EE3C, Power Electronics and Power Systems

Assignment on Power Electronics, 2024-25

Task 1 (Marks: 20)

A three-phase 6-pulse diode rectifier, connected to a 3-phase AC supply, having a voltage of 415 V (line-to-line RMS), a frequency of 50 Hz, and a per phase series inductance of Ls = 5mH, feeds a static RL load.

Question 1

Draw the circuit diagram of the AC-DC diode converter.                                    [2]

Question 2

Implement this rectifier in Simulink. The diodes have a forward voltage drop of 1.0 V when conducting. Model the load as the series of a resistor R = 10 Ω and an inductor L = 100 mH.

Question 3

Using the circuit parameters of Question 2:

Task 2 (Marks: 40)

A three-phase 6-pulse, fully controlled thyristor rectifier supplies a static RL load, from a three phase 415 V (line-to-line RMS), 50 Hz, AC supply having a per phase series inductance of Ls = 2.5 mH.

Question 1

Draw the circuit diagram of the AC-DC thyristor converter.                             [2]

Question 2

Implement this rectifier in Simulink. The thyristors have a forward voltage drop of 1.0 V when  conducting.  Model the load  as the  series  of a  resistor R and an inductance L.

Investigate the following cases in the simulation study:

a) R = 50 Ω, L = 2 mH andLs = 2.5 mH;

b) R = 50 Ω, L = 200 mH andLs = 2.5 mH;

c) R = 10 Ω, L = 200 mH andLs = 2.5 mH;

d) R = 10 Ω, L = 200 mH andLs = 10 mH.

For all cases, the firing angle of thyristors has to be chosen to get an average voltage of 500 V across the load.

In your report, you  have  to  show  and  comment  (maximum  2  sentences)  the following for all the cases:

1.    the firing angles to achieve the desired load voltage;                       [1+1+1+1]

2.    the waveforms of the DC voltage across the load;                           [2+2+2+2]

3.    the values of the THD of the currents of the three phase AC supply;  [1+1+1+1]

4.    the power factor seen by the AC supply, remembering that the voltage

is sinusoidal but the current is distorted.                                           [2+2+2+2]

Question 3

Using the rectifier model of Question 2 and assuming Ls = 2.5 mH, R = 50 Ω, and L = 200 mH:

Task 3 (Marks: 40)

A pulse-width modulated (PWM) three-phase inverter, shown in Fig. 1, supplies a three-phase, Y-connected static RL load, connected to the nodes A, B, C. The input DC voltage Vd is smooth and equal to 600 V.

Fig. 1. Three-phase inverter supplying a static RL load

Question 1

Develop a Simulink model for the inverter, using IGBT as power devices and sinusoidal  PWM  with  triangular  carrier  as  a  modulation  technique.  The  load parameters  are R = 25 Ω   and L = 200 mH.   The  modulation   frequency  and amplitude ratios are mf = 9 and ma = 0.8, respectively. For a fundamental frequency of the output voltage of 25 Hz and with reference to the circuit in Fig. 1, show in the report:

Question 2

The inverter is modulated with a sinusoidal PWM with triangular carrier. Assume R = 25 Ω, L = 50 mH, ma = 0.8 and fundamental frequency output of 25 Hz.

1.   Design the value of the frequency ratio mf to keep the THD of the output current below 2%.                               [10]

2.   Verify your design using your computer simulation.                                    [6]

Question 3

The inverter is modulated with a sinusoidal PWM with triangular carrier. Assume R = 25 Ω, L = 50 mH, mf = 31 and fundamental frequency output of 25 Hz.

Remarks

These instructions have been tested in Matlab 2023a. Other Matlab versions might be slightly different.

1)   Remember to add units and titles to all diagrams included in the report.

2)   A simple way to improve the legibility of the figures it to change the settings of the scopes:

a.    Click  on  “view”, “Configuration properties”, “Time”, to add the time-axis label and select the x-axis unit

b.    Click on “view”, “Configuration properties”, “Display”, to add they-axis unit and the title;

c.    Click on “view”, “Style” will enable you to change the background colour of the figure, the linewidth and colour of the lines.

3)    Some  Simulink  examples  of AC-DC  converters  and  DC-AC  converters  are available on Canvas.

4)   Use the tutorial notes for Simulink and Matlab to help you for the development of the simulations.

5)    Starting from the example for three-phase diode rectifier, change the diodes to thyristors. The thyristors can be controlled by the “Pulse generator (Thyristor 6- pulse)”, placed in “Simscape”, “Electrical”, “Specialized Power Systems”, “Power Electronics”, “Power Electronics Control” . Alternatively, you can search the block from the search bar at the top of the “Simulink Library Browser” .

6)   The frequency of synchronisation (input “wt”) can be obtained with 3-phase a  phase-locked loop algorithm, block “PLL (3ph)” from the AC power source. An  angle duration of 10 degrees is often enough to turn the thyristors on. A “constant” block can feed the input “block”, putting the constant equal to zero.

7)   A good  example  of a  6-pulse  controlled  rectifier  can  be  found  by  typing  in “power_ThyristorRectifiers” in the main Matlab window.

8)   The “PWM generator (2-level)” block can be found in the same folder of the pulse  generator forthyristors. Change the generator mode to “3-phase bridge (6 pulses)” and tick “internal generation of reference signal” .

9)   To change the resistance as a step, you can use two resistors in parallel, with one of the  two resistors  series  connected  to  an  ideal  switch  (“Specialized  Power systems”, “Power Electronics”). The switch is open when the input “g” is 0, it is closed when “g” is 1. The switch is initially open, so only one of the two resistors is connected to the rest of the circuit (e.g. 50 Ω). When the switch is closed by changing the input to port “g” from 0 to  1, the second resistor is connected in parallel, reducing the total load resistance. For example, if the second resistor is 33.3 Ω and the first resistor is 50 Ω, the equivalent resistance is 20 Ω .

10) PID controller blocks are already available in Simulink in the folder “Simulink”, “Continuous” .  These  controllers  have  all  the  functions  already  implemented, including saturation and anti-windup.

11) PID controllers work for the control of both DC and AC quantities.

12) To control a quantity “x”, you need to see “x” as the effect and you have to adjust the quantity “y”, where “y” is the cause of “x” . For example, in an electric circuit the current is the effect and the voltage is the cause; if you want to control the current, you have to regulate the voltage. Therefore, the output of the PID controller is the voltage reference that is generated by the converter.

13) In the model answers, the number of sentences is indicative of the expected length of each answer and it is not prescriptive.