Hey guys, it's Julia and welcome back to my channel and for today's video I'm going to be giving you guys like a quick little update and also some of my recent reads So I've been away for a bit and like we don't have to talk about all the reasons I just feel really shitty about this channel and Like what it was and then how dead it is now and I know that's really my fault But at the same time it just it feels weird So I feel a little weird sitting in front of the camera today I've been spending like all my time on Twitch in terms of like the time I used to put into YouTube It's been just going into Twitch So if you want to like see me like three times a week or something definitely go over there And like I'd be happy to chat with you guys and play games with you over there But today we're gonna talk about some of the books that I've read in the past a little bit I have five here to talk about first. I have here is a manga series and this is called I am a hero. So this one I read volumes one and two these guys actually got on sale That's why like I've had them for a bit. I got them on sale. That's the reason why I own them, but they are zombie mongas You know like apocalyptic zombie horror is what these are our main character is This dude on the cover here and he makes a lot of questionable decisions He's uh the back describes and I was mentally unhinged.  So like it wasn't really a great time, but in the second one We saw a little bit of character development just just a little so there's more dynamics and more relationships in this one And like the series is clearly going somewhere. So there's like this is volumes one and two And this is three and four and the bind ups But I definitely would continue with this series if I could find the third one for a good price if not, though probably not but I really like the art style in it I'll show you guys art from the first one. Yeah, I really I really like the art style in this one I ended up giving the first one like a three three star rating like wasn't that great but if you If you have them or you think it sounds interesting and you could get to the second one I think the second one is a little bit better. So if I get a hold of the third one I'll definitely let you guys know my thoughts on that one, but they're really fun to read. They're really fast reads I like horror manga like a lot So it like I didn't have a bad time reading them at all I think this one like a little bit over like a three star rating because it was it was better, but yeah Next up here. I have fence volumes three and four This series is about like an academy of fencers all male fencers and they compete and they're trying to get on this team That's what like the whole series is about So we follow each like the fencers and their dynamics their relationships their rivalries their competition their Romances a little bit. So there's lots of stuff happening in this series. I really really like it. I can't wait to read the next volume It's so so good I think it's just really interesting too to see like a bunch a bunch of people that are all talented just trying to prove their place and I really like sports graphic novels Surprisingly, I want to read that hockey one that is out as well that like he's a baker too. I think but So good if you're interested in fence at all, I'd recommend checking it out I never thought I'd really care to read a book about fencing, but it's so good like so good So I gave both of those four stars each because they were Beautiful lastly I read I hope this reaches her in time by R. H sin This was a reread for me. I was going through a little bit of a rough time and you know I'm reading poetry in bed who what I'm really sad kind of kind of helps me feel a little seen So that's what I was doing when I read this one just crying in bed reading this But it was it was very good. I I really like Ari sin's work. You know, he just Focuses on trying to like just let you know your worth and he gives like a lot of motivational quotes Obviously a lot of motivational poems, but his sort like his poems usually are about like love loss relationships and then like That kind of thing also like some of them are more focused on breakups But this one was more this one was more about like sadness and love and relationships These are also this one is also really inexpensive Like I think you can get the e-book for like really really cheap. You've never read R. H sin before I definitely recommend reading something by him. I've read mostly everything He's come out with unless there's been like some new like I don't think I've read his most recent stuff that's come out in like the past like six months But other than that I've read everything he's put out and I highly recommend him for especially like beginner people who want to get into poetry For modern poetry like I think he's just pretty good and I would recommend checking him out So there you guys have it. Those are some of the books that I've been reading Thank you so much for watching this video. I know it was short definitely let me know videos that you would like to see in the future because like I don't want to stop uploading on this channel and The reason why I haven't been is mostly me shitting on myself, so I've had some people come into my twitch chat and say they really mess my videos and some people tweet me and message me So thank you guys so much if you message me or just watch or care about my videos at all Like I really really appreciate it and I honest like Yeah, I'm just Like self sabotage.   Thank you and I Hope to be back with a new video soon. Bye


that even that is too much okay yeah so hi everyone my name is Martin I'm running a work development agency in Singapore called Bitmask and well today as the final talk today I want to just give some very quick and easy super fast tips for Python beginners so I guess most of you will probably know all of this but I know that we have some beginners here today so this might be helpful for some of them okay tip number one is use virtual so maybe a quick show of hands who is using virtual and okay so that is probably 90% pretty good yeah I believe for newcomers this is the very first thing I do should probably teach yourself and it's not very difficult anyways so why should you use it it's to avoid the thing that we call dependency health so imagine you have two projects one project you need Django 1.5 the other project needs Django 1.6 and then in the morning you start working on the first project and the afternoon you want to switch to the other one and you would always have to pip install the old Django pip install the new Django and you would have to do it all the time waste time waste bandwidth waste this space so that's not a good solution virtual amp will help you to create isolated environments so as I said you can that is basically a result of avoiding dependency health now you have buckets of environments and they don't interfere with each other so they are isolated it also means that you won't pollute your global environment so I don't really know if this is really an issue but every time I do Sunoo pip install something I'm kind of scared what of my operating system is actually using requests version one point whatever and now I'm installing an older version for some reason am I breaking my operating system right now so maybe polluting your global environment might not be the best idea as well and you also it helps you to create reproducible environments so usually you will have this so-called requirements dot text file and with a tool like pip or easy install you can just say pip install everything that's in this requirements text and there's like 50 different packages in them and then you go and grab a tea and you come back five minutes later and everything has been installed so it's pretty good if you have a bigger team and you need everyone to be on the same page working on the same project so how do you use this you just run pip install virtual and you go into any project folder where you want to start working on your project and then you call this new command virtual and and you give it a name usually we would use the end and this will install a new folder called the end which contains its own Python library and whenever you run when you activate this environment which we will do with source the end been activate your shell will get will have some new environment variables and the path to the Python very Python executable will be changed to the one that is in this Vm folder here so when you run which Python your terminal it will no longer go to use a local Python or wherever it's installed it will go to projects my project the end been Python and then when you run pip install it will no longer end up in whatever is your global folder will end up in this Vm folder so that means all the crap that you have installed during this project you can easily delete it you can just delete the Vm folder and you can reinstall everything again start from scratch if you mess it up somehow and by typing deactivate you will stop using this virtual environment and you will go back to your global environment so yeah as I just said it creates a folder Vm what you can call it you can give it any name uses its own Python executable it installs packages only into that folder and by the way if you're running a virtual control system like it you should not add this folder to your repository because when you have many developers they might have different operating systems and they might compile the Python packages differently so you don't want to commit this into your repository that's everybody's own business to install the packages into this into their own virtual environments right so this is not not something that is shared with the team everybody sets this up on their own computer and yeah there's the link where you can use it so maybe a very quick demonstration so when I go to my project folder and I start a new folder and then I say virtual and Vm and now I have this Vm folder here and inside of the Vm folder there's a bin folder which has the Python executable and deactivate script so now I can use source Vm bin activate and usually you can see that your prompt changes and it tells you now you are basically running a virtual environment and now when I do like in so requests for example yeah okay I'm not online why is that I'm running my own spot okay never mind so yeah so it would it would be installed into the Vm lip Python site packages and then you would find all the things that you have installed in this folder so if you want to browse the code and one dive into the into the things that you are using you can actually have a look at it very easily okay so that's the first tip second tip is building on that so if you are using virtual and already you should also use virtual and wrapper raise of hands who knows about virtual and wrapper okay so that's like only maybe 30% and I would have expected that most people somehow don't use it I don't know why this is really awesome you will no longer have your VMs in that folder where you are currently working you will you will have a environment variable called work on home and a virtual and wrapper will help you to just install all your virtual environments into that single folder right which makes it is I find it easier that I know where are all my virtual environments where on my computer are they if I want to go into one of them want to delete them want to mess around with them I have one central folder I just go into that folder and I know where I am and you don't have to remember the past to this activate script like source projects my project been activated it's confusing so virtual and wrapper basically gives you one commands called work on and you say work on project one and boom the virtual environment was the name project one will be activated no matter where you are in your channel right now and so with yeah with zsh it has plug-in and I think with bash there's also way to set up auto completion for this so when you are like me and you have tons of virtual environments it's super easy to activate them by installing this is also pretty easy as usual pet install virtual and wrapper then you need to put a few for few lines into your bash profile or if you are using this I'm putting it into this HRC or you can put into bash RC any file that is executed when you start a new shell right so you would use these new and new environment variables here this is the most important one work on home and then when you have done that you can use this new command called MK virtual and so you don't have to use virtual and because virtual and creates a new virtual environment in the folder where you are right now right and pay virtual and creates a new virtual and in this folder work on home which is your central folder for your virtual environments and then you can activate it with work on and deactivated with deactivate as usual so when I run work on and have a press double tap I see all my virtual environments and if I activate one of them you can see that it has been activated and I don't have it doesn't matter in which folder I am right so I'm just going to my home folder and I can say work on this this one for example and that is activated so then I have this central folder here where all these virtual environments are together yeah go to the folder you don't know it you stay in the same folder so no matter where you're working currently you can work on you can just activate this environment and from then on this other Icelandic Python executable will be used but if you want to go to the floor yes you should you can see this one I can I think I'm not sure if this works why not I have done it for a long time I think you can put a dot file VN visit dot VN yeah that worked so when there is a dot VN file which has a name of one of your virtual environments and you CD into that folder the environment will automatically be started so you don't even have to type work on anymore I think this is a feature of the end but there's also the I'm in a different directory and I want to go to the directory of my project right there's the CD project oh yeah there's something like that and that's also there's also removed virtual and so you can delete them without having to go into your central folder and it's the CEO there's CD virtual and so if we want to have a look at that it's interesting it doesn't have a complete it doesn't seem to work I have never used it before it doesn't work you just if you just see virtual and it goes into the virtual that you're currently oh yeah oh the current activity that was when he said the CD virtual and building was friendly going to build these types of building which doesn't get I see okay that's pretty cool all right so sorry okay so because you use these tools all the time in every virtual and then okay okay I never use that because I always have a requirements text file anyways which I need to run when I start a new virtual and so I don't need hooks okay last tip lint your code Python already has this awesome pep8 coding conventions brought to us by our benevolent dictator uniform rossum and many more people probably and I think this is the one of the great things about the Python ecosystem you can look at anybody's code and it just looks familiar because most of the people are following the pep8 coding conventions so you don't have to waste time in your own company your own team to set up a central document where you decide how the code should look like it has already been decided for you and it will also find some nasty syntax errors for you and it keeps your code beautiful so there's a there's a tool that helps you sticking to beautiful code and it's called flake 8 so you would run it install flake 8 and then you can run this command flake 8 on the current folder and then it will look into all Python files and see if they are compliant with the pep8 conventions so let's try that so let's say I have a file here which has pretty bad code we will import star which you should never do and then we we will have a super long line and then we have some white space here and some white space here for example so that's pretty ugly and when I run flake 8 it finds this file and it finds the lines okay sorry sorry like this so it finds this file that code and tells me exactly on which line which syntax error has been found usually they are already very easy to understand so you don't have to go to some other documentation to find out what is this error all about so it's telling me oh I have invalid syntax why do I have any valid syntax okay what I actually wanted to do was this so now I'm flake 8 and it says I'm using star imports and this makes it very difficult for my IDE to figure out which which modules are imported right now like which which classes are available in this file because I don't know what's behind star right so I should be more precise about what I'm actually what I actually want to use so we will change that to this and then when I run it again it says decimal has been imported but it's never being used this is one of the most the one that I like the most because when your projects grow you tend to import all kinds of stuff you mess around and then you get to a final solution which is so easy and all the stuff that you have imported before is no longer being used so flake 8 makes it very easy and tells us that we are not using it at all so let's remove it right and then it's saying there's a line which is too long so with strings we can use something like this it's still too long it's here so we put it here and then we have a blank line at the end of the file finally it will not find any hours and we are good to commit our beautiful code yes okay sure yeah that's what I want to say last most editors have flake 8 plugins so for supply I guess you have one for eclipse probably as well and even for my ugly little vim when I press when I press F7 it leaves the file for me and says flake 8 is okay so let's introduce an error again and now it tells me line too long in this small window here when I the cursor jumps here immediately when I press enter it jumps back to the line that is wrong so when you have a file with lots and lots of errors you can just step through those press enter and you will jump to the error and you can fix them super fast yeah we did that as well in the beginning we were using two or three different ones but in the end we settled on flake 8 the latest version I think they have it covers everything and it has the best error outputs and I think there's even a way to exclude some of the errors if you say in my project I I don't care about line too long for example there's a way I forgot how to do it because I'm good with all the things that it suggests to me but if you really want to exclude some of the errors there's also a way to do it is probably the documentation yeah right yeah yeah that's it for me you're like plugging in a little bit if you do gender development you check out his youtube page for his company because they open source almost everything they do by the way is anyone here toying with the idea of visiting picon later this year in June okay because we are still as we are inside the beginning we are still looking for proposals for talks and I mean we have super awesome keynote speakers but that doesn't mean that everybody who's giving a talk has to be a super awesome rockstar programmer right I mean it's an event driven by us by the community for the community so anyone who's doing anything interesting I thought the talks today were all super interesting and they would have been good fits for picon talks so if you do something awesome like you should submit your talk for picon definitely yeah if you think you're doing something similar it like with this scope this will be a really good talk for picon as well you should consider submitting something it's good for the community so what what do you do now


would incentivize farmers to transition from animal production or animal feed production into producing crops that could be used as plant-based inputs and to provide financial incentives and technical assistance. So I think sometimes in the agriculture community there's a sense that alternative proteins means an end to like rural livelihoods and farming communities and that's not the case, you know, especially with plant-based meat that inputs are plants and they need to be grown by people and we want farmers to be stewards of the land and to produce these crops that are going to be in demand for plant-based products.


in the last lecture, we were looking at rewriting the equations of the induction machine in a different frame of reference. The original induction machine equations we had written in the so called natural reference frame where the stator variables being 3 voltages Va, Vb and Vc and the stator variables Ia, Ib and Ic, these are all written in the so called ABC reference frame that means we look at the actual voltage applied across the stator a phase, the voltage applied to the stator b phase, voltage applied to the stator c phase, the flow of current in the stator a phase, b phase, c phase and so on. And similarly we have rotor variables which are again the rotor a phase, a phase voltage, b phase voltage, c phase voltage and the flow of current in the 3 phases of the rotor. So with this we had a fairly large expression describing the voltages, the relationship between the voltages 3 here and 3 here and the flow of current 3 here and 3 here, a fairly large description we were thinking of how one can try to simplify these expressions and for that purpose we then try to look at the MMF created by or generated by 3 phase winding, the net MMF generated by the 3 phase winding and we found that the MMF created by the 3 phase winding could be approximated or could be equivalently thought to be generated by a 2 phase winding itself. So the 3 phase winding MMFs are generated by windings that are situated actually separated by 120 degrees whereas the equivalent 2 phase MMF is generated by windings that are situated such that their axis are separated by 90 degrees in space. So we call these as the a axis and the b axis whereas the original axis of the machine is then a axis, b axis and c axis. So we describe or we derive the way of transforming variables from the a, b, c or the natural reference frame axis to the a, b axis there are only 2 axis here. And in that we found that if MMF has to be invariant that is the MMF generated by windings that are there on the a, b, c axis is the same thing that is thought to have been generated by windings on the a and b axis so it should generate the same MMF. And if that is going to be the case we found that the ratio of turns between the 3 windings on the a, b, c axis and the 2 windings on the a, b axis that ratio of number of turns was something that could be decided based on some requirement of the other. We also found that if you want to go from a, b, c to a, b and then also go back having found out variables in a, b frame of reference if you now want to find out a, b, c you need to do a matrix inversion and that was not feasible unless you introduce a 0 sequence component as well. So we introduced a 0 sequence component to complete the description thereby from the a, b, c 0 reference frame so to say reference frame meaning it is just some place from which you observe instead of observing the mechanics of the machine electro dynamics nature of the machine from a, b, c frame of reference that is where you describe these variables you might as well describe it from the a, b and then now added 0 frame of reference. In order to describe the ratio of number of turns we found that there are 2 ways that are generally used one is then known as the power invariancy approach power invariant transformation and another is then the non power invariant transformation and we had seen how these 2 work and what happens to the ratio of number of turns if we use either one transformation or the other and we saw that if you are using the non p i method then we have the vector i a, b, 0 being described by 2 by 3 times the matrix m into i a, b, c this is a vector containing where i a, b, 0 is a vector of i a, i, b and i 0 and i a, b, c is a vector i a, i b, c and then if you want to find out the inverse that means having found or known i a, b, 0 in some way if you want to get what would be the equivalent 3 phase current we have to do the inversion and then you have 3 by 2 times m inverse i a, b, 0 should be equal to i a, b, but then we also know from the description in the earlier class that m inverse is equal to 2 by 3 times m transpose and therefore i a, b, c is 3 by 2 into 2 by 3 into m transpose into i a, b, 0 which means this is simply equal to m transpose into i a, b, 0. So one can transform a, b, c to a, b, 0 or a, b, 0 to a, b, c and we also have used the requirement or we have used an idea that in order to derive the number of turns that the way in which the vector i is getting transformed should be the same in the way in which the vector v is getting transformed and therefore we had defined the relationship v a, b, 0 is 2 by 3 times m into v a, b, c which therefore would mean that v a, b, c is m transpose into v a, b, c. So this we had seen in the last lecture. We see that the transformation from a, b, c to a, b, 0 is not really the same as transformation from a, b, 0 to a, b, c not really the same in the sense here there is a factor 2 by 3 coming and here there is no factor 2 by 3 coming. Other than that you have m and m transpose we know that m transpose and m inverse are related in some manner. On the other hand if you use the other approach that is the power invariant approach then what you have is i a, b, 0 as we had derived in the earlier lecture is root of 2 by 3 times m into i a, b, c and therefore this means that i a, b, c is root of 3 by 2 times m inverse into i a, b, 0 and since m inverse is equal to 2 thirds of m transpose we can substitute that expression. So this is root of 2 by 3 into i a, b, c is m inverse of this this is sorry this is root of this expression is wrong this is root of 2 by 3 times I have made some mistake let me check yeah i a, b, 0 is root of 3 by 2 times m inverse into i a, b, c which is root of 3 by 2 m inverse is 2 thirds of m transpose so that is 2 by 3 times m transpose into i a, b, 0 and this in turn gives us this is root 2 by 3 m transpose into i a, b, c. So what we have is if you define that i a, b, 0 is root 2 by 3 times m into i a, b, c the inverse transformation root what you have is i a, b, c is root of 2 by 3 times m transpose into i a, b, 0 similarly therefore you would also get v a, b, c is equal to root of 2 by 3 times m transpose into v a, b, c here what we see is this factor root 2 by 3 occurs both in the transformation from a, b, c to a, b, 0 and also from a, b, 0 to a, b, c and what was m here now becomes m transpose so this transformation is a little easier to have in mind it is easier to remember because root 2 by 3 factor comes always and it is either m or m transpose whereas in this earlier case in one root you have 2 by 3 in the inverse you do not have 2 by 3. So in this manner one can transform variables in the a, b, c reference frame to the a, b, 0 reference frame. Now we have not at this point of time said whether this a, b, c are belonging to the stator or belonging to the rotor they could be anything any 3 phase variable set can be transformed to an equivalent 2 phase so to say 2 phase variable set we normally refer to this as 2 phase variable because in most cases this i, 0 term happens to be 0 because in most cases electrical machines are excited by balanced ac supplies in which case va plus vb plus vc is equal to 0 and if you remember i0 or v0 is equal to whatever scale factor here into 1 by root 2 times va 1 by root 2 times vb plus 1 by root 2 times vc which means va plus vb plus vc divided by root 2 and since this is equal to 0 v0 will be 0 and if v0 is 0 then i0 would also be 0 and therefore this variable is invariably 0 and therefore this is referred to as a 2 phase set of variable so this is normally called as 3 phase to 2 phase and this transformation is also known as clocks transformation so this 3 phase to 2 phase could mean 3 phase of the stator or 3 phase of the rotor it could be any one of those the stator flow of currents generates its own MMF the rotor currents also generate their own MMF and each of those could in turn be thought of as being generated from 2 phases in the case of the stator the since a b and c axis are fixed in space the a and b axis are also fixed in space in the case of the rotor the a b c axis are fixed to the rotor and since the rotor is going to rotate the a b c axis are rotating in space and therefore this a and b axis are rotating along with the a b c axis so the 2 phase system on the stator is fixed to the stator and a stationary whereas the 2 phase system of the rotor is fixed to the rotor and hence it is rotating so both these can then be described by a similar set of equations you can have either stator or the rotor here. So having said all this how do we apply this to the case of induction machine now at this point before we get into the induction machine let us introduce define certain notations now we are going to have stator variables and rotor variables sometimes we may have we may want to write the stator variables in a certain frame of reference rotor variables in certain other frame of reference and therefore the notation can become very involved so we will define certain ways in which we are going to write these variables. Now if we have an input variable or an output let us say v which is the phase voltage that is applied now this letter itself stands for voltage now this may refer to stator or to the rotor and in each case we have an a phase b phase and c phase or a beta 0 and therefore what we will do is we will attach a subscript and a superscript this in turn will refer to we will mean it to refer to stator variables the superscript will refer to rotor so which means that if I write v a since this is coming below and it is stator we will infer that v a refers to the a phase voltage of the stator on the other hand if I write v a it would then refer to a phase of the rotor if I write v a it would refer to the a phase of the stator and v a would refer to the a phase of the rotor similarly we will define variables i a and i a, i a, i a needless to say you could have v b, v beta, v c, v 0 and so on the location of a beta or 0 or a b and c will refer will determine whether we are talking about stator or whether we are talking about the rotor so we will keep this in mind later on we will introduce some more notations when we have occasion to refer to more frames of reference right now we have defined or described two frames of reference one is the so called natural reference frame the natural reference frame is the actual frame of reference when you can measure the variables that you are applying to the machine so the natural reference frame we will always call it as the a, b, c reference frame because generally machines are three phase machines and we will refer to the three phases as a phase, b phase and c phase so the natural reference frame is the three phase a, b, c reference frame. We also have the a, b reference frame or the a, b, 0 reference frame the a, b, 0 reference frame is always a reference frame which we will consider that is fixed to the member which we are looking at if it is a, b, 0 for the stator it is fixed to the stator if it is a, b, 0 of the rotor it is fixed to the rotor and therefore the a, b, 0 of the rotor is going to be rotating a, b, 0 of the stator is going to be stationary that is that arises from the member to which this a, b, 0 is attached so these are two reference frames that we have so far introduced. So now how are we going to apply this to the case of induction machine in the case of induction machine we have this vector v which is the vector of voltages at all phases of the machine both stator and rotor and therefore this vector we will denote as v, a, b, c, a, b, c to denote that this vector contains both stator variables and rotor variables the stator variables are in the a, b, c reference frame the rotor variables are also in the a, b, c reference frame similarly you have the vector i which again is in a, b, c reference frame a, b, c, a, b, c. So the induction machine description that we have is a relationship between v, a, b, c and i, a, b, c which we wrote as this is equal to r into i, a, b, c plus p times psi which is a vector of flux linkages that is again in the a, b, c reference frame which we have expanded it as r into i, a, b, c plus p times l into i, a, b, c if you remember in one of the lectures we had written down elaborate expressions for r and l a fairly big description. Now what we have done is we have tried to transform this a, b, c to a, b, c and we have defined it for a set of three phase variables which could be interpreted as either stator phases or the rotor phases and therefore we can now define the vector v which is a, b, c in the stator a, b, c in the rotor this can be thought of as being derived from the vector v, a, b, c, a, b, c by a transformation matrix c. How do we find out what goes into c that is easy to find out since we know how that has been derived. So let us now define this matrix c we know that the three phase variables of stator voltages for example stator is denoted by the subscript so v, a, v, b and v, c we know that this is equal to root of 2 by 3 times we will use in this course transformation that is invariant with respect to active power so we will use this factor root 2 by 3 times 1-1.5-1.5, 0, root 3 by 2 and – root 3 by 2, 1 by root 2 times I am sorry this is v a, b, c is equal to this matrix times v a. So this is the description that we have this relates the stator a, b, c similarly therefore we can also write v a, v, b, c now we are writing variables in the rotor therefore I am putting this in the superscript this is also equal to root of 2 by 3 times 1 the same –1.5-1.5, 0, root 3 by 2, – root 3 by 2, 1 by root 2, 1 by root 2 times v a, a, b and v. So the transformation for the three phase stator variables and the rotor variables is the same. Now what we have what we need to do in order to get a matrix description c like the one that we have written before that is we want to say a, b, 0, a, b, 0 is equal to c times v a, b, c, v a, b, c then what we can do is this matrix we will define as a matrix c11 and then therefore we can combine these two descriptions into one equation where we write a sub vector v as v a, b, 0 and this sub vector v as v a, b, 0 these are the three vectors consisting of three variables of the stator vector consisting of three variables of the rotor this can as a matrix c11 which is this matrix 0, 0 and c11 again multiplied by v a, b, c, v a, b. So the rotor variables vector that comes here the stator variable vector comes here therefore now you can see that v a, b, 0 is c11 times v a, b, c that is what you have here and v a, b, 0 of the rotor is also equal to c11 times v a, b, c of the rotor that is what you have here. So effectively we have combined these two into one description here similarly then we can write an expression i a, b, 0 and a, b, 0 is equal to c times i a, b, c and a, b, c the same kind of description also apply. So now that we have these two equation which say how to transform a, b, c to a, b, 0 we can substitute this in our expression equations for the induction machine and try to see what happens. So if we do that from this equation we can write v a, b, c a, b, c is equal to c inverse times v a, b, 0, b and c. Now c inverse is nothing but the inverse of this matrix and this matrix is in the block diagonal form and therefore we can write this as c11 inverse c11 inverse and we know what the inverse of c11 is because we have defined all the transformations between the a, b, 0 to a, b, c. This is nothing but root 2 by 3 times m and c11 inverse is root 2 by 3 times m transpose and therefore the c11 inverse is nothing but c11 transpose and c11 transpose which is same as c transpose. Therefore we know c11 inverse c or c inverse is easy to write. Similarly we can write i a, b, c, a, b, c equals c inverse times i a, b, 0, i a, b, 0 and our earlier expression says that the induction machine equation v a, b, c a, b, c equals r times i a, b, c plus p times l into i a, b, c. But now we have written i a, b, c in terms of i a, b, c in terms of this so we substitute these expressions here. So what you have is c inverse v a, b, 0 is equal to r times c inverse i a, b, 0 a, b, 0 plus p times l c inverse i a, b, 0 a and you can remove this inverse by multiplying throughout by the matrix c and therefore you have v a, b, 0 a, b, 0 equals p times r c inverse i a, b, 0, 0 plus this is c times p l c inverse. Now this is derivative of a product of these 3 and being vectors or square matrices one cannot, one has to maintain the order in which these occur and therefore this can be expanded further as c r this term remains as it is you can write this as c l c inverse p of i a, b, 0 plus c times p of l c inverse multiplied by i. Now remember that the operator p stands for the derivative operator it is d by dt and both l and I mean c is not dependent on t because c is something that is fixed matrix so that does not depend l alone depends on t because l has the rotor angle inside it and as the rotor is going to rotate the rotor angle will change with respect to time and therefore this l depends on t and if you differentiate therefore since the only term that depends on t in the matrix l is the rotor angle you will then have derivative of the rotor angle which is nothing but speed and therefore this term can be further expanded as expanded so this is c r c inverse i a, b, 0 i a, b, 0 plus c l c inverse derivative of i a, b, 0 plus this term alone can be expanded as p of l into c inverse plus l into p of c inverse and l into p of c inverse is 0 because c inverse does not depend on the rotor angle and therefore this term simply evaluates to that and therefore that is c times p of l into c inverse i a, b, 0 so this is the expression that we land up with. Now one has to simplify these terms in order to find out what this description is going to look like and that simplification is not a simple algebra why it is fairly involved algebra so we will just indicate how to go about doing that simplification so if you take this matrix c r c inverse the matrix r consists of or can be written as r a, b, c, 0, 0 and r a, b, c of the rotor stator off diagonal terms are 0 and r a, b, c itself is the stator resistance r is multiplied by identity matrix u which is identity matrix which is 3 rows and 3 columns 1, 0, 0, 0, 1, 0, 0, 0, 1.  So if you now write the term c r c inverse is c 1, 1, 0, c 1, 1 and then you have r a, b, c, 0, 0, r a, b, c, r c inverse and we know that c inverse is nothing but c transpose so c 1, 1 transpose 0, 0, c 1, 1 transpose so this is equal to c 1, 1, 0, 0, c 1, 1 multiplying these 2 so you have r a, b, c, c 1, 1 transpose and then 0 and then you have r a, b, c, c 1, 1 no this term is 0 and here you have r a, b, c, c 1, 1 transpose and this can further be simplified is c 1, 1, r a, b, c, c 1, 1 transpose and this is 0, this is 0, I have c 1, 1, r a, b, c, c 1, 1 transpose and r a, b, c is nothing but a scalar multiplied by identity matrix and therefore this is nothing but r s multiplied by c 1, 1 into identity matrix multiplied by c 1, 1 transpose which is nothing but c 1, 1 into c 1, 1 transpose which is an identity matrix again so you get r s into u, 0, 0 and by similar argument this is r r into u and therefore this matrix is the same as what we started out with. So as far as this term is concerned this matrix is the same as r so there is no difference here. Now how to find out this so let us look at that matrix we will not complete the algebra but we will see how that has to be done. The matrix L can similarly be subdivided into matrix L11, L12, L21 and L22 we have seen what the form of L11, L21 and all that look like and we also notice that L12 is equal to L21 transpose or L21 equal to L12 transpose that also we have seen. So similar to the way we had done CRC inverse this also has to be done so you would then have c 11, 0, 0, c 11 multiplied by L11, L12 we can write this as L12 transpose L22 and then you have c 11 transpose so this becomes your CLC inverse and one can expand this. So this would then be c11, 0, 0, c11 and then L11, c11 transpose and then L12, c11 transpose and L22, c11 transpose and then if we expand this also further you get c11, L11, c11 transpose and then e11, L12, e11 transpose, e11, L12 transpose, c11 transpose so this is the expression but what do each of these terms look like one has to expand this and try to find out what it looks like and similarly this term here try to find out what it looks like. I will just show the net result of doing all this algebra I would urge you to verify yourself by performing this equation expanding this form in terms of individual element of L and c. So let us look at how this algebra is going to work out so here we have the expression for the induction machine written in the natural reference frame and as we had seen the matrix L can then be written as L11 instead of L12 I have put it as M12 so M12 and M21 L22. This matrix L11 looks like this you have leakage inductance plus magnetizing inductance this is the mutual inductance of the stator phases and then again leakage and magnetizing it assume to be a three phase balance machine therefore these inductances are the same. We had also seen why MS is equal to minus LMS by 2 we had looked at that and then the matrix M12 is MSR which is the maximum value of mutual inductance multiplied by some function of the rotor angle and then all these are functions of rotor angle so that is M12 M21 is the transpose of M12 matrix and the rotor inductance that is L22 now looks like this very similar to L11 and where MR is again minus LMR by 2 this is the form of the original description of the machine in the natural frame of reference. And now having transformed this to the two phase variables or the aß0 reference frame the matrix L so this is what we have in the aß0 reference frame this can then be written as the same matrix R multiplied by aß0 aß0 so this term is going to multiply the derivative of aß0 therefore this is another inductance matrix let us then call it as L aß0 aß0 this matrix is going to have derivative of the inductance matrix and we said that in the inductance matrix only term which will give a non zero derivative are the terms that involve the angle of the rotor and therefore you would then have a dθ by dt term that comes out of this so you are going to have a dθ by dt multiplied by i aß0 aß0 and this term out of which dθ by dt has been taken out the remaining we will call it as the matrix G and this matrix G is then called as the speed matrix because it is being operated on it is being then multiplied by this dθ by dt term which is nothing but the rotor speed and therefore G is called the speed matrix so what we need we have already seen what is the structure of R we need to find out what is the structure of L what is the structure of G so if you look at the structure of L you see that you have a self inductance term consisting of a leakage inductance and a magnetizing inductance but that magnetizing inductance is not just LMS but 3 by 2 times LMS here again you get a same term and the zero sequence only the leakage inductance enters the picture similarly this part has LLR plus 3 by 2 times LMR similarly here and only the leakage inductance for zero sequence part of the rotor side these two matrices is 3 by 2 times MSR into cosθ and then sinθ that is how this matrix looks and this matrix is then the transpose of this one so this is how the inductance matrix itself looks like and the speed matrix you note that in the speed matrix all these terms are zero the speed matrix is likely to have all the term all these terms zero because the derivative of the inductance matrix in the inductance matrix these terms do not depend on the rotor angle and therefore in the derivative all these become zero similarly here all these terms are also zero note that the zero row has all zero entries both for the stator and as for the rotor these terms are again dependent on the rotor angle so this is how the matrix L and G is going to look like. Now once we know this we can write down the full expression L aß0 G aß0 we can now write this full term now this particular expression though we have derived it from the equation of the three phase induction machine by applying this transformation from a b c to aß0 we will see in the next lecture that this equation could have been written down directly by observation without having going required to go through this elaborate conversion from a b c to aß0 why it can be written down by observation because this expression now refers to a machine which has two windings two windings on stator and two windings on rotor and these two windings are located along axis that are 90 degrees displaced these are again 90 degrees displaced with respect to each other and therefore one can see that in the inductance description L matrix you see that the mutual inductance term here this term would refer to the mutual inductance between the a axis and the a axis that term is 0 why is that 0 because two coils which are located 90 degree with respect to each other flux linkages will not happen by exciting one and saying in the other so mutual flux linkage or the mutual inductance is 0 when the two axis are displaced by 90 degree similarly here also you find that the mutual inductance term is 0 you will see why this term happens to be 0 in the next lecture. So in the next lecture we will start by looking at how this expression can be written down directly from observation so with that we will stop for this lecture.