s that are personalized at their level and then they they move forward from there that wind time also provides time for EL and special education teachers to work with their students in a smaller group setting one to one so again another opportunity there and then there was professional development around both of those programs some of our ELA teachers really focused on ELA and math focused on lexia for ELA and math for alex now we have our science teachers also doing alex our social studies teachers also doing lexia so we expanded some of that professional development and then as you saw on the board schools our schools are also focusing on that cisa seven professional development with co-plan and co-serve so that we have maybe an EL teacher or a special education teacher teaming with a classroom teacher to plan and serve their students in their classroom at the same level i'm on the next slide slide 15 just really kind of a summary of of the story of middle school at first month of how we started um we i think a lot of students and teachers have noticed that some of the unstructured and transition times are different because we didn't have that last year students were co-ordered we maybe didn't have those transition times um they really the beginning of the year again just like at an elementary level we emphasize some of those daily routines i was at farnsworth on the first day of school and was helping some sixth graders as it normally is on day one of school how to open their lockers and find their lockers but then i went up the third floor and saw seventh grade students also being helped because they weren't they didn't have lockers last year so again that's that transition time of uh you know really kind of coming back to it's always a transition to go to middle school but for seventh graders many of them it was a transition as well um but also the the schools have gone back to focusing on building that climate and culture so trying to bring back some spirit days some incentive pieces really trying to build that community piece which which maybe wasn't there when we were in different settings um and then again really focusing on those individual learning gaps so our teachers in the classroom have some data where they know and especially nealy and math where students need extra support we can provide that in the intervention time in the middle of the day but we can also still get that grade level um access to grade level curriculum all right eric's gonna go on with the high school all right so on slide 17 uh it's a bit repetitive from what jim and kelly have said but our our high schools uh last i looked it was north south and warner have all completed the panorama panorama survey already um so that data will be to us sooner rather than later and we'll share it with you when we have it if you flip to page 18 i'm really going to focus on our college and career readiness indicators as we've shared many times with you um at the high school level we really focus on that uh broad educational experience from academic programming to personalized and career specific experiences and i think our college and career readiness indicators are a good marker on on how we're doing on these pieces we shared the data with you in the spring but really a lot of the data for a senior class is completed by the end of their senior year with some classes they may be finishing up etc so really we just wanted to update you on the data and where things are at and where we ended up so on page 18 we're looking at career readiness data uh just as a reminder uh the the definition that we're using in terms of being career ready is meeting at least two of these indicators again i'm not going to read through every single piece with you um but the attendance piece uh seems to be right on track for where things have been a community service is something we're finally moving forward with this year um the tracking piece of that has been the challenge uh workplace learning uh our senior class last year in 2021 um had had opportunities for that i think um to be honest i think part of last year offered some more opportunities and maybe have been in the past for kids to have some of those workplace experiences the actual industry credentials dropped just because of those connections with the schools i weren't weren't as clean our pathway courses and our extracurriculars our numbers stayed pretty consistent there the one thing i will point out is this is a measurement of four years so right so if you're looking at extracurricular participation overall you see the 2021 class is higher than 2020 2019 that doesn't necessarily mean we had an increase last year in co-curricular participation but over the course of those four years our students are getting involved and to be honest with you i think as we talk about a final summary at the end are excited to re-engage in many of those opportunities again uh the next two pages you'll find are are kind of the exact same thing we start looking at college readiness indicators there's really one main difference between the two slides and that is uh the the population that we're pulling data from so on page 19 uh what we're looking at for college readiness indicators are students that indicated they were on a two or four year uh path uh post high school uh you'll notice in pretty much every single category we have a significant dip in the year 2020 uh the the reason for that is our our data for that year is uh incomplete from the standpoint of we're relying on students to indicate their path post high school uh much of that indication happens in the spring of the year and when things got shut down in the spring of of that year uh the vast majority of our attention was pertaining to how do we help students successfully navigate that environment that we're in so we had over i think was over 350 students that didn't indicate whether or not they were uh choosing career whether they were choosing service whether they were choosing a two or four year so our our data set isn't the same for that year so i'll kind of refer to that on the next slide um so it would really i guess on page 19 encourage you to compare 2021 uh to 2019 as much as possible um again as you can see there i think the the numbers are are fairly consistent again these are our indicators of of four years of high school in that whole high school experience how question indicators that um like based on past kind of clearing house data you probably had more kids going to four-year school than were probably you know was the right path for them and it was kind of showing out as well in terms of the retention and how many were actually completing that um and it was pretty interesting based on the numbers it was almost spot on in terms of predictor are we still seeing similar trends of numbers of students that are choosing that path or is this perhaps helping them see different options that might better suit them and transitory learning or getting to a immediately into the workforce in a different career path that might you know better suit kind of where they're where they're at i know that was a large conversation right was for a long time everything was only four year that's an exceptional option but we've got a lot of different opportunities for kids and hopefully this counseling process opens up that opportunities for them and helps them make that decision yeah so i don't i don't think we've seen a drastic change in the number of kids stating that they want to go to a two or four-year college i think what's really shifted is the conversation that we have with those kids right so they put down that's what they want the conversation with them is look this is what the data tells us you need to be able to do to be successful in college these are the areas that you're lacking what can we do to support you and help you in that area we really encourage our counselors to have that conversation and not a conversation of well you know college might not be for you um yeah so that's the the piece there i think kids are are looking at things um a little differently but again i think the really hard part with the data that you're talking about is going to be the kids that decided yeah i'm not going to pay for college tuition to learn from home virtually last year so right then the college enrollment numbers go down and we i know of a number of kids personally that did that right or kids that yeah i'm gonna go to ltc and take my gen eds or uw sheboygan uh and take my gen eds and then transfer so the data's going to be a little wonky there um but the good news is here is our data across all these metrics so is pretty much up so we're feeling pretty good about that up and kind of compare slides 19 and 20 so the difference on 19 and 20 and i'm not intending to lead off the act piece because we'll come back to here um so page 20 includes all students so now when we're comparing 2019 2020 2021 you have a comparison data set to look at i think when you come back to you know some of the college level pieces there when you compare pages 19 and 20 obviously some of the dual credit or advanced algebra courses and act scores um are a little bit lower when we're comparing all students um but again i think that that's kind of fits what we what we've talking about is is a student that's not going um to that college path some of those things aren't as important as a as a work experience might be for them so i think again trying to really try to compare what's important to students and help them be successful on the path that they're on but i think the overall summary of those three pages is really that our 2021 class um was right on par with what we had seen in previous years so then the last piece i guess just in terms of a qualitative summary again i think you heard a couple of parents shared us with you tonight but i think just from from my experiences being in a high school um over the last few weeks just the the amount of of kids being excited to be able to be back and interacting with each other um has has been exciting uh i think one of the funny things is just that unstructured time um the first couple days of of getting back to to lunch um prior to prior to last year we had open campuses and kids moving back to that setting weren't really exactly sure what what to do in that setting those first couple days um i think the the whole idea of co-curriculars and building culture uh you heard homecoming being referenced um there's a north south volleyball game this week that both of our athletic directors said it was probably the best atmosphere they've seen at a sporting event in a long long time so those kind of things i think are exciting for our students exciting for our schools and really that return to normalcy um on the academic side of things uh i think the one piece that our our high schools both of them are really working hard on i should say both all of them are working hard on is really to make sure that any of our students that did fall behind from a credit standpoint have opportunities to get caught up sooner rather than later so that we put them on a path to graduate with their class um as we we progress on here we're talking virtual instruction and very briefly here as we said about 120 um kids participating in the online elementary and then uh Warners numbers up 10 15 20 percent depending on the day but there's they're relatively small numbers i think 75 at the middle school about 130 at the high school um and our third friday report will will be out soon and that'll give you a little bit more information there i think you know we're in the same predicament that that we have been we've seen some families last year that that wanted out because we were taking maybe too many precautions in this year we've seen some families dip out because they didn't feel the precautions were enough but overall i think our enrollment is is pretty stable and will be around um 9600 last piece is the budget implement uh implications and we uh shared this with you last year as well so we have our lexie subscription uh we retain current staffing levels to help with class sizes as kids transition back um kid stop has uh been a challenge to staff uh but it's a great opportunity and you can see a ton of interest from our families and uh you know obviously uh a way for our elementary students to gain additional educational opportunities after school tutoring program is being set up at the middle school and really they're they struggle i think to get kids to stay after school so they're trying to also incorporate it into lunch and times when kids are at school to um help with any remediation there kelly and i continue to work with um different companies as far as possibly bringing in act workshops um one thing we know right is you're going to benefit from from those workshops or from that study but it's expensive um so some families can afford it some can't we're trying to remove those barriers for our kids and and have all kids get access to that with this covid funding um and then we had our smaller class sizes during summer school which was a success as far as enrollment numbers go uh bridges looks good by all intended purposes eric and and his team made a great uh purchase there when they went through that adoption process and um that's supported with these funds and then our guided region materials really focused on hitting our kids at their at their readiness levels um have been a nice addition to our elementary schools as well then would um will we get our next group poured out give a timeline in mind hopefully um end of october would make the most sense so basically in a month yep just waiting for um right some extra data to come in and state hasn't said when they're going to take them bar go off the forward data so that's that's always a piece as well right thank you this is great good information to have and look forward to you know i could see this being kind of a regular regular i've done that i'm moving forward to kind of keep tabs on to the degree that you think you've got new information to report out right and so i think one of the things we really want to get back to and and jake and his team have done a great job putting it together and and working but as you recall we've had presentations always throughout the year from our high school so i'm offering college readiness elementary schools talking about their goals and what they're focused in on will have that additional district data and from the those factors that you saw or those critical areas you saw tonight as well as our internal report card data some of the state stuff so as they look as a team to be able to bring that back it really helps you stay on top of where we're at and it helps us be able to share all the wonderful opportunities we have and also where those challenges and struggles are in areas that we need to continue to focus in on to ensure all our students are through in college running thank you i think we'll do d and e together since their second readings we got a motion for the adoption of d which is second reading of new board of ed policy 75 44 use of social media and e which is second reading of revised board of ed policy 91 30 public request suggestions or complaints any questions on the second read all those in favor say aye opposed motion carry dates um can you help me one meaning so i march is always shepherded this process and i spoke to her and she is going to respectfully not shepherd the process anymore which i am thankful we're all thankful to her for um all the work she's put into it but she's going to let it go so i if someone wants to be kind of the new champion the dates process let me know i guess offline otherwise i will keep my name next to it and i can take notes as part of their job description well do we formally say that well when i was vice president that's hoping i kept it we'll talk okay good we'll talk anyway i think what we need to do tonight is we need to adopt the document that was in our packet correct line the four goals for the coming school year and then set in motion essentially the process that hopefully now we're all you know some of the new board members are still getting into because you've only done the font but the rest of us should be fairly familiar with so really david if i can interject the two the two things you really want to do tonight is one is the four goals that i have there for for my personal goals that you would adopt or approve tonight or ask questions about um and then two is to be ready to at the october meeting to be ready to provide feedback and you facilitate a conversation enclosed regarding that formative performance report so we would do that in a month you do that in typically we've done that the first meeting of the month as opposed to the second but that's up for debate work fits best on the agenda okay board five right last two pages right those last two pages those what are there six performance standards yes yep board members you would write down comments specific evidence of regarding those six performance standards and what we would do is we would discuss those through any questions regarding the four goals that were submitted that were in our packet was um the role the district administrator in achieving the goal has that always been there or was that a new feature sure that was added by dave's just really to try to solidify is this really something i'm personally doing all the work for this is something where i have the direct responsibility this is something i help me to facilitate or is that really you know i'm either guide on the side sort of but you know ultimately i'll rest that at the end of the day with myself but where where's my role within this goal because there's many things that occur across the district obviously that i need to help facilitate you need to help guide or i'm directly doing so that that was new i like it it really helps you understand a little bit more about where my role is in that as opposed to what the role is in right thing yeah yes correct and i like that as well yep the quick question set i mean i appreciate and uh support all of these and i think it makes sense here over your continuity and most of your job is a long term strategic role um one just quick question on the development refinement leadership succession plan if i remember correctly we did have a closed session when we talked through succession planning is there is there a change to that or is that a different indicator of success or i'm just just curious if that um is tied to what that was or is this addressing a different piece yeah one of the reasons i want to keep this and this would be a goal that i had last year and we added to don as a result of the board really asking for more clear levels of communication around succession planning what does that mean not only for the my role but for all the roles within the district so i wanted to maintain putting you know having this on here as a way for us to continue to refine that as we see people seeking out other opportunities what does that look like how do we help develop we're going to have some potential retirements in the next couple years are there internal people that we want to provide additional opportunities for or are we looking at this point in time that might be an external role but how do we maintain this this notion especially around our our leadership of our close to 70 administrators across the district how do we ensure that we've got continuity and that we're providing people the opportunities to grow and develop but i would envision that same thing kyle in addition to the reporting out on specific opportunities for leadership growth but for us to also have some conversations about succession planning what does that look like thank you questions not an inner emotion to adopt this document is presented questions you're not all those they were saying you post motion carried so again board members we'll get back to you on the timeline again normally we would do that report out in two weeks but we'll we'll see how that where that can be the whole agenda lands and whether or not we want to do that night night or do we want to do it a month okay reports of committees curriculum and instruction kyle item number one is for information seclusion and restraint report no crazy outliers here in terms of numbers it's pretty standard year over year for newer board members that is our annual report out on times when a student is secluded or physically restrained and a lot of times we're seeing that more with students that have certain disabilities that involve their behavioral disorders but pretty standard there and number two is the graduation requirements this is required by state statute these are not any different than pre-covid and actually we're kind of returning back to it there were some adjustments as a result of what it impacted that that march of 2020 so i would move approval of item two graduation requirement hearing none all those they ever say hi hi you post post curate thank you item b re human resources committee mark i would move approval of item number one appointments and item number two leave of absence that were listed in the committee minutes can you post motion carry hands william started today itself his first day as associate principal we're happy to have william join our team and he was one of those appointments under number one we'll have him be introduced with the board at the act over 12 meeting we're shipping them coming he will give an introduction of himself and speaking to meet william facilities recreation and theater committee ryan approval of item number one the fund balance request with five-year capital schedule and what this is is there's only one item that's being requested as as a capital expenditure using using their fund balances here and what it is it is a a field liner which john tells me it is fancy is all get out but it will save time and paint apparently so it's it's so whatever you were lining the fields at north urban or field dreams or whatever it it saves a significant amount of time apparently it's all gps run and everything else so it's got bells and whistles but in the long run it it's it's needed is it'll it because if anything it'll save time for the workers who have to run it question all those in favor say aye any opposed motion carry anything else ryan finance and budget committee marsha thank you items one two and three are we're in the audit right now so it's we don't have any information till the audit is completed item number four we're going to address an item number nine and i have three first readings that i'll read individually i'd like to move approval of first reading a revised board of education policy 72 30 gifts grants and be plus shins all those in favor say aye i me impose motion carry first reading of revised board of education policy 75 50 joint use of facilities interlibrary loans questions all those in favor say aye i be opposed motion carry item number seven i move approval of first reading of revised board of education policy 84 05 environmental health and safety program questions all those in favor say aye i me opposed thank you and then i'd like to um move approval of gifts in excess of 2,500 dollars by the urban family in the amount of four thousand dollars for james madison school and acuity for the shaboy and the amount of ten thousand dollars for the shaboy and theater company questions those who've ever say aye i be opposed motion carry it and then i would like to move approval of item number nine budget revisions and transfers of appropriations this was not cited correctly at our committee meeting so we need to take action this evening on that line item any questions all those who've ever say aye aye any opposed motion carry and that's it thank you marshal kyle anything for committee of the whole nope legislative i don't know ryan if you were there or south got it go ahead hi thank you mr president um i was a little bit late to the meeting because i had to download i think my eighth different uh streaming meeting meeting app so i missed the first part of the meeting most of it was actually talked about um is a discussion that was generated by um by mr rugink over at um over at usberg you know just and it was a it was talking about how do we you know with everything that's been going on with you know with the public and being very you know very involved in covid and crt you know how can we reduce the temperature um and like with many things that are you know that that's been going on in in our society the we didn't come up with an answer we're not going to anytime soon but but that was a significant part of the of the discussion from when i was able to participate and so we talked about uh towards the beginning we're just updates from districts around their you know what they're seeing the welcoming back of students opening of school etc a couple things to point out the legislature was meeting today number of bills that are being put forward will be interesting to see where the senate that was in the assembly today senate was trying to vote on some as well many of those bills talk about you know implementing mandates at the state level that will have a direct impact on us whether that's curriculum transparency and posting of of resources whether that's what we can and can't do around the work of of race equity etc handwriting first of bill fiscal transparency bill there is a and one of them for the life or reading assessment bill and civics education bill all around what are what schools should do or what schools shouldn't do all applied to the public schools and charters but not applied to our voucher program schools so that was a point that i brought up for our legislators as well as you know we've got more than three million dollars of shabuigan area school boundary dollars if you will going to private schools who are involved in the parent choice program and none of these bills impact them even the fiscal transparency bill does not impact them and so i've got some concerns just all the taxpayer dollars and you heard some people talk tonight about taxpayer dollars and yet very little has ever talked about our voucher schools and more than three million dollars that are being used and nobody knows a lot about it was there anything that they were actually proposing that they believe would actually be not vetoed by the governor that there's actually changes being proposed that could actually be implemented because i mean i i don't anticipate any of that would even if approved through the house and the assembly or through the assembly and through the senate that it's going to be approved by the governor so i mean it's going to be just a yeah i don't know at that point where it ended up but that really goes back to ryan's point when the question was asked you know tell us more information about the bills where do they stand locally and how do they support them or not and it was really a conversation around well this is what there are fellow legislators are doing if we support it we've probably signed on but they have been receiving unanimous votes usually on party lines either side so it was one of those discussions about how do we get to the real the meat of it and there were questions raised about local controls i.e the school board setting those parameters about different curriculums that we want to see as opposed to the legislator saying this is what you should do as a school board so some of that at times does does make for interesting conversations about who should control those those decisions was what happens after the covid money runs out as if we're all aware um joint finance and they all were signed by the governor didn't give us a rate you know they're not they're not um you know they basically said well you have this covid money that you can use for you know for your per student expenses um we're not going to do we're not going to increase your um you know your per student your per capita expenditure are you either whether it's a limit or the the amount that you're able or the amount that the state is giving through a um and this and that was a concern that was brought up by pretty much every single district you know conservative areas not so conservative areas it's the what is your plan now that you've done this you know as you know as the legislature where you're going with that yep good summary of the meeting right if you're paying anything off on legislative for questions uh citizens facility advisory committee mark you referenced it a little bit so the minutes were included in your packet we met last monday at farnsworth middle school so uh principal Todd de Bruin and uh representative from bray and uh joe volmer and dave albright from facilities led the group on a tour of the building we just looked at some of the challenges with the size of the rooms there and those facilities that related to um classrooms and then uh joe uh and dave focused on some of the more of the infrastructure difficulties they have in that aging building and then we discussed uh we went outside and kind of showed what parts of that building in the uh suggested draft by bray would stay so that newer newer section that includes the gym would remain and then a new school would be built to the south of the gym and then when that was completed they would take down the the old part that is basically all the classroom space us north of the gym so so the group had a nice tour they kind of understood the plan that that bray brought forward um and again we'll just continue to meet uh we're still deciding on the location of our next meetings so thank you mark questions for mark and then finally looking public education foundation um i wasn't able to be there yeah i arrived this uh extremely late myself so um the minutes are there for your um reading enjoyment and just remember all in for education is the first friday and put the pine hills new location and you want to buy raffle tickets um buy them for myself first though maybe the grand raffle prize is an autograph jersey by yannis on the buck i think could be a pretty cool uh pure bucks person that would be a nice that's the grand prize that's the grand prize there's a bunch of other bunch of other communications uh are listed that we have been receiving lately future meeting dates uh committees on the 12th and the regular board on the 26th at our regular times um we'll see where we plan in terms of location for the communities on the 12th it'll be in one of the buildings to accommodate a bigger group we'll just have to see where we do it so just be on the lookout for different locations then downtown yeah just a shout out to our electronics guys yeah to really work and get everything set up and yeah thank you guys yes um it takes a lot and hopefully you know based on feedback and and we don't do this enough to get in rhythm but you can tell it was much better tonight the sound here and perfect process yeah yep yep i need a motion to adjourn all those in favor post for your adjourn thanks everyone


Welcome to the course on power system dynamics and control. Power system dynamics and control is a subject which is concerned with the transient processes which occur in a power system. A power system is continually subjected to some disturbance or the other. The disturbance could be quite severe like lightning which may result in the tripping of some of the power system components or it could be very benign in the sense that a load change also is a kind of a disturbance on a power system. So, if you for example, switch on a bulb you are actually subjecting the power system to a kind of a disturbance and we would expect that whenever a power system is subjected to any disturbance you would expect that it would settle down to some kind of equilibrium. So, even without going through the whole you know detail of what is stability and what is equilibrium what is instability we have a kind of intuitive notion about stability in the sense that we expect that voltage magnitudes which are available to us are going to be steady the frequency also is steady. So, the fact that for example, in this classroom the bulbs and lights are absolutely steady in a sense shows that the power system at present is stable. However, there are situations in which a power system may lose stability and it can happen quite dramatically. In fact, if you look at the past few years past 10 years you will find that some large or small grid disturbances have taken place in which some kind of instability has occurred and there has been consequent loss of load to a customer. So, you will see that it is important to learn the subject you will notice that a power system is in fact, a very very very large system it can it consists of many components diverse components and is spread over of huge geographical area. So, typically you know power system could span a entire nation for example, tens of thousands of kilometers. So, it is important to learn the subject of power system stability so that we can design operate a power system in a reliable fashion. The word plug and play has been in vogue for almost two decades, but in a way a power system has been a plug and play system for more than a century to make a power system work normally one has to control it. As we shall see there are some inherent phenomena which occur in a power system which lead it to instability. So, we should operate or control the system so that it is stable before we go ahead with what is stability and what are the basic phenomena which occur in a power system. Let us first understand what is the structure of today's power system. As I mentioned it is a large system having a large number of diverse components. The first lecture is usually an overview of what we are going to study in this whole course about 40 lectures. So, I will not deviate from the tradition we will have a overview of the course in this lecture as well as the next. Today I will concentrate on showing to you a nice phenomena we will even have a small video clip to display to you a certain kind of phenomena which occurs in power system it is very interesting, but first let us have a look at what we are going to study in this particular lecture. We will have an introduction to power system problems stability problems in power system in particular we will concentrate on one particular phenomena today. Then around the end of this lecture I will give you a course outline some prerequisites and the reference books. So, as I mentioned some time back let us first try to understand the structure of a bulk power system. So, the next point which we are going to study is the structure of bulk power systems. If you look at power systems of today they are spread over a huge geographical area and consist of generators interconnected to each other they all interconnected to each other through a bulk transmission network. For example, here there is a generator which generates power electrical power at a voltage of around 16 kilo volts a single unit could be generating as high as 1000 megawatts I mean there are generators unit sizes 500 megawatts 1000 megawatts 210 megawatts. So, this each unit could be itself generating 100s or even 1000 megawatts and there could be several such units within a power plant though here I have just shown you one. The voltage 16 kilo volts is inadequate for power system transmission otherwise it will cause a large amount of losses if you try to transmit this electricity over large distances. So, what we have is a step up we step up the voltages to around 400 kilo volts or 220 kilo volts. So, that we can transmit it over large distances load centers could be sometimes several hundreds of kilometers away from where the generation is. So, you cannot avoid transmission. So, you what you see is that you have high voltage transmission lines. So, that you can transmit bulk power over large distances with lesser losses they can be actually several e h v voltage level extra high voltage levels for example, 220 and 400 k v system. In fact, the 200 k v system may be embedded in a 400 k v system, but to interconnect the 400 k v and 220 kilo volt system you do require a transformer in this case it is a auto transformer. Do you know why we use an auto transformer in case we want to transform voltages say from 400 k v to 220 k v whereas, we use a two winding transformer when we want to step up voltages from 16 to 400 k v. The answer lies in the fact that whenever the voltage step up ratio or step down ratio is relatively small in this case around 2 and auto transformer gives you a cost advantage a substantial cost advantage. Moving on we see that a power system may be meshed in the sense that they may be two parallel parts two transmission parts from point say a to b you can go it go from here or you can go here. So, in some sense a power system being meshed is also quite reliable in the sense that if one of the transmission parts say this transmission line is tripped you do have alternative power transmission parts. Now, you in addition to AC lines you could have in special circumstances DC lines. DC lines essentially are transmission lines which are operated at DC voltages obtained by rectifying the high voltage AC and inverting it at the other end. So, you have got a kind of an HVDC link here. So, large power systems typically will have one or two HVDC links embedded in there. We shall see later that HVDC links may also be used for special interconnections called asynchronous interconnections. Now, one of the most important thing of course, is that loads are supplied at relatively lower voltages they are 66 k B which is step down further right down to 230 volts phase to neutral which appears in your electricity outlet in your home. So, this is the structure of the bulk part system from here onwards the load is at lower voltage and from here onwards the power system is more or less radial, but at the bulk level there is some level of meshing that is there are parallel parts from point any point any node from say A to B. So, some of the characteristic of synchronous grids today are they are three phase AC they are essentially synchronous systems which are I shall elaborate on this point and that usually connected by AC lines except for special situations like very long distance transmission or asynchronous connections DC links are used. So, you will find that you will find that mainly the AC power system of today is consisting of synchronous machines interconnected by AC lines. Now, one of the most important implications of this is that all the synchronous machines in steady state operate at the same frequency this appears almost surprising, but if you kind of a take a special situation or you take a typical situation you will find that if two synchronous machines are connected to each other and they are running at different frequencies we will not have steady magnitudes of voltages or power flows. To see this let us consider a simple example consider two synchronous machines one operating at 50 hertz and the other operating at 51 hertz the question is what is the nature of power flow between the two generators. In fact, in this particular diagram you have got a synchronous motor and a synchronous generator. So, if one of the synchronous machines is operating at 50 hertz and the other at 51 hertz what is going to be the nature of power flow and the voltages at certain points in the network. You notice here that the synchronous machine has been represented by a voltage source. In fact, most of my or other a large part of my course is going to tell you how a synchronous machine is not actually a voltage source, but something much much much more complicated. So, let us actually analyze this situation where you have got one synchronous machine which is operating at 50 hertz and the other at 51 hertz. If you have got two sources connected to each other by a transmission line which is represented by its reactance x. In fact, there is a big story of how we come to this representation of a transmission line by a lumped inductor, but we will keep that for some other time. In fact, x is nothing but the frequency omega into the inductance of the line. So, the inductance in fact is the inductance per unit length into the length of the line. Suppose you have got two sources v 1 bar and v 2 bar. So, this is a phasor representation. Suppose v 1 bar is equal to v 2 bar.  What does this actually mean the phasor representation? Let us assume of course, that the frequency of both the sources is equal that is say f 0 could be say 50 hertz. So, the instantaneous value of the voltage waveform here is root 2 v 1 sin omega t plus phi 1 and v 2 is equal to root 2 v 2 sin omega t plus phi 2. So, v 1 bar and v 2 bar essentially is equal to v 2. What is the expression for power flow from source? The first source to the second source in case your phasors are defined in this way and both these sources are at the same frequency.   Remember that in a three phase system cumulative three phase power flow is a constant. Remember in a three phase formula of power v 1 and v 2 represent the line to line RMS voltage magnitude at ends 1 and 2 respectively. Now, if you have got a source v 1 bar has a frequency f 1 and v 2 bar has a frequency f 0. There is a difference of frequencies here in that case the question arises how do you get the power flow expression? Now, to a very good approximation if f 1 and f 2 are near equal in that case I can directly use this formula v 1 v 2 sin phi 1 minus phi 2 by x. But remember now this phi 1 is changing with respect to phi 2 how is that so?     So, you have when I apply this formula this is formula I should use phi 1 minus phi 2 by x this is the way you will apply this formula even here you will notice that this is an approximation you cannot have power equal to this expression exactly. One of the objection which you will immediately see is that when I use this value of x should I use omega 1 or should I use omega 0 l. So, there is a this formula cannot be exact, but I leave it to you to show that this formula is approximately true you can directly use this formula for power flow. If omega 1 is approximately equal to omega 0 they are not equal, but then here equal. Now, what do you see in this formula? The power flow is not a constant remember phi 1 dash is phi 1 is changing with time. So, what you have is in case the frequency of the two sources is not equal power flow three phase power flow will not be a constant it keeps jumping around can you also show that if you got a source rather two sources with two different frequencies the midpoint voltage the magnitude of the midpoint voltage also will not be a constant. So, magnitude of the midpoint voltage is also not a constant if the frequency omega 1 of this source and omega 0 of this source is not equal. So, the basic thing which I wish to tell you here is that if I do connect two synchronous machines together and they are operating at different frequencies they may be very close to the frequencies may be very close to each other, but they are slightly different then you will find that both the power flow as well as the voltages along the transmission line this something you can generalize are not going to be constant they are going to keep jumping around. So, your voltage will not be a constant at a particular location. So, you cannot have a situation you cannot have a steady situation if your voltages rather the synchronous machines are not operating at the same frequency this is a bit intriguing because it means that if I got synchronous machines which may be thousands of kilometers away, but if they are interconnected by AC lines then in steady state they have to be at the same electrical speed. See I just plugged in these values with two sources 50 hertz and 50 one at 50 hertz and the other at 51 hertz and the waveforms which you get are these. So, this is something which I have explained to you analytically that your power flow is not going to be a constant and the midpoint voltage for example, also keeps jumping around it actually jumps around at the difference frequency. So, if you got two sources one at 50 hertz and one at 51 hertz and you connect them together then you will find that the voltages jump around at the difference frequency. So, the point of course, here is that we cannot operate steadily in case you have got synchronous machines connected by AC lines if they are operating at different frequencies. So, something which obviously comes to your mind is what keeps the machines in synchronism can we lose synchronism. The answer to the first question is something which you will learn in this course the physical equations which describe the motion of synchronous machines as well as the behavior of the electrical network really determine the fact that synchronous machines tend to stay in synchronism if they interconnected. So, if you take two synchronous machines and interconnect them properly then they tend to stay in synchronism unless they are subjected to some large disturbance certain large disturbances. If the disturbance is very large it may so happen that synchronous machines may lose synchronism. So, what you have is once the machines lock on to synchronism they move together if there is a disturbance they could be a transient but eventually the system stays in synchronism. So, a system operator does not have to do any manually intervention to ensure that the synchronous machines in our system are remaining in synchronism. However, a system operator has to know and understand that a system can the synchronous machines can lose synchronism under certain circumstances. In fact, I will show you a situation in which synchronous machines are going to lose synchronism. In fact, the highlight of this lecture in fact is a small video clip which I am going to show of a synchronous machine losing synchronism in a laboratory. So, this is the first and one of the most interesting stability phenomena which you have you are going to learn in this course. Of course, by the time you are able to analyze this particular phenomena in a more rigorous fashion remember I took recourse to somewhat you know approximate expressions for power flow in case of synchronous machine operating at different frequencies and try to prove to you that the synchronous the system will be very unsteady in case your frequencies are different. But later on in this course we shall take a more rigorous modeling approach and we will try to rigorously show that this in fact is true. But today I will show you a video clip in which you can actually see this loss of synchronism and once you lose synchronism of course, things are not steady and when you have synchronous machines not in synchronism you have to disconnect them. So, before we show you that video clip of the experiment let me just tell you a bit about the experiment. So, that you can appreciate what is really going to be shown to you what we have in the laboratory is a synchronous machine. The synchronous machine I will just show you a very simplified kind of single line diagram will be interconnected to the laboratory three phase supply. So, three phase synchronous machine running at 1000 rpm roughly 1500 rpm it will be interconnected to the lab supply. The lab supply of course, is obtained from the western region power grid of India. So, here when I am going to connect the synchronous machine to the lab supply I am in fact connecting it to the huge western regional grid of India. This synchronous machine is run by a prime mover in a real power system this prime mover could be a steam turbine it could be a hydro turbine. In the laboratory it is in fact a DC machine a DC machine which is connected to a rectifier which gets its supply from a transformer which is again being fed from the laboratory supply. So, what you have here is the laboratory supply is supplying power to the DC machine the DC machine runs as a prime mover to the synchronous machine and eventually of course, we will put this power back to the lab supply. In a real system this would be a turbine a steam or hydro turbine we are able to we are able to vary the voltage applied to the DC machine by actually this is not a two winding transformer actually it is a it is actually a we will just redo this. This is a laboratory supply it is in fact connected to an auto transformer. So, this is in fact connected to an auto transformer this connected to a diode rectifier this is in fact connected to a DC machine the DC machine runs the synchronous machine. The same lab power supply also feeds the field winding of this DC machine. So, the field winding of this DC machine is actually being fed from the lab supply also this auto transformer of course, is a variable auto transformer. So, actually I can change the voltage to the DC machine by changing the trans auto transformer taps. The field of this synchronous machine is also fed through a control of rectifier which is also being fed from the laboratory supply. We can actually control the field current to this field winding of the synchronous machine by controlling it through a control rectifier. The reason why we need to control it actually is that once we load a synchronous machine the voltage tends to fall at its terminal. So, we are actually having a closed loop regulator which roughly not perfectly regulates the output voltage of the synchronous machine. The synchronous machine is driven at roughly 1500 rpm which is the frequency of a laboratory supply. I would say 50 hertz is the laboratory supply frequency and this is the 4 pole machine. So, we have to actually run it at 1500 rpm. The synchronous machine has to be connected to the lab supply. Now, it is connected to a lab supply, but can you connect it directly? You must have done this experiment in your undergraduate years. It is called synchronization of a synchronous machine to a power grid. You have to do it carefully. In fact, if you do not do it carefully you will you may find that the transients may be undesirable and unwelcome and you may not be in fact able to synchronize properly also to the grid besides giving a big shock to the shaft of the synchronous machine. So, you have to actually do this synchronization process very carefully. One thing you have to check is that the voltage at this point the voltage phasor here and the voltage phasor here should almost be equal. So, if I connect this synchronous machine when the voltage phasor here and the voltage phasor here is almost the same then you will find that it will be a fairly bumpless transfer. Of course, it is implicit that this is a 3 phase system. So, actually this has to be insured at in all 3 phases. The frequency of both the systems the lab supply as well as the synchronous machine output also must be near equal and the phase sequence also should be the same. In that case we can have a steady state power flow. We can actually have a steady state power transfer between the synchronous machine and the grid. Now, how do you ensure that before you connect the voltages are almost the same? The voltage phasors in each phase are almost the same. You do it by measuring the voltage across both points or one simple way of doing it is you connect some high resistance bulbs in each phase. So, if you got point A and B in parallel with this switch you connect a bulb. If this bulb is always dark absolutely dark it would mean that the voltage is voltage across A and B is equal all the time and in that case it is a good time to switch on this. But of course, if the frequency of this synchronous machine and the lab supply is slightly different from each other the phasor voltage A with respect to the phasor at B will be continually changing and you will find that the lamps will glow bright and dark. So, you should connect at the point or you should adjust the speed so that the voltages here and here are almost equal. So, you should switch on at a point at which the voltages here and here are almost equal and that occurs when you have got the dark period. This will become very clear when we actually do the experiment. Now, one or two small points the synchronous machine on its shaft I have mounted a plate on which I made a cross mark. When the machine rotates you will not see this cross mark normally because it rotates at a fairly high speed you will not actually be able to make out the cross mark it is a white cross mark. But if I have got a device called a stroboscope the stroboscope which is essentially a device which gives flashes of light at the frequency at a certain frequency you will find that suppose for example, this is moving at 1500 rpm and this flashes at 25 hertz it gives a very narrow pulse of light at 25 hertz. So, it is giving a narrow pulse strain in fact of light at 25 hertz. So, what you will find is that whenever there is a pulse of light you will see this cross. The next time the pulse of light comes this cross would have completed one revolution and it will be exactly at the same point again. So, using a stroboscope which is flashing at 25 hertz if you look at a cross mark which is rotating at 1500 rpm which is again 25 hertz you will find that it is look stationary. So, in fact if I you connect this stroboscope such that it flashes at the frequency of the lab supply. So, it flashes at the frequency of the lab supply I can make out whether I am in synchronism or not by looking at whether this cross is stationary or not. If this cross is slowly moving it would mean that the frequency of this rotation is almost equal to the frequency of the lab supply. So, what I will do is I will arrange. So, that this stroboscope is in fact flashing very narrow pulses of light at the same frequency as this lab supply. In fact it is since this is a 4 pole machine I will be actually reducing the frequency by half and making it flash at 25 hertz or whatever the laboratory frequency half of it. So, this is something you will notice in this experiment before we show you the video clip I will just show you how this setup looks like. So, this is the still photograph of the laboratory setup I will quickly show it to you this is the synchronous machine this one here this is the DC machine this is the DC motor which is the prime mover this is the cross mark I was talking about this is the stroboscope which flashes at half the frequency of the laboratory supply. So, that if the 4 pole machine runs at the same frequency or rather the electrical frequency if it is near 50 hertz which is the near about the laboratory frequency you will find that this cross mark is moving very slowly and when of course, the frequencies are equal this cross mark appears absolutely stationary. This is the panel which we use to control and measure the synchronous machine parameters using this auto transformer I am able to do armature voltage control of the DC machine. Remember by changing the armature voltage I can increase the amount of torque provided by the DC motor at a particular speed. So, if the DC motor is running at a particular speed and I increase the armature voltage it will increase the armature it will increase the torque of the DC machine motor. So, I can actually increase the amount of power mechanical power available at the shaft of this machine once I synchronize the synchronous machine to the grid I will in fact increase the power input to the DC motor by increasing the armature voltage and I will try to push more power into the laboratory supply. The current and power of this alternator are viewed by looking at these 2 meters this is the frequency this is the synchronization switch this is the dark lamp corresponding to 3 phases dark lamps corresponding to the 3 phases this is a terminal voltage of the machine this is the field voltage and field current of the machine. So, I hope you will get a kind of a feel of the laboratory setup which you are going to see. So, now over to the video clip what you are going to see here is that if I once I synchronize the machine to the grid if I increase the power flow beyond a certain point you will find that the machine which actually is in synchronism with the grid after it is connected falls out of synchronism. The important thing is that while I am increasing power a little bit the synchronous machine does not lose synchronism you will only find that the cross mark is moving showing that there is some temporary acceleration of the machine. But the machine still remains in synchronism once it is connected to the laboratory supply but after a point you will see something happening. So, over to the video clip we start the machine the DC machine by armature voltage control the DC machine field has already been switched on. So, the machine has started the cross mark on the machine is not stationary indicating that the speed of the machine is not equal to that of the grid. We now excite the synchronous machine the voltage builds up in a control fashion we are increasing the field through a controlled exciter. So, it gradually increases it is ramped up there it goes approximately up to 150 it is programmed to increase that way. We now give step changes to the voltage reference of the controlled field. So, that we get the voltage near about 230 volts which is equal to roughly the voltage of the power supply the lag power supply. We now switch on the laboratory supply and as I mentioned in my sometime ago the dark lamp starts start glowing at and a blink and glow at the difference frequency. We control the speed of the armature by armature voltage control and we get the speed almost equal to that of the grid and we synchronize and you will notice now that the cross mark is absolutely stationary. Once we have synchronized we can feed power into the grid by increasing the power output of the synchronous machine this is done by actually increasing the power input to the DC patient motor. So, you see how the power is increased and simultaneously you will find that the cross mark is moving if we increase it beyond the point. However, so he is doing that so increasing the power input beyond the point after the point it just loses synchronism. See how the current and power meters move quite widely even the terminal voltage of the machine keeps jumping around note that we are still connected to the lab supply, but we have gone out of synchronism and we cannot operate this way actually because the talks the power voltages all fluctuate very widely so eventually we have to disconnect. So, this is basically a illustration of the loss of synchronism phenomena of a synchronous machine connected to the lab supply. What we saw was if we synchronize the machine it locks on to the frequency of the lab supply, but if we go on increasing the power beyond the point the machine can lose synchronism. So, we now stop and shut down the machines. A natural question which may come to your mind is when you have a large system can you use lose synchronism in the same way as the synchronous machine in the laboratory which you saw some time ago the answer is yes. For example, in the western region of India we have seen that in the past decade there have been several instances where this has happened. When there is a large disturbance groups of machines on one side of the grid fall out of synchronism with other groups of machine on the other side of the grid. Here of course, I have just shown you a few machines there are lots and lots of synchronous machines interconnected by lots and lots of AC lines what I am showing here is just a schematic. So, you find a group of machine the big group of machines fall out of synchronism with another group of machines. This is in fact, the manifestation of the same phenomena which you have seen in the laboratory. So, you have got a set of machines they tend to remain in synchronism when connected by AC lines when the synchronous machines connected by AC lines, but when subjected to a large disturbance these may fall out of step. Once they fall out of step the power flow in the AC lines as well as the midpoint voltage keep on jumping around and you will have to actually separate out the systems you cannot operate that way. In fact, when machines lose synchronism they can cause large transient power and therefore, shaft arcs which may damage a synchronous machine. So, that is the reason why we do not we cannot continue to operate under loss of synchronism conditions, but as you saw in the laboratory when you connect a machine to a laboratory supply it does tend to remain in synchronism and slight changes or disturbances which occur do not cause the machine to go out of synchronism right away. Only after you go beyond a certain limit or the system is subjected to a large disturbance that you may fall out of step. If you fall out of step as I said some time ago you will have to separate out the machines which have fallen out of step. Although I have discussed a particular phenomena of interest that is loss of synchronism it is important to point out that you can have a synchronous operation that is synchronous machines not running in synchronism under certain circumstances and still be stable. So, you can have synchronous machines interconnected to each other, but they are still stable every power flows are stable terminal voltages are stable. When can this occur one of the most notable examples is when you connect synchronous machines via what is known as an asynchronous link. So, if you have got two synchronous machines say two synchronous machines or two systems. So, you have got system one and system two consisting of a large number of synchronous machines interconnected by AC lines. So, if you got a this is only a schematic if you got a large number of system synchronous machines interconnected by AC lines the frequency throughout here that is the electrical speeds of all the synchronous machines will have to be equal if they are interconnected by AC lines similarly here. So, this is system one and two themselves are synchronous grids. So, they have got many synchronous machines interconnected together by AC lines. Suppose this is running at 51 hertz and this is running at 50 hertz they are happily running at different frequencies, but if I decide to interconnect them by an AC line there is going to be a problem I cannot just connect them just like that they may they may they may not synchronize. And the second thing is that if they do not synchronize you are going to have a large number of power and voltage variations. So, instead of doing what is known as an AC interconnection instead if I rectify the voltage here and I invert the voltage here using controlled rectifiers thyristor based controlled rectifiers I can have what is known as an asynchronous link. The asynchronous link basically uses rectification of AC into DC and again inversion of AC into DC, but the important point is power flow through the link is no longer a function of the phase angle here or the phase angle here nor is it dependent on the frequency because you are rectifying the AC voltage and making it into a DC voltage. So, really the frequency at this point and this point do not matter the power flow is actually going to be determined by the DC voltage here and the DC voltage magnitude here the difference of the DC voltage magnitude is actually going to determine the power flow through the line. So, in fact you can operate stably with this at 51 hertz and this at 50 hertz or any other pair of frequencies the power flow will not fluctuate. In fact, the power flow can be maintained constant by controlling the firing angle of these rectifiers which in turn control the DC voltage at the two ends of the DC line. So, this is what is known as an asynchronous link. So, remember you can have an asynchronous link in case you have got what is known as a DC interconnection. So, the question which I would like to ask you is what I am going to show you in the next slide is it a synchronous grid or is it an asynchronous grid please have a look. So, you have got a DC line as I mentioned sometime ago two areas connected by a DC line, but importantly in this particular example there are AC lines in parallel as well. So, is this a synchronous grid or is it an asynchronous grid? The answer is that it is a synchronous grid the reason is that the power flow in the parallel AC lines is still determined by the phase angular difference at the two ends. So, the frequencies of the synchronous machines on either side of the grid are different you will find that the power flow will keep will be unsteady in the AC lines and as a result we will not be able to operate stably in this fashion. So, this what I showed you was an example of a HVDC link embedded in a synchronous grid in such a case this is still a synchronous grid. An exercise for you find out how many synchronous grids are there in India and how many HVDC links are there in India. Out of those HVDC links which of the which of them are embedded in the synchronous grids and which form an asynchronous grid. So, we will try to answer these questions in the next lecture, but I request you to survey it survey and find out these answers to these questions. You can have a look at them again how many synchronous grids are there in India the number of HVDC links in India and how many of these HVDC links in India are asynchronous links and how many are embedded in a synchronous grid. You can of course, if you are not a student of India you can do the same exercise for your own country. So, the point is I have given you one case of an asynchronous grid in which loss of synchronism is not an issue because if you have got a synchronous two synchronous machines or two synchronous grids connected only by a DC link they can be operated at independent frequencies. Similarly, there are two more cases which you can consider in which synchronous operation is not necessary. The first case is a single machine a single synchronous machine which is simply connected to a load. So, it is a synchronous machine connected to a load. For example, if the load is a fan which is an induction machine typically or a incandescent bulb these loads they are not functions of phase angle, but they are functions of voltage magnitude. So, if you have got a single synchronous machine connected to a bulb or a fan in that case loss of synchronism is not an issue. Loss of synchronism is only when you have got two synchronous machines connected to each a two or more synchronous machines connected to each other. This is a situation in which loss of synchronism is not an issue, but remember if you have got a synchronous motor generator connected to a synchronous motor you can have a loss of synchronism situation under certain circumstances. Remember just a small point just because you have got synchronous machines connected to each other does not mean that you always have a loss of synchronism problem loss of synchronism can occur if there is a large disturbance some large disturbances not always. So, that is something you should remember I am just hinting to you and showing you possible scenarios wherein a large disturbance causes a loss of synchronism. Right now for example, the lab supply is steady and the lots and lots may be hundreds of synchronous machines in our grade and they are all running in synchronism. So, loss of synchronism takes place under certain disturbances certain large disturbances. One more situation where loss of synchronism does not occur is when a synchronous machine is connected to say an induction machine an induction motor or a induction generator for that matter. For example, you have got wind generators wind mills which are actually driving induction machines which are connected to your synchronous grid. These machines are in fact not running in synchronism with the synchronous machine in fact an induction machine generates power only if the frequency of it is slightly different from the synchronous machine. So, these are two situations in which loss of synchronism is not an issue in fact we shall see later that there are issues even in these small systems they are related more to voltage and frequency that is something we will do in the next lecture. You may have got the impression that the major problems rather the only problem in the system is loss of synchronism of synchronous machines connected by ac lines. The answer is no there are lot many other stability issues which may crop up in a synchronous grid. In fact you may have problems of unsteady or unstable voltages unsteady or unstable frequency even if loss of synchronism is not an issue. So, these are independent issues stability problem which you do encounter in a power grid. Then you have the effect of feedback controls improperly designed feedback controller using a power system can in fact cause loss of synchronism. Also in certain circumstances you can have adverse interaction between the electrical part of the system and a mechanical part. For example, the shaft connecting the turbines to the generator may have problems of torsional oscillations when connected to electrical grids which are series compensated by series capacitors. So, these are some phenomena which do take place which hopefully this course will give you adequate background to study. The course outline is as follows initially I will of course give you a introduction to power systems ability which I am which is already ongoing and we will also of course learn a bit more about this in the next lecture. We will also learn in the next lecture a bit about power system operation and control and then in the third lecture we will start move on to the nuts and bolts of this lecture that is modeling of physical systems. The principles of modeling and a simple analytical tools which I use to analyze dynamical systems. So, we will try to understand basic concepts of equilibrium stability in fact interesting point is I am not actually described to you what is stability or what is equilibrium, but I have hope that you with a intuitive idea of these concepts at least intuitively you would be able to understand. But we will do a formal analysis of these things in the lectures to come. A major chunk of our course is going to be in the modeling of synchronous machines, excitation and primer controls, transmission line, loads and other components. So, this will in fact take out take a big chunk of our time. The important point is that in modeling all these the most important thing is of course what approximations do we make. We will of course not be able to model all systems in their full glory otherwise you will find that soon the problems become intractable. In fact we will set ourselves the goal of trying to analyze a fairly large system.  For example, the western region of India or the complete central synchronous grid of India which is fairly large. So, let us set set ourselves that kind of a target in this particular course. The other things of course once you learn about modeling we will learn all the stability issues anew when you interconnect power systems. In fact the phenomena which I showed to you today will do it in much much more detail and much much more rigorously later on. We will also learn a few stability tools common stability tools for analyzing rotor angle stability or even electromagnetic transients. And eventually of course we should the whole aim of this course is not only to understand power system stability problems rigorously, but also try to find out solutions for some niggling power system stability problems. So, that is the last part of this course. So, we are setting ourselves to a very very big target in this course, but I am sure you will enjoy it. The prerequisites which you need for undergoing this course is basically knowledge of electrical machines synchronous machines DC machines induction machines basics of power systems transmission line modeling at least the sinusoidal steady state modeling of most components control systems and numerical methods. So, these are the things you would actually need to know if you want to really understand the power system power system dynamics. There are many books on power system dynamics and control I recommend three of them, but of course there are other books which are just as good, but I will be following the notation etcetera of the first book by K. R. Padilla, but all the books which I mentioned here are good and I am sure it is a good idea to read from all the books. So, that you get a good variety of topics which are covered to recap what we have done today is analyzed not analyzed I would say just had a brief overview of the structure of power systems and in particular synchronous power systems and we just mentioned hinted at several problems which are encountered in power systems, but we concentrated on a particular very interesting and intriguing phenomena which is the loss of synchronism phenomena in a power system and of course I gave you a course outline books and the prerequisites. So, our journey begins in earnest now and I think all of you all will enjoy doing this course. We will not sacrifice too much on rigor we would like this course to be not just an overview as in the first lecture, but allow you at the end of the course to actually use some of the tools or even develop some of the tools from scratch to analyze power systems stability problems. With that we come to the end of this first lecture see you again for the second lecture.