 I invite you to view the lectures of this course on modeling and analysis of electrical machines. I am Dr. Krishna Vasudevan from the department of electrical engineering at IIT Madras. So this course as I said is called as modeling and analysis of electrical machines. In the lecture today we will look at understanding the objectives of this course. The material we are going to see throughout these lectures and how they are going to be different from the material you might have seen definitely on the lectures at the undergraduate electrical machines course may be one or may be two. And we will also see the utility of the material that we are going to study in this course. So first the objectives, the objectives of this course which means what are we going to see in this course. As is given by the heading we are going to look at modeling and analysis of electrical machines. So let us understand that in little more detail. Now let us say you have an electrical machine. As you know the electrical machine may be a DC machine or may be an AC machine of the varieties that you had seen earlier. We will generally call that as a machine and we know that the electrical machine has an electrical port. Electrical port is where you give electrical supply to the machine and then there is a shaft available in the machine where you would then connect your mechanical may be mechanical load if it is a electrical motor or a mechanical source if it is an electrical generator. Now an electrical machine is inherently an electromechanical energy conversion system which means that you may have energy flowing in from the electrical side to the mechanical side or you may have energy flowing from mechanical side to electrical side. Now if the flow of energy is from electrical to mechanical then you would call that as an electrical motor and if it is from mechanical to electrical then you would call that as a generator. All machines are inherently able to do both. You may be able to use a given machine as an electrical motor or you can use the same machine as an electrical generator. Now this electromechanical energy interaction it is able to do because of the presence of a magnetic field inside the machine. If there is no field the machine will simply not work. The magnetic field is essential to the operation of the machine it is only in the when the magnetic field has been established it is able to do this electromechanical interaction. And the machines should normally therefore have a way of establishing the field inside the machine that may be done through the same electrical port which supplies electrical main electrical energy or in some cases there may be another input available where you give an electrical supply in order to establish the magnetic field so that is given the name as a field port. So an electrical machine then has these three places where it interacts with the external world there is in the mechanical side where some load may be rotated there is an electrical side where you can give an electrical supply or take the electrical output available and then you will have to give an electrical input may be in order to establish the magnetic field. So we have a system where all these three interact any description of an electrical machine should therefore be able to describe how this interaction happens you should be able to reduce it to the form of some equations whereby you can know having given an electrical input supply how the mechanical side will behave having given a field of course or having given a mechanical input how much electrical output are you going to get. So these are the essential aspects which we will look for when you say that you are going to model a machine or when you say you are going to analyze a machine analyze how this system is going to behave. So essentially then we are trying to look at generating a mathematical equation set a mathematical equation set which will describe the interactions from one port to the other port this port is not going to interact in the main transfer of energy between the mechanical and electrical side but this is essential in order to establish this interaction there is no main energy consumed from this to convert on to the mechanical side of the electrical side. So we are trying to look at generating a mathematical equation set if you look at the operation of electrical machines for example let us say we are going to consider a motor right which means that you have this machine here you have an electrical port you have a mechanical port I am not going to mark the other port which is the field which is well understood that it is there it is not going to take part in the electromechanical interaction. Now if you now supply an input to this machine and you are going to derive a mechanical output from the machine let us say you are going to connect it to some load may be a wheel or may be a fan blade or some other kind of load which means that on this side you are going to have rotational motion and for rotational motion the machine basically has to generate torque only if it is able to generate torque the load would rotate. And therefore in response to the supply that has been given it will draw a power that is electrical power from the electrical source and deliver mechanical power to the load in order to do this or in the way of doing this for in establishing this interaction the machine generates heat there is lot of heat generated inside the machine the machine temperatures can rise up may be 100 degrees or more depending on the machine design. So the machine is also going to generate heat apart from that you have the machine shaft and the shaft will have mechanical stress on it right. So if one wants to describe how this machine is going to behave in all its entirety then you need to describe all these aspects you need to know how much of stress is going to be developed you need to know how much heat is going to be developed you need to know how much input power is drawn how much mechanical power is delivered all that needs to be established and in the machine the magnetic field is not just situated in one location it is distributed throughout the machine which means inside the machine the magnetic field or the magnetic flux density the magnetic flux density is going to change inside the machine. You know that electrical machines are generally circular in nature in shape that is and inside you have a magnetic field and the field levels may change at different locations inside the machine. So there is a spatial distribution of magnetic field inside the machine and one needs to know if you want to understand the machine is in its entirety how this magnetic field is distributed. So these are all various aspects of trying to understand and model an electrical machine but in this course we are not going to look at heat that is generated we are not going to look at how the magnetic flux is distributed throughout the machine in various locations these are not of interest we are rather trying to look at the machine from its input output behavior that if you give input of this much an AC supply or a DC supply of so much level what is the mechanical output that is going to be obtained. So we are sort of attempting to look at input output behavior the output behavior obviously has to take into consideration the load that is given without knowing what is the load you would not be able to describe how this mechanical side is going to behave. So we are going to look at input output behavior and this input output behavior we want to represent as a mathematical equation set which means a set of equations describing the relationship between what is happening here and what is happening there so this is the overall objective of this course but may be some of you will say have not you done this before right in the first or the second course on electrical machines. Let us take for example you are looking at DC machines now if you are looking at DC machines I am sure in the first or the second course on DC machines you would have come across machine equations the machine equations read VA equals RA x IA plus a back EMF which is generally called as EB so this is something that you would have come across which is nothing but an equation now along with this you have another equation which says that EB equals some induced EMF gain EMF constant multiplied by speed this is just the electrical part and then there has to be something which translates this electrical part to the mechanical part and there you write the generated electromagnetic torque TE is nothing but some KT multiplied by IA now these are machine equations that I am sure you would have seen in your first or second course on electrical machines are these not enough right these are after all an equation set and these do describe the behavior of a DC machine more specifically one could say that this describes a separately excited DC machine but if you take a look at these equations what we are saying is that there is a DC voltage that is applied to the machine in response to which it draws a DC IA EB is the induced EMF which is also DC the induced EMF arises because of rotation therefore some omega and in response to this flow of current IA you have a generated torque the equations do not tell us anything about how this speed actually came into existence it simply says that if this is the speed this is the EMF right the DC machine would not have been in existence operating all the way from T equal to – infinity from a long long time ago somewhere at some point of time you must have turned this machine on which means if you are having a DC supply which is VA this DC supply must have been switched on to the machine this equation says that VA must be equal to R into I if there is a current flowing and then there is an induced EMF a controlled voltage source which is KE times omega plus here this is your resistance RA and now you close this which let us say at some T equal to 0 this should have been the case you could not have had the machine operating from time immemorial sometime you should have switched this on and before you switched on obviously there would not have been speed the machine would not have been rotating before you turned it on and now the question is if you are going to turn this switch on at some instant of time let us say call it at T equal to 0 how does this speed rise from 0 value to whatever it is right so that is not answered by these set of equations similarly if this DC voltage is not a pure DC voltage it has some ripple which normally or DC supplies will have or in the case of modern DC machine operation you definitely do not give a pure DC source you derive it from some other circuitry for example you do not have this kind of a DC source you have another box here which is some electronic circuitry which may in fact derive it supply from AC and this electronics is going to supply what is so called DC voltage to the machine which is not really pure DC but fluctuating DC so if you are going to give something like that how does this machine behave how is this generated electromagnetic torque TE is it smooth or is it going to have lot of ripples if it is going to have lot of ripples how does it really affect the performance of the load now these are all aspects which this set of equations do not review so this set of equations actually describes what is called the steady state behavior steady state equations it only talks about if the speed is held steady at some particular level then this is the back emf and in response to that and the steady applied voltage there is a steady DC current that flows and these are the expressions that then describe the machine behavior under steady state condition whereas what we are trying to see here is non steady state that is under dynamic condition how the machine behaves these are also otherwise known as transient condition how the machine behaves for example if machine is operating and you suddenly throw a load on it increase the mechanical load what happens to the speed how fast does it drop how low does it go and how fast is it able to pick up again these are all again issues that are not described by these equations so we are going to try in this course to develop equations to understand machine behavior to model the machine in order to be able to answer these questions also the same equations will definitely be able to give us the steady state behavior as well but if you want only steady state behavior you have already learnt these machine equations in your first or second course but what you have missed is this part which is what we will focus in this again let us look at induction machine the induction machine is a much more involved machine than the DC machine you know that the induction machine takes well we look at three phase induction machine there are also single phase induction machines which we are not going to look at in this course we will basically look at the three phase machine in which case it takes a three phase AC supply and then delivers a mechanical load on the other side and you would have seen in the first course or the maybe the second course in UG electrical machine that this induction machine can be analyzed or understood its behavior can be understood through an equivalent circuit in the case of DC machine the equivalent circuit is very simple the variables are DC and therefore you have a DC supply a simple resistance and an EMF source this is all there is in the equivalent circuit of a DC machine under steady state condition. Now that you have an induction machine the induction machine being an AC system apart from the resistance you would also have an inductance coming into picture therefore you have seen the equivalent circuit of the induction machine to have a stator resistance and then a stator leakage inductance and then the magnetizing branch the rotor resistance the rotor leakage inductance and then the resistance representing mechanical output all this is your equivalent circuit of the induction this resistance is of course variable that is a variable resistance and the symbols given are standard RS or sometimes call let us call it as R1 and then L1 one represents the stator and here you have R2 dash where 2 represents the rotor and dash represents the fact that the rotor resistance is referred to the stator and here you have LL2 dash that is the leakage inductance of the rotor referred to stator this is the core loss resistance I will call it as Rm and this is the magnetizing inductance and call it as Lm and this resistance represents the mechanical output from the machine which is given as R2 dash into 1 – s by s where s is the slip of the machine which is given by the synchronous speed – the rotor speed divided by the synchronous so it is a ratio of a slip that is occurring in the machine the rotor is slipping behind that of the synchronous speed by some number ratio of that with respect to the synchronous speed is then the slip so now you have this is an equivalent circuit which is per phase how to determine values for this you would have studied in your UG course doing block rotor test and no load test of the induction machine one tries to extract values for all these elements and having extracted values for all these elements one can now go ahead and understand the behavior of this machine by doing a circuit analysis this is a fairly simple circuit not too complicated and this circuit you know is called the exact equivalent circuit of the induction machine and one can because these numbers are pretty high and therefore the flow of current in this is small and the stator impedance also does not normally drop too high a voltage when rated voltage is applied and therefore if this drop is going to be negligible then one can shift this magnetizing branch to the input and the circuit as shown here is called the approximate equivalent circuit of the induction machine one can analyze this using normal circuit analysis right but you see that in order to analyze this circuit you need to know what is the value of SA you need to know the slip which means you need to know the rotor speed so once you know the rotor speed once you know the AC supply once you know values for all this one can get the performance of the induction machine again you see that you need to know the rotor speed a priori in order to understand or analyze the circuit you cannot answer for example if you want to know how the machine is going to accelerate you cannot answer that from this circuit this circuit does not say what is the relationship between the generated torque and the input supplies that are given for example IS as a function of time it only says that if so much current is flowing here then you can find out how much mechanical power is output provided you already know the speed and in a general case for example here if you want to say the induction machine is going to start you have no way of knowing how the machine is going to accelerate you have no way of knowing how it will respond to a sudden change in the loading conditions that are there at the output. In the same way if you now have a mechanical source as is used in the wind generation systems today there are lot of wind generators available and most of them use an induction machine so you have blades that are connected here like that and due to rotation of the blades you now get electrical power output from the machine so how does this interaction happen again this equivalent circuit can be used provided steady state is all that you are interested but wind speeds are not normally steady things are going to change and it would be good from other view point as well to have a more detailed model of the machine in order to understand the system behavior with this. Similarly let us also look at the synchronous machine which is the third variety of machine that you would have seen in the UG course the synchronous machine is normally described by or rather is mostly used as a generator this is a variety of machine that is used in the electricity grid in order to generate the supply that you get everywhere in your home in your work places it is used to generate electricity so this is primarily used to convert mechanical input to electrical output you have an equivalent circuit for this also which looks like this again on a per phase basis you have an AC source and then you have the armature resistance and then the armature inductance and then the electrical output the equivalent circuit is fairly simple unlike the case of induction machine where there is a slip of operation here there is no slip the word synchronous I am sure you will recall refers to the fact that it rotates at one single speed which is the synchronous speed which is the speed related to the frequency of the AC supply. Now how does one understand this again you have equations that are describing the regulation of the machine and then the armature reaction effects all these things are well known and then if you have this machine already connected to an infinite grid then one knows how much of active power transaction is going to take place how much reactive power is going to take place how the field excitation is going to control the flow of reactive power how the mechanical input controls the flow of active power all these things one would have seen but what one has not seen in the UG course is again suppose there is a fault you have the synchronous machine not looking at this you have the synchronous machine connected to a bus and some long line there is another bus may be connected to some loads may be some other generator is also there now if there is a fault at this point what happens to the synchronous machine how does this machine behave with respect to a faulted condition does the speed still remain the same will the speed go down will the speed increase will the supply voltage is changed how will it behave now in order to understand this this equivalent circuit does not tell us anything again you need to have more detailed equations of the machine in order to understand this behavior right. So again transient behavior is unanswered by this equivalent circuit so to sort of summarize what we have seen so far is that the major difference between the first course or the second course on electrical machines where you would have studied about various machine varieties and this course is that one is going to be look at in this course at dynamic behavior in this course as opposed to what we saw in the UG courses you would have mainly focused on steady state behavior and the equations that we are going to derive equations that we are going to develop will require an understanding of how the machine works will require an understanding of how the machine is built and these equations we are aiming to develop primarily input output relations we are not going to be interested in looking at the internal distributions of field the stresses that are developed that is not the goal of this course in short we are not going to be looking at the machine design aspect of it we are only going to look at input output relations why this material is useful let us just briefly look at it this material is useful or the knowledge that you would gain from this course is very useful in application areas a machine is not going to be used in isolation you do not want to have a machine sitting on this bench simply applying an electrical supply to it and say yes the machine is moving the machine is going to rotate there is no fun you will have to connect it to some kind of a load and it is the load that you are interested in controlling the machine exist in order to operate the load and you cannot just allow the machine to operate the load unless you are looking at an application like a home fan where you do not really bother about what is the speed at which the fan is rotating may be the fan is rotating at some 300 rpm may be 500 rpm you want only a medium fan speed or low fan speed or a high fan speed you are not interested in saying I want a fan speed which is 600.5 rpm or 603 rpm not deviating from that so there are application where you want to have a precisely controlled machine speed and how do you get that obviously you need to have if you say that you want a precisely controlled speed the speed must be precisely controlled in spite of variations around it variations to the environment which means variations to the supply variation in the load irrespective of any of these things you still want the speed to be held fixed and how would you do that you would need to have a closed loop control system you would need to sense if there are disturbances that are happening and then control the input supply given to the induction machine may be if it is an induction machine this is the only thing that you can control so you need to sense disturbances around and then control this if you are going to do that and you want a good response from the machine you need to be able to estimate how this machine will respond to changes in my supply to changes in my load for all that you need equations describing the dynamic behavior without having equations describing dynamic behavior you cannot attempt a control system design it is essential induction machines especially are now being used in very high performance systems and there are methods of controlling induction machines which fall under the class of vector control applications or sometimes called a field oriented control. So these are high performance applications for which you need to look at the machine in a totally different way this vector control kind of application or vector control kind of operation on the induction machine converts the induction machine to look something like a DC machine we will understand in this course how all that is going to have and what are what is the basis of vector control how to do vector control you would probably do it in some other electrical drives based course but not here but here we will look at the basis similarly in large electrical systems if there is a disturbance how is the entire system going to behave there is lot of discussion today on what is called as micro grid which is a small grid containing several distributed electrical sources how does this system behave if there are going to be disturbances you cannot avoid disturbances on a grid if it is a large grid it is able to withstand some amount of disturbances but if it is a small grid it may not be able to withstand so how do you assess the stability of the micro grid for that again you need to have dynamic equations of machine if they are connected to the grid alternative I mean additionally in addition to these machine descriptions the material that we will study will also help to understand how distributed sources can be connected to the grid for example solar photovoltaics how do you connect them to the grid there is an inverter that is going to interface to the grid and the inverter has to be controlled in a fairly complicated manner how do you establish all those things though it is a machines based course the material that we will learn here will also help us understand how this has to be done so in short then this is a course on machine modeling where we are going to try and look at the dynamic behavior of the machine and understanding this will help us apply or design and understand how machine control needs to be done whether it is for motoring or whether it is for generating the material that we will see in this course is going to be extremely important machine control grid operations and what we now have as distributed electrical source so with that we will end this lecture and we will continue in the next hour.