PowerPoint Presentation

[Audio] Good day ladies and gentlemen. My name is Mahinda Vilathgamuwa and i am responsible for delivering lectures for e g h 4 4 8 this semester. My contact details are shown here and you are encouraged to raise your queries anytime..

[Audio] I conduct lectures on thursdays from nine to eleven in the morning at lecture hall p 4 1 2 in gardens point campus. Rough lecture schedule is shown here but I expect some slight changes. I have scheduled a consultation time for you just after the lecture in my office at s 8 0 7..

[Audio] This slide shows the assessment schedule. Quizzes have a weightage of twenty percent. There are 4 quizzes altogether in this semester. The project weighs twenty percent. The project includes computer labs, simulations, hardware circuit and a report. The breakdown of project marks is given in the project c r a sheet. You need to conduct two pracs for this unit. Each prac has a weightage of ten percent. The final examination at the end of the semester weighs 40 percent..

[Audio] You need to form a group with another two fellow students so that each group has three members. This formation needs to be done before thirty first of march. All group members are required to put equal effort in the completion of the project as it is compulsory to submit the project contribution form at the end of the semester along with your final report..

[Audio] As I mentioned earlier the computer labs are part of the project assignment and they are assessed. Although the two computer labs are scheduled to occur in weeks 5 and 10 respectively you would be able to conduct the labs at your convenience in these weeks..

[Audio] This slides shows the schedules of the computer lab, practical lab and the project. Computer labs take place in weeks five and ten. Pracs take place in weeks 8, 9, 11 and 12. We will upload the submission timeline of these assessments on the blackboard soon..

[Audio] Here, we will try to refresh your knowledge about a c circuits. In the first diagram we show a single phase R L series circuit. The next diagram shows the phasor diagrams for lagging and leading power factor circuits respectively..

[Audio] The first equation is the basic ohms law applied to an a c circuit. Here, you can see that the current is obtained by dividing the applied voltage by the impedance of the circuit. The second equation describes the real power of a single phase circuit. It is given by the multiplication of voltage, current and power factor of the circuit. The power factor is cos theta and theta is given by the inverse tangent of reactance divided by resistance of the circuit..

[Audio] Why we need to use three phase power. The first reason is the three phase power is not pulsating. On the other hand you will find that single phase instantaneous power is pulsating at twice the line frequency. The second reason is that a large amount of power can be supplied through a three phase system economically. For example, the amount of conductive material needed to transfer a certain amount of power using a three phase system is less compared to that using a single phase system..

[Audio] The first picture shows how a y connected three phase source is schematically represented. The second diagram shows the variation of three phase voltages with time. As you can see, there are 3 sinusoids that have same amplitude and frequency but are phase shifted by 120 degrees to each other. This kind of three phase supply is known as a balanced supply. In the third diagram, we show how a three phase system can be represented in phasor domain. As you can see. The phasors have equal amplitude but they are 120 degree apart..

[Audio] In this slide we show how a y connected load is represented schematically. There is the neutral point n in the centre. The voltage v a that is the voltage between the neutral point and the line a is called the phase voltage while the voltage between lines a and b v a b is called the line voltage. The current i a is the line current and is the same as the phase current in the y connection. In the phasor diagram, we show how the line voltage v a b is obtained using the phase voltages v a and v b vectorially. The line voltage amplitude is square root three times the phase voltage and is shifted by 30 degrees to the phase voltage v a..

[Audio] If the load is balanced, the impedances, impedance angles and the phase currents are equal. So you can write the total power as three times the phase voltage, current and the power factor. In terms of line quantities, the total power is square root 3 times the line voltage, current and the power factor..

[Audio] This is the circuit representation of a 3 phase delta connected load. Here again we assume a balanced load. Here line current is shown as i a and phase current is shown as i a b for an example. They are different for a delta connected load. However, the line voltages and phase voltages are the same for this connection. The phasor diagram shows how the line current i a is obtained using the phase currents i a b and i a c. The line current is square root three times the phase current and is phase shifted by 30 degrees to the line current..

[Audio] For a balanced load the three phase power expression is the same as that of the y connected load..

[Audio] In power electronics, we need to deal with periodic signals most of the time. Fourier series expansion provides a beautiful way to decompose a periodic signal into primitive periodic components..

[Audio] A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series is known as harmonic analysis and is extremely useful as a way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical..

[Audio] In this slide we show, how the fourier coefficients a nought a n and b n are obtained using some simple fourier integrals..

[Audio] The root mean square value of a voltage or its r m s value can be calculated using the first formula on this slide. First we take the square and then the mean and finally the root. That is why it is called the root mean square. In the second expression, how the same r m s value is calculated using its fourier components is shown. Detailed analysis of fourier series is discussed in the lecture and tutorials..