 Good morning and welcome to this course, Electrical Equipment and Machines FEM Analysis. Now, these are NPTEL MOOC course exclusively devoted to finite element analysis and its application to electrical machines which is static and rotating machines as well as some other equipments like high voltage you know devices. Now, all these devices that we are going to analyze by using FE analysis in this course they are used in generation, transmission and distribution of electrical energy. Now, what are we going to study in this course? The focus will be on principles of electromagnetic relevant to finite element method. Now, electromagnetic is a vast subject and we are going to only focus in this course on low frequency electromagnetic and to that extent we will cover some basics of electromagnetic which are relevant to FE analysis of low frequency apparatus. I will also you know suggest those who are new to electromagnetic, they can quickly you know see this website at leisure time which is a virtual electromagnetic slab. The address is mentioned here it is you know if you just type VEL IIT Bombay you will get this link and then you can you know see many software experiments and related theory mentioned in each of these experiments with interactive you know mode like you know for example if you click these buttons you will get the field plots with the relevant explanations below. So, those who are not so well in basics of electromagnetic they can either read any book on basic book on electromagnetic or you know refer any such web based material like virtual lab and upgrade themselves, but they need not worry too much because I am going to cover in about six half an hour lectures all the basics of electromagnetic which is required for this course. So, that will bring all of us on same platform and that that will be good I think then in the second focus will be on development of theory of finite element method and the corresponding procedures. Now, procedures that we are going to see are basically for one dimensional and two dimensional problems three dimensional problems can also be solved by developing our own course, but amount of computational efforts in terms of coding and not from the point of your electromagnetic are quite high when you do coding for three dimensional FEM analysis. So, we are not actually going to develop 3D course as part of this course for that many commercial softwares are available and they are best suited to solve your practical 3D problems. The idea of this course is when researchers and practicing engineers they are using commercial software they should know what they are doing and understand the result that they are getting from the commercial software. So, once you understand the FEM procedure then you will be a better researcher or a practicing engineer to exploit various features of commercial FEM softwares. The third focus is going to be on solving some practical problems related to static and rotating machines and we will you know solve various problems from static transient time harmonic coupled and in the increasing order of you know difficulty and computational efforts. As I mentioned it will be desirable if you refresh yourself with basics of electromagnetic vector calculus and of course machines I am sure most of you are exposed to principles of electrical machines, but in case you are not you may want to you know refresh or you know if there are some doubts of course they can be addressed as part of this course during the interactive sessions. The course is of eight weeks and there will be introductory lectures on basics of electromagnetic and then we will get on to the FEM theory first we will see 1D, 2D then we will also see from static calculations we will go to time harmonic then transient coupled and so on. This course as I said earlier would be useful to practicing professionals who are actually solving industry problems as well as to undergraduate and postgraduate students. To undergraduate students they will understand the potential of this finite alien method and suppose if suppose they go on further to do research take the research career or join industry they would be in position to use this tool effectively. Postgraduate students of course many PhD students who are dealing with electrical machines and apparatus they have to design optimize improve performance of this equipment and for such reasons they will come across at some point of the time with this finite element method and I am sure this course would be useful to them. Now what is the need for FE analysis? Now this finite element method amongst all numerical techniques is one of the most popular techniques for particularly low frequency. For high frequency electromagnetic analysis for example when you are analyzing antenna and waveguides particularly antennas where you know you have open boundary problem there the integral equation methods like method of moments are more useful. But here since our focus is on electrical machines and we have bounded structures typically you have you know finite element finite difference but among these finite element has emerged as most popular and will concentrate in this course only on finite element method. As I said this is being used extensively by researchers and industry many commercial FE softwares are available and why finally computation of electromagnetic fields is essential. Initially when computational tools were not advanced the designers of electrical machines they used to have analytical formulae thumb rules or curves derived based on experimental data and then they used to you know design machines. But you know that there used to be always some kind of factor of ignorance and for that factor of ignorance can be minimized by using numerical techniques like finite element method. Using finite element method you can exactly know the field distribution and the stress levels. Stress when I mean stress could be electromagnetic stress it could be thermal stress it could be structural stress it could be you know any other stress related to engineering field and although we are going to discuss here only electromagnetic and coupled systems. As you are aware finite element method is equally applicable to other domains of engineering and in fact it was first well developed and initiated for structural engineering and then it got adopted and adopted for electrical engineering and electronics engineering. So, computation of EM fields is essential for improvement in performance parameters like calculation of reactants, calculation of losses, calculation of temperature rise, calculation of forces, torques and what not. It can be also used for enhancing quality and reliability I will give some examples in the next slide and then it can be also used for investigative analysis that is failure analysis. Some equipment suppose it fails at the test bed during the test or at the site then how do we investigate and come to the root cause for such failures that can be also done by using finite element method. So, finite element method as is well known for is used for is basically a non-destructive testing and evaluation method. That means, we are not actually physically stressing the machine we are actually simulating or emulating a given device in that finite element software and then actually subjecting that machine to stresses and in that sense it is non-destructive testing and evaluation and this has obvious advantages because you know if it is a very costly device like a large generator or a large transformer costing few you know crores or millions of dollars then it is not possible to you know completely design build test that equipment and then find out oh there is some mistake and then do rework that rework would be very costly or you know in today's world where there is there is a global competition and competition is very cut throat. You need to optimize the material cost and again you have this FEM coming to your rescue. Now, one of the first applications as I mentioned of F E analysis is parameter estimation of any device that you are simulating. Now, here is the case of a transformer which all of us know and is the equivalent circuit of the transformer. Now, this equivalent circuit has many parameters and these parameters generally we have studied in our basic course on electrical engineering. We basically based on the theory of transformers we evolve this equivalent circuit, but to a practical designer this equivalent circuit is a result of design and test that means this equivalent circuit is of practically of no use to a practicing designer who wants to design a transformer. This equivalent circuit can be derived based on test and design data. So, what is required for a designer or a person who is trying to optimize a product like transformer he needs to understand each of these circuit parameters in depth. Now, when we are actually are writing these reactances and resistances they are already doing some approximations like when we are actually talking of reactance and we are calculating by some formula simple analytical formula. We are approximating like that the flux is entirely axial there are no you know leak edges at the end or there are no you know ampere turn per mm imbalances and what not. So, we basically tend to assume things which make analytical formula application possible. Similarly, when it comes to these resistances R 1 and R 2 dash as we know these are AC resistances. So, it is basically DC resistance of binding plus skin and proximity effects they add to or they lead to what is known as AC component of resistance. And believe me to understand and compute this AC resistance in a practical device it requires thorough knowledge of Maxwell's equations theory of eddy currents which we are going to see in this course. Similarly you know if you see this shunt branch of this equivalent circuit which shows magnetizing reactance X m and core loss resistance R c. Now, these two parameters are also they are extremely demanding in terms of understanding field behaviors and governing electromagnetic materials. As you we know the ferromagnetic material that is used in core material of static and rotating machines it exhibits that the material exhibits hysteresis characteristics. So, there is not only there is a nonlinearity, but there is remnants and hysteretic behavior. So, in order to address this behavior and be able to take into account into your numerical method it requires lot of understanding of basics of electromagnetic fields, basics of material science, basics of governing physics. As I mentioned here this is a typical leakage field plot of a transformer. These are transformer window, core window and I am showing only one you know set of windings that means there are other set of windings on the other side. So, this is the low voltage winding and high voltage winding is in two parts with taps. Now, because of this taps and because of this gap which happens because some turns may be out of the circuit. You can see here the leakage field is basically turning here in this gap and there is a corresponding radial component of field in this zone. That makes the calculation of reactants as well as the eddy current losses in the windings difficult by using standard analytical formulae. And here again that is why you need to use a numerical technique like finite element method. So, the second focus of finite element analysis is typically reliability or quality enhancement. So, here you know I am showing a typical you know high voltage lead to ground arrangement in a typical high voltage equipment. So, this is a high voltage lead, this is a ground plane, these are Q potential contours and these are electric field contours. We will see you know background theory of this electromagnetic and the corresponding basics in next few lectures. So, typically a high voltage equipment like transformer or condenser bushing they have oil plus sol sol sol sol insulation. And as we are aware that insulation breakdown phenomena is highly statistical or stochastic in nature. It is a function of not only design parameters, but it is a function of how the equipment is manufactured, whether the clearance that that that are designed are actually you know you are getting or are there some impurities in the insulation which got introduced during the manufacturing. So, all those aspects make the insulation breakdown phenomena highly statistical and unpredictable. So, that is why you need to have sufficient margin between the strength of the insulation and the corresponding maximum stress. Now that difference between strength and stress is what decides the probability of failure. So, probability of failure will be high if the margin between the strength and stress will be smaller. So, by using finite element method since we are actually going to get exact value of stresses and the corresponding stress distribution at various points we will be able to find out the exact margins that are available at various points within the high voltage equipment. And be able to find out the margins between the strength and the stress. And a good insulation design is the one wherein you know in more or less throughout your electrical equipment if the margins between the strength and stress are more or less equal. That means you should not have a case wherein somewhere you are unnecessarily stressing the insulation very high and at some other places we are actually you know under utilizing the insulation. So, that is not a good insulation design. So, finite element analysis like the one that we are going to see in this course will be able to tell you the stress distribution and then you will be able to find out the corresponding margins that are available at various points in the insulation structure and then you can optimize or improve the insulation design. So, in case of such typical high voltage equipment you have oil and cellulose insulation and then you can actually. So, there are as shown here there are two cases one is the bulk oil stress wherein this is the oil between the high voltage lead and the ground and that is getting stressed. And then you have to find out the maximum stress which occurs at this point at the surface of the lead and then you can actually minimize the probability of failure as mentioned by finding out the maximum stress by using FE analysis and the strength you can find out by various means may be experimental curves that you may have or may be using some theory like stress toil volume which we will see later in one of the tutorials how to do that. There is another phenomena what is called as surface creepage. Now, the same high voltage lead is basically supported by an insulating structure here that structure on the surface of this insulating structure you have this equipotential contours crossing. So, along this surface you have potential difference and the corresponding creepage. So, this creepage phenomena is very important and it is well known that the creepage strength is less than the bulk oil withstand and that makes the creepage phenomena important to analyze. So, such things can be analyzed using finite element method. Similarly, you can do investigative analysis for example, here we see how to do analysis of rotor bar breakage in case of squirrel cage induction motor. Now, this is as you can see this is a very you know latest paper published in 2019 and people are researchers are exploiting finite element capability to help investigate the problem that are commonly observed in rotating machines. So, basically you can have rotor breakage because of manufacturing defects or thermal stress or due to frequent starting at the rated voltage or may be due to fatigue. A crack that gets developed due to such irregularities and stresses that basically reduces cross sectional area and increases the resistance. That increase in the resistance leads to lower induced currents and lower torque. Now, what one can do is by a series of F E simulations wherein you can emulate the increasing crack by increasing resistivity. You can get a reference curve of torque versus resistivity and wherein this dash line is representing the open bar that is open circuited bar. So, once you get this kind of curve and now you have test results of a machine having such expected problem, you can basically verify this with reference curve and be able to predict the level of problem in case of the analyzed machine. So, with this introduction we will see whether briefly the course outline. The course outline is basically we will cover first revisiting. We will revisit some important concepts in electromagnetic. We will study finite elementary 1D and 2D predominantly and the corresponding procedures for 1D and 2D. Then FEM coding using free wear software. Now, what are the free wear software that we are going to use? One of course is going to be Sylab which is equivalent of MATLAB. Those participants and those who have registered for this course if they have MATLAB or any other commercial software they are free to use that. But those who are not having such commercial softwares for them we are also giving the option of using Sylab as part of this course. Then there is something called as Gmesh which is a meshing software that also we will see how to use that in conjunction with Sylab to develop your own 1D or 2D course. Then we will cover FE analysis for electrostatic, magnetostatic, time harmonic, transient, non-linear problems as well as for machines involving permanent magnets, voltage and current coupled devices and so on. Then as I said we will also see tutorials and case studies involving computation of inductance, force, torque, inrush current, eddy current losses and so on. These are the reference books for this course. If you really see this list of books, of course there are many books available. But during my academic and research career I have mostly used these books. So, the first book by Professor Sadikou is on various numerical techniques particularly useful for low frequency electromagnetic. So, in books also you will find two distinct sets of books. One set of books are devoted to low frequency electromagnetic and other set you can say it is devoted to high frequency electromagnetic FE analysis. So, these books that are listed these are mostly for low frequency electromagnetic analysis. So, the first book basically covers nicely the various techniques that are available for low frequency electromagnetic analysis. The second and third book they are quite good for analysis of rotating machines by using finite element method. The fourth book is good for understanding FE procedures. The fifth book is good for understanding basics of electromagnetic and theory related to finite element method at the introductory level and the chapter 15 of this book is particularly good for finite element method. The sixth book is exclusively dealing with transformer engineering and in this you have you know fourth chapter, fifth chapter devoted to analysis of eddy currents and chapter 12 on basics of electromagnetic fields and finite element method including coupled analysis. So, this book also will be a very good reference book for this course and of course there are so many other books exclusively devoted to finite element analysis of rotating machines like one is this SJ Solon second one and there are so many other books. So, those also can be referred and this is just a reference representative book on one of the products that is transformers. Thank you.