Good morning and welcome to this course, Electrical Equipment and Machines:

FE Analysis. This is a 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 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 electromagnetics relevant to

finite element method, electromagnetics is a vast subject and we are going to only focus in

this course on low frequency electromagnetics. And to that extent, we will cover some basics

of electromagnetics which are relevant to FEM analysis of low frequency apparatus.

I will also suggest those who are new to electromagnetics,

they can quickly see this website at leisure time which is a virtual electromagnetics lab.

The address is mentioned here, it is if you just type VEL IIT Bombay,

you will get this link and then you can see many software experiments and related theory

mentioned in each of these experiments with interactive mode. Like, 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 electromagnetics, they can either read any book on

basic book on electromagnetics or 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 electromagnetics, which is required for this course.

So that will bring all of us on same platform and 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 codes,

but the amount of computational efforts in terms of coding and not from the point of

electromagnetics are quite high when you do coding for three dimensional FE analysis.

So, we are not actually going to develop 3D codes 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 results 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 FE software.

The third focus is going to be on solving some practical problems related to static

and rotating machines. And we will solve various problems from static, transient, time harmonic,

coupled and in the increasing order of difficulty and computational efforts. As I mentioned,

it will be desirable if you refresh yourself with basics of electromagnetics, 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 refresh or 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 from basics of

electromagnetics and then we will get onto 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 element 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 these 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 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 finite element, finite difference, but among these finite element has

emerged as most popular and we 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 design machines,

but that there used to be always some kind of factor of ignorance and 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, stress could be electromagnetic stress, it could be thermal

stress, it could be structural stress, it could be any other stress related to engineering field.

And although we are going to discuss here only electromagnetics 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 adapted and adopted for electrical engineering and electronics engineering.

So, computation of EM fields is essential for improvement in performance parameters,

like calculation of reactance, calculation of losses, calculation of temperature rise,

calculation of forces, torques, and whatnot. 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 if it is a very costly device like

a large generator or a large transformer costing few crores or millions of dollars,

then it is not possible to 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 a global competition and competition is very cutthroat,

you need to optimize the material cost and again you have this FEM coming to your rescue.

One of the first applications as I mentioned of FE 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 this 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.

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 actually

are writing these reactances and resistances, we 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 leakages at the end or there are no 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 R1 and R2 dash,

as we know these are AC resistances. So, it is basically DC resistance of winding 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, if you see this shunt branch of this equivalent circuit,

which shows magnetizing reactance Xm and core loss resistance Rc.

Now, these two parameters are also they are extremely demanding in terms of understanding

field behaviors and governing electromagnetic fields. As we know the ferromagnetic material

that is used in core material of static and rotating machines, it exhibits the material

exhibits hysteresis characteristics, so there is not only there is a non-linearity but there

is remanence and hysteretic behavior. So, in order to address this behavior and be able

to take into account into your numerical method, it requires a 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. This is a transformer

window, core window and I am showing only one set of windings that means there are

other set of windings on the other side. So, this is the low voltage winding and the high

voltage winding is in two parts with taps. Now because of these 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 reactance 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 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

equipotential contours, and these are electric field contours. We will see background theory

of this electromagnetics and the corresponding basics in next few lectures. So, typically a high

voltage equipment like transformer or condenser bushing they have oil plus cellulose 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 clearances 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

break down 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 is 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, 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 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 maybe experimental

curves that you may have or maybe using some theory like stressed oil 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 these 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. This is as you can see,

this is a very latest paper published in 2019. And people or researchers are exploiting finite

element capability to help investigate the problems 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 maybe 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 FE simulations wherein you can emulate the increasing

crack by increasing resistivity, you can get a reference curve of torque versus resistivity

and wherein this dashed 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 a reference

curve and be able to predict the level of problem in case of the analyzed machine.

So, with this introduction we will see briefly the course outline,

the course outline is basically we will cover first revisiting.

We will revisit some important concepts in electromagnetics, we will study finite

element theory 1D and 2D predominantly and the corresponding procedures for 1D and 2D.

Then FEM coding using freeware software. So, now what are the freeware software that we

are going to use, so one of course is going to be Scilab, which is equivalent of MATLAB,

those you know 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 Scilab as part of this course,

then there is something called as Gmsh, which is a meshing software that also we

will see how to use that in conjunction with Scilab to develop your own 1D or 2D codes.

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. And 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 Sadiku is on various numerical techniques, particularly

useful for low frequency electromagnetics. So, in books also you will find two distinct

set of sets of books. One set of books are devoted to low frequency electromagnetics

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 electromagnetics and theory related to finite element method at the

introductory level and 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 S.

J. Salon, 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.