Training D2: Synchronous Machine Modeling

all right so Tom got to provide them a theoretical overview or the broad overview I'm gonna be about as much math as you guys assessments grad school and undergrad before I do that though I wanted to mention when I talked to Ashley we've done training on how to use the software here before some of the younger people here have never had that maybe so the training we're doing we're gonna have some hands-on stuff like Tom was doing but a lot of it is not going to be so I wanted to point out you guys may know this already but you come to our website power will calm you just come to the regular website if you go over to training and events and then online training along the left you'll see some various courses that we have one of which is a transient stability course actually most of the video that's on here was recorded here in 2015 you guys did this basically when BPA says can I take the training I always say yes as long as you give it to us we can share it with our other customers too so if you come in here and you wanted to learn more about you know transient stability basics you'd come in click here and there will be there we go you click on here there's a YouTube video on all of our training for all of our courses above the YouTube video there'll be two links one of which is slides that were used in recording this video and then updated slides because you know over time we update them but we don't rerecord because it's a bigger process so if you click down here I suspect this is BPA 2015 and there it is you guys did like went all out producing it and everything Gordon so this is ha but anyway you can go in here yes they added the music after Tom didn't come out to light show but anyway that's all on our website you can go do that you can you know bother your neighbors who are more experienced but all of that click here do this that really just software training is all on our website alright so I wanted to make sure you need so this presentation is the presentation I wish I had in grad school because it presented the way I understand it we're gonna go all the way back to how transient heard synchronous machines work and we're gonna start with synchronous machines because that is the vast majority of the devices that turn mechanical energy into electrical energy you know as a new engineer the fact is most of the new generators you deal with our solar and wind right now but you know most of the generators there in the existing fleet are some sort of a synchronous machine and there's you know a huge amount of literature on this dating back a hundred years so a couple good books the two books I tend to go to first well the book I go to first on any topic and transients and dynamic Stability is cool just because it's it's the biggest one it covers DC lines loads it just covers a very wide set of things it's a good reference book I suspect most of you have it it's actually not a good classroom book because the reason people buy textbooks like Tom is for the homework solution guide and the things at the end of the textbook because that's less work for him whereas this book is not it's it's not really it's a reference book it has problems but it's a great reference book a good theoretical book on synchronous machines is my old professor professor pie and Sauer wrote a book and a lot of it the reason I like this one is because the nomenclature tends to follow what actual commercial software does I'm not positive they chose that on purpose but that's it matches better what is actually written in code like power world pslf in pieces so a lot of the derivation I walk through really comes out of this book all right a few topics a lot of there's a lot of words in synchronous machine thoughts there's talk about stator and rotor stator and rotor really have to do with you know that where is the thing physically located in the vast majority of synchronous machines there are other terms related to the armature and the winding these are functional terms most of the time will present in a couple slides the armature is the stationary part of the generator and the rotor will have the field winding on it I assume it's possible to flip that and actually see motors DC motors will flip it okay yeah but so functionally as a power engineer dealing with these big synchronous machines you tend to think armature is the stator doesn't have to be true it is true in the motors we do for generators we do all right there are then other windings we're going to talk about in the math coming up they're called damper windings is what I like to call them mostly because when you say I'm worse or you just I think I assume that's just the French word for damping is it does anybody know so anyway it's a it's a it's an extra a winding that's added we'll talk about it a little bit that basically makes the Machine want to be at 60 Hertz so if you move away from 60 Hertz it creates a torque that tries to bring you back it's good for stability it's also good for startup you think you start out at zero this winding is creating a torque that's bringing you up so it wants you to go to 60 Hertz so it's it was created engineers figured out hey if I add a winding here it makes my machine behave better yep big scheme you've got the very ground I think so I think never seen their clan just work for you they're not in there okay I never saw no mortis or wine okay okay I mean the end of that exists but I would say yeah I mean I'll kind of have pictures of where they would be if they're in there you know so there's a novels we have we don't include those the model that we're going to derive here is basic it's going to have the field winding and it's going to have two damper windings on the Q axis and one on the D axis depending on how you set up the parameters you're essentially saying some of those damper windings are not there and then another topic is poles if you want your team to spin more slowly and you're gonna have extra poles actually let me just show some pictures up here in a second so like here is a round rotor where it's saying there's rst my hunch is I copy this off in a different language I bet they use this instead of ABC it's European okay so the eight you know the a phase is right here the B phase coming out and going in is right here and the seat base is right here so so there are three phases and there's one actually they call this a two pole machine of each winding has two poles in a in a winding that would spin more slowly like hydro plant would do normally view like this you'll have many poles and I what is the maximum number of poles that someone might have it was a lot so they they might have literally four or five there's four six eight poles even more okay yeah so if you have more poles that basically means that you can spin more slowly and still create a 60 Hertz wave form so now once you get to the models we have all of that is gonna go away but there's a whole bunch of math that goes there so alright just start with let's just assume we have a component machine so we have a base the dot and the arrow these represent windings so if you remember make sure you use your right hand put your left hand behind your back arrows coming out here so we have current that's going like this kind of down the armature up and back out and we create the a axis then is the right hand rule from that the B axis is right here it's going like this so the B axis is up this way and you can draw these positional axes that way and then finally in the middle we have a rotor the rotor winding is coming but arrows are going in and out this way so the d axis is in this direction all right from there so the D axis is related to the rotor and these ABC are related to the stator or the armature of the outside all right we then need to choose some other things the Q axis all right the Q axis is chosen as being 90 degrees out of phase with the D axis so then we have to make a choice do we make it behind or do we make it in front leading lagging is what people like to use the term so we're gonna use leading and we're gonna put the Q axis in front of that that is an arbitrary choice after that we need to define what is the rotor angle of the machine and again it's like well how do you how do you define it it's like Tom slack angle angles have to be with respect to what and the rotor angle is defined in the equations we use as the angle between the a axis and the Q axis so it's this angle right here all right be careful when I first started so kind of the history of transient stability our world existed from 96 until probably about 2006 and we didn't do anything with transient stability a couple things happened at that point kind of three two of which really are just kind of random first of all we could see wind and solar was starting to pick up and that was meaning more people were doing transient stability so I mean if I came to BPA in 1996 and I had a room like this probably two or three of you would ever run transient stability it's that very dimitri more okay but it was my point is it's grown probably twice as many people are more or more many utilities just didn't do it at all so from our commercial standpoint was like okay they're gonna be more customers that was the good reason to do the other reasons we started doing it is Tom got called and he's like offered to be a on the textbook but he had to write the book on transient stability the chapter on that so then tom was like oh crap I need to remember how transmissibility work cuz that was not the field that he worked it at that point in his career so he had to go back and remember how it worked and so naturally that got into simulator and the other issues we were trying to sell the China the time and our folks in China told us you can't sell the software toy without transient stability the irony is we did sell it there and no one ever bought transient stability so great that was all right so at that point then Tom's looking it up you know a couple years later I started looking at it as well if you look at textbooks on this topic those two choices I just made about where is the Q axis is it leading or lagging and where is the rotor angle textbooks define it differently in Kunar he defines the Q axis leading but when he talks about rotor angle he talks about this angle instead of this angle it's not wrong it's just an arbitrary choice so what he calls rotor angle is really 90 minus R rotor angle if you go look at another book the anderson book they define Q axis as lagging again perfectly fine the reason I bring it up is if you take equations out of Sowers book or the equations I'm gonna present and then go look at the con Kunda or Andersen Fuad book we're gonna have random sign differences all over my equations and some places they say Q will say D it's wildly confusing as a new person coming into this very technical field that the textbook nomenclature really isn't consistent be careful if you look at that alright basics of the synchronous machine so the synchronous machine kind of has two main inputs to it I should say that the output is on the armature that's the power going out into the system the two inputs are we have some device that is creating a DC voltage to apply to the windings on the rotor so this goes all the way back to like high school physics class where you took a you know a piece of iron wrapped wires around it and hooked up your battery and you're like 16 years old and then you sat and spun that device and you created some power coming out of it so this device we call it an exciter is creating this DC voltage here we then have another device somewhere that's applying a torque to spin this rotor and we call that device a turbine or and there's a control system on it called the governor so we have some mechanical power come in here spinning a rotor that's got a DC voltage applied and that's gonna because we've got a DC voltage that's spinning that's going to create an AC voltage going out the ABC phases of this device and that is that's the basics of a synchronous machine so tom later is going to talk a lot about the exciter and the governor I'm in this presentation only going to be talking but well how do we model the physics of this rotor as it's spinning all right comment about the rotors rotors are created in different ways some rotors are round rotors they tend to be bigger machines and I'm kind of just talking it but why are they round my hunch is because they're really big and the mechanically it's easier to make them round because any like really really fast yeah so if you were spinning this really really fast unless you creep unless you produced it perfectly symmetrically you would get vibrations whereas if you don't make this perfectly symmetrical you'll get less vibration and it's also I think the one on the bottom the way they connect those whole pieces there's a sliding you're spending really fast they go don't break their the mechanical engineers figure in this stuff yeah impressive yes so basically really fast spinning devices will be round the Hydra units would spin a little slower will tend to be this this has an advantage because there's less iron and it's cheaper as a result whereas this is more expensive to make so one or the other you will have that has an impact on the equations we'll talk about the equations we derived really err for both of these and then if two values happen to be equal to each other then they're modeling this so this is just one out time I think Tom got these this is a big synchronous machine so the stator is going this way you can kind of see the windings in here on the stator this is the babe giant state that's huge yeah that's a big old probably for a nuclear power plant that's my guess synchronous machine rotors you can design them like this because there's a slip rings you're kind of talking about he went right big old pieces you come okay so the top part could be a cold piece and it would slide into the spider we call okay seven so this is for a salient murder and this would be more where you've got the windings in here actually I think this is meant to represent like a permanent magnet rotor where these pieces are actual magnets anyway there's different ways to actually build the rotor itself this is a picture of a of a rotor this would be more salient actually I'm learning things so these are the pole pieces that are getting put on and clearly there are locked if I were to count all these and divide by three that's the divide by six I guess actually that's the number of poles so there's there's a lot of pieces on there because it's the DC well correct but there's one on here and one over here and that's whole time oh you're right pole pairs yes so yes so you just count them all Wow so that's probably like a 64 it looks like as a website or what this has made up looks like you see one yeah guessing this is creating the DC voltage which is being applied to this room there it doesn't show up 30 comment click to the ones winding this way yeah there's some they're just bars and reporters faces with ball piece and you can kind of see some photos on the water to the trophies yes and that's where they're driving a little more discerning okay and there looks like a squirrel cage winding so I'm the very end of the pole yep you can see sort of where the squirrel or missing the windiest bolted together yeah we're around okay so this is what it physically looks like and then what we're gonna drive in the equations we're not really going to talk about how is it physically made they figured that stuff out eighty years ago there's probably six or ten companies in the whole world that know how to build these things so mathematically we're going to think of it as we have the ABC phases we've got the field winding this is the one that the external exciter is actually hooking up to to provide a DC voltage in here and then our equations we're gonna say well they might have another damper winding in the D axis and they might have to deduct up to two damper windings in the Q axis where they're wound like this instead so the D axis is our wound in the same way as the field winding and the Q axis windings are 90 degrees out of phase I shouldn't say a phase just physically they're 90 degrees different so we have to D two cues and two DS and one of the D windings is actually physically connected to the exciter and that's basically the equations that we have so we start there and then we just start applying math to it the first equation for math is the easiest one this is just Newton's method its force is mass times acceleration except we're dealing with a rotating system so we're gonna do torque is moment of inertia times angular speed that's the first equation we have and then the second equation we have is that the rotor angle if we're at you know synchronous speed and it's not changing but if it increases then the rotor angle is going to be moving as well so this is the derivative of the rotor angle is the speed other than that we have a whole bunch of electric circuits here they have seven of them we've got the ade the B and the C so three circuits on the armature winding and then we have four circuits on the rotor 2 D and 2 Q axis so ultimately we have 19 sets of equations that we have here and in the end we're gonna get general at the other end of this in about 40 minutes all right so the stator winding is we're not including any capacitance here this is just a piece of wire round wound around some iron so it's basically an inductor so you go way back to circuits all you have with an inductor and our resistance is you have a voltage is equal the current times resistance as everybody knows that Plus think back we have flux voltage is the derivative of flux with respect to time so that's what this equation is so it's got a resistor and an inductor we have one of those on the eight and the B and the C circuit and then similarly we have one on the for rotor circuits as well and then finally we have the derivative of the shaft is we have to do two divided by the number of holes because if we have lots of extra poles than it actually spins slower but the speed then scaled so you have to scale the two divided by the number of poles and then finally we have the the main mechanical equation which is saying that the derivative of you know how fast it is spinning is the mechanical power minus the electrical power and then textbooks usually throw in a term called friction and windage very shortly we're gonna throw that away because we just assume they build them so there isn't anything there's I think there's very little I don't actually know anybody have it I think I mean they're built so precisely that the amount of loss mechanical loss is just de minimis we just ignore I've never seen a model that includes this T here's took these are torque equations all right at this point if you go look at a textbook they're gonna apply all of that stuff and they're gonna start defining an inductance like between the a phase and each rotor phase and the problem that you're going to have when you look at these books is that if you think about what is the inductance between the a phase and one of these windings on here well this winding is spinning so that inductance is going to be a function of where the rotor physically is at and so when you draw out all the equations I remember doing this in peeps class they're terrible they're just they get really complicated they look like stuff like this if I want the flux on a it's this I've got and here's an inductance the self inductance on the a phase the self inductance to the second textbooks but the point is you then have a positional term that says as it's spinning it varies with the position of the rotor and they're very very complicated and what's gonna happen here is we're gonna thank all the engineers in the 1910s and 20s it literally took them decades to figure this out we're like you know what if we just create this transformation matrix kind of like Tom's a positive negative zero sequence that I think most undergrads at least talk about that at the end of a class you're like okay we can do this it's like the last two weeks of your senior level course that you talk about fault analysis this is similar similar idea at Tom's Tom talked about the number one paper was the positive negative zero sequence number two was this paper on the parks trip people call it the parks transformation but I think if you go back Park kind of introduced the idea but we don't actually use his transformation it's a little different than this but he had the idea of creating a matrix that takes all these ABC quantities runs them through a matrix and comes up with dq0 quantities and I'm going to skip all that I think I think I watched peak write on the board for about one or two lectures and showed that if you take all this mess run it through some equations I'm going to show in a second it turns into this okay but we don't have ABC values anymore we have D Q and zero values so the D axis and the Q axis are related to what I was just talking so we're gonna skip all that basically I tell you to when you go home tonight just say thanks to those engineers 80 years ago we'll figure this out because but then also remember it took them decades to do so it's not like they just sat down like okay here's how to do it it's like no they thought about it and then they retired and somebody else picked it up and they thought about it and then you know it took a generation of engineers to figure this out all right so I'm gonna introduce this equation in a second this is a matrix but we're gonna turn our ABC values into dq0 values by multiplying by a transformation matrix and we're gonna do the same thing if you want it to go in the opposite direction you take the inverse of that matrix and we're going to apply this exact same matrix for voltage for current and for flux we're basically taking the things that means something physically and you know really turning it into math at this point that means a definition oh this we are defining it it's not that these are equal because we figured it out we're defining it oh the definition is this is equal to this because we sit yeah so the transformation matrix is this now this is a descent again if you go back look at the papers from the 1910s and 20s people were debating you can use different transformations and they think all kind of work this one just happens to work out the best and you can imagine it's like how they come up with 2/3 here and a half and a half why didn't we just do one one one that's it seems more complicated than it needs to be and the answer is they argued about this I'm sure there were probably industry meetings where people argued about what to do so you can think that at least we're arguing about less complicated things but this is the transformation matrix it's you know it's not the same as positive negative zero sequence but if you look at it it's somewhat inspired by it you still see that 2 PI over 3 that was similar to but positive negative zero sequences and but in verse of it happens to be this and if you look at it this transformation matrix though is much more complicated than the positive negative zero because it is it itself is spinning as the rotor spins these equations are changing so in some respects when you first see this you're like isn't this just making it more complicated but it in the end it does not so if you take the equations we started with earlier you take these equations you take this ABC value put it in a matrix to multiply it by that 3x3 matrix do some algebra for about an hour you will figure out that the equations become this they look very similar I've got these rotor windings these are all the same all I'm messing with the stuff stator windings here the ABC values are becoming DQ zero so they look kind of the same but there's some extra terms that show up I'm not going to go through that algebra I did it when I was in grad school I just believed it now yes exactly good that goes back to that's definition of fear it's not exactly this it's like it's related to the angle between that's the wrong picture that's out of Kunar this is not between them no it is right it's between the q and the y-axis yeah I mean I'm drawing it here on a two-pole machine so it's a little more complicated if you add poles but it's it's related to it's related to the physical angle of the rotor at that at that time all right so those are our equations kind of waved their hands the equations are we have electrical system as equations that look like this mechanical system where I'm messing with them and skipping some more things but adding in the fact they're functions at the pole as well here so the electric torque derivation again I'm going to skip a lot of things here that's in it or in a textbook friction and wind aides were kind of gonna start ignoring that from here the mechanical torque that's coming from the GUP in the software it's coming from the governor model but you know it's the steam that's the amount of mechanical torque being created by whatever is pushing on the rotor the electrical torque needs to be derived all right and if you go read papers it it's actually rather complicated it ends up being that you create if you look at all the variables over here we get the electrical system there's a certain amount of electrical loss maybe from the resistance there's the mechanical or the electrical system going out into the system so then there's a certain amount of power that's being run through a magnetic field that's turning the electrical power into mechanical power or vice-versa over here we have the torque coming from the mechanical system this is the friction and windage loss we're ignoring that this is the sort of amount that's being turned into the electrical system sorry though this is the amount that's going out to the mechanical system anyway the point is in the middle here this is an electromagnetic field all of the theory on this machine starts with the assumption that we don't lose any power in the transformation inside these electrical fields and there's a lot of there's a huge amount of calculus that I mean when I started making these slides it took me like about a week to understand what it was saying which made me go I'm not going to talk about that in the presentation but the point is you start with this fundamental assumption then it makes sense it's not like the air is heating up there's not there's not loss in that in that electric field and again skipping the derivation using that it's called the conservative coupling field using that assumption you can calculate that the torque has to be this if that is a suit and in the end say okay it kind of makes sense power is voltage times current we know that flux is ends up being voltage divided by speed because it's the derivative of if you think through voltage voltage is the derivative of flux with respect to time so if these are AC waveforms they're end up being the speed ends up being related in there so it ends up making a lot of sense that it is equal to flux times current like this and then the pole value is in here and this three-halves value is just kind of showing up it's it's part of the reason and the transformation matrix you use two thirds because events I'm cancelling out later and then we're also going to define a new variable called Delta that's real is it's the synchronous reference frame is what we're do this is what this is called so we're gonna assume that there is an angle that is equal to the synchronous speed so this is 2 pi 60 right here and then as the shaft physically moves the the rotor angle what we actually call the rotor angle is equal to this now in reality the shaft is spinning it's not like it's going anywhere it's just sitting there spinning around and we're gonna make this definition so again you see the belt again this is just defined as this alright so if you take these equations and substitute them back into the mechanical equations we have or now here if I jump back here I'm taking these equations and then messing with them a little bit by putting in the electrical to work and then Delta changed here previously we were looking at previously we had this equation right here but the derivative of shaft with respect to time is this and now we have this one down here instead and then we're gonna add some different per unit values all of these values here are actually not in per unit yet I'm going to skip about two or three pages in the textbook here where they talk about how do I pre unitize things and when we've convert everything to per unit you end up getting this so now all these values that we have here are in per unit so when I talked about P mechanical and I say one that means whatever the MVA base of the machine is I'd say 0.5 shouldn't say MD a the megawatt base of the governor is right here and a comment about Omega alright all of our software tools meaning ours PS all the different software vendors are usually but not always consistent about saying when we say Omega we mean the deviation from synchronous speed so if you look pull up a block diagram of a governor in simulator and you see Omega somewhere most of the time that's going to be zero at steady state because they're at 60 Hertz and so if we want something that's per unit eyes to be actual speed we'll try to draw a 1 plus Omega and that is true except for when it's not somebody just made a buck diagram and forget to do it so you're looking at a block diagram and you see speed if you look at it usually you can go well that will never be 0 so if there if it just says Omega and maybe it's you got a number divided by Omega clearly the block diagram is wrong it's 1 plus Omega so usually Omega means deviation from synchronous speed we no longer previously we had a value that was J in these equations that was the moment of inertia that's now been per unit eyes and things I'm not really presenting am and of having it each usually don't is anybody know why we didn't just say why don't we always have to H why didn't we just say this is H tilde or something I have no idea do you have any idea okay it's always 2h because that's what somebody decided could be the poles maybe I don't know it's always 2h the electrical power or torque is over here a comment about we have P we have to divide by speed here because this is a torque value so power divided by speed is it and then a comment about this D term all the software tools use this equation right here as their mechanical equation and if you go look at a general agend cell all of our rope machine models include a damping term it's really historical back in 1955 people did not go through and model this rotor that I'm going through right now modeling all the damper windings they didn't do it because they didn't have computers they could have been literally doing this by hand so they didn't include the damper winding so they would often introduce like an extra term that was just well there's about this much damping so that if the speed goes up then it's minus here so then the speed would try to come back so what it means for you as a software user is if you get a synchronous machine model from someone who's done a test in the last 40 years but D value should be zero because they are including the damper windings we're going through and talking about it so you don't need this extra term because the damping is built right into the equations so if you see a D value it might I don't want to say it does me but it might mean that an engineer was just tweaking a parameter so that the plots matched nice but they really shouldn't have been doing that that should be zero all right if you go look at Pete's hours book and the equations that we present I mean power world psst EPS I love everybody kind of uses similar notation you won't find a textbook that's exactly the same Pete and PI's book is as close as it gets however there's an extra minus sign they don't use the exact same notation that's us there's one difference there if you happen to go look at theirs so what are all the per unit values I didn't really talk about how we got to these but the model that you end up using in software like ours they're gonna have Omega s whenever you see that that's usually 2 pi 60 or it could just mean that it's one if it's pretty unitized in the equations I'm gonna do in these slides I will try to put a Delta Omega when I need speed deviation just to make that clear we're gonna have a stator currents we're not going to talk about the ABC phase currents because then we'd have all those cosine of opposition terms in there we're gonna be in the DQ 0 world and we're going to have these are the terminal voltage we have flux on the stator and these are flux values on the rotor really and then we have a field voltage in a mechanical power then we have all these input parameters but they user adds to the equations so I just skipped several pages in the textbook so go through per unit izing everything and the equations that we had before tonight doors through tonight no I don't even want to do it again it's like if you go to grad school you do it once and then never do it again because it yeah it's pages and pages of algebra but basically it's taking these equations so we got three stator four rotor to mechanical I just skipped a whole bunch of math but we're still gonna have to mechanical three stator and four rotor so this is just the exact same equations but with different per unit eyes values and we do a whole bunch of math and to get to here and we're getting very close now to what is used in the software tools the only the difference is down here the equations up here these are there's there's four different fluxes on the yeah I'm the rotor and you know we're assuming that the fluxes are that all the flux on the rotor eventually comes over to the stator and comes back it's not like leaking out and disappearing somewhere because again the conservative coupling field assumes there's no loss in this in this transformation so these fluxes up here are just the flux on the stator so it's the relationship between the stator flux and the rotor fluxes the other thing you might notice here is the zero values all went away I said this was the DQ 0 transformation I don't see any zeroes that's cuz I just skipped those we're assuming we have a balanced three-phase synchronous machine so if it's balanced then all the zero values are zero so in all of the software tools like ours we don't include this term so they're not up here all right next thing all right I know I'm waving my I'm trying to put like literally in a half a semester of a graduate course and they're like one and a half hours okay I remember doing a machine class you would go through this in detail all right another equation that we're gonna mess with is right here these are the stator fluxes and how actually we have including the zeros up here still completely all right these differential equations on the stator one of the things that shows up is the derivatives here get multiplied by 1 over the synchronous speed all right what is synchronous speed synchronous speed in our world is 1 over 2pi 60 so that is the time constant on this differential equation is about 2 milliseconds so one of the approximations that we're going to make as does everyone is we're going to assume that these stator equations are really really fast I think these are taken out of I'm pretty sure this is out of so if you were to look at the actual speed deviation versus time what you're gonna see in a software tool like simulator is this dashed line if we're doing clue these standard dynamic there would be some really fast dynamics that died way very quickly and you know things are gonna be off a little bit so this goes again back to Tom's comment so by making this assumption we just made the model wrong and then it's like well how wrong all right if you go read a text book they're gonna talk about things like integral manifolds and all kinds of stuff that's really confusing I'm always like you know I know this isn't theoretically right but basically we're saying you know what this multiple this term is really small small enough that you basically just say well why don't we just approximate that it's approximately zero all the time and all of the math they talk about in a paper or a textbook really comes down to making this assumption they just prove its that it's okay to do this but this is the assumption we make about the stator dynamics basically we make them go away by assuming that they're infinitely fast and so instead of having instead of having missed these two differential equations this term just goes away and then we're going to have this equation which just means that the terminal voltage is equal to the negative of this so we just created these two equations instead and these are the network interface equations that are going to show up in our transient stability if you multiply these out so now I have flux something these are the stator fluxes but remember there is also a bunch of algebra here that said the relationship between the stator and the rotor fluxes is this so then you take these and substitute them down here you group turns together and then we get these equations down here and eventually I'm going to get to the end here I'll pull up the round rotor block diagram and say okay that says where all this stuff came from so trust me so then we're gonna define all right we've got a voltage is equal to resistance times the current okay I got it that makes sense I've got with a speed times an X q IQ all right that looks like a complex number math there I can see that that's maybe something I haven't seen before and we come over here and this looks kind of complicated so what we're gonna do with this term is say well why don't we define that as some internal voltage e d double prime is equal to this and V Q double prime I should have put a delta here we're just defining these and then our equation becomes this and this right here is close to what everybody does in software tools so now we have these two terms here where we're multiplying by essentially the per unit speed because the you know it's two these three these four values here are the fluxes inside the rotor and they're constant they're changing this is that this definition is defining how are these four fluxes created to create some kind of a flux out on the stator essentially so they're they're changing all right so we have these two speakers this purple speed term right here that comes out in the derivation in most software tools we ignore this all right I I've never really seen a paper that says this is why we ignore it but like I think I know why they ignored it back in the seventies when they figured this out this is the kind of the it this is going to show up as the internal impedance of our model we're gonna have a voltage source behind an impedance that's where we're going with this and so what it's saying is that that reactance is a function of the frequency well you know what so is the transmission line reactance right the two equations Tom add up where you have transmission lines if the frequency in the system is varying then the reactance of a transmission line would vary most people never modeled that in a transient stability simulation because you're assuming it's not varying that much and so we're gonna make the assumption that well you know what the internal impedance of its synchronous machine would also vary with frequency but we're gonna ignore that and just turn it into this and essentially treatment this term is always one so the actual equations that get used in software tools is down here so there's a I'm gonna get to it picture I should we just your Google search on general you second link is power so we're eventually getting to this Jen ro you equations what I'm showing right here is really this it's this we're getting to the point where we're gonna model a synchronous machine as a voltage behind the reactance that's where we're trying to get here and we're almost there alright so now we have these six differential equations so we used to have nine differential equations as we had three stator four rotor and two mechanical and we just took three of the stator equations and turned them into algebraic so we still have four rotor equations and two mechanical equations and then these relationships up here are just algebra all right we then have to talk about the field cold ocean all right the field voltage is down here this is the the field voltage actually coming from the exciter another term we need is something called the field current and we're gonna define that as this term right here it's like everything else in here all right so at steady state there is a relationship between the field voltage and the field current that's defined by mutual inductance it's it's an X value so it's the mutual inductance times Omega L so typically we will define this whole term right here as the field voltage it's really the field voltage scaled by the mutual inductance but usually we just call it the field voltage per unit eyes it that way not the field we call it the field current and that that field current this term right here is going to go back into the exciter model so what Tom will present later there's a field voltage coming out of an exciter and a field current going back to if you look at if you look at block diagrams good time on our our picture you'll see the field current compare voltage coming in here this field current is going out and so if you were to sum up everything coming into this summation Junction it's it's this it's this big equation right here so why we get to the block diagram is a little easier to talk about all right they hate to tell you but all we've talked about right now is one machine by itself against an ABC voltage out there so it keeps getting more complicated next but then there's lots of beautiful math that's in the classes so next is all right we need to synchronize all of these machines thousands of them across the system all to one common reference and this creates a whole bunch more math so we're going to do a conversion that converts from that ABC values into I'm using capital letters here to represent something different than the rotor values where we're going to take this equation and multiply it by the ABC values to turn them into these capital letter values and if you do that and you make the assumption that the AVC voltages are balanced so we're going to start with that assumption so they are all have exactly the same magnitude and they're shifted by a hundred and twenty degrees from each other and if I multiply it by this matrix and I do a bunch of math and I hate textbooks because they always say and you do some math it's not that hard and get this it's like no I'm putting the derivation steps and then letting you read them later do you do all that math it ends up being this exactly do much a trig and we've now turned our ABC balanced things into a magnitude and an angle and also if you notice that speeds gone there's no frequency here anymore at all the frequency terms cancel out and if you think about it if I have two terms that are like this where I have one value that's magnitude times the cosine of an angle and I have a second value that's the same name two times the sine of the angle complex numbers we can say that's a complex number so another way to think of it is yeah this right here we can treat that as a complex number essentially I mean everything I just talked about here this is exactly what a power floor does we don't talk about sines and cosines and the power flow around we talk about magnitude and angle that you were making this assumption it's the same one okay so that's great that takes us from have this this is what we talked about earlier this was the dq0 transformation on the rotor then I have a transformation here that takes the ABC values and turns them into a DQ zero across the whole system its standard across everywhere I can then take let me jump ahead here to explain why we care so what we're doing here is we're trying to get to the point where we have things on the rotor the equations that I talked about the previous half-hour and then we have equations out here on the network and we're trying to build a mathematical relationship of how we get back and forth between them and in order to do that we have to go through this ABC reference frame along the way and most of the time you will see people who've studied all this kind of skip all the steps that there was something that came from so in order to get from my rotor reference frame to what's called this network reference frame I have to take the two giant matrices I had and multiply them together so this was from before this was the DQ zero where we took the ABC on the rotor and turned him into DQ zero and then this is the inverse of that and then we then have to multiply this times that thing that took us to the synchronous reference frame we have to multiply these two matrices together and again you do a whole bunch of math and at the very end you get this and this says that if I'm on the network and I want to convert from my network reference frame over to the rotor reference frame I just multiply by this matrix and then we're going to ignore the zero terms and kind of get rid of that in just a moment so the beauty is all the math that I just waved my hands at and kind of skipped because we're gonna ignore from now to an eternity many many textbooks will skip all of this and just say to get from the synchronous reference frame to the rotor reference frame you multiply by this and I was other where did that come from it comes from a whole bunch of math that's going on behind the scenes if you happen to want to hook us to like simulator up to an EMT P tool the MTP is working in the ABC reference frame so you would have to go back and do these kinds of conversions every time step two be updating what that ABC values is ABC values are but most of our customers in there so our final result of huh how do we get from the network reference frame into the machine as we multiply by these matrices that represent a rotation and if you look at them for a little while and eventually eventually you realize that you can do this is complex number math you're just taking a machine value and multiplying it by you know just rotating it by an angle and the thing to realize is the rotor angles right here so as the system spinning are getting in or out of synchronism that this this relationship is actually changing I don't really expect a lot of questions here it's just an it just yeah it's right here it's that it's like at every rent and some random bus out there there is a balance voltage ABC voltage that's at you know synchrony at 8:00 Kwong's at a frequency and it's at some angle it could be any angle so it's literally the Aang it's it's equivalent to the angle of a powerful bus it's like every bus has a different day yeah but I mean the beauty of going through all the staff is that doesn't show up here it's you know whatever your dq0 stuff is the bus angle doesn't matter all right so now I have these equations well--that's we got those before so then we have the network interface all right so these are the equations we have that describe how to take I go back to my round rotor here the the fluxes that I'm talking about are the states on these block diagrams so they literally represent the flux inside the river and they're dynamic and if you take some algebraic combination of those because of this state and this stage is getting multiplied by a constant come out here and they're kind of be represented as a voltage then inside the machine so we're then going to treat yeah so we have a voltage inside a mission we have an impedance find a voltage behind it impedance all right if we make some assumptions about this we can make our life easier so it's 1965 I'm John and roll writing the first software tool on this perfectly reasonable to go you know what these two values are usually equal to each other maybe maybe not but if they are equal to each other it's gonna make my math way easier it's gonna make it easier to code things so Jen Rao Jen Sal always make the assumption that X Q double Prime and X D double prime are equal to each other and the reason they do it is because the software is easier to write I completely understand what and it's usually closed and if you also make the assumption that as the system becomes saturated which we'll talk about next that those two terms don't change that much then you can rewrite these two equations as a complex number equation right here and that this equation right here is a voltage with a complex impedance and a complex current so the network interface is literally exactly this and they don't I can change from a feminine equivalent over to a Norton equivalent and lots of things get very easy by making this by making these two assumptions okay when I wave my hands a little later at things but the more modern models like Jen TPF gentie PJ Jen qec do not make these assumptions and they make the equations a lot harder and I'm not going to talk about that in this presentation but it mean it's not it's hard and then it took someone like Tom or me or John under or a couple of months to figure it out we don't have to figure it out once and others have figured it out too so it's not like you all right so here's our equations - yeah go ahead typical parameters for the XD and X Q double prime how different are they third in the more come their model I don't do you have any idea tend to be a little different I mean they're not going to be mine I think literally in our code and power role we hard code it so they cannot be more than a certain fraction different than each other okay I think it's somewhere between like 1/2 and 2 times yeah because as they diverge from one or another the approximations we make in order to handle that and start causing miracle trouble but they can't be a little bit okay and aside later tomorrow better talk about renewable models all right one of the really nice things about the synchronous machine model is we're modeling it as a voltage behind an impedance so if I come in there and fault that make this voltage go to zero there's actually not a problem numerically I got a voltage I got an impedance okay I just get currents you know moving around in there no big deal doesn't numerically fall apart all right the renewable models we're gonna model as a constant current injection and that causes all kinds of trouble when you fault it because suddenly you're trying to push current into zero volt digital what does that even mean what is the yeah for instance what is if the voltage here is zero the magnitude is zero what is the voltage angle who the hell knows it's the different you know it's the angle between the two vectors but it's gone so there's there are all kinds of numerical trouble that it's going to happen with those and I'll talk about those and I kind of already mentioned this if we allow this then things get more complicated alright so next we have to go to saturation and this is where things get very common these are the equations that we kind of waved our hands at modeling I have now turned them in from those equations into a block diagram it's a little easier to kind of look at the pictures then so when you're right here this the derivative of this state is whatever's going into the integrator Tom's gonna talk about block diagrams in a little bit so I'll let him mention that but just something to tell you for someone like me I went to grad school in the 1990s if you were in grad school in the 1990s you worked on economics that was that was what people worked on so I worked out with the electricity trading it's like I should have gone off and been an electricity trader one of my students he didn't go to jail he took the topic that I started on of like how to how to basically intentionally create congestion so you can make more money and he just went too far but anyway my point is I went to grad school I got a PhD in electrical engineer and took stuff like this yeah I took stuff like this I came back to this ten years and Tom's like we're gonna work on transient stability now they put stuff up like this I was like what the hell is that what is s what is that so if you look at something like this and you go what the hell is that then so did Tom and I when we first started looking at transient stability ten years removed from having studied so don't don't feel bad if you're like wondering what this is so episode of me alright so anyway on this block diagram this is all representing derivatives of States and things we haven't included a topic called saturation yeah and this is again where my pause from I thank everybody 80 years ago we're gonna pull this stuff out okay so we haven't included saturation yet it's a whole bunch of synchronous machine models the general Jen sale models are kind of what I'm going over really and we'll talk a little bit about these other models here shortly but the first thing we need to do is talk about saturation and we're going to kind of wave my hands in a lot of this but the idea is we usually talked about on an inductor that the voltage is the derivative of flux which is the number of turns times even forgetting that some of these things are and we make the assumption that the flux is equal to some constant times current this constant is what we call inductance all right in reality though if you look at how does the flux and you know going through a magnetic material as you wrap wire around it change as the current increases if you're talking about an inductor you've got a straight line it's a linear relationship or what is my sixth grader says directly proportional I'm like you mean linear know we call it directly first they're not talking linear again directly proportional goes up and reality is you push more and more current or eight more magnitude of an AC current through it it saturates essentially again I don't I don't really remember exactly why it's like the flux like gets crowded it bumps into what this is sensory I don't really remember but there's something about the magnetic material that at some point that you have to push more and more and more current in order to get flux out to no saturate and different material will saturate in different ways so this is a slide Tom had gotten off Wikipedia that looks at out of sheet metal steel silicon steel all these different kinds of materials the kind we're talking about here is iron so ours look something like this Kurt around number six so actually what I'm presenting if we were using a different kind of material some of these curves would be hard to represent so the initial part that's linear is what we are modeling up until this point so we're going to talk about what happens when it saturates oh you're right okay anyway you know century it's important another thing that a magnetic material will do is as you go up it's got this something called hysteresis where it kind of some of it gets stuck in there alright they are going to build these generators in a way with laminations and ice and that's more for eddy currents that's something different but anyway that all I'm gonna do is wave my hands and say we're not gonna model this we're not gonna model the fact that there's like return paths it's like this we're just gonna model it as though there's one path so models like ours do not include hysteresis so what we're gonna have is I'm going to start talking more about current and voltage if you think about we're talking about AC waveform so if I have an AC waveform right so we have a voltage waveform that some magnitude times let's just ignore the fact that there's angles and stuff it's cosine Omega T but actually all that flux remember we're talking about voltage the derivative of voltage is the derivative of flux with respect to time now we're going to be talking about phasers and things that at sixty Hertz so the derivative of this is just a Omega derivative of cosine is minus sine so voltage is if you can think of it as box times Omega e to the J PI over 2 I can't remember it's plus or minus there but the point is all you're doing is taking the flux if you take cosine and sine they're just 90 degrees out of phase with each other and the magnitude increase by Omega so really when we talk about flux and voltage in a synchronous machine they're similar to each other they're scaled by speed and they're shifted by 90 degrees but we're looking right here at magnitude so the magnitude of the field current versus the magnitude of the AC so this is a DC current and an AC waveform magnitude so we're just going to talk about terminal voltage instead of flux but they're related to each other if you go do generator testings I was just talking to to Steve at BPA here he's going off to do generator testing tomorrow are they gonna do this test tomorrow they got an open circuit generator so they're gonna increase the field voltage which increases field current and they're going to look at what is the terminal voltage they're gonna trace this curve and if there was no saturation that get a straight line but there's gonna be saturation they're gonna do a physical test out there that gets this blue line all right yeah because it's off okay alright so this is a test that will be done all right I like to take this curve that you traditionally see because in software it's easier if you flip the axes so I'm gonna do the voltage for our current versus voltage instead so this is the same curve just flip the axes are flipped so if you think about it what the way we're gonna represent it in Sachin and software's we got a straight line those are all of our X values that you put in in a synchronous machine they're the unsaturated inductance values so when you start saturating them we're gonna have to add some extra term but these the values we're giving are related to these lines all right the actual amount of current needed to get this voltage is the blue line so essentially the green stuff is the extra current need so if you think about it the grey line is what we have if we split that up into two pieces and say I've got a red dashed line and I have this purple line and I add them together then I get what we actually have and this purple line is the extra stuff that's coming from the fact that the magnetic material etc so different software tools are gonna do it differently I like I like to joke about this if this was today and people like Dimitri and I were in a room somebody in the room would be like we need to define that really accurately we should put in a 10 point piecewise linear curve to define the saturation super accurate that is what would happen today thankfully in 1970 people didn't have as good at computers so they said you know what why don't we just pick two points choose those and we're going to define a function so that the advantage is there's only four input values here or actually there's only two not a synchronous machine because we assume that the X values are 1 per unit 1.2 and you just give us these two points and then you have to pick a function that describes how how the extra current needed as you increase voltage varies and you just define the shape by a function and one of the things that Tom found out when he did that was a BPA funder project to think in early 2010 when Tom was validating power World PSoC EPA's / tool pslf one of the things he found out was the software tools don't use the same function great time we found out that pslf uses this function and PTI uses this function and as long as you're in between it doesn't matter that much but you will get different answers so this function here is one we call scaled quadratic it's a quadratic function with ins divided by the input also so the function will look something like this green line right here and as long as you're between these two points all of these functions give similar answers all right this is just describing how to derive from input data what this function is we want the curve that's increasing in here not this other one that matches the interpretation this is what we call the quadratic function again the values look similar in between you have to compare this curve to this curve the green part in the between the points is about the same and then some people like to use an exponential function instead but you're just you're all that these things are doing is they're trying to describe this public error with only two points and just to comment one of them assumptions is is that as the voltage goes up the saturation goes up but that doesn't mean that you user can't put in input data that flips those which makes no sense so software tools have to deal with that so Jamie it's just hard coded for all time that the the voltage guys are one in 1.2 on the synchronous machine model on the exciter models there's four input parameters at the Jedi ro you model down here there's two input parameters for what is the saturation at 1.0 per unit field voltage and what is it at one point two but if I go look at and say an exciter there's d1 saturation one e to saturation - but they're similar concepts and they're giving it two points yeah I mean it didn't have to be that way that's just what software vendors decided all right so if you have this test that says in order to get this field voltage I need this amount of current then it's very natural to take the general you model that we derived earlier and just add in some extra current or extra these extra current and that is what happened in 1960s they they had a test it made perfect sense just take the flux and the stator run it through here and add in some extra field voltage that is needed to get this AC voltage at the output so this what was chosen for this model came right from the empirical test so remember this is the field current right here so we have flux which is related to the voltage magnitude at the terminal it's a bit of hand waving here but the test that is done is an open circuit test which means that the a stator current is zero if you go through a lot of math you figure out that at during open circuit the Q axis is actually all de-energized so this whole thing down here is like not there when you're doing the open circuit test so really all you're doing is up at the top you're just saying I've got a voltage at the terminal and I'm gonna run it to get a magnitude but I already have them in two because this one down here is zero and then I'm just gonna add in some extra value from the saturation function so I mean it was done that way because that is the test that is used to create tomorrow all right down here I just said that when you do the open circuit and saturation test this entire stuff is de-energized so that value right here where you're saying oh and there's also some saturation down here in the Q axis we're not testing for that at all the assumption that is made is well there is a certain amount of scaling from saturation on the D axis it's probably the same on the Q axis probably all that the whole iron is getting saturated it would make sense that the angle that the flux is going probably doesn't matter that much so that ratio right here it's not clear when you guys are looking at it because it's like it's X cubed plus XL but these two values happen to equal the mutual inductance so that's the inductance that's inside the iron so that scaling term is just coming from that there's no there's no test behind that it's just that it's an assumption all right other things related to this this the saturation is not a function of the current at all - so as the armature current as you load up the machine it's only a function of the voltage at the terminal which testing the Demitri and focus of BC Hydro they know that's not true when they look at saturation it changes with loading I don't think anybody has a great handle on why they have some guesses but as an aside is funny people I love his book but what I think happened is he worked on this like the first half is of his career and you can see kind of at the end of the book he had a lot of pieces that he kind of just abandoned I think he just got sick of this topic because when I would ask him about it the only thing I always tell me is that the general and Gen cell models are wrong that's we would always tell me that until about two years ago I didn't know what he was talking about and what he's talking about is what was done right here to take this test and just insert some extra current right here who actually violates a whole bunch of assumptions made during the derivation because it's essentially saying that only this particular flux is saturating but really all four of these represent fluxes on the rotor and there's a relationship between them so they should all know saturate together and he had a paper he wrote in the early 90s that described this and said Jenna I was wrong but I think that's like the last time he thought about transient stability because he kind of moved on but the fact is actually if you look at his paper what he didn't get to hear but what he was saying was instead of adding it in over here which is great where the test is at instead if you just sort of add in some extra current then it it still satisfies all of this theory and this model would have been just as easy to do that but no one ever did all right this I'm just gonna kind of skip a lot of these slides but they're useful if you want to initialize this model and you were writing your own software but you buy R so you don't have to this is walking through how do I take a saturated model and actually initialize it and in the end you get a rotor angle that's down here this is the general thing but I'm just gonna skip through this if you ignore saturation it's actually much easier as most things are you ignore saturation all those equations end up being you can just calculate it with a circuit equation this is not the same circuit equation we use on the general model you look back the limp Eden's here is our plus X Q double prime but to get this steady-state value you have to use XQ itself but it just so happens if you run this then the angle you get right here is the rotor angle but when you have saturation it gets more complicated and then you have to initialize all of the rest so what's going on here on the block diagram do you want to initialize this value do you have the flux on the D and Q right here it's actually you don't have them initially because you have the ABC values in order to get the DQ values you have to run it through that matrix that include the rotor angle so you don't know the rotor angle that's part of initializing so it is kind of complicated to initialize this because the rotor angle has to be calculated as part of relation all right the comment on the gentie PFF ingenta pj models alright the advantage of this model was it included the ability to allow saturation to vary with stator current this model you know it just it came from testing that Dmitri and John undergo and others did and I think they just kind of added a term because it matched the testing so that was an advantage there was another advantage of the model was you could have that to double prime impedance does not be equal to each other and the big advantage was it matched tests that were done better so it was matching things better the biggest thing it was matching better was the field formations so this is the gem TP F and J model so a lot of the models in wacker like this one of the things with the model is if you look at the block diagram for this model the leakage reactance is not in there so I think somewhat unintentionally they made an approximation in the differential equations that later on we were finding maybe we didn't need to make but the big changes right now that the saturation function itself is no longer just a version of the voltage but it's also a function of the terminal current the stator current so as the machine is loaded the saturation changes all right so several years ago Quincy Wang and he was that power tech then he went to BC Hydro that was noticing some troubles with the gem TPF in jail and mostly because this again the field voltages and currents didn't match all of these changes with related to saturation that we've been kind of thinking through in the last five years it'll be another five or ten years before people switch to this model but all of them they they make the system a little more accurate in mapping how the field voltage at current changes alright so one of the questions that would be natural would be why does anyone care why does it even matter and I think historically it hasn't mattered that much I think the reason it's starting to matter is cuz people keep telling folks like you we need to model over and under excitation limiter z-- alright so in an old general you model slave Tom doing dick studies the first gig studies he did were included this stuff in transient stability he was like applying a a big solar flare coming and hitting Wisconsin and he expected a voltage collapse and he ran the studies and everything was fine and he was like this is ridiculous and then he then he went to look at the generator var outputs and they were all like five and ten times higher than the steady-state limits as because in your models in transient you don't model over excitation limiters so if you look at the VAR output of a generator during a transient during the fault it goes really high and you're not modeling the fact that something's gonna clip it because the term the field voltage will go too high so the first thing Tom had to do to do that study was to go in put some sort of crude over excitation limiters to prevent that from happening but if you're going to start modeling these suddenly your results matter whether you get the field voltage and current correct so if you start adding those it's gonna matter more so I don't know you could listen to this and go okay that's a good reason not to monetize because then that could keep using the synchronous machine models like that but you know as you start modeling these things then it matters so the genkyu-en is a new model in simulator it builds off of the gen TPF and j model essentially i'm going to skip these slides but right here this is gen route instead of adding in saturation as like an extra additional term here it's gonna assume that all the impedances in my model are scaled so that there's a leakage reactance that's the part that's represented by the air gap so that is not going to saturate so if I have X D double prime if I subtract off the leakage reactance essentially that's the part that's inside the rotor if I assume that that just scales with some multiplier and I do that to all the constants including the time constants including the field and current and voltage and I scale them by some multiplier for saturation then I can do this instead so instead of the addition term that I did with the general and Jen sale because that was the test that I had if I instead to scale by moulting a multiplier and literally this sat value is the same everywhere in there this is essentially what the gentie PF and J model did but I'm applying it to the general model instead because it includes the leakage term so these differential equations will match whereas the gentie PF and J they did not this is the saturation current function its exam it's the exhibits the saturation term is 1 plus the saturation and so that will work I think we think that will work better the thing that Quincy at power Tech has found is that as he loads the open circuit tester down here as you vary the voltage when you come up here at zero voltage I mean you can't really get to zero as you bury the field current when you're loaded what he's finding is if the ID is negative then you tend to be over here and if you're positive you tend to be over here so the whole curve is shifting all the time so what Quincy talked us into was just adding an extra term right here it kind of literally changes the slope of that curve as this thing is loaded my coworker sarve and I really didn't like this for a long time and we tried to come up with something that was a little more beautiful theoretically but we've given up this matches his test data one of the things we don't like about it is it kind of violates the idea that the D and Q axis century the same together because we have a term here but we don't have a term right here to make it symmetrical I never really understood why Quincy did that until I sat down to code it and if you include a term here it makes the code really really so I quit see that's why it's like some of these decisions get made because the software gets more complicated and it's like is it worth it for the accuracy you get so if you've got an extra term here that's similar to the kis term that's in Gen TPF so one last comment about the synchronous machines if you want a switch from a model you have now over to say the Gen qec model it is not appropriate to just take the parameters you have and copy them over Tom mentioned this kind of in passing and is its earlier presentation but all the input parameters go on with the model they're intimately tied so just because the parameter names happen to be the same doesn't mean they mean exactly the same thing they're tied to the model so one of them I mean a problem that happened in whack when people switched over to the Gentiles I think a lot of people just took their general you and Jen sale model per input parameters and copied him over because that was way cheaper than paying somebody a hundred thousand dollars to do a new test it would have been better to leave the old model with the parameters that were fit to it and wait until the next time you do a study and then your fitting the parameters to that model so you can't can't just switch if you save the test results can you just read to the other new model absolutely we could go back and retune it i mean someone like BPA would have the staff in-house to do that most of yeah most other utilities have to pay someone every time do that all right so I guess my hope is my hope was we'd come up with something better than Quincy's after sorrow that I working on it off and on for a couple years when we had time we eventually gave up we'll leave it nobody's revisited this model in like 30 years well wait somebody else can read this and the last one just kind of walks through if you're inside simulator you can app when you're in a simulation you can actually go look at these DQ guns if you want you come in here the terminal values it actually lists the direct and quadrature in internal and internal voltages most of the time you're not going to look at that but these these all come from there so here's the DNA this is the voltage magnitude angle so I can get the RDI I can then transform that over to the DQ values and get the values on the dialog this is showing you that these are truly related with all this math that most of the time you will never look at it is called qec because it allows for quadratic or an exponential saturation there's an input parameter and Quincy and sarra band I kind of settled on this being it's like a compensation term so the C is there's an extra term that's compensating for as the the load as the stator current changes the saturation changes yes it's it's I was trying to call it Jen tpw for power role like that that's why it's called that so has it been used I don't know he's a testing to show that it does a better fit Quincy has done some testing to show that on his I mean granted Quincy has a particular generator that had particular problems with the old models I suspect most generators it wouldn't make a big difference but I know what could be quadratic exponential compensation I suspect that we you'd have to go it's the cool thing about power roles here it is there's Quincy's the cool thing about putting our help documentation on a public website is we're always the first link and I do the search yeah so I think he's calling it a walkthrough what's he thinks about things more in in these diagrams I always get confused by these but it's another way of thinking about the block diagram yet single theaters authentic or exponential of any calls with compensation yeah a simple field current compensation all right I know that's really technical but it's kind of a gives you a flavor as to where of these models come from and mostly I always go back to the slide to thank people for figuring it out before us I mean it took me I started working on this Tom started in 2006 I probably started looking at it in about 2008 I don't think I understood any of this until about 2016 it's like I can code these equations without understanding where they come from so you know it's there's a lot of history behind it that isn't really taught anywhere because people already figured it out all right so where are we supposed to eat lunch

Channel: PowerWorldCorp

Views: 3,249

Keywords: software training, PowerWorld Simulator, power flow

Id: F03f47CSSUw

Length: 107min 16sec (6436 seconds)

Published: Tue Mar 10 2020