Introduction to PM-Synchronous Machines

now today we are going to start talking about sink permanent magnet synchronous machines for a couple of reasons actually it's easier to understand in terms of you know out of the different AC machine types it's easier to understand and it's also going to correlate well with what we have been talking about in terms of synchronous reference frame transformation and all that so we can go directly into understand how reference frame transformation can be applied with a real motive both for the machine model as well as the control of it okay so we will talk about ppm so P M s M so this stands for permanent magnet synchronous machine guess or PMS and theory and we will talk about characterization what all this looks like for us okay now people call these brushless DC machines as well this is a general term that people interchange and there are certain variants and say BL DC and it all comes down to you know what school what professor taught you this and then what they believe is true and I don't want to get entangled in that discussion as long as what you are talking about is accurate and you know what the they are referring to I think that's sufficient enough of an explanation and then the reason it's called brushless DC is when we look at it look at the motor model it'll look like a DC motor but in the rotor reference frame it'll look like a DC motor however the are no brushes as you know we know with a synchronous machine at least with the permanent magnet rotor you don't need any brushes to conduct or pass any current to the rotor right so if I'm to draw my three-phase machine you are essentially you will see that we have a set of conductors I'll draw a very simple version you're going to see three sets of conductors so we'll call this a prime this is a and then we will call this B and this C and then you know this is C this is V prime this is C Prime right so we have our stator which is attached to the motor frame so if I am to draw a stator this would look like that and typically this is what gets mounted so let's say you know we have a little mount where the machine is you know sitting on and this is bolted down to to a table or a bench or something right so you have your stator and we talked about the complexities that you can see with stator windings and then if you look at the rotor I want to try to get this as accurate as possible so and we talked about the different magnets that you're going to see but I'm gonna draw a little bit of a motor like that a rotor like that where you know you have some magnets mounted you know let's say like this okay so you have a north and a south magnetic like that for example okay so this is our rotor and of course you know if you look at an actual motor it's not this this saliency is not going to be as significant because you're not gonna see it very clearly because it's a material property but depending on how the magnets are placed you're going to see salient see or it might be a nonce alien motor ok and we talked about those in some of our previous lectures and now so since the rotor field we know we need two fields to generate talk into anything any motor right whether it's brushed or brushless OAC or DC and we are establishing our rotor field through these permanent magnets ok so back in the days when these DC motors and AC motors were invented they didn't have strong enough material or mega permanent magnets to build these permanent magnet synchronous machines so they they were very weak magnets therefore most of the synchronous machines were wound rotor which means the rotor had another set of windings and those windings built so by passing current through those windings they built an electromagnet so it's like you know instead of the rotor they pretty much you know they had something like this so they had a coil like that no very densely packed coil another essentially another set of windings that you have current pass through but you need a wine you need brushes to maintain the polarity okay so you're kind of getting the same result so you'll have a north and a south built up and in order to maintain that polarity you need brushes to move along with this right as the rotor is rotating you need brushes and you need slip rings so that's how they achieved it back in the days and then with the advancement of material we were able to replace those with permanent magnets which has much higher flux density and can perform way better so with that now we have this brushless right we we have gotten rid of this bound field and therefore we have brushless machines so no brushes means it can improve your performance lifetime significantly okay all right so we have that so and depending on how these machines are designed they they are named differently you call them surface mount magnet PMS em sir or surface mount permanent magnet synchronous machine or interior magnet P MSM or interior permanent magnet synchronous machine there are different names out there you will see when you work with these types of motors what else so the IPM and then now when you come to look at or when you try to characterize whether it's P MSM or brushless DC primarily it comes down to the back EMF okay so some people will call brushless DC depending on the back EMF because if the back EMF has a trapezoidal shape okay so if you if you spin the motor your back EMF let's say looks not that much sinusoidal but it has kind of a trapezoidal look right it has a trapezoidal shape instead of a very nice sine wave like this okay instead of a sine wave like that then people tend to call them brushless DC or trapezoidal back EMF machines now the advantage is actually not advantage but the difference is you can drive you can drive both types of machines with a trapezoidal voltage you don't need to apply a sinusoidal voltage to either machine and I know this is gonna be a little this this might be a too much information but just bear with me [Music] rather than applying so this is the back EMF right this this is we are talking about back p.m. back EMF both the green and brown waveform this is for a trapezoidal machine this is for a sinusoidal machine right this is a science now either type of machine can be driven by applying a sinusoidal voltage so that means you can apply a sinusoidal three-phase set of currents or voltages oh if you don't want to generate this sinusoidal current so let's call this applied voltage applied voltage you can apply a very simple trapezoidal waveform it's not as sinusoidal as this as a voltage you can apply a trapezoidal voltage and still drive the motor now why do you want to do the trapezoidal waveform it's cheaper right you don't have to go through generate this complex sinusoidal waveform you can have a linear ramp or you can even ramp up directly and hold the PWM at a certain value so this scheme is much cheaper much easier to implement than generating a sine wave so algorithm wise or code wise it might be cheaper but you might have a lot more torque ripple at the output so the motor talk might have much more ripple so that's why people tend to go to a sinusoidal Drive voltage and sinusoidal back EMF however you can drive either type of these machines with either of these voltages or either of those currents okay so just keep that in mind the only difference is going to be in your toe how much repel you are going to get will depend on the machine as well as the design of the machine so so you have a bit of a difference here now here we are saying you're looking the back EMF is going to be trapezoidal right and that also this is also an ideal discussion so we are just talking about this for the learning perspective if you are to take a motor and look at the back EMF it may not exactly look like this even if it's called a trapezoidal motor it might not look like that because depending on the motor design sometimes you will see something like this so this is practically speaking okay so you might see a little bit of a notch they are depending on how the windings are set up and then they still call these trapezoidal motives okay so just keep keep that in mind when you look at back EMF sand you try to characterize there is the theory and then when you look at it from practice point of view there are certain subtleties that you have to keep in mind okay so there are certain variations but all of them at least what I think is you can call them a PMS em you can call them a brushless DC but ultimately you know the way we model it in the linear region will be the same and I will highlight the linear region with nonlinearities certain things change in the machine model okay and that's for an advanced class and we are not going to cover that all right so that's kind of a little bit of information there to get us set up in this discussion kind of background so again going into PMS M's why is this preferred over other machines I don't know if you have come across this many applications are now going towards permanent magnet synchronous machines whether it's surface mount magnet interior permanent magnet a lot of them are going towards these permanent magnet based synchronous machines because it has high density high density I talked density it has high power density right power density and this high density is actually coming from this compact design this is coming from the compact design because of the permanent magnet technology is so advanced you can now you know pack a lot of power a lot of torque with a small footprint or in a small volume which is much more advantageous you know in looking at these days in applications right you look at the car you look at a robotic system everything is trying to be compact very small designs right and space means or space materials means cost so compactness brings in another big factor along with efficiency these are very efficient compared to some of the counterparts like induction machines and efficiency also depends remember we talked about the top speed regions and how efficiency changes depending on operating point right so if you are looking at torque and the speed you will see certain regions where or contours right efficiency contours depending on the motor design so this is something a motor design I would look at when they are optimizing their machine design so you have talk density efficiency and also this can be controlled electronically it's called an electronically commutated commutator means you know you you move the motor right drive the motor through electronic commutation and you can drive them with an inverter right you can invert you can use an inverter control speed you can control talk by controlling the current that you apply the amplitude of the current and the speed is synchronous with the frequency so having a variable frequency drive VFD you might have heard of that vft now you can control the speed of the motor okay so there are advantages there as well alright so [Music] that's a little bit of an info another little bit more information on why we wanna or why people are moving towards permanent magnet synchronous machines and we also don't have you know the arcing and all those problems of DC machines so there is another advantage in p.m. in synchronous machines at least PMS m's compared to DC machines can you guys think of one I can give you a hint this is thermal related if you think of the thermal perspective these are an advantage of the permanent magnet synchronous machine versus DC machine well depending on the current both will get hotter right both will get hotter but if you think of the DC machine right for a DC machine your magnets are outside your windings are inside right your windings are going to be inside the rotor now for a PMS M for a synchronous machine your windings are outside your magnets are inside right so it's very difficult to cool higher he dissipate more llx in terms of the cooling properties right now you can cool something that's actually on the stator much easily then something on the route because we have we don't have much room inside the inside the motor to cool it so it's going to be very difficult to cool DC machines because you have to get through this air gap or you have to find some way to take that heat out through the shaft but here we can have a fan we can have some cooling system around the motor to take that heat out so p.m. that that's another reason that prevalent magnet synchronous machines are popular so there are a whole lot of advantages and when it comes to PMS m's okay so a little bit more information and so now we are talking about machines that have the stator out star outside and you have the rotor inside right this is a PMS M that have the stator this is the stator and we have our rotor right and there have been designed where they they swap the two they are again three phase three phase machines and then they are called outer run outer runner so that means you have your magnets I'm going to try to get accurate outer runner means so the magnets are mounted on this surface and then you have a set of windings inside okay so this is a three-phase winding still a brushless it still brushless and these are very popular in drones in drones and in come in like laptops you know laptop fans laptop fans for cooling they have this what else and and then there's a there are in veal machines in veal so if you look at certain vehicles they have electric machines inside the tire so in such machines they use these kind of outer runner machines to get you know to get that space reduced but however you do need you have the problem of cooling the thermal effect is still there so it's not going to be able to you're not going to be able to cool as you would the inter in a runner or the normal type of a synchronous machine and then I think I have a couple of these outer runner machines in the lab in three to six kilo machines if you want to look at them okay and then I have a direct experience on I have with control I've controlled that that was one project that I did for my PhD in controlling them those in wheeled machines and read they're really good he knew he bikes actually Alex it was a new back in 2008 so I don't know if you can still call it nuit bikes that they had them in 2008 oh yeah so a lot of these technologies have existed for a period of time you know and depending on new advancements new sensors new modulation techniques they come and you know they come and they both come and go so you tend to see that with technology and then three and I don't want to get into a lot more details I will just mention these things for you so that you remember we are talking here about three-phase right and there are two phase brushless DC machines as well when you know you might come across this as well there are certain they have a little bit tricky to get to start up and commute it and drive you need sensors to do that but there are two phase brushless DC machines they tend to be cheaper and they go into applications for fans where you don't need and you don't care about torque ripple because there's a lot of torque ripple here and then there are this technologies for control called trapezoidal control and we will talk about them when we talk about the different control strategies okay so depending on type of control you to achieve you get they'll have their own advantages and disadvantages okay so a little bit of a background before we begin to talk about the designs and what you can do with the machine so let's start with what the electrical circuit diagram would look like okay so this is the electrical circuit diagram electrical circuit diagram so it's a three-phase machine right so you have a resistance we have inductance and then so you have three phases of course data you know three v is v phase seven phase you can multiply the number of phases but you know the underlying concept is fairly similar depending on the number of phases you change your voltage phase shift between the applied voltages and then everything else is almost the same okay and then we'll call this me yes they'll call this VBS because this VCS okay and then one more thing to remember is that we do have coupling between these inductances right this magnetically coupled they have their mutual inductances right this is coupled to this this is copper this and likewise so they have their own mutual inductances so call this RS RS and then we have a we have inductances the same inductance let's assume they have the same inductance but so we are talking about a balanced three-phase system okay now one thing we are not seeing here is the back EMF and then will capture the effect of back EMF when we represent it in the mathematical form okay we have we have the inductance there so with the flux linkage we can capture that now if we want to write the relationship or try to mathematically model this and these variables are in state a frame which means they are going to be sinusoidal right they're going to be sinusoidal and if you look at the back EMF or the currents they are also going to be sinusoidal okay and we can say that if this is VA s right you can say these currents IAS IPs and I see us okay those are the currents going in and then we can write the voltage draw and keep in mind we are considering the phase voltages here phase voltages right and this is called the neutral point neutral point in some machines you do have access to the neutral point from the outside but certain machine designers don't give you access to the neutral point if so you are only going to see the phase voltages Oh line to line voltages okay you know from your Power Systems class you from your 341 lectures that phase to phase voltage and the line to line voltages are different okay so remember that whenever you look at a back EMF or when you look at the applied voltage if you are considering line to line versus phase that is a difference so these subtleties can actually trip you up and cause certain errors when you implement in so you have to be very careful so let's write the phase voltages so we are looking at VA s vb s and VCS right so these are the three voltages and they are essentially equal to the current ahrefs times sorry the resistance the phase resistance time current right and then there are no other effect from the currents on resistance so this is zero right you know how to multiply matrices and then of course we're gonna have our flux linkage change right yes OBS and the C yes and if you remember we we did something similar when we studied the reference frame transformation right so we have our VA s and then similar to VA s we can write the BS right and again we can write this here yes right so we can see the relationship there okay sorry now we want to look inside what we get here for lambda s and we are going to assume a linear machine model for our basic understanding but in applications when you go into real-life your view most cases you're gonna want to consider these nonlinearities that you see in these systems so there is a lot of mathematics as a lot of engineering that goes behind such systems yes BS number C yes yes so let's look at the flux linkages and then we can apply the derivative the P is basically DS over DT we looked at this right so I'm you know since I studied at Purdue this is the standard notation I'm using a textbook called analysis of electric machines by Paul Kraus back in the days I believe that was third edition and I think there are new revisions of the book but you know I'm kind of referring to that there might be other textbooks that use different notation just keep that in mind so here yes yes that is the self-inductance yes yes okay and then a SBS this is the mutual inductance between the let me go back to the figure the SBS is the inductance the mutual between a and B because when that's current flowing B it will link flux through it because of the state how the static is designed right there is some magnetic coupling you have your beads so when there's current going through one winding ET that flux will link through not all of it some of it will link through B right therefore there will be some mutual inductance that's what we wanna remember okay and that's what this mutual inductance is capturing similarly you are going to see la s CS okay and then we have our currents IAS IPs Phi C yes so there is some coupling between the BS current and that current influence on a s the flux linkages on a s and then when current is flowing through C phase C there is a certain flux that links through a winding that has this SCS coupling term which again influences the a s flux okay and on on this so this is the electromagnetic flux linking we have another flux right guys that rest of the flux coming that is coming from our permanent magnets so let me go to a different page because I need so let me try to try all the way here lambda KS and the BS and the CS s CS and then this is la s es el es es es si es okay and then when you look at the flux linkage of B this is l BS KS right because current through a linking through the windings B which influences that flux right so l vs vs l vs c yes okay LC yes yes LC s PS l CS c yes so these are the self-inductances the flux due to the current through its own windings versus flux due to currents through other windings if you want to think of it that way okay so that's the flux linkages flux linkage includes currents and the number of windings keep that in mind when the motor is rotating this might be changing okay and then we have another source of flux the permanent magnet okay so I'm going to use lambda M Prime here and then we are assuming ideal okay so we'll have sine theta R then here sine theta R minus 2 PI over 3 sine theta R minus 4 PI over 3 and so now this is due to the permanent magnet flux the flux linkage due to the permanent magnet flux and then we are we are using a sinusoidal distribution here considering that because of the permanent magnets and if you want to kind of visualize this let me see if I can get this right and give a hand waving explanation just to be brief here so you have especially you will have your a winding right and then depending on how your rotor magnets are aligned that is specially going to be your gonna call this 0 right that direction is 0 now with that if we consider be winding B winding B prime then there is a spiritual shift right it's a special shift from that so that b and b b b prime that winding will have a 2 pi by 3 shift for the same magnet right because we have the same rotor magnet but because of the windings that are out of phase we have the flux linkages obtained and phase shift there ok so that's why we are not changing the magnet for that winding but since the winding is specially displaced that phase shift will carry on to the flux linkage of that phase if you don't think of it that way ok so you'll have a north and south that links and then similar B for C right for C you're going to see a 4 PI over 3 shift because of the spatial displacement of the sea winding right so the key point is flux linkage not just flux flux linkage captures the permanent magnet flux from for this part times the winding placement so that's yeah and then we call this matrix and L the LS the inductance matrix okay inductance matrix capital LS bold because it's matrix and we for analysis perspective we assume this is this is oops I lost you guys we assume this is cement to stop that from happening now when you look at the toke generated this toke generation is based on the currents and the magnetic fields so you have a stator magnetic field generating stator magnetic field generated by the currents and you'd have a rotor magnetic field that interact right so that interaction generates the electromagnetic torque that gets applied onto the motor so if you want to come up with the electromagnetic torque equation based on the stator variables this is going to be a very long expression very complex expression and you can find this in several textbooks you know and if you need this and if you can't find it let me know I can provide that to you I don't want to get into that yet if need be we can talk about that okay so like before that I think what we want to do is we want to try to understand the Machine a little bit better before we go and try to see what the state of frame currents are it's going to be a very long expression with IAI space squared IB IB squared so I don't want to get into that okay all right so now with that so we kind of saw what the motor model would look like in the stator frame you take a machine and you look at it this is what its gonna look like yeah this is in linear region and certain assumptions this is what you're going to see now if you are to analyze this and study and control this in this form it's going to be somewhat difficult because we have our currents be AC voltages and currents they are going to be AC it's not impossible you can still do it but it's going to be a lot of computations and you have AC currents so what we have done is in order to analyze and model these motors a little bit better we have gone into this rotor reference frame transformation okay and I hope you remember that from our previous discussions we were able to convert our machine into at least the inductances and resistors network we converted that to the rotor reference frame right we applied the KSR transformation matrix we use the KS inverse transformation matrix and we converted that machine into the rotor reference frame what is transformed it to the rotor reference okay so we want to apply the same concept to that state machine model that we just came up okay and I don't expect you to know this know these concepts just try to absorb as much as possible and then when you start working with these things and if you have more questions now you can have you can think and try to you know understand what exactly going on with these approaches okay so what we're trying to do next is actually go into looking at rotor reference frame motor models Road reference frame even myself when I learned about you know this machine model this machine model with you know these equations I had to go back many times just to explain it to myself so if it just didn't make sense right away you don't take your time think about it try to understand and maybe you know I can try to help clarify certain things okay all right so we have we're going to look at the rotor reference frame now in order to transform you know the approach right we looked at how to do that we can left multiply with KS both sides and then apply the inverse to the right hand side and you can come up with this relationship so I won't do the application or the transformation from scratch I'll show you what that transformation or once you transform the motor model to this rotor reference frame what it would look like okay so this is the transforming to the rotor reference frame so we typically use Q s R to indicate that it is in rotor reference frame this is the quadrature axis voltage you've seen this before this is the direct axis voltage and this is the zero sequence voltage okay typically in applications people don't talk about the star it's implied for up with PMS em no rotor reference frame is the go-to frame to analyze it better and model it with a simpler model and we know that our resistance network since it's balanced it's not much influence it's going to remain or as as it is if we showed that last time and then our currents since we are considering dynamic variables which means your variable can be dynamic not a steady state we are going to use simple letters and if we go into steady state variables you know we will show can use we use capital letters that's kind of the standard format and I'm sure you are familiar with it from your 358 cosas site so we have our rotor reference frame currents and then we have our voltages remember the flux voltages from the flux linkages right lambda t s prime 0 and we have permanent magnet flux which is P so this is our Q is our lambda Q so any most applications people don't even use the 0 sequence they tend to ignore that assuming it's a balanced system ok so we have our flux linkage this way so let's let me expand on this a little bit k expand this a little bit and specifically on lambda q sr then the DSR lambda 0 s okay so this is what its gonna look like we are looking at the flux linkages right assuming the linear models you're gonna see L LS l mq l LS l MV so the LM pew this is the Q axis inductance this whole term this is d axis inductance and then we have our leakage l LS is typically the leakage terms that you're going to see now if you have heard you know in Q axis current Q axis inductance Q axis current is basically IQ the axis current is ID 0 sequence current is not much spoken about because for a balanced system this is zero and it's assumed for most cases unless it's a faulty machine or a drive system for that matter and then we have IQs our IDs are zero and of course we have our flux linkage lambda M prime ah this is zero one zero okay so now you can see couple of things here your flux linkage your back EMF due to the permanent magnet is only reflected on the D axis okay this is an important point to remember because we said that D axis is directly along the permanent magnet flux okay so that's why this is reflected that way and QX is where we place our stator flux right there or we align the currents so that the stator flux is 90 degrees out of phase from these flux because quadrature it means 90 degrees out of phase from the direct axis okay so now everything is kind of linked together in this analysis and hopefully it will paint a better picture okay so this is the motor model in matrix matrix form and what I want to do is I want to stop here for now I want to let you guys think about this a little bit and we'll go into a little bit more discussion on what this model will look like you know feel free to write these equations out independently so vqs are if you had to write this out as an equation what are the terms that you are going to see right for each of them try to write that write that out and see what you get okay because we will actually try to do that next time and try to understand what is this vqs what is this VDS what does that tell us about the Machine behavior okay now we are not changing the machine here we are not modifying the structure the machine is there in the stator frame we are not changing this setup we are only transforming into this hypothetical frame to study it better to control it better okay so in the real world it's gonna look like this but when we do the transformation that representation is going to look like this mathematical okay and then this will help us understand the Machine and control the machine in a much more robust way then you would try to control these in the sinusoidal form they it gets a little bit tedious to do that all right good do you have any questions any questions

Channel: Sandun Kuruppu

Views: 2,314

Keywords: motor control, AC machines

Id: Brro9D059y4

Length: 49min 42sec (2982 seconds)

Published: Wed Jun 03 2020