah, we on boss talk one on one, one on one. Yeah, we gon' talk.


I don't know why, but my YouTube channel just grew massively in like a few days. It used to grow at like five people, four people a day. And then in two days I look and it grew from 380 people, subscribers to 430 in two, three days. And I don't know why, I like it. And that's why I tell people all the time, take massive action consistently and you're going to get lucky.  And once in a while you get lucky and you get these breaks where you just like grow massively.  Do it!


a place I shouldn't have been. I guess it depends on, like for me, it was a lot of places I shouldn't have been, but the first place I can remember that I shouldn't have been is pulling a gun on my stepdad at age eight. You on boss talk one on one, one on one. Here we gon' talk. Same thing with Smoke D. Like what's something that transpired in your life? And I don't know, you don't know where to start. He like, I don't know, I just don't know where to start, you know what I'm saying? Like at a time in your life where you came to a roadblock or you came to a stumble, you came to a place where you shouldn't have been or you came to a place where you had a show that changed your life. Probably, like.  So you overcame it. Because people are watching this show, kids are watching this show, adults are watching shows that's going through choices right now that could end them up in a casket. Um, a place I shouldn't have been. I guess it depends on, like for me, it was a lot of places I shouldn't have been, but the first place I can remember that I shouldn't have been is pulling a gun on my stepdad at age eight. Eight years old? Yes, man. To protect my mom, right?  You know, when the men are the protectors, we're not allowed to look below the waist of the women in our family. So no, no. And I'm just what I was raised to be. A protector, you know?   You understand what guns can do. And so I guess I was kind of like, it was more of a mental incarceration, trying to figure things out that I didn't understand. And my mind couldn't, it couldn't register them because I didn't know what it meant.  So that was kind of my first understanding of fear because at age, I was fearful. But then like, I knew in my heart, I was going to shoot him. I feel that way now, but my mom didn't let me.  What's up, mom? Yeah, she got in front of him and that confused me.   But it wasn't about him. It was about me. And it took me years. So those kind of traumatizing things, they like psychologically, they just put you in a place. So you already kind of just set up based on the way the system has your neighborhood, the social security, all of these things system, systematic things set up in play to even aid, you know what I'm saying?  The whole time you're saying that, he always tell me, I watch too many movies. I'm like, I've seen that in a movie. Exactly what you just described.  Exactly the same thing. She was trying to prevent him throwing his life away. His life away. Off of raw emotion. Exactly. And reacting off of raw emotion. You know what I'm saying? Exactly. She was willing to save your life and through no matter what you just experienced, you were still more important in that situation. But you know what, bro? She fixed my, it's here. I mean, we was just downstairs. You seen how the dudes came. We was just here. I'm just saying this because I'm a real time thinker, right? Now I noticed the man that's sitting there and he didn't took a drink and the drink didn't took him. You see? So he figured he smooth and he dabbed over there to where he see a bunch of women over there. Maybe drunk, maybe blind or whatever he is, but he came wrong. His spirit was wrong. Absolutely wrong. And I reacted in a way that I don't want to react no more. You know? That incarceration, it took my smiles. It took the emotions that I wanted to use. My mom ain't give us no hugs. We ain't got time for no hugs. You better, you know? Because she's trying to raise men. Right. We couldn't come back home with a loss.  Don't come back home losing. You know, and that puts you in a situation to where, you know, it's unnatural because my father should be telling me that, not her. And she, God bless her soul, them broke daylight to be dark to provide a way for us. Now we had a great life.  She didn't have time. She spent time working. And I got, you know, whoever she was mad to, I had to be scared of him until I was 16. Then I really tried to kill him. Like for real, for real, to the point she had to leave him, right? So it's that kind of aggression that's carried over from a childhood trauma to a situation right now. I don't like to play.  Man, you better go. Yeah, pull it in. Like go, I don't know. You want this. And I don't want to be like that, bro. No, I get it, man. I want a more diplomatic way to handle situations when I proceed them as a threat, right? But let me ask you a question and this goes to all of you. Do you think in situations like that, it would have been helpful if or hurtful because when you're dealing with boys, it's a thin line, especially with a woman, you don't want to turn them soft. You're trying to make them into men. But like to turn around and explain to a child, the reason why I did this is because of this. I don't know if your mom explained to you at that moment in time. Of course, after she de-escalated the situation, it's not because of him, it's because of you. Right. Did she explain that at that moment in time? Communication isn't usually never there in the black family. I'm not sure. I'm not sure my mom is mean or the better.   I'm not sure. I think I just figured it out.  You gonna get my granddad and them and grab them on them whoop you for doing anything. You gonna get a whooping even though you done it. And your brother too, if he were with you, whatever, whoever in there can get it. You know what I mean? At eight?  Whoever, he get hit, all that. So that's what I'm saying. Like, I get it, you know, mom didn't explain it. My mom shouted, my dad, I was five, so I get it. You know, like, I was standing there. Like four. But if we're not left with our own imagination and trying to figure stuff out, because a lot of times, even as adults, when somebody do something, say your spouse and she react a certain way, in your mind you're thinking, that's the reason why, but it's really not the reason why and that can make you react differently instead of actually coming to her and say, why did you do that? And having her explain herself honestly, you know what I mean? It's miscommunication in any situation, in any household that causes, you know, that outcome. That's the reason why I was asking that. Tim Smolley used to say communication rules the nation. You know, and you got the patience to wanna have that. Exactly. Some people don't feel like they're obligated to tell you nothing, you know what I'm saying? Because of what they learned. Their parents didn't, you know, talk to them so why am I trying to do this to you? Correct, correct.


In the previous class, we could draw two inferences about the behavior of a synchronous machine from its constituent equations. In fact, the analysis which we did was a steady state analysis. What we did last time was, we obtained the open circuit voltage at the terminals of a synchronous machine when a voltage V f is applied at the field. The machine of course, is rotating at a speed say omega naught. In such a case, it was shown that the voltage open circuit voltage which appeared at the terminals of a machine was given by V a is equal to omega naught m a f i f sin omega naught t. This was with the assumption of course, that theta is equal to omega naught t. Of course, remember that i f in steady state is nothing but V f by R f. So, the expression which we got was of V voltage, the voltage which appeared across the A winding. Of course, if it is a star connected winding, the root 2 by 3 times this would be the line to line voltage. So, line to line voltage magnitude would be root 2 by 3 into omega naught m a f I am sorry, this should be root 3 by 2 m a f into I f. So, this would be the line to line voltage R m s magnitude whereas, the voltage across the A winding would be this. The second and more interesting inference about the steady state behavior was a machine was that if a machine was connected to a three phase balance voltage source and we studied a particular situation in which the rotor is aligned at an angle delta at the time when the voltage source to which the synchronous machine is connected to undergoes a negative to positive 0 crossing. So, if that situation exists t dash into omega naught is equal to V line to line R m s square into sin 2 delta by 2 into this term. Remember that this term is equal to 0 in case x t and x q are equal. So, this is a saliency dependent term. The other term for in fact, this is the power if you multiplied by omega naught it is the steady state power. The second term of this steady state power equation is V line to line R m s of the applied voltage into x d f into I f x d f into I f as we saw sometime back was nothing but the open circuit line to line R m s voltage. Please remember that we did an open circuit analysis of the machine and we got root 3 by 2 into omega naught into m a f into I f as a line to line R m s voltage magnitude.  So, what we have here is the steady state torque torque of power expression looks like this with this should have a sin delta sin into sin delta term here which was missed out. So, this particular term has got V line to line R m s multiplied by the open circuit line to line R m s voltage into sin delta by x d. So, these were the 2 simple and important results of a synchronous machine. We now move on to an important part of our course in fact in the previous class we have previous lectures we have obtained the synchronous machine equation the differential equations both the flux equations and the torque equations. So, in fact we have come to a point where we can analyze the machine completely but there is one important engineering aspect which we should go through before we start actually applying these equations for the analysis of a synchronous machine. It may appear very trivial especially for a theoretically inclined person what we are going to do now. The basic point we are going to do is try to obtain the parameters which are required for the analysis of a synchronous machine. So, if I want to obtain certain parameters then I need to do a certain amount of testing and once I do a testing I will have to fit whatever I get as a test results into my model and obtain the parameters for it. So, this is what is going to be the aim of this particular lecture. In fact what we see in the literature on synchronous machine analysis is that often we will not be given the inductances of the machine. For example, LAA to LAB, LAB, LAA 0, MAF all these inductances are rarely given what instead are given are some of the parameters obtained from some tests which are applied to a synchronous machine. For example, you will be given things like the open circuit time constant of the synchronous machine or the short circuit time constants of a synchronous machine or the transient and sub transient reactances of a synchronous machine. Now, how do you correlate these parameters or these variables which are given I would not say variable the parameters which are given as a result of testing of a synchronous machine. How do you correlate them to the model that we have derived so far? So, that is basically the aim of this particular lecture. So, we will try to understand a synchronous machine in terms which is written the equations of which are written in terms of what are known as the standard parameters or the parameters obtained from standard tests. So, this is our lecture today the modeling of synchronous machine in terms of standard parameters.  So, my equations are constituting in fact, a combination of differential and algebraic equations. There is nothing sacrosanct about representing the algebraic equations you can always eliminate current by expressing it in terms of flux and ensuring that your flux equations are in pure state space form, but generally people like to write the flux equation in terms of differential equations in flux which contain current and separately write current as algebraically related to the fluxes. Now, let us say I want to obtain these parameters of a synchronous machine they have several ways you can do it one you can of course, you know do an electromagnetic analysis of a machine and try to using say some computational methods for electromagnetic fields accurately calculate the inductances and other parameters of the machine, but another simpler and better way of doing things is to actually physically test the machine and obtain its parameters. So, for example, one of the ways you can do it is what is known as the stand still frequency response test of a synchronous machine. So, let us see what we can do suppose you have got a synchronous machine which is at stand still that is its speed is 0 and what we do is also for example, keep the field voltage 0 that is short circuit the field binding in such a case the stator flux equations can be written down like d psi d by d t there is no speed emf term because speed is 0. So, suppose you have a situation where speed is equal to 0 v f is equal to 0 this one the equation of a synchronous machine the stator fluxes are going to look like this of course, if you assume that the resistances of a synchronous generator are very small for large synchronous machines they are indeed very small resistances then you get d psi d by d t is equal to minus v d and d psi q by d t is equal to minus v q. We shall arrange our tests in such a way that the fluxes the 0 sequence fluxes and currents are 0. So, we shall arrange everything in such a manner. So, we do not have to bother about the 0 sequence variables here. Now, suppose I excite the stator winding in a certain fashion for example, I take my stator winding and I excite it in this fashion I connect the v a b c windings in star keep the star point open and of course, this is I a this is I b and this is I c and I apply a voltage here which is equal to v and I short this winding here. So, I apply a voltage here v short this winding. So, this is what I will do the other thing I will do is I will align my field winding axis to the a winding axis. So, what I will do is the field winding is aligned to the a axis. So, what is theta? So, theta will be 0. See remember it is it is also at stances. So, theta will always remain 0. Now, what I will do is apply voltages of various frequencies here and try to take out the frequency responses between the currents and the voltages. In this case, since v b is equal to v c, and v s, s is the Laplace variable is equal to v a of s minus v b of s. This is condition number 1, this is condition number 2 and there is a third condition I a I will call as I and I b which will be equal to I c will be equal to half of I of s. So, if you look at this figure here this is I. So, the current will split equally between these two windings and you will have these conditions. So, there are 3 or 4 conditions let me just write them down here v b is equal to v c and this. Now, since theta is equal to 0, we have I of d is equal to root 2 by 3. This current will take in this direction, current will take in this direction into the machine that case you will have minus I cos of 0 theta 0 remember plus I by 2 cos of minus 120 degrees plus I by 2 cos of plus 120 degrees. So, this will be equal to minus root 3 by 2 rather I should say minus of root of 3 by 2 into I. So, we have got let us just write it again v d I d of s is minus root 3 by 2 into I and I q you can take this out very quickly I will just write it down minus of I into sin of 0 plus I by 2 into sin of 120 minus plus of I by 2 into sin of minus 120. So, this turns out this turns out to be equal to 0. Similarly, v d is equal to root 2 by 3 into v a cos of 0 plus v b into cos of minus 120 plus v c into cos of plus 120 and that comes out to be equal to root 2 by 3 times v. So, what we have is this and v d of s where s is a Laplace variable is this. So, if you apply Laplace terms forms here on the basic time dependent quantities these are the time dependent quantities we will have this this is of course of s.  So, what we will do is in this setup this test setup I will apply a voltage v this is voltage which I will apply v and obtain the current I what I will do is I will do this for various frequencies of voltage which are applied. So, what we will get is some kind of the frequency response v s by I s. So, this is what we will get if we do this test since v f is shorted that is the field winding is shorted here you do not have any term corresponding to v f. So, this test is done with the field winding shorted. So, what we can do is obtain v of s by I of s and recall from one of the equations which we wrote previously we have minus d psi d by d t is equal to v d and minus d psi q by d t is equal to v q this is if of course resistance is neglected and the speed is 0. So, these two things are obtained from those equations. So, the point is once I get this transfer function can I correlate it with what we get from actually what I get from the model what is the transfer function I get from the model we shall see shortly. But, basically what I wanted to say is since psi d and v d are related in this fashion we can get the transfer function from this because we have this relationship and we also have this relationship I will just write it in Laplace domain minus of psi d of s is equal to v d of s upon s. So, actually you can get the relationship psi d of upon I d of s by actually doing a measurement of this transfer function. So, what I can do is take out this frequency response of this transfer function and try to fit it into the transfer function I get from the model which we have. So, that is what we can do in fact it is an easy it is easy to see that in case I align my field winding at theta is equal to 90 degrees. If I align my theta at 90 degrees in such a case I can get this transfer function the reason of course, is that under these situations I d will turn out to be 0. So, what we will get effectively is the transfer function which is of importance is actually going to be this. Now, it is in fact one important point which I missed out was in case the field winding is aligned axis is aligned to the a winding v q is also 0. So, this is something I did not show. So, in fact that is something I did not explicitly show, but it is easy to see. So, now I have got these transfer functions from these tests the question is from these transfer functions can I obtain the parameters of a synchronous machine. Now, the obvious thing which we ought to do whenever we try to equate the transfer functions which are obtained by testing. In fact you will get what is known as the frequency response of this transfer function by testing. So, suppose you get some frequencies once of any transfer function like this. Suppose there is a transfer function y s upon u s which is of this kind for various frequencies you evaluate this transfer function by putting s is equal to j omega and you get the magnitude of this transfer function and you get the phase of this transfer function. What you need to do is you can fit say a rational function like 1 plus s t 1 upon 1 plus s t 2 and try to see by choosing appropriate values of t 1 and t 2 can I get a response which is identical to the one obtained from measurements. The answer is that in general in physical systems whenever you take out these transfer functions actually the frequency response of transfer functions by testing the physical system you will find that it usually will not match exactly with the transfer function obtained analytically via some model because there are always some kind of approximations implicit whenever we obtain a model of a synchronous machine. So, for example if we take the model of a synchronous machine that is we have got what are known as the flux and the current relationships we have got the differential equations of the flux fluxes that is we have got equations in d psi by d t we also have got a flux current relationship. The question is can I get the same transfer function analytically the answer is yes you can in fact if you look at the rotor equations of a synchronous machine in the direct axis the rotor equations are given by these two differential equations and the quadrature axis by these two differential equations. Moreover as I mentioned sometime back the currents which appear in these differential equations are related to the fluxes by this relationship. So, this is the relationship you have got for the fluxes. So, if for example I wanted to find out the transfer function between psi d and this what would I do what I need to do is take out the apply Laplace transformation to the direct axis differential equations as a result of which I will get s into psi f of s plus r f into i f of s is equal to v f of s. Now of course, if voltage applied to the field winding is 0 in that case we said this equal to 0 in such a case you will have psi of f s is equal to minus of r f by s into i f of s. Similarly, the other equation that in psi h of s differential equation in psi f of s if you take the Laplace transform you will get minus of r h upon s into i h of s. Now you have got these equations and you wish to now obtain this transfer function. So, what you need to do is use these equations in conjunction with the algebraic relationship which is again sorry. So, you have got this relationship too. So, you can substitute what we have got sometime back this into this.  And as far as these two equations are concerned in psi f and psi h it is easy to see that you will have this is by simply transferring the or expressing psi f of s in terms of i f and i h. So, this is basically what you get of course, this is multiplied by just use the word capital. So, as to denote that these are Laplace variables Laplace transformed currents. Now what you can do is express i f and i h of s in terms of i d of s and then what you do is effectively eliminate them from the first equation. So, you can write get psi d of s wholly in terms of i d of s. So, what you effectively have to do if you focus on this equation which I have to get i f and i h in terms of i d I will have to take this this term on to this side then invert this matrix and write i f and i h in terms of i d of s and substitute here. So, I have to substitute for i d and i h. So, I will cut a very long story short and directly tell you that psi d of s will have the following form. In fact, it will be l d into a transfer function it will have this form this is of course, obtained provided you keep the field winding shorted otherwise you will have another term in v of s. So, you got a what is known as a second order numerator and a second order denominator polynomials which relate psi d of s to i d of s. Now, just we will do it once.  So, this particular equation. So, in fact, you will get this as l d into 1 plus s t d dash plus t d double dash plus t d dash t d double dash. So, the general form into s square this is square. So, this is the general form, but the point is I have defined this new time constants we shall see the significance of this time constants a bit later, but the fact is that transfer function which you will get when you actually evaluate this you know when you actually substitute for i f and i h here you by using this particular equation will look like this where I will call this as a d of s square. So, what is a d and b d a n and b n well hold your breath this is what it will look like. So, a n is nothing, but this it is a very complicated looks a very complicated equation in terms of the basic parameters of the machine and b n.   So, please note that this error. So, although these expressions look very complicated they can actually be found out by applying by in fact substituting for the field and h damper winding currents in terms of i d f s. So, let me just tell you that. So, the point is that this second order transfer function we have got the coefficients b n a n b d n a d can be written in terms of these, but the general you can factorize them in this form and I define this time constants which will come out as a result of this factorization as t d dash t d double dash for the numerator polynomial and t d 0 dash and t d 0 double dash in the denominator polynomial. So, let me just summarize what I have done.  So, these are the basic parameters of the machine it turns out that psi d by i d from the model which I have used will give you a second order it will have the form in which you have got a second order polynomial in s divided by a second order polynomial in the denominator both in the numerator and the denominator you will find it that a second there are second order polynomials. So, I can actually what I can do is I can do an experiment do a test on the machine obtain the frequency response of the machine that is obtain the frequency response of psi d of s upon i d of s for various omegas that is I do an experiment obtain psi d. In fact, I should say j omega upon i d this is basically a transfer function. So, if I apply various the voltages voltage as I showed sometime back or various frequencies and a compute this transfer function or other I obtain this transfer function from the measurements which I take. So, what I need to do is actually measure v the magnitude and phase of v and measure the magnitude and phase of i for various frequencies for the test I described sometime back. So, once I do that I can actually try to correlate the frequency response with the transfer function which I have got. In particular I could get the parameters of the transfer function which I theoretically obtained by comparing it with the transfer function I obtained by measurement. So, I have to in some sense fit the model to the experimental data. Now, one important point which I should mention here that I took when I model a synchronous machine I model in the q axis for example, two damper windings it may. So, happen especially for if you look at hydro turbine driven generators that you will be able to fit the data obtained from experiment to the model very easily by just one damper winding on the q axis. So, that that can happen. So, what we have assumed is a kind of a model in which there are two damper windings on the q axis one damper winding on the d axis and a field winding and obtain the transfer function and the transfer function show obtained when we correlate it with experiment it may so turn out that we get a lot of error or other we are not able to fit the experimental data to the model which we have got. So, this may indicate that our is assumption which we made right in the beginning of having two damper windings on the q axis and one field winding and one damper on the d axis may require revision you may require more windings or in some cases you can even model a synchronous machine adequately with just one winding on a certain axis. So, this does happen, but what we will take right now what has been found in the literature in or reported in the literature is that this two damper windings on the q axis and one damper winding on the d axis with along with the field winding is adequate or rather models a steam turbine driven generator quite well. For a hydro turbine driven generator you can in fact show that you can in fact observe that one damper winding on the q axis is adequate to model the hydro turbine driven generator in fact even if you have modeled a higher order machine you know machine with more number of windings one can always reduce the order of the or rather reduce the order of the model by open circuiting one of the damper windings. For example, if I set R h equals to infinity or a very very large value it is equivalent to opening that damper winding. So, depending on what experimental data we get we will be able to in most cases or most practical generators fit you know the experimental data to the theoretical transfer functions. So, what we will get in fact after doing all these measurements is the parameter values l d t d t d double dash by fitting it in fact this fit may not be exact, but you can always tune these values of t d dash t d double dash t d zero dash and t d zero double dash tune it in such a way that they match with what is obtained in by doing the experiment. So, we have got the transfer function psi d s upon i d s from experiment and we are tuning in the parameters of the model. So, that the model and the experimental data matches. So, that is done by what is known as the standstill frequency response test which I mentioned sometime back. Now, that is only one issue I will get l d t d dash t d double dash t d zero double t d zero dash and t d zero double dash by fitting the model to the experimental frequency response.  So, I should not call l f h is equal to and then you have got r h and r f of course, there is a parameter r a the resistance of a synchronous machine and that we assume also has been measured can be measured separately the resistance of the state of winding is something you can measure separately. So, we will not worry about resistance of the state of winding now. So, we have got 1 2 3 4 5 6 these are equal so 6 7 8 8 parameters in our original synchronous machine model by doing the tests we can fit the experimental data and obtain these or rather tune the time constant. So, that they fit exact more or less they fit very well with the experimental data. So, we will try to tune these parameters. So, we here you have got 1 2 3 4 5. So, actually you have got from the tests you will get the parameters of these parameters these parameters of the transfer function. So, they are only 5. So, if you just you know obtain these parameters you will of course, manage to replicate in the model using the model or transfer function which gives almost the same responses that obtained experimentally, but you will not be able to get all the parameters of the original model. Now, this is not very surprising it is in fact, a transfer function model in some sense is collapsing the whole state space model into a input output relationship and some of the nuances which are there present you know the nuanced information which is present in the state space model is in some sense destroyed because of this. So, just by doing this frequency response test just this is one test you know of the frequency response we are not going to get all the parameters required of the original state space equation or let me put it this way we will not get all the parameters specified in the original state space in which the states are the damper winding field winding fluxes. So, before we go into a more deeper discussion into this particular aspect let me just tell you one thing that if I obtain these parameters L D T D dash T D double dash T D 0 double dash and T D 0 dash am I going to get a workable state space model of a synchronous machine. The point is I cannot get the original model of a synchronous machine because all these parameters are not obtainable from these, but it would be useful to understand what exactly can I obtain from this these measurements we have got this time constants from this time constants I cannot back calculate 8 values from these 5 values. Remember of course, that whenever we have a transfer function can we obtain the state space representation. So, if I have got a transfer function representation of a dynamical system in fact, that is what I have got right now if I actually do this frequency response test I can infer the transfer function of a synchronous machine a particular transfer function of a synchronous machine on the d axis with the field winding shorted. So, the question is from the transfer function can I get back the state space with reference to a previous discussion I just one can say that obviously, one cannot get the original state space because the number of parameters obtained from this test are not adequate they are not adequate to obtain in fact, all the parameters of the original state space model. So, what we have done in fact, let me just tell you from the original state space which had in fact, 8 parameters which I just listed down I got a transfer function in fact, I took a I got this transfer function by shorting the field winding I got a transfer function in 5 parameters. Now, I cannot get back of course, to this state space of 8 parameters using these 5 parameters of the transfer function, but the question is can I get to a state space in which we are just 5 parameters the answer is yes it is possible. So, the key to this is to remember that if you have got a state space representation of a system like this the transfer function y s upon a u of s is nothing, but c into s i minus a inverse b. Now, one thing one interesting thing is if I use a transformation of variables x is equal to r into z in such a situation you will have the same system when written in terms of the z variables will be z dot is equal to r inverse a r z the same system plus r inverse b u and y is equal to c into x which is nothing, but c into r into x into z. The transfer function of this system is c into r into s i i is of course, an identity matrix into r inverse a r inverse r inverse b which is nothing, but c into s into r inverse this will be r r inverse into r into r inverse a r into b inverse. So, this is of course, using simple rules of matrix algebra. So, we will get c into s i minus a inverse b. So, what you have here is the same transfer function this transfer function and this transfer function in fact match exactly. So, the same system rather if you have got a transfer function you can either get to a state space of this kind or you can get a state space of this kind and both are in fact valid representations of your system, but the point we should remember is that the original variables and the new variables are related by this relationship here. So, let me get back to our original issue from the state space of 8 variables we got into a transfer function of using 5 parameters. So, using these 5 parameters of course, it will not be able to back calculate all the 8 variables of the original state space equations, but you can if you so wish write down the state space equation using only 5 parameters, but the state variables of this state space system using 5 parameters is not the same as the state variables here they will in fact be some kind of linear combination of the states in this. So, your state space equations here and the state space equation here are written in terms of different variables. So, that is one important thing you should keep in mind. So, using these transfer I can get a state space representation using just these 5 parameters. In fact, it is a nice thing if you can write down the state space with lesser number of parameters, but it is important that the state space equations which you will get will be in terms of states which are related in some way by some linear transformation to the original state space variables that is psi f psi h psi d, but of course, which is require lesser number of parameters. Now, in power system analysis it is often required to at least you know have a nice neat interpretation of the states. So, often people would insist that well I do not want a state space which use only 5 parameters, but the states are not easy to interpret you know the states for example, psi f and psi f psi h for example, are variables which are easy to interpret they are in fact the fluxes linked with the f and g by f and h winding, but of course, if I write the state space in terms of only 5 parameters the states in this state space representation will be a linear combination of these states and it may be difficult it is not really very nice to have for example, state space equations in which one of the states is say 5 times the field flux plus 3.5 times the you know the damper winding flux. So, there is a in fact problem here and power system engineers have tried to solve this problem in a bit round about fashion. In fact, the solution to this problem is to in fact try to do try to in fact obtain more transfer functions by various other tests may be similar setups some more tests and get get more parameters which can be correlated to the original 8 parameters which I have already said. So, if I through more tests obtain more parameters then I would should be able to obtain the original 8 parameters which I mentioned by back calculating. Remember that all the transfer functions which we have for example, if you recall this is the coefficient of the numerator polynomial in s. So, if we have got in fact, you know just t d dash and t d double dash one will not be able to get all these parameters. If you have got for example, sorry t d dash t d double dash t d 0 dash and l d and t d 0 double dash you are not going to get all these 8 parameters which are which are a part of this. So, it is not possible to back calculate 8 parameters, but one can take out other transfer functions you can you know you know try to think of other tests. For example, you do this test with the field winding open in that case you will get another transfer function you can actually obtain the same transfer function using the analytical model which we have then correlate both of them. So, you can actually have many more tests and actually get all the parameters, but unfortunately power system engineers have with a limited number of tests and limited number of parameters attempted to get an approximate synchronous machine model. And therefore, because of that we will in fact have to make certain approximations in the kind of state space equations we are finally, going to get which are in terms of what are known as the standard parameters. So, there is only one way of getting meaningful state space representations with a larger number of parameters than what are obtained by measurement and that is by making certain approximations. So, we will redo or rather recap what you have done today in the next lecture and try to obtain a state space representation of a synchronous machine a meaningful state space representation of a synchronous machine may be with a few approximations in fact, with a few approximations which will be in terms of states which we can directly interpret. So, there will be not some transform states which use lesser number of parameters, but we will try to get approximate state space equations with a few approximate with lesser number of parameters. So, this is what we will do in the next lecture.