1. Marry the right person . This one decision will determine 90% of your happiness or misery.
2. Work at something you enjoy and that’s worthy of your time and talent.
3. Give people more than they expect and do it cheerfully.
4. Become the most positive and enthusiastic person you know.
5. Be forgiving of yourself and others.
6. Be generous.
7. Have a grateful heart.
8. Persistence, persistence, persistence.
9. Discipline yourself to save money on even the most modest salary.
10. Treat everyone you meet like you want to be treated.
11. Commit yourself to constant improvement.
12. Commit yourself to quality.
13. Understand that happiness is not based on
possessions, power or prestige, but on relationship with people you
love and respect.
14. Be loyal.
15. Be honest.
16. Be a self-starter.
17. Be decisive even it it means you’ll sometimes be wrong.
18. Stop blaming others. Take responsibility for every area of your life.
19. Be bold and courageous. When you look back on your life, you’ll regret the things you didn’t do more than the ones you did.
20. Take good care of those you love.
21. Don’t do anything that wouldn’t make your Mom proud.
Just open Task Manager (Ctrl+Alt+Delete) & in the that press (Alt+U)
a drop down menu appears & press (Ctrl) & without releasing it Click
Shut Down
& count
5….4….3….2….1!
& WOW! Its off…
checked and works well with Windows XP !
Hope you find it useful…
After Windows Explorer opens, in the right window pane, right click and select New / Shortcut
In the "Type the location of the item" enter the Web Site URL you want to create. An example would be (without quotes) "http://my.opera.com/piyushssb/"
Click Next
In the "Type a name for this shortcut:" enter a name for the link that you want to display in the Start menu.
Click Finish
Now click on the Start menu and you will see the new link you just created. Click on it and it will open up to the website.
After Windows Explorer opens, in the right window pane, right click and select New / Shortcut
In the "Type the location of the item" enter the Web Site URL you want to create. An example would be (without quotes) "http://my.opera.com/piyushssb/"
Click Next
In the "Type a name for this shortcut:" enter a name for the link that you want to display in the Start menu.
Click Finish
Now click on the Start menu and you will see the new link you just created. Click on it and it will open up to the website.
Method 1
1.open your rapid share link
2.then click on free.
3.As soon as timer start type this in address bar and click enter
javascript:alert(c=0)
4.a pop up message will come click ok your counter is zero just download the stu
mega
upload Links, Download, Rapid share Links, rapid share movies, rapid
share free, hack rapid share, hack mega upload.
Method 2
1.Delete the cookies in your browser internet explorer or Firefox or opera or whatever u use).
2.Press start->run,type cmd.
3.In the command prompt,type ipconfig/flushdns press enter.Then type
ipconfig/release,then ipconfig/renew .Now type exit.
4.Now try downloading, for many people this may work if their ISP provides a dynamic ip.
mega
upload Links, Download, Rapid share Links, rapid share movies, rapid
share free, hack rapid share, hack mega upload.
Method 3
1.Just switch off your router or modem) and switch it back on.
2.This may work for some users Mtnl and Bsnl) and maybe some others too.
Actually these methods generally work for those people whose ISP gives them dynamic ip.
If these don't work then one more thing that can be done is to use proxies.
mega
upload Links, Download, Rapid share Links, rapid share movies, rapid
share free, hack rapid share, hack mega upload.
Method 4
1.Download the software Hide ip platinum from here http://rapidshare.de/files/34451917/hideipv32.rar
2.Run it, then it will automatically chose a proxy (ip of a different
country) for you. So you can easily download without any restrictions.
You just have to change the proxy each time you download.
cls
@ECHO OFF
title Folder Locker
if EXIST "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}" goto UNLOCK
if NOT EXIST Locker goto MDBLOG2BEST
:CONFIRM
echo Are you sure to Lock this folder? (Y/N)
set/p "cho=>"
if %cho%==Y goto LOCK
if %cho%==y goto LOCK
if %cho%==n goto END
if %cho%==N goto END
echo Invalid choice.
goto CONFIRM
:LOCK
ren Locker "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
attrib +h +s "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
echo Folder locked
goto End
:UNLOCK
echo Enter password to Unlock Your Secure Folder
set/p "pass=>"
if NOT %pass%== BLOG2BEST goto FAIL
attrib -h -s "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
ren "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}" Locker
echo Folder Unlocked successfully
goto End
:FAIL
echo Invalid password
goto end
:MDBLOG2BEST
md Locker
echo Locker created successfully
goto End
:End
çççççççççççCode ends line aboveçççççççççççç
A method of determining the angular position of the rotor of a brushless direct current motor
Abstract: A method of determining the angular position of the rotor of a brushless direct current motor having a stator with multi-phase windings, control circuitry that provides excitations switched after one another to the motor phases such that the excitations produce stator flux vectors lying in different directions in the full 360 electrical degree range, and a measurement circuit that delivers responses for the phase excitations is provided. The position is estimated by selecting the main excitation stator flux vector which results in the minimal inductivity shown by the measured response, and selecting the two other vectors in the previous and subsequent directions with respect to the direction of the main vector, and by computing the ratio between differences of measured responses for the selected stator flux vectors.
Claim: What is claimed is:
1. A method of determining an angular position of a rotor of a brushless direct current motor having a stator with multi-phase windings, control circuitry providingexcitations switched one after another to motor phases such that the excitations produce stator flux vectors lying in different directions in a full 360 electrical degree range, and a measurement circuit that delivers responses for the phase excitations,the method comprising the acts of: selecting a main excitation stator flux vector resulting in a minimal inductivity shown by a measured response; selecting two other stator flux vectors, one of which is in a previous and another of which is in asubsequent direction with respect to a direction of the main excitation stator flux vector; and computing a ratio between differences of measured responses for the selected stator flux vectors in order to estimate an angular position of the rotor of thebrushless direct current motor, wherein the selection of the main excitation stator flux vector is done by selecting a vector that corresponds to a maximal value among {i.sub.0, . . . i.sub.2p-1}, where if more than one equivalent maximal value isfound, then any of their indices are selectable for the index of the main excitation stator flux vector; the ratio between differences of measured responses for the selected stator flux vectors being computed as a fraction, the numerator of which isi.sub.n minus i.sub..lamda., and the denominator of which is i.sub.m minus i.sub.n, if i.sub..lamda. is greater than i.sub.n, else if i.sub.m does not equal i.sub..lamda., then the denominator is i.sub.m minus i.sub.x, else the denominator is 1, where mdenotes the index of the direction of the main excitation, and .lamda., n denote indices of the directions before and, respectively, after the direction of the main excitation; and wherein the estimated position is obtained as m times .pi. over p plusthe calculated ratio between differences of measured responses for the selected stator flux vectors times .pi. over 2p.
2. The method according to claim 1, wherein the motor works in a non-linear (saturation) region of inductivity characteristics at least in a part of a position range.
3. The method according to claim 1, wherein the measured responses are proportional to an actual inductivity or counterinductivity of the multi-phase windings of the motor.
4. The method according to claim 3, wherein a measured response proportional to the inductivity is the time period of an excitation pulse to a stator phase until the response signal transient reaches a fixed maximum level.
5. The method according to claim 3, wherein a measured response proportional to the counterinductivity is the maximum of the current response transient of a stator phase for an excitation pulse of a fixed time period.
6. The method according to claim 3, wherein position dependent motor values are inverted before being applied in a further calculation, if they are proportional to the inductivity of the windings; the measured or calculated position dependentmotor values that are proportional to the counterinductivity of the windings being denoted by {i.sub.0,. . ., i.sub.2p-1}.
7. The method according to claim 1, wherein a measured response proportional to the inductivity is the time period of an excitation pulse to a stator phase until the response signal transient reaches a fixed maximum level.
8. The method according to claim 1, wherein a measured response proportional to the counterinductivity is the maximum of the current response transient of a stator phase for an excitation pulse of a fixed time period.
9. A method of determining an angular position of a rotor of a brushless direct current motor having a stator with multi-phase windings, control circuitry providing excitations switched one after another to motor phases such that theexcitations produce stator flux vectors lying in different directions in a full 360 electrical degree range, and a measurement circuit that delivers responses for the phase excitations, the method comprising the acts of: selecting a main excitationstator flux vector resulting in a minimal inductivity shown by a measured response; selecting two other stator flux vectors, one of which is in a previous and another of which is in a subsequent direction with respect to a direction of the mainexcitation stator flux vector; and computing a ratio between differences of measured responses for the selected stator flux vectors in order to estimate an angular position of the rotor of the brushless direct current motor, wherein the motor phases areexcited with at least 3 stator flux vectors selected from the 2p stator flux vectors lying at electrical angles of k.pi./p, k =0,. . ., 2p -1, where p denotes a number of phases of the motor, where selection is made such that at least the main vectorand the vectors lying in the previous and subsequent directions are chosen for excitation, wherein the selection of the main excitation stator flux vector is done by selecting a vector that corresponds to a maximal value among {i.sub.0,. . .,i.sub.2p-1}, where if more than one equivalent maximal value is found, then any of their indices are selectable for the index of the main excitation stator flux vector; the ratio between differences of measured responses for the selected stator fluxvectors being computed as a fraction, the numerator of which is i.sub.n minus i.sub..lamda., and the denominator of which is i.sub.m minus i.sub.n, if i.sub..lamda. is greater than i.sub.n, else if i.sub.m does not equal i.sub..lamda., then thedenominator is i.sub.m minus i.sub..lamda., else the denominator is 1, where m denotes the index of the direction of the main excitation, and .lamda., n denote indices of the directions before and, respectively, after the direction of the mainexcitation; and wherein the estimated position is obtained as m times .pi. over p plus the calculated ratio between differences of measured responses for the selected stator flux vectors times .pi. over 2p.
10. The method according to claim 9, wherein position dependent motor values are inverted before being applied in a further calculation, if they are proportional to the inductivity of the windings; the measured or calculated position dependentmotor values that are proportional to the counterinductivity of the windings being denoted by {i.sub.0,. . ., i.sub.2p-1}.
11. A method of determining an angular position of a rotor of a brushless direct current motor having a stator with multi-phase windings, control circuitry providing excitations switched one after another to motor phases such that theexcitations produce stator flux vectors lying in different directions in a full 360 electrical degree range, and a measurement circuit that delivers responses for the phase excitations, the method comprising the acts of: selecting a main excitationstator flux vector resulting in a minimal inductivity shown by a measured response; selecting two other stator flux vectors, one of which is in a previous and another of which is in a subseauent direction with respect to a direction of the mainexcitation stator flux vector; and computing a ratio between differences of measured responses for the selected stator flux vectors in order to estimate an angular position of the rotor of the brushless direct current motor, wherein position dependentmotor values are inverted before being applied in a further calculation, if they are proportional to the inductivity of the windings; the measured or calculated position dependent motor values that are proportional to the counterinductivity of thewindings being denoted by {i.sub.0,. . .,i.sub.2p-1}, wherein the selection of the main excitation stator flux vector is done by selecting a vector that corresponds to a maximal value among {i.sub.0,. . . i.sub.2p-1}, where if more than one equivalentmaximal value is found, then any of their indices are selectable for the index of the main excitation stator flux vector; the ratio between differences of measured responses for the selected stator flux vectors being computed as a fraction, thenumerator of which is i.sub.n minus i.sub..lamda., and the denominator of which is tm minus i.sub.n, if i.sub..lamda.is greater than i.sub.n, else if i.sub.m does not equal i.sub..lamda., then the denominator is i.sub.m minus i.sub..lamda., else thedenominator is 1, where m denotes the index of the direction of the main excitation, and .lamda., n denote indices of the directions before and, respectively, after the direction of the main excitation; and wherein the estimated position is obtained asm times .pi. over p plus the calculated ratio between differences of measured responses for the selected stator flux vectors times .pi. over 2p.
The invention relates to a method for determining rotor position for a brushless direct current (so-called BLDC) motor without using a position sensor. The determined position information can be applied to controlling the motor.
The control of BLDC motors includes an electronic commutator, which determines the necessary excitations of the windings of the different phases according to the actual position of the rotor. The classical way to determine rotor position is touse position sensors that trigger the switch from one commutation state to another. Using such position sensor mechanisms increases the price especially if the motor is located separately from the controlling electronics in the given application.
Rotor position determination without using special position sensor mechanism is based on the fact that a position can be obtained basically from the electromagnetic characteristics of the machine itself.
Maybe the most widely spread method is the back-EMF method, where the rotor position is determined on the basis of the induced voltage functions by rotation (Lenz's law). The disadvantage of this method is that the amplitude of the inducedvoltage is practically too low for determining the position at low rotational speed. So, this method cannot be used to start the motor.
During standstill and at low speed, typically, extra excitation is inserted to get information about the rotor position. One classification of these methods can be done along the property if they include excitation of only one phase or severalphases of the motor for calculating the position estimate. The methods that excite several or all phases of the motor have the advantage that no initial information is necessary about the flux and/or inductivity characteristics of the motor.
The general pre-assumption is only that inductivity of the stator windings varies in the function of the position, and that its periodicity is 360.degree. el (and it is not 180.degree. el). Sufficient condition for this is if the inductivityof the windings of the phases enters into the nonlinear (saturation) region of the characteristics at least in a part of the position range.
European patent specification EP-0251785 proposes a method to determine commutation on the basis of the highest measured value among the responses for the excitation pulses. The excitation pulses are provided for each phase in both polaritiesand have the same fixed time period. Here, the estimated position data is selected out of a discrete set having a resulting of 180.degree. el/p, where p denotes the number of stator phases.
European patent specification EP-0536113 bases its method also on 2p number of measurement data. Here, continuous position estimation is provided by calculating the phase of the first harmonic out of the inverse discrete Fourier transform of theresponse values. The calculated position information is used to determine starting commutation command. After this starting commutation command, it is proposed to control the change of the commutation with an experimentally predetermined series ofcommutation time periods until a limit speed is reached. After reaching the limit speed, the back-EMF method is applied for commutation control.
The basic idea described in WO-2003052919 is similar to that of EP-0251785. But here the maximal amplitude of the responses for all test pulses is fixed to the same value, and the necessary time periods to reach the limit are measured. Then,commutation is selected according to the phase excitation with the smallest time period. After initial measurement, it is further proposed here to reduce the number of measurement pulses to three if the direction of rotation is not known, and to two ifthe direction is known.
There is therefore needed a method to determine the rotor position through simple calculation using reduced number of excitations, but still resulting in a continuous estimate, that is, more advantageous than the above methods.
This need is met by a method of determining the angular position of the rotor of a brushless direct current motor having a stator with multi-phase windings, a control circuitry that provides excitations switched after one another to the motorphases such that excitations produce stator flux vectors lying in different directions in the full 360 electrical degree range, and a measurement circuitry that delivers responses for the phase excitations. The position is estimated by selecting themain excitation stator flux vector, which results in the minimal inductivity shown by the measured response, and selecting the two other vectors in the previous and subsequent directions with respect to the direction of the main vector, and by computingthe ratio between differences of measured responses for the selected stator flux vectors.
As such, the method of the invention determines the maximum of the nonlinear curve of the counterinductivity characteristics out of the small number of measured data. The displacement of the maximum of the curve is equivalent to the angulardisplacement of the rotor from the position, where rotor magnetic polarity is aligned with the direction of the 1st stator flux vector.
Accordingly, the rotor position is determined by simple calculation using reduced number of excitations resulting in a continuous estimate.
According to a further aspect of the invention, the motor works in the non-linear (saturation) region of the inductivity characteristics at least in a part of the position range.
According to a further aspect of the invention, the measured responses of the stator phases are proportional to the actual inductivity or counterinductivity of the motor windings. A measured response will be, for example, proportional to theinductivity if the time period of the response signal transient is measured until reaches a fixed maximum level. On the other hand, a measured response will be, for example, proportional to the actual counterinductivity if the maximum of the currentresponse transient is measured for an excitation pulse having a fixed time period.
According to a further aspect of the invention, the motor phases are excited with at least 3 stator flux vectors selected from the 2p stator flux vectors lying at electrical angles of k=0, . . . , 2p-1, where p denotes the number of phases ofthe motor. Selection of the excitation directions is made in such a way that at least the main vector and the vectors lying in the previous and subsequent directions are chosen for excitation.
According to a further aspect of the invention, the position dependent motor values are inverted before being applied in the further calculation, if they are proportional to the inductivity of the windings. Thus, a data set with valuesproportional to counterinductivity of the windings is always used in the position estimation. The measured or calculated position dependent motor values that are proportional to the counterinductivity are denoted by {i.sub.0, . . . , i.sub.2p-1}
According to a further aspect of the invention, the selection of the main excitation stator flux vector is done by selecting the vector that corresponds to the maximal value among {i.sub.0, . . . , i.sub.2p-1}. If more than one equivalentmaximal values are found, then any of their indices can be chosen for the index of the main excitation stator flux vector. Then, the ratio between differences of measured responses for the selected stator flux vectors is computed as a fraction, thenumerator of which is i.sub.n minus i.sub..lamda., and the denominator of which is i.sub.m minus i.sub.n, if i.sub..lamda. is greater than i.sub.n, else if i.sub.m does not equal i.sub..lamda., then the denominator is i.sub.m minus i.sub..lamda., elsethe denominator is 1, where m denotes the index of the direction of the main excitation, and .lamda., n denote the indices of the directions before and, respectively, after the direction of the main excitation. Finally, the estimated position isobtained as m times .pi. over 2p.
Other objects, advantages and novel features of the present invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings.
BRIEF DESCRIPTION OF THEDRAWINGS
FIG. 1 is a block diagram illustrating a method of controlling a BLDC motor;
FIG. 2 is a schematic diagram of the commutation driver and measurement circuit; and
FIG. 3 is a graph of one period of the inductivity of a phase in the position of the function showing the method of position estimation according to the invention.
DETAILED DESCRIPTION OF THE DRAWINGS
Referring to FIG. 1, the motor 1 consists of a rotor 2 and a multi-phase stator 3. The rotor 2 may, e.g., be of a salient pole type with permanent magnet or excited with DC, or it may, e.g., also be of an exterior type with surface permanentmagnet. The motor 1 is driven with a driver circuit 4, which is controlled with a control device 5.
The motor 1 is controlled in such a way that subsequent commands to the driver circuit 4 on the command lines 6 switch current from the external power supply UB to those stator phases that build a magnetic field for providing the maximal momentfor rotating the rotor 2. Therefore, excitation of the phases must be changed synchronously with the rotation of the rotor 2 (by switching among the commutation commands), and its timing needs position information of the rotor 2.
If rotor 2 already rotates above a certain speed, information for timing of the switching of the commutation commands can be obtained from the measurements of the phase voltages 7 (Back-EMF method).
If the speed of the rotor 2 is below the level where the induced voltages can be used to time the commutation change, commutation control is suspended for a certain period of time, during which rotor position is determined out of the responsesfor forced excitations of the phases. The responses are measured with measurement circuitry 8 and fed back with a feedback signal 9 to the motor control device 5. Motor control device 5 calculates the position estimate out of a series of feedbackvalues and determines the proper control command accordingly, which is sent to the motor driver circuit 4. This procedure is repeated with some frequency starting from standstill until motor 1 reaches the speed where the back-EMF method can already beused.
The driver circuit 4 is depicted in more detail in FIG. 2. FIG. 2 shows the example of a so-called half-bridge circuit for a 3-phase motor having stator windings connected in delta 31, 32, 33, but the invention is equivalently applicable formotors with a star-connection, and for motors having other than three phases with different driver circuits. In the case where a half bridge type motor driver is used, motor control device 5 switches on one of the high-side switches (SH1, SH2, SH3), andone of the low-side switches (SL1, SL2, SL3) of driver circuit 4 to energize the actually needed motor phases. Simultaneous switching of SHi and SLk is forbidden with i=k. The allowed other combinations result in six possible stator flux vectorsdisplaced with equivalent angle distances of 60.degree. electric after one another. A commutation command selects always the proper stator flux vector for excitation to provide maximal moment for rotating the rotor 2.
Position measurement is necessary to start the rotor 2 from standstill without pulling it into an initial position, and frequently during commutation at low speed. In the latter case, normal commutation control does not work, thus a time periodis waited until windings are de-energized, and a measurement procedure is inserted.
To be general in the formulation of determining the position, the number of phases of the motor 1 is denoted by p. Motor values proportional to the actual inductivity or counterinductivity of the stator windings are measured by applyingexcitations in different directions in order to determine the rotor position. In the preferred embodiment, the motor phases are excited with the motor driver 2 applying short pulses in electrical angles of k.pi./p, k=0, . . . , 2p-1. As will be seenlater, excitations in only three to four directions are sufficient after position is once initially determined.
In case of an excitation pulse in any of the selected directions, the current flows through a shunt-resistance 51. In the preferred embodiment, two solutions are proposed to provide the feedback signal for the motor control device 5 to calculatethe position estimate. Either the built voltage transient of this resistance can be amplified and then fed back after to the motor control device 5. Thus, the feedback signal is proportional to the actual counterinductivity of the excited windings. Motor control device 5 samples the feedback signal after a constant delay from the beginning but before the end of the excitation pulse. Then, feedback circuit 52 consists of an amplifier and possible filtering. Another solution is when the amplifiedvoltage is compared with a pre-selected fixed reference voltage, and the output of the comparator is fed back to the motor control device 5. Then, the excitation pulse is kept until output of the comparator changes, and the measured resulting period ofthe pulse is proportional to the inductivity. Then, feedback circuit 52 consists of a possible amplifier and filtering, the comparator, and the reference voltage source or input. In any of these or other possible cases for measuring inductivity orcounterinductivity, the measured value is finally transformed to be proportional to counterinductivity within the motor control device 5.
This way of measurement is repeated in such selected direction of the stator flux vectors resulting in a data set with values {i.sub.k, k=0, . . . , 2p-1} proportional to the counterinductivity. (Reducing the number of measurements will bediscussed later.) The measured values are stored after each measurement, and the position estimation algorithm is started after the measurement sequence is finished.
The preferred algorithm for determining the rotor position out of the set of data {i.sub.k, k=0, . . . , 2p-1} proportional to the counterinductivity can be derived using geometrical operations depicted in FIG. 3. The nonlinear curve 91represents an exemplary function proportional to the counterinductivity characteristic in the function of the rotor position with a selected stator flux vector. The maximum of the curve 91 shows the angular displacement of the rotor 2 from the position,where rotor magnetic polarity is aligned with the direction of the 1st stator flux vector (direction of 0). During the measurement process, discrete points (92, 93, . . . , 97) of this curve are measured (assuming symmetrically in the characteristic ofthe different phases).
The algorithm for determining the rotor angular position may be formulated as follows: A. Search for the maximal value among the data set. Denote its index with m (Note that indices go from 0 to 2p-1). B. Calculate the following ratio among thedata of the set: where .lamda.={m-1 if m>0,2p-1 if m=0, and n={m+1 if m<2p-1, 0 if m=2p-1 C. Position is estimated as .theta.=(m+r/2).pi./p.
It can be seen that after Step A (selection of the maximal value) response values of excitations in only three directions are used to calculate the position information. If a previous position estimate is given, then the measurement values inthe same three directions can be used to calculate the new estimate until the middle one is the largest among them. If the one with an electrical angle of .pi./p earlier than the previous maximum becomes the new largest value, then an additionalexcitation 2.pi./p earlier than the previous maximum should be applied to receive the new necessary value for calculating the actual position. Similarly, if one with an electrical angle of .pi./p later than the previous maximum becomes the new largestvalue, then an additional excitation 2.pi./p later than the previous maximum should be applied to receive the new necessary value for calculating the actual position. That is, only three to four excitation pulses are sufficient after the position isonce initially determined, resulting in a reduction of the total time period for the measurement process.
The foregoing disclosure has been set forth merely to illustrate the invention and is not intended to be limiting. Since modifications of the disclosed embodiments incorporating the spirit and substance of the invention may occur to personsskilled in the art, the invention should be construed to include everything within the scope of the appended claims and equivalents thereof.
/* program to display a matrix of any order*/
/* it is not for the experts*/
#include
#include
void main()
{ clrscr();
int i,j,n,a[20][20],m;
cout<<"get the order"<<"\n";
cin>>n;
cout<<"get the order"<<"\n";
cin>>m;
cout<<"get matrix elements"<<"\n";
{for(i=1;i<=n;i++)
{
for(j=1;j<=m;j++)
cin>>a[i][j];
}
}
{for(i=1;i<=n;i++)
{
for(j=1;j<=m;j++)
cout<<"\t"<
} getch();
}
}
if u have a better solution,
post ur solution as comments...
special thanks to ....... Mr.J.Mannickaraj BE(for his valuable support)
Tell me about yourself ?
Start from your education and give a brief coverage of previous experiences. Emphasise more on your recent experience explaining your job profile.
What do you think of your boss?
Put across a positive image, but don't exaggerate.
Why should we hire you? Or why are you interested in this job?
Sum up your work experiences with your abilities and emphasise your strongest qualities and achievements. Let your interviewer know that you will prove to be an asset to the company.
How much money do you want?
Indicate your present salary and emphasise that the opportunity is the most important consideration.
Do you prefer to work in a group?
Be honest and give examples how you've worked by yourself and also with others. Prove your flexibility.
Describe the ideal Job
Ideally, I would like to work in a fun, warm environment with individuals working independently towards team goals or individual goals. I am not concerned about minor elements, such as dress codes, cubicles, and the level of formality. Most important to me is an atmosphere that fosters attention to quality, honesty, and integrity.
What type of supervisor have you found to be the best?
I have been fortunate enough to work under wonderful supervisors who have provided limited supervision, while answering thoughtful questions and guiding learning. In my experience, the best supervisors give positive feedback and tactful criticism.
What do you plan to be doing in five years' time?
Taking the PE exam and serving in supervisory/leadership roles both at work and in professional/community organization(s).
What contributions could you make in this organization that would help you to stand out from other applicants?
In previous interships, my industriousness and ability to teach myself have been valuable assets to the company. My self-teaching abilities will minimize overhead costs, and my industriousness at targeting needs without prompting will set me apart from others. Additionally, one thing that has always set me apart from my scientific/engineering peers are my broad interests and strong writing abilities. I am not your typical "left-brained" engineer, and with my broad talents, I am likely to provide diverse viewpoints.
What sort of criteria are you using to decide the organization you will work for?
Most importantly, I am looking for a company that values quality, ethics, and teamwork. I would like to work for a company that hires overachievers.
Job Interview Tips
An interview gives you the opportunity to showcase your qualifications to an employer, so it pays to be well prepared. The following information provides some helpful hints.
Preparation:
Learn about the organization.
Have a specific job or jobs in mind.
Review your qualifications for the job.
Be ready to briefly describe your experience, showing how it relates it the job.
Be ready to answer broad questions, such as "Why should I hire you?" "Why do you want this job?" "What are your strengths and weaknesses?"
Practice an interview with a friend or relative.
Personal appearance:
Be well groomed.
Dress appropriately.
Do not chew gum or smoke.
The interview:
Be early.
Learn the name of your interviewer and greet him or her with a firm handshake.
Use good manners with everyone you meet.
Relax and answer each question concisely.
Use proper English—avoid slang.
Be cooperative and enthusiastic.
Use body language to show interest—use eye contact and don’t slouch.
Ask questions about the position and the organization, but avoid questions whose answers can easily be found on the company Web site.
Also avoid asking questions about salary and benefits unless a job offer is made.
Thank the interviewer when you leave and shake hands.
Send a short thank you note.
Information to bring to an interview:
Social Security card.
Government-issued identification (driver’s license).
Resume or application. Although not all employers require a resume, you should be able to furnish the interviewer information about your education, training, and previous employment.
References. Employers typically require three references. Get permission before using anyone as a reference. Make sure that they will give you a good reference. Try to avoid using relatives as references.
Transcripts. Employers may require an official copy of transcripts to verify grades, coursework, dates of attendance, and highest grade completed or degree awarded.
A C/C++ Program and Source Code for Computing Ybus and Zbus Matrices
Below is a C/C++ program and source code that computes the Ybus and Zbus of a given electrical network of any size. The input system is written on “rx.txt” with the following column format; ‘From bus’,'To bus’,'r’, and, ‘x’. The ‘From bus’ and ‘To bus’ must be a consecutive positive integer starting from zero. Bus zero is assume to be the slack or swing bus. A complex header file was used to assist the matrix operations. Zbus was computed by simply inverting the Ybus.
//-----------------------------
#pragma hdrstop
//-----------------------------
#pragma argsused
#include < stdio.h >
#include < conio.h >
#include "matrix.h"
#include < complex.h >
using std::complex;
using namespace math;
typedef complex Complex;
typedef matrix Matrix;
void main(void)
{
//declare variables
int cnt,i,j,matsize=1;
double tmp3,tmp4;
Complex tmp6;
Matrix Y,Ybus,Zbus;
FILE*in;
Y.SetSize(matsize,matsize); //set a temporary matrix size
//get the branch data
in=fopen("rx.txt","r"); //open file
if(in==NULL)
{printf("nrx.txt not found");
getch();
}
cnt=j=i=0;
for(;;)
{if(fscanf(in,"%d",&i)==EOF)
{break;}
if(i>matsize)
{matsize=i;}
fscanf(in,"%d",&j);
if(j>matsize)
{matsize=j;}
Y.SetSize(matsize+1,matsize+1);
fscanf(in,"%lf",&tmp3);
fscanf(in,"%lf",&tmp4);
tmp6=Complex(tmp3,tmp4);
Y(i,j)=1.0/tmp6;
cnt++;
}
fclose(in);
//end of getting branch data
//Create Ybus
Ybus.SetSize(matsize+1,matsize+1);
//Diagonal entries
for(i=0;i<=matsize;i++)
{for(j=0;j<=matsize;j++)
{Ybus(i,i)=Ybus(i,i)+Y(i,j);}
}
for(j=0;j<=matsize;j++)
{for(i=0;i<=matsize;i++)
{Ybus(j,j)=Ybus(j,j)+Y(i,j);}
}
//end
//off diagonal entries
cnt=0;
for(j=cnt;j<=matsize;j++)
{for(i=0;i<=matsize;i++)
{if(j!=i)
{Ybus(i,j)=Ybus(j,i)=-1.0*Y(i,j);}
}
cnt++;
}
// end
//end of creating Y bus
//bus 0 is not included in the Ybus Matrix
//because it is the reference bus
for(j=1;j<=matsize;j++)
{for(i=1;i<=matsize;i++)
{Ybus(i-1,j-1)=Ybus(i,j);
}
}
Ybus.SetSize(matsize,matsize);
Zbus.SetSize(matsize,matsize);
printf("nnYbus Matrixn");
cout << Ybus << endl;
Zbus=!Ybus; //get the inverse of the Ybus
printf("nnZbus Matrixn");
cout << Zbus << endl;
getch();
}
Nokia Mobile Phone Prices in India Price List
is the world's leading mobile phone supplier and a leading supplier of mobile and fixed telecom networks including related customer services. compare Nokia prices. We will help you find the best deal available. Here you will find Indian Mobile Market rates, Nokia, Prices, Mobile Rates in Indian Market of Nokia Pak Rupees Cost Value Indian Mobile Market Nokia. Here you will find Price list of Nokia in Pakistan India, Prices of Nokia phone, Rates of Nokia in Pakistan and India.
These Prices are in Indian Rupees
Nokia 8800 Rs.36399
Nokia E90 Communicator Rs.34949
Nokia N95 Rs.27844
Nokia N93i Rs.26624
Nokia N77 Rs.20000
Nokia N91 8GB Music Edition Rs.19999
Nokia E61i Rs.17749
Nokia N76 Rs.17674
Nokia 9300i Rs.16974
Nokia N73 Music Edition Rs.16654
Nokia E61 Rs.16069
Nokia E65 Rs.15724
Nokia N73 Rs.15669
Nokia N80 Rs.13619
Nokia 5700 Rs.12374
Nokia N70 Music Edition Rs.12094
Nokia N70 Rs.11099
Nokia N72 Rs.9474
Nokia 7500 Prism Rs.9449
Nokia E62 Rs.9389
Nokia 6300 Rs.8649
Nokia 6233 Rs.8224
Nokia E50 Rs.8174
Nokia 7610 Rs.7294
Nokia 5300 Rs.7174
Nokia 3230 Rs.6814
Nokia 3110 classic Rs.5817
Nokia 5200 Rs.5639
Nokia 6085 Rs.5224
Nokia 2630 Rs.4449
Nokia 6080 Rs.4119
Nokia 2760 Rs.3964
Nokia 6070 Rs.3719
Nokia 6020 Rs.3714
Nokia 5070 Rs.3712
Nokia 6030 Rs.2918
Nokia 2626 Rs.2774
Nokia 2310 Rs.2399
Nokia 1600 Rs.1869
Nokia 1112 Rs.1774
Nokia 1200 Rs.1674
Nokia 1110 Rs.1574
Nokia 1110i Rs.1549
ARE U A STUDENT OF LOCAL ENGINEERING COLLEGE BECAUSE OF YOUR MARKS AND CUTOFFS
NO PROBLEM
WHATEVER MARK YOU HAVE SCORED , I WILL JOIN YOU DIRECTLY INTO
"INDIAN INSTITUTE OF TECHNOLOGY (IIT-MADRAS,DELHI,KARKPUR)
"INDIAN INSTITUTE OF SCIENCE (BANGALORE)
THROUGH MY WEBSITE.
click the below url
http://nptel.iitm.ac.in/
Internal RAM
In addition to logic, all new FPGAs have dedicated blocks of static RAM distributed among and controlled by the logic elements.
Internal RAM operation
There are many parameters affecting RAM operation. The main parameter is the number of agents that can access the RAM simultaneously.
• "single-port" RAMs: only one agent can read/write the RAM.
• "dual-port" or "quad-port" RAMs: 2 or 4 agents can read/write. Great to get data across clock domains (each agent can use a different clock).
Here's a simplified drawing of a dual-port RAM.
To figure out how many agents are available, count the number of separate address buses going to the RAM. Each agent has a dedicated address bus. Each agent has also a read and a write data bus.
Writing to the RAM is usually done synchronously. Reading is usually done synchronously but can sometimes be done asynchronously.
Blockram vs. Distributed RAM
Now there are two types of internal RAMs in an FPGA: blockrams and distributed RAMs. The size of the RAM needed usually determines which type is used.
• The big RAM blocks are blockrams, which are dedicated areas in the FPGA. Each FPGA has a limited number of these, and if you don't use them, you loose them (they cannot be used for anything but RAM).
• The small RAM blocks are either in smaller blockrams (Altera does that), or in "distributed RAM" (Xilinx does that). Distributed RAM allows using the FPGA logic-cells as tiny RAMs which provide a very flexible RAM distribution in an FPGA, but isn't efficient in term of area (a logic-cell can actually hold very little RAM). Altera prefers building different size blockrams around the device (more area efficient, but less flexible). Which one is better for you depends on your FPGA application.
How FPGAs work
Logic-cells
FPGAs are built from one basic "logic-cell", duplicated hundreds or thousands of time. A logic-cell is basically a small lookup table ("LUT"), a D-flipflop and a 2-to-1 mux (to bypass the flipflop if desired).
The LUT is like a small RAM and has typically 4 inputs, so can implement any logic gate with up to 4-inputs. For example an AND gate with 3 inputs, whose result is then OR-ed with another input would fit in one LUT.
Interconnect
Each logic-cell can be connected to other logic-cells through interconnect resources (wires/muxes placed around the logic-cells). Each cell can do little, but with lots of them connected together, complex logic functions can be created.
IO-cells
The interconnect wires also go to the boundary of the device where I/O cells are implemented and connected to the pins of the FPGAs.
Dedicated routing/carry chains
In addition to general-purpose interconnect resources, FPGAs have fast dedicated lines in between neighboring logic cells. The most common type of fast dedicated lines are "carry chains". Carry chains allow creating arithmetic functions (like counters and adders) efficiently (low logic usage & high operating speed).
Older programmable technologies (PAL/CPLD) don't have carry chains and so are quickly limited when arithmetic operations are required.
Generation, Transmission
and Distribution of
Electric Power an
Overview
2 Generation, transmission and distribution of electric power 2
2.1 Goals of the lesson ………………………………………………………………... 4
2.2 Introduction .............................................................................................................. 4
2.3 Basic idea of generation …………………………………………………………... 4
2.3.1 Changeover from D.C to A.C ........................................................................ 5
2.3.2 A.C generator ……………………………………………………………… 5
2.4 Thermal, hyddel & nuclear power stations ………………………………………… 6
2.4.1 Thermal plant ……………………………………………………………… 7
2.4.2 Hydel plants ……………………………………………………………….. 7
2.4.3 Nuclear plants ……………………………………………………………… 8
2.5 Transmission of power …………………………………………………………….. 10
2.6 Single line representation of power system ……………………………………….. 13
2.7 Distribution system ………………………………………………………………… 14
2.8 Conclusion …………………………………………………………………………. 15
2.9 Answer the following ……………………………………………………………… 16
Version 2 EE IIT, Kharagpur
Chapter 2
Generation, Transmission and Distribution of Electric
Power (Lesson-2)
2.1 Goals of the lesson
After going through the lesson you shall get a broad idea of the following:
1. Different methods of generating electrical power.
2. Issues involved in transporting this power to different types of consumers located
generally at far off places from the generating stations.
3. Necessity of substations to cater power to consumers at various voltage levels.
2.2 Introduction
In this lesson a brief idea of a modern power system is outlined. Emphasis is given to create a
clear mental picture of a power system to a beginner of the course Electrical Technology. As
consumers, we use electricity for various purposes such as:
1. Lighting, heating, cooling and other domestic electrical appliances used in home.
2. Street lighting, flood lighting of sporting arena, office building lighting, powering PCs
etc.
3. Irrigating vast agricultural lands using pumps and operating cold storages for various
agricultural products.
4. Running motors, furnaces of various kinds, in industries.
5. Running locomotives (electric trains) of railways.
The list above is obviously not exhaustive and could be expanded and categorized in detail
further. The point is, without electricity, modern day life will simply come to a stop. In fact, the
advancement of a country is measured by the index per capita consumption of electricity – more
it is more advanced the country is.
2.3 Basic idea of generation
Prior to the discovery of Faraday’s Laws of electromagnetic discussion, electrical power was
available from batteries with limited voltage and current levels. Although complicated in
construction, D.C generators were developed first to generate power in bulk. However, due to
limitation of the D.C machine to generate voltage beyond few hundred volts, it was not
economical to transmit large amount of power over a long distance. For a given amount of
power, the current magnitude (I = P/V), hence section of the copper conductor will be large.
Thus generation, transmission and distribution of d.c power were restricted to area of few
Version 2 EE IIT, Kharagpur
kilometer radius with no interconnections between generating plants. Therefore, area specific
generating stations along with its distribution networks had to be used.
2.3.1 Changeover from D.C to A.C
In later half of eighties, in nineteenth century, it was proposed to have a power system with 3-
phase, 50 Hz A.C generation, transmission and distribution networks. Once a.c system was
adopted, transmission of large power (MW) at higher transmission voltage become a reality by
using transformers. Level of voltage could be changed virtually to any other desired level with
transformers – which was hitherto impossible with D.C system. Nicola Tesla suggested that
constructionally simpler electrical motors (induction motors, without the complexity of
commutator segments of D.C motors) operating from 3-phase a.c supply could be manufactured.
In fact, his arguments in favor of A.C supply system own the debate on switching over from D.C
to A.C system.
2.3.2 A.C generator
A.C power can be generated as a single phase or as a balanced poly-phase system. However, it
was found that 3-phase power generation at 50 Hz will be economical and most suitable. Present
day three phase generators, used to generate 3-phase power are called alternators (synchronous
generators). An alternator has a balanced three phase winding on the stator and called the
armature. The three coils are so placed in space that there axes are mutually 120° apart as shown
in figure 2.1. From the terminals of the armature, 3-phase power is obtained. Rotor houses a field
coil and excited by D.C. The field coil produces flux and electromagnetic poles on the rotor
surface. If the rotor is driven by an external agency, the flux linkages with three stator coils
becomes sinusoidal function of time and sinusoidal voltage is induced in them. However, the
induced voltages in the three coils (or phases) will differ in phase by 120° because the present
value of flux linkage with R-phase coil will take place after 120° with Y-phase coil and further
120° after, with B-phase coil. A salient pole alternator has projected poles as shown in figure
2.1(a). It has non uniform air gap and is generally used where speed is low. On the other hand a
non salient pole alternator has uniform air gap (figure 2.1(b)) and used when speed is high.
Driven at n rps by
prime mover
(a) Salient pole generator
Field
coil
N
S
Y
R
B
Driven at n rps by
prime mover
(b) Non salient pole generator
Y
R
B
Field
coil
N
S
Figure 2.1: 3-phase generators.
Version 2 EE IIT, Kharagpur
Frequency, voltage & interconnected system
The frequency of the generated emf for a p polar generator is given by 2
p f = n where n is speed
of the generator in rps or 120
p f= n when n is in rpm. Frequency of the generated voltage is
standardized to 50 HZ in our country and several European countries. In USA and Canada it is
60 Hz. The following table gives the rpm at which the generators with different number of poles
are to be driven in order to generate 50 Hz voltage.
Number of poles of Generator 2 4 6 8 10
rpm at which generator to be driven 3000 1500 1000 750 600
A modern power station has more than one generator and these generators are connected in
parallel. Also there exist a large number of power stations spread over a region or a country. A
regional power grid is created by interconnecting these stations through transmission lines. In
other words, all the generators of different power stations, in a grid are in effect connected in
parallel. One of the advantages of interconnection is obvious; suppose due to technical problem
the generation of a plant becomes nil or less then, a portion of the demand of power in that area
still can be made from the other power stations connected to the grid. One can thus avoid
complete shut down of power in an area in case of technical problem in a particular station. It
can be shown that in an interconnected system, with more number of generators connected in
parallel, the system voltage and frequency tend to fixed values irrespective of degree of loading
present in the system. This is another welcome advantage of inter connected system. Inter
connected system however, is to be controlled and monitored carefully as they may give rise to
instability leading to collapse of the system.
All electrical appliances (fans, refrigerator, TV etc.) to be connected to A.C supply are therefore
designed for a supply frequency of 50 Hz. Frequency is one of the parameters which decides the
quality of the supply. It is the responsibility of electric supply company to see that frequency is
maintained close to 50 Hz at the consumer premises.
It was pointed out earlier that a maximum of few hundreds of volts (say about 600 to 700 V)
could be developed in a D.C generator, the limitation is imposed primarily due to presence of
commutator segments. In absence of commutators, present day generated voltage in alternator is
much higher, typically around 10 kV to 15 kV. It can be shown that rms voltage induced in a coil
is proportional to φ and n i.e., Ecoil ∝ φ n where φ is the flux per pole and n is speed of the
alternator. This can be justified by intuition as well: we know that mere rotating a coil in absence
of magnetic flux ( φ) is not going to induce any voltage. Also presence of flux without any
rotation will fail to induce any voltage as you require rate of change of flux linkage in a coil. To
control the induced voltage one has to control the d.c field current as speed of the alternator gets
fixed by frequency constrain.
2.4 Thermal, hyddel & nuclear power stations
In this section we briefly outline the basics of the three most widely found generating stations –
thermal, hydel and nuclear plants in our country and elsewhere.
Version 2 EE IIT, Kharagpur
2.4.1 Thermal plant
We have seen in the previous section that to generate voltage at 50 Hz we have to run the
generator at some fixed rpm by some external agency. A turbine is used to rotate the generator.
Turbine may be of two types, namely steam turbine and water turbine. In a thermal power station
coal is burnt to produce steam which in turn, drives the steam turbine hence the generator (turbo
set). In figure 2.2 the elementary features of a thermal power plant is shown.
In a thermal power plant coil is burnt to produce high temperature and high pressure steam in
a boiler. The steam is passed through a steam turbine to produce rotational motion. The
generator, mechanically coupled to the turbine, thus rotates producing electricity. Chemical
energy stored in coal after a couple of transformations produces electrical energy at the generator
terminals as depicted in the figure. Thus proximity of a generating station nearer to a coal reserve
and water sources will be most economical as the cost of transporting coal gets reduced. In our
country coal is available in abundance and naturally thermal power plants are most popular.
However, these plants pollute the atmosphere because of burning of coals.
Boiler Turbine Generator
Steam in
3-phase A.C
Electric power
Condenser
Water Steam
out Feed
pump
Chemical energy
in coal
Heat energy
in steam
Mechanical energy
in turbine
Electrical
energy
Figure 2.2: Basic components of a thermal generating unit.
Coal
Stringent conditions (such as use of more chimney heights along with the compulsory use of
electrostatic precipitator) are put by regulatory authorities to see that the effects of pollution is
minimized. A large amount of ash is produced every day in a thermal plant and effective
handling of the ash adds to the running cost of the plant. Nonetheless 57% of the generation in
out country is from thermal plants. The speed of alternator used in thermal plants is 3000 rpm
which means 2-pole alternators are used in such plants.
2.4.2 Hydel plants
In a hydel power station, water head is used to drive water turbine coupled to the generator.
Water head may be available in hilly region naturally in the form of water reservoir (lakes etc.) at
the hill tops. The potential energy of water can be used to drive the turbo generator set installed
at the base of the hills through piping called pen stock. Water head may also be created
artificially by constructing dams on a suitable river. In contrast to a thermal plant, hydel power
plants are eco-friendly, neat and clean as no fuel is to be burnt to produce electricity. While
running cost of such plants are low, the initial installation cost is rather high compared to a
thermal plants due to massive civil construction necessary. Also sites to be selected for such
plants depend upon natural availability of water reservoirs at hill tops or availability of suitable
Version 2 EE IIT, Kharagpur
rivers for constructing dams. Water turbines generally operate at low rpm, so number of poles of
the alternator are high. For example a 20-pole alternator the rpm of the turbine is only 300 rpm.
Discharge of water
in down stream
Generator
Up stream
water level
3-phase A.C
Electric power
Water head
H Dam
Water
Turbine
Potential energy
of water
Kinetic
energy
Electrical
energy
Figure 2.3: Basic components of a hydel generating unit.
2.4.3 Nuclear plants
As coal reserve is not unlimited, there is natural threat to thermal power plants based on coal. It
is estimated that within next 30 to 40 years, coal reserve will exhaust if it is consumed at the
present rate. Nuclear power plants are thought to be the solution for bulk power generation. At
present the installed capacity of unclear power plant is about 4300 MW and expected to expand
further in our country. The present day atomic power plants work on the principle of nuclear
fission of 235U. In the natural uranium, 235U constitutes only 0.72% and remaining parts is
constituted by 99.27% of 238U and only about 0.05% of 234U. The concentration of 235U may be
increased to 90% by gas diffusion process to obtain enriched 235U. When 235U is bombarded by
neutrons a lot of heat energy along with additional neutrons are produced. These new neutrons
further bombard 235U producing more heat and more neutrons. Thus a chain reaction sets up.
However this reaction is allowed to take place in a controlled manner inside a closed chamber
called nuclear reactor. To ensure sustainable chain reaction, moderator and control rods are used.
Moderators such as heavy water (deuterium) or very pure carbon 12C are used to reduce the
speed of neutrons. To control the number neutrons, control rods made of cadmium or boron steel
are inserted inside the reactor. The control rods can absorb neutrons. If we want to decrease the
number neutrons, the control rods are lowered down further and vice versa. The heat generated
inside the reactor is taken out of the chamber with the help of a coolant such as liquid sodium or
some gaseous fluids. The coolant gives up the heat to water in heat exchanger to convert it to
steam as shown in figure 2.4. The steam then drives the turbo set and the exhaust steam from the
turbine is cooled and fed back to the heat exchanger with the help of water feed pump.
Calculation shows that to produce 1000 MW of electrical power in coal based thermal plant,
about 6 × 106 Kg of coal is to be burnt daily while for the same amount of power, only about 2.5
Kg of 235U is to be used per day in a nuclear power stations.
Version 2 EE IIT, Kharagpur
The initial investment required to install a nuclear power station is quite high but running
cost is low. Although, nuclear plants produce electricity without causing air pollution, it remains
a dormant source of radiation hazards due to leakage in the reactor. Also the used fuel rods are to
be carefully handled and disposed off as they still remain radioactive.
The reserve of 235U is also limited and can not last longer if its consumption continues at the
present rate. Naturally search for alternative fissionable material continues. For example,
plutonium (239Pu) and (233U) are fissionable. Although they are not directly available. Absorbing
neutrons, 238U gets converted to fissionable plutonium 239Pu in the atomic reactor described
above. The used fuel rods can be further processed to extract 239Pu from it indirectly increasing
the availability of fissionable fuel. Effort is also on to convert thorium into fissionable 233U.
Incidentally, India has very large reserve of thorium in the world.
Total approximate generation capacity and Contribution by thermal, hydel and nuclear
generation in our country are given below.
Method of generation in MW % contribution
Thermal 77 340 69.4
Hydel 29 800 26.74
Nuclear 2 720 3.85
Total generation 1 11 440 -
Non conventional sources of energy
The bulk generation of power by thermal, hydel and nuclear plants are called conventional
methods for producing electricity. Search for newer avenues for harnessing eco friendly
electrical power has already begun to meet the future challenges of meeting growing power
demand. Compared to conventional methods, the capacity in terms of MW of each nonconventional
plant is rather low, but most of them are eco friendly and self sustainable. Wind
power, solar power, MHD generation, fuel cell and power from tidal waves are some of the
promising alternative sources of energy for the future.
Turbine Generator
Steam 3-phase A.C
Electric power
Condenser
Exhausted steam
from turbine
Water feed
Coolant
Control rods
pump
Coolant
circulating pump
Moderator
Reactor
Fuel
rods
Heat Exchanger
Figure 2.4: Nuclear power generation.
Version 2 EE IIT, Kharagpur
2.5 Transmission of power
The huge amount of power generated in a power station (hundreds of MW) is to be transported
over a long distance (hundreds of kilometers) to load centers to cater power to consumers with
the help of transmission line and transmission towers as shown in figure 2.5.
Transmission tower
steel structure
R Y B
R Y B
Disc insulators.
Transmission line
(bare conductor)
Ground
Figure 2.5: Transmission tower.
To give an idea, let us consider a generating station producing 120 MW power and we want
to transmit it over a large distance. Let the voltage generated (line to line) at the alternator be 10
kV. Then to transmit 120 MW of power at 10 kV, current in the transmission line can be easily
calculated by using power formula circuit (which you will learn in the lesson on A.C circuit
analysis) for 3-phases follows:
I =
3 L
P
V cos θ
where cos θ is the power factor
=
6
3
120×10
3×10×10 ×0.8
∴ I = 8660 A
Instead of choosing 10 kV transmission voltage, if transmission voltage were chosen to be
400 kV, current value in the line would have been only 261.5 A. So sectional area of the
transmission line (copper conductor) will now be much smaller compared to 10 kV transmission
voltage. In other words the cost of conductor will be greatly reduced if power is transmitted at
higher and higher transmission voltage. The use of higher voltage (hence lower current in the
line) reduces voltage drop in the line resistance and reactance. Also transmission losses is
reduced. Standard transmission voltages used are 132 kV or 220 kV or 400 kV or 765 kV
depending upon how long the transmission lines are.
Therefore, after the generator we must have a step up transformer to change the generated
voltage (say 10 kV) to desired transmission voltage (say 400 kV) before transmitting it over a
long distance with the help of transmission lines supported at regular intervals by transmission
towers. It should be noted that while magnitude of current decides the cost of copper, level of
Version 2 EE IIT, Kharagpur
voltage decides the cost of insulators. The idea is, in a spree to reduce the cost of copper one can
not indefinitely increase the level of transmission voltage as cost of insulators will offset the
reduction copper cost. At the load centers voltage level should be brought down at suitable
values for supplying different types of consumers. Consumers may be (1) big industries, such as
steel plants, (2) medium and small industries and (3) offices and domestic consumers. Electricity
is purchased by different consumers at different voltage level. For example big industries may
purchase power at 132 kV, medium and big industries purchase power at 33 kV or 11 kV and
domestic consumers at rather low voltage of 230V, single phase. Thus we see that 400 kV
transmission voltage is to be brought down to different voltage levels before finally delivering
power to different consumers. To do this we require obviously step down transformers.
Substations
Substations are the places where the level of voltage undergoes change with the help of
transformers. Apart from transformers a substation will house switches (called circuit breakers),
meters, relays for protection and other control equipment. Broadly speaking, a big substation will
receive power through incoming lines at some voltage (say 400 kV) changes level of voltage
(say to 132 kV) using a transformer and then directs it out wards through outgoing lines.
Pictorially such a typical power system is shown in figure 2.6 in a short of block diagram. At the
lowest voltage level of 400 V, generally 3-phase, 4-wire system is adopted for domestic
connections. The fourth wire is called the neutral wire (N) which is taken out from the common
point of the star connected secondary of the 6 kV/400 V distribution transformer.
Power Station
step up
transformer
Step down
transformer
400 kV/33 kV
Step down
transformer
33 kV/11 kV
Step down
transformer
11 kV/6 kV
Step down
transformer
6 kV/ 400 V
3-phase, 4 wire
400 V, power
To
Big industries
To
Medium
industries
To
Small
industries 400 kV
HV transmission
line Generator
10 kV
Domestic consumers
R
Y
B
N
Figure 2.6: Typical voltage levels in a power system.
Some important components/equipments in substation
As told earlier, the function of a substation is to receive power at some voltage through incoming
lines and transmit it at some other voltage through outgoing lines. So the most important
equipment in a substation is transformer(s). However, for flexibility of operation and protection
transformer and lines additional equipments are necessary.
Version 2 EE IIT, Kharagpur
Suppose the transformer goes out of order and maintenance work is to be carried out.
Naturally the transformer must be isolated from the incoming as well as from the outgoing lines
by using special type of heavy duty (high voltage, high current) switches called circuit breakers.
Thus a circuit breaker may be closed or opened manually (functionally somewhat similar to
switching on or off a fan or a light whenever desired with the help of a ordinary switch in your
house) in substation whenever desired. However unlike a ordinary switch, a circuit breaker must
also operate (i.e., become opened) automatically whenever a fault occurs or overloading takes
place in a feeder or line. To achieve this, we must have a current sensing device called CT
(current transformer) in each line. A CT simply steps down the large current to a proportional
small secondary current. Primary of the CT is connected in series with the line. A 1000 A/5 A
CT will step down the current by a factor of 200. So if primary current happens to be 800 A,
secondary current of the CT will be 4 A.
Suppose the rated current of the line is 1000 A, and due to any reason if current in the line
exceeds this limit we want to operate the circuit breaker automatically for disconnection.
In figure 2.7 the basic scheme is presented to achieve this. The secondary current of the CT is
fed to the relay coil of an overcurrent relay. Here we are not going into constructional and
operational details of a over current relay but try to tell how it functions. Depending upon the
strength of the current in the coil, an ultimately an electromagnetic torque acts on an aluminum
disc restrained by a spring. Spring tension is so adjusted that for normal current, the disc does not
move. However, if current exceeds the normal value, torque produced will overcome the spring
tension to rotate the disc about a vertical spindle to which a long arm is attached. To the arm a
copper strip is attached as shown figure 2.8. Thus the arm too will move whenever the disk
moves.
Power line CB CT
Relay
Trip signal to circuit
breaker if current
exceeds the rated
current.
Figure 2.7: Basic scheme of
protection.
Power line
CB
CT
Trip coil
Figure 2.8: Relay and CB.
Main
contact
Battery
Moving
arm
Spindle
Relay
1
2
+ -
Copper strip
The relay has a pair of normally opened (NO) contacts 1 & 2. Thus, there will exist open
circuit between 1 & 2 with normal current in the power line. However, during fault condition in
the line or overloading, the arm moves in the anticlockwise direction till it closes the terminals 1
& 2 with the help of the copper strip attached to the arm as explained pictorially in the figure 2.8.
This short circuit between 1 & 2 completes a circuit comprising of a battery and the trip coil of
the circuit breaker. The opening and closing of the main contacts of the circuit breaker depends
on whether its trip coil is energized or not. It is interesting to note that trip circuit supply is to be
made independent of the A.C supply derived from the power system we want to protect. For this
reason, we expect batteries along with battery charger to be present in a substation.
Apart from above there will be other types of protective relays and various meters indicating
current, voltage, power etc. To measure and indicate the high voltage (say 6 kV) of the line, the
voltage is stepped down to a safe value (say 110V) by transformer called potential transformer
Version 2 EE IIT, Kharagpur
(PT). Across the secondary of the PT, MI type indicating voltmeter is connected. For example a
voltage rating of a PT could be 6000 V/110 V. Similarly, Across the secondary we can connect a
low range ammeter to indicate the line current.
2.6 Single line representation of power system
Trying to represent a practical power system where a lot of interconnections between several
generating stations involving a large number of transformers using three lines corresponding to
R, Y and B phase will become unnecessary clumsy and complicated. To avoid this, a single line
along with some symbolical representations for generator, transformers substation buses are used
to represent a power system rather neatly. For example, the system shown in 2.6 with three lines
will be simplified to figure 2.9 using single line.
400 kV
Figure 2.9: Single line representation of power system.
Transformer
G
Transmission
As another example, an interconnected power system is represented in the self explained
figure 2.10 – it is hoped that you understand the important features communicated about the
system through this figure.
line 1
400 kV/33 kV 10 kV/400 kV
33 kV/11 kV 11 kV/6 kV
400 V/6 kV
To
Sub1 Sub2
Sub3 Sub4
Sub5
To big
industries
To medium
industries
To small
industries
LT consumers
Figure 2.10: Single line representation of power system.
Step up
transformer
G1
Transmission line 1
Power station 1
To
loads B2
HV
G2
G1 G2
To
loads
To
loads
Step down
transformer
To
loads
Power station 2
HV transmission line 3
B3 B1
Line
interconnecting
two stations
Version 2 EE IIT, Kharagpur
2.7 Distribution system
Till now we have learnt how power at somewhat high voltage (say 33 kV) is received in a
substation situated near load center (a big city). The loads of a big city are primarily residential
complexes, offices, schools, hotels, street lighting etc. These types of consumers are called LT
(low tension) consumers. Apart from this there may be medium and small scale industries
located in the outskirts of the city. LT consumers are to be supplied with single phase, 220 V, 40
Hz. We shall discuss here how this is achieved in the substation receiving power at 33 kV. The
scheme is shown in figure 2.11.
33 kV/6 kV
Underground cable
feeders
6kV
Service main Distribution
transformer
Figure 2.11: Typical Power distribution scheme.
Sub 1 Service main
Service main
(4-wires: R, Y, B & N)
6kV
feeders
6kV
feeders
6 kV/400 V
Δ / Y
Power receive at a 33 kV substation is first stepped down to 6 kV and with the help of under
ground cables (called feeder lines), power flow is directed to different directions of the city. At
the last level, step down transformers are used to step down the voltage form 6 kV to 400 V.
These transformers are called distribution transformers with 400 V, star connected secondary.
You must have noticed such transformers mounted on poles in cities beside the roads. These are
called pole mounted substations. From the secondary of these transformers 4 terminals (R, Y, B
and N) come out. N is called the neutral and taken out from the common point of star connected
secondary. Voltage between any two phases (i.e., R-Y, Y-B and B-R) is 400 V and between any
phase and neutral is 230 V(= 400 3). Residential buildings are supplied with single phase
230V, 50Hz. So individual are to be supplied with any one of the phases and neutral. Supply
authority tries to see that the loads remain evenly balanced among the phases as far as possible.
Which means roughly one third of the consumers will be supplied from R-N, next one third from
Y-N and the remaining one third from B-N. The distribution of power from the pole mounted
substation can be done either by (1) overhead lines (bare conductors) or by (2) underground
cables. Use of overhead lines although cheap, is often accident prone and also theft of power by
hooking from the lines take place. Although costly, in big cities and thickly populated areas
underground cables for distribution of power, are used.
Version 2 EE IIT, Kharagpur
2.8 Conclusion
In this lesson, a brief idea of generation, transmission and distribution of electrical power is
given - which for obvious reason is neither very elaborative nor exhaustive. Nonetheless, it gives
a reasonable understanding of the system for a beginner going to undertake the course on
electrical technology. If you ever get a chance to visit a substation or power station – don’t miss
it.
Some basic and important points, in relation to a modern power system, are summarized
below:
1. Generation, transmission and distribution of electric power in our country is carried out
as 3-phase system at 50 Hz.
2. Three most important conventional methods of power generation in out country are: coal
based thermal plants, Hydel plants and nuclear plants.
3. Load centers (where the power will be actually consumed) are in general situated far
away from the generating station. So to transmit the large amount of power (hundreds of
MW) efficiently and economically over long distance, high transmission voltage (such as
400 kV, 220 kV) is used.
4. Material used for transmission lines is bare is bare copper conductors which are
supported at regular intervals by steel towers. Stack of disk type ceramic insulators are
used between the HV line and the steel tower.
5. Level of current decides the section of the line conductor and the level of voltage decides
the amount of insulation required.
Version 2 EE IIT, Kharagpur
2.9 Answer the following
1. Name three conventional ways of generating power. Of these three, which one
contributes maximum generation in India.
2. What number of phases and frequency are adopted to generate, transmit and distribute
electrical power in modern power system?
3. Name the types of generators (alternators) used in (1) thermal plant and (2) in hydel
power plant.
4. In a hydel power station, the number of poles of an alternator is 24. At what rpm the
alternator must be driven to produce 50 Hz voltage?
5. Give some typical value of generated voltage in a power station. Why is it necessary to
step up the voltage further before transmitting?
6. What is a substation? What important equipments are found in a substation?
7. With the help of a schematic diagram explain how a overcurrent relay protects a line
during short circuit fault.
8. What are the functions of CT and PT in a substation?
9. The ammeter reading connected across a CT secondary is 3 A and the voltage reading
connected across a PT is 90 V. If the specification of the CT and PT are respectively
1000 A/5 A and 6.6 kV/110 V, What is the actual current and voltage of the line?
10. What is a pole mounted substation? At what voltage levels are the found in a power
system?
11. Why are batteries used in a substation.
12. Are different power stations interconnected? If so, why?
13. What are the differences between a coal based thermal plant and a nuclear power plant.
Version 2 EE IIT, Kharagpur
Module
1
Introduction
Version 2 EE IIT, Kharagpur
Lesson
1
Introducing the Course on
Basic Electrical
Version 2 EE IIT, Kharagpur
Contents
1 Introducing the course (Lesson-1) 4
Introduction ………………………………………………………………………........... 4
Module-1 Introduction ……………………………………………………………........... 4
Module-2 D.C. circuits ………………………………………………………………….. 4
Module-3 D.C transient …………………………………………………………………. 6
Module-4 Single phase A.C circuits …………………………………………………….. 7
Module-5 Three phase circuits …………………………………………………………... 8
Module-6 Magnetic circuits & Core losses ………………………………………........... 8
Module-7 Transformer …………………………………………………………………... 9
Module-8 Three phase induction motor …………………………………………………. 10
Module-9 D.C Machines …………………………………………………………........... 11
Module-10 Measuring instruments ………………………………………………............ 12
Version 2 EE IIT, Kharagpur
Introduction
Welcome to this course on Basic Electrical Technology. Engineering students of almost all
disciplines has to undergo this course (name may be slightly different in different course
curriculum) as a core subject in the first semester. It is needless to mention that how much we are
dependent on electricity in our day to day life. A reasonable understanding on the basics of
applied electricity is therefore important for every engineer.
Apart from learning d.c and a.c circuit analysis both under steady state and transient
conditions, you will learn basic working principles and analysis of transformer, d.c motors and
induction motor. Finally working principles of some popular and useful indicating measuring
instruments are presented.
The course can be broadly divided into 3 major parts, namely: Electrical circuits, Electrical
Machines and Measuring instruments. The course is spread over 10 modules covering these 3-
parts, each module having two or more lessons under it as detailed below.
Contributors
1. Modules 4, 5 and 8 by Prof. N.K. De
2. Modules 2, 3 and 10 by Prof. G.D. Ray
3. Modules 1, 6, 7 and 9 by Dr. T.K. Bhattacharya
Module-1 Introduction
Following are the two lessons in this module.
1.1 Introducing the course
Currently we are in this lesson which deals with the organization of the course material
in the form of modules and lessons.
1.2 Generation, transmission and distribution of electric power: an overview
This lesson highlights conventional methods of generating 3-phase, 50 Hz electrical
power, its transmission and distribution with the help of transmission lines and
substations. It will give you a feel of a modern power system with names and function
of different major components which comprise it.
Module-2 DC circuits
This module consists of seven lessons (2.1-2.7) starting with the fundamental concepts of electric
circuit (active and passive) elements, circuit laws and theorems that established the basic
foundation to solve dc network problems or to analyze the voltage, current and power (delivered
or absorbed) in different branches. At the end of each lesson a set of problem is provided to test
the readers understanding. Answers to these problems are located therein. The contents of each
lesson are described below.
2.1 Introduction to electrical circuits
This lesson provides some basic concepts on Kirchoff’s law, difference between linear
and nonlinear circuits, and understanding the difference between current and voltage
Version 2 EE IIT, Kharagpur
sources. The mathematical models of voltage and current sources are explained and
subsequently the basic principles of voltage and current dividers are discussed. Each
topic of this lesson is clearly illustrated by solving some numerical problems.
2.2 Loop Analysis of resistive circuit in the context of dc voltages and
currents
In this lesson, loop analysis method based on Ohms law and Kirchoffs voltage law is
presented to obtain a solution of a resistive network. This technique is particularly
effective when applied to circuits containing voltage sources exclusively; however, it
may be applied to circuits containing both voltage and current sources. Several
numerical problems including both voltage and current sources have been considered to
illustrate the steps involved in loop analysis method.
2.3 Node-voltage analysis of resistive circuit in the context of dc voltages and
currents
Node voltage analysis is the most general and powerful method based on Kirchhoff’s
current law is introduced in this lesson for the analysis of electric circuits. The choice
of one the nodes as reference node for the analysis of dc circuit is discussed. The
procedure for analyzing a dc network is demonstrated by solving some resistive circuit
problems.
2.4 Wye (Y) – Delta (∆) or Delta (∆) – Wye (Y) transformations
The objective of this lesson is to introduce how to convert a three terminal Delta (∆) /
Wye (Y) network into an equivalent Wye (Y) / Delta (∆) through transformations.
These are all useful techniques for determining the voltage and current levels in a
complex circuit. Some typical problems are solved to familiarize with these
transformations.
2.5 Superposition Theorem in the context of dc voltage and current sources
acting in a resistive network
This lesson discusses a concept that is frequently called upon in the analysis of linear
circuits (See 2.3). The principle of superposition is primarily a conceptual aid that can
be very useful tool in simplifying the solution of circuits containing multiple
independent voltage and current sources. It is usually not an efficient method. Concept
of superposition theorem is illustrated by solving few circuit problems.
2.6 Thevenin’s and Norton's theorems in the context of dc voltage and
current sources in a resistive network
In this lesson we consider a pair of equivalent circuits, called Thevenin’s and Norton’s
forms, containing both resistors and sources at the heart of circuit analysis. These
theorems are discussed at length and highlighted their great utility in simplifying many
practical circuit problems.
Reduction of linear circuits to either equivalent form is explained through solution of
some circuit problems. Subsequently, the maximum power transfer to the load from the
rest of circuit is also considered in this lesson using the concept of these theorems.
Version 2 EE IIT, Kharagpur
2.7 Analysis of dc resistive network in presence of one non-linear element
Volt-ampere characteristic of many practical elements (Carbon lamp, Tungsten lamp,
Semiconductor diode, Thermistor etc.) exhibits a nonlinear characteristic and it is
presented in this lesson. A common graphical procedure in case of one nonlinear
element or device in a circuit is also introduced in this lesson to analyze the circuit
behavior. This technique is also referred to as load line analysis method that is
intuitively appealing to analyze some complex circuits. Another method based on
analytic technique is described to analyze an electric circuit that contains only one
nonlinear element or device. These techniques are discussed through worked out
problems.
Module-3 DC transient
The study of DC transients is taken up in module-3, consisting of two lessons (3.1 and 3.2). The
transients in a circuit containing energy storage elements occur when a switch is turned on or off
and the behavior of voltage or a current during the transition between two distinct steady state
conditions are discussed in next two lessons. At the end of each lesson some problems are given
to solve and answers of these problems are located therein. The contents of each lesson are
described below.
3.1 Study of DC transients in R-L and R-C circuits
This lesson is concerned to explore the solution of first order circuit that contains
resistances, only single energy storage element inductance or capacitance, dc voltage
and current sources, and switches. A fundamental property of inductor currents and
capacitor voltages is discussed. In this lesson, the transient and steady state behavior in
a circuit are studied when a switch is turned on or off. The initial condition, the steady
solution and the time constant of the first order system are also discussed that uniquely
determine the system behavior. The solution of differential equation restricted to
second order dynamic systems for different types of forcing function are included in
Appendix of this, lesson. Some problems are solved and their dynamic responses are
plotted.
3.2 Study of DC transients in R-L-C circuits
The solution of second order circuit that contains resistances, inductances and
capacitances, dc voltage and current sources, and switches is studied in this lesson. In
this lesson, the transient and steady state behavior of a second order circuit are studied
under three special cases namely, (i) over damped system (ii) critically damped system
(iii) under damped system that can arise depending upon the values of circuit
parameters. Some examples are solved and their dynamic responses are shown.
Version 2 EE IIT, Kharagpur
Module-4 Single phase AC circuits
There are six lessons (4.1-4.6) in this module, where the various aspects related to ac circuits fed
from single phase supply, are described.
4.1 Generation of single phase ac and fundamental aspects
The principle of generation of sinusoidal (ac) waveforms (single phase) in an ac
generator is first presented. Then, the two aspects – average and root mean square (rms)
values, of alternating or periodic waveforms, such as voltage/current, are described with
typical examples (sinusoidal and triangular).
4.2 Representation of sinusoidal quantities in phasor with j operator
As the phasor relations are widely used for the study of single phasor ac circuits, the
phasor representation of sinusoidal quantities (voltage/current) is described, in the lesson,
along with the transformation from rectangular (Cartesian) to polar form, and vice versa.
Then, the phasor algebra relating the mathematical operations, involving two or more
phasors (as the case may be), from addition to division, is taken up, with examples in
each case, involving both the forms of phasor representations as stated.
4.3 Steady state analysis of series circuits
The steady state analysis of series (R-L-C) circuits fed from single phase ac supply is
presented. Staying with each of the elements (R, L & C), the current in steady state is
obtained with application of single phase ac voltage, and the phasor diagrams are also
drawn in each case. The use of phasor algebra is also taken up. Then, other cases of series
circuits, like R-L, R-C and R-L-C, are described, wherein, in each case, all methods as
given, are used.
4.4 Analysis of parallel and series-parallel circuits
The application of phasor algebra to solve for the branch and total currents and the
complex impedance, of the parallel and the series-parallel circuits fed from single phase
ac supply is presented in this lesson. The phasor diagram is drawn showing all currents,
and voltage drops. The application of two Kirchoff’s laws in the circuits, for the currents
at a node, and the voltage drops across the elements, including voltage source(s), in a
loop, is shown there (phasor diagram).
4.5 Resonance in electrical circuits
The problem of resonance in the circuits fed from a variable frequency (ac) supply is
discussed in this lesson. Firstly, the case of series (R-L-C) circuit is taken up, and the
condition of resonance, along with maximum current and minimum impedance in the
circuit, with the variation in supply frequency is determined. Then, the problem of
parallel circuits and other cases, such as, lossy coil (r-L), is taken up, where the condition
of resonance is found. This results in minimum current and maximum impedance here.
4.6 Concept of apparent, active and reactive power
The formula for active (average) power in a circuit fed from single phase ac supply, in
terms of input voltage and current, is derived in this lesson, followed by definition of the
Version 2 EE IIT, Kharagpur
term, ‘power factor’ in this respect. The concept of apparent and reactive power (with its
sign for lagging and leading load) is presented, along with formula.
Module-5 Three phase AC circuits
There are only three lessons (5.1-5.3) in this module. Only the balanced star-and delta-connected
circuits fed from three-phase ac supply are presented here.
5.1 Generation of three-phase voltage, line and phase quantities in star- and
delta-connection and their relations
The generation of three-phase balanced voltages is initially presented. The balanced
windings as described can be connected in star- and delta-configuration. The relation
between line and phase voltages for star-connected supply is presented. Also described is
the relation between phase and line currents, when the windings are connected in delta.
The phasor diagrams are drawn for all cases.
5.2 Solution of three-phase balanced circuits
The load (balanced) is connected in star to a balanced three-phase ac supply. The currents
in all three phases are determined, with phasor diagram drawn showing all voltages and
currents. Then, the relation between phase and line currents is derived for balanced deltaconnected
load. The power (active) consumed in the balanced load is derived in terms of
the line voltage and currents for both cases.
5.3 Measurement of three-phase power
The total power (in all three phases) is measured using two wattmeters only. This is
shown for both unbalanced and balanced cases. The phasor diagram with balanced threephase
load is drawn. Other cases are also described.
Module-6 Magnetic circuits & Core losses
In this module there are two Lessons 21 and 22 as enumerated below.
6.1 Simple magnetic circuits
It is often necessary to produce a desired magnetic flux, in a magnetic material (core)
having a definite geometric shape with or without air gap, with the help of current
passing through a coil wrapped around the core. This lesson discusses how the concept of
circuit analogy can be introduced to tackle such problems. Both linear and non-linear
magnetic circuit problems are discussed through worked out problems.
6.2 Eddy current & hysteresis losses
These two losses are produced in any magnetic material which is subjected to an
alternating time varying fields. Generally in all types of A.C machines /equipments
working on electromagnetic principle these losses occur. In D.C machine armature too
these losses occur. In this lesson the origin of these losses are explained and formula for
estimating them are derived. Finally methods adopted to minimize these losses discussed
as losses bring down the efficiency of any machines.
Version 2 EE IIT, Kharagpur
Module-7 Transformer
Transformers are one of the most important components of the modern power system. In this
module having 6 lessons, various aspects of a transformer are explained and discussed as per the
break up given below.
7.1 Ideal single phase transformer
Clear concept of ideal transformer goes a long way to understand the equivalent circuit
representation of a practical transformer discussed in the next lesson. In ideal
transformer all kinds of losses are neglected and permeability of core is assumed to be
infinitely large. To have a rough and quick estimate of primary current for a given
secondary current of a practical transformer one need not consider detail equivalent
circuit but rather pretend that the transformer is ideal and apply simple relation of ideal
transformer.
Properties of ideal transformer and its principle of operation along with phasor diagram
are discussed both under no load and load condition.
7.2 Practical single phase transformer
A practical transformer has various losses and leakage impedance. In this lesson, it has
been shown how these can be taken into account in the equivalent circuit. Phasor
diagrams under no load and load condition developed. Concept of approximate
equivalent circuit discussed and meaning of equivalent circuit referred to primary and
secondary side are explained.
7.3 Testing, efficiency and regulation of transformer
Two basic tests called open circuit and short circuit test are discussed and then it is
explained how equivalent circuit parameters of a single phase transformer can be
obtained from the test data. Importance of selecting a particular side for a particular test
is highlighted.
Importance of efficiency and regulation are discussed and working formula for them
derived. Concept of all day efficiency for distribution transformer is given. Regulation
is essentially a measure of change of magnitude of the secondary voltage from no load
to full load condition and its value should be low. From the expression of regulation it
is easily identified the parameters on which it depends.
7.4 Three phase transformer
Generation, distribution and transmission of power are carried out with a 3-phase, 50
Hz system. Therefore, stepping up or down of 3-phase voltage is required. This of
course can not be done using a single phase transformer. Three separate identical
transformers can be connected appropriately to serve the purpose. A 3-phase
transformer formed by connecting three separate transformers is called a bank of 3-
phase transformer. Another way of having a three phase transformer, is to construct it
as a single unit of three phase transformer. The relative advantages and disadvantages
of the two are discussed.
Version 2 EE IIT, Kharagpur
Various important and popular connections of 3-phase transformer (such as star/star,
star/delta, delta/star etc.) are discussed. The importance of dot convention while making
such connections are pointed out. Simple problems involving a 3-phase transformer
connection are worked out assuming the transformer to be ideal.
Vector grouping of various three phase transformer connection are generally not meant
for a first year course and can be avoided. However, for completeness sake and for
students who want to know more, it is included.
7.5 Autotransformer
There are transformers which work with a single winding. Such transformers are called
auto-transformers. The lesson discusses its construction and bring out differences with
two winding transformer. Here, ideal auto transformer is assumed to show how to find
out current distribution in different parts of the winding when it is connected in a
circuit. It is also pointed out how three single phase auto transformers can be connected
to transform a 3-phase voltage.
7.6 Problem solving on transformers
Few typical problems on single phase, 3-phase and auto transformers are worked out,
enumerating logical steps involved.
Module-8 Three phase induction motor
In this module consisting of six lessons (8.1-8.6), the various aspects of the three-phase induction
motor are presented.
8.1 Concept of rotating magnetic field
Before taking up the three-phase induction motor (IM), the concept of rotating magnetic
field is introduced in this lesson. The balanced three-phase winding of the stator in IM are
fed from a balanced three-phase supply. It is shown that a constant magnitude of
magnetic field (flux) is produced in the air gap, which rotates at ‘synchronous speed’ as
defined in terms of No. of poles of the stator winding and supply frequency.
8.2 Brief construction and principle of operation
Firstly, the construction of a three-phase induction motor is briefly described, with two
types of rotor – squirrel cage and wound (slip-ring) one. The principle of torque
production in a three-phase IM is explained in detail, with the term, ‘slip’ defined here.
8.3 Per phase equivalent circuit and power flow diagram
The equivalent circuit of a three-phase IM is obtained, which is explained step by step.
Also the power flow diagram and the various losses taking place are discussed.
8.4 Torque-slip (speed) characteristic
The torque speed (slip) equation is obtained from the equivalent circuit of the rotor. The
characteristics are drawn, with typical examples, such as variation in input (stator)
voltage, and also in rotor resistance (with external resistance inserted in each phase).
Version 2 EE IIT, Kharagpur
8.5 Types of starters
The need of starter in a three-phase IM to reduce the stating current drawn is first
explained. Then, three types of starters – Direct-on-line (DOL), star-delta one for use in
an IM with a nominally delta-connected stator, and auto-transformer, are described.
Lastly, the rotor resistance starter for a wound rotor (slip ring) IM is briefly presented.
8.6 Single-phase induction motor and starting methods
It is first shown that starting torque is not produced in a single phase induction motor
(IM). Then, the various types of starting methods used for single-phase IM with two
stator windings (main and auxiliary), are explained in detail. Lastly, the shaded pole
single-phase IM is described.
Module-9 DC Machines
9.1 Constructional features of DC machines
The lesson discusses the important construction features of DC machines. The induced
voltage in a rotating coil in a stationary magnetic field is always alternating in nature. The
functions of commutator segments and brushes, which convert the AC voltage to DC
form, are explained.
The examples of lap and wave windings used for armature are presented. It has been
shown that the number of parallel paths in the armature will be different in the two types
of windings. For the first time reading and depending upon the syllabus, you may avoid
this portion.
9.2 Principle of operation of D.C machines
The lesson begins with an example of single conductor linear D.C generator and motor. It
helps to develop the concept of driving force, opposing force, generated and back emf.
Concept of Driving and opposing torques in rotating machines are given first and then the
principle of operation of rotating D.C generator and motor are explained. Condition for
production of steady electromagnetic torque are discussed.
9.3 EMF and torque equations
The derivation of the two basic and important equations, namely emf and torque
equations, which are always needed to be written, if one wants to analyse the machine
performance. Irrespective of the fact that whether the machine is operating as a generator
or as a motor, the same two equations can be applied. This lesson also discusses armature
reaction, its ill effects and methods to minimize them.
The topic of calculation of cross magnetizing and demagnetizing mmf’s can be avoided
depending upon the syllabus requirement and interest.
9.4 DC Generators
The lesson introduces the types of DC generators and their characteristics. Particular
emphasis has been given to DC shunt and separately excited generators. The open circuit
characteristic (O.C.C) and the load characteristics of both kinds are discussed. It is
Version 2 EE IIT, Kharagpur
explained that from O.C.C and the field resistance line, it is possible to get graphically
the load characteristic.
9.5 DC motor starting and speed control
In this important lesson, problem of starting a DC motor with full voltage is discussed,
and the necessity of starter is highlighted. The operation of a three-point starter is
explained. Various methods of controlling speed of DC shunt and series motors are
discussed. At the end, a brief account of various methods of electrical braking is
presented.
9.6 Losses, efficiency and testing of D.C machines
To calculate efficiency of any machines, it is essential to know various losses that take
place in the machine. Major losses in a DC machine are first enumerated, and
Swinburne’s test and Hopkinson’s tests are explained to estimate them.
9.7 Problem solving in DC machines
In this lesson, some typical problems of DC motors and generators are worked out. This
lesson should be consulted from other relevant lectures of the present module whenever
you feel it to be necessary.
Module-10 Measuring instruments
The magnitude of various electric signals can be measured with help of measuring instruments.
These instruments are classified according to the quantity measured and the principle of
operation. The study of DC and AC instruments for measuring voltage, current signals and
subsequently induction type energy meter, are described in this module consisting of three
lessons (10.1 10.3). at the end of each lesson (10.1 10.3), a set of problem is provided to test the
readers understanding.
10.1 Study of DC and AC measuring instruments
The general theory of permanent magnet moving coil (PMMC), moving-iron (MI)
instruments and their constructions are briefly discussed in this lesson. PMMC
instruments are used as a dc ammeter or dc voltmeter where as MI instruments are
basically used for ac current or voltage measurements. Various torques involved in
measuring instruments are classified and explained. Subsequently, the advantages,
limitations and sources of errors of these instruments are studied therein. Idea behind the
multi-range ammeters and voltmeters are introduced by employing several values of
shunt resistors or several multiplier resistors along with the meter resistance. In this
context some problems are solved to illustrate the meaning of multi-range meters.
10.2 Study of electrodynamics type instruments
Electrodynamics meters can measure both dc signals and ac signals up to a frequency of.
The basic construction of electro-dynamometer instruments and their principles of
operation are studied in this lesson. Torque expressions for such instruments (as an
ammeter, voltmeter and a wattmeter) are derived and then mode of meter connections to
the load as an ammeter, voltmeter and a wattmeter are presented. Shunts and multipliers
Version 2 EE IIT, Kharagpur
can be used for extension of meters range. A compensation technique is introduced to
eliminate the errors in wattmeter readings. In this lesson, the constructional features and
principle of operation of electro dynamometer instruments (ammeter, voltmeter and
wattmeter) have been discussed. The sources of error and their corrections are
highlighted. Some problems have been worked out for better understanding.
10.3 Study of single-phase induction type energy meter or watt-hour meter
The basic construction with different components of a single-phase induction type energy
meter is considered in this lesson. Development of torque expression and errors in energy
meters are studied. Some adjustment techniques are discussed to compensate the errors
in energy meter. Finally, the extension of meter range using instrument transformers is
discussed.
Version 2 EE IIT, Kharagpur
Labels
- group discussion (1)
