THE UNIVERSITY OF NEW SOUTH WALES FINAL EXAMINATION JUNE/JULY, 2003 ELEC4240/ELEC9240 POWER ELECTRONICS 1. Time allowed: 3 (three) hours 2. This paper has six questions. Answer any four. 3. All questions are of equal value. 4. A separate examination book should be used for each question. 5. Candidates may bring only slide rules, drawing instruments and approved electronic calculators into the examination room. 6. Answers must be written in ink. Except where they are expressly required, pencils may only be used for drawing, sketching or graphical work. 7. This paper may be retained by the candidate. See over for Question 1
QUESTION 1 The single-phase diode bridge rectifier of Figure Q1 is to be used to supply 24 c to a load of resistance R = 0.5 Ω and inductance L = 3 mh. The available ac supply is at 240 V rms, 50 Hz. 240V 50 Hz i p Input Transformer i s v s D 1 D 3 i L Load D 2 D 4 N:1 Figure Q1 Assuming that the load current is smooth and ripple-free, find the following i. Find the required RMS secondary voltage of the transformer. [2 marks] ii. Hence find the required input transformer turns ratio and its kva rating. [3 marks] iii. Sketch a diode current waveform and hence find the diode rms current rating. Find the required Peak Reverse Voltage (PRV) rating of the diodes. [3 marks] iv. Find the input transformer utilisation factor (TUF) at full load iv. Find the rectifier input power factor at full load. It is required that the load current ripple due to the dominant load ripple voltage must not exceed 5% of the full-load DC current, find v. the inductance of an L-filter in series with the load vi. the inductance and capacitance of an LC-filter between the load and the output terminals of the converter. See over for Question 2. ELEC4240/9240 Power Electronics 2
QUESTION 2 A three-phase, half-controlled thyristor bridge rectifier (such as indicated in Figure Q2) supplies DC current to a large electromagnet. The load circuit is highly inductive, so that the load current can be assumed to be smooth and ripple-free. The AC supply to the rectifier is from a 415V, 50 Hz source. The coil resistance and inductance of the electromagnet are 1.5W and 0.6 H, respectively. The firing angle of the converter is continuously adjusted to regulate the magnet current. +V D /2 v o n v an v bn v cn i a i b i c T 1 T 3 T 5 D 4 D 6 D 2 D f i L R L Electromagnet Coil V D /2 Figure Q1 (ii) Derive an expression for the out DC voltage,, of the converter, assuming continuous conduction of load current. In which quadrant(s) does this converter operate? Find the DC output voltage of the converter when it delivers a DC load current of 350A. Hence find the required firing angle a of the converter for this load. (iii) The application requires that the electromagnet current be brought down to zero quickly from its steady value after it has been ON for some time. Calculate the quickest time in which the coil current can be brought down to 5% of its nominal value, from the instant the firing pulses of the converter are blocked. (iv) In order to bring the magnet current down to zero faster than the time found in (iii), it is suggested that the converter of figure Q2 may be replaced by a 3-phase fully controlled thyristor converter. Describe the modification and explain how it might work. (iv) With the modification suggested in (iv) included, what will be the smallest time in which the magnet current can be brought down to 5% of its nominal value? See over for Question 3. ELEC4240/9240 Power Electronics 3
QUESTION 3 Consider the regenerative converter of figure Q3. The load current is continuous and can be assumed constant at a level of 200 A. The converter is supplied from a 230V, 50 Hz AC source with source inductance of L s = 1.2 mh/line. v an 0.0012 H i a T 1 T 3 T 5 v o I L v bn 0.0012 H 0.0012 H i b i c R = 0.1Ω Load L = 0.3 H 230V, 50 Hz v cn T 4 T 6 T 2 220 V + Figure Q3 Show that the output DC voltage of the converter for a firing angle a is given by 3Vmax 3 Ls Vd = ω cosα IL π π. (ii) Show that the commutation overlap angle, µ, is given by 2ωLs cos( α + µ ) cosα = I L V max (iii) For the given load current (200A), calculate the converter output DC voltage, the firing angle α and the overlap angle µ. [6 marks] (iv) Using the waveforms supplied with the question paper in page 9, sketch output voltage waveform and one of the AC input current waveforms, indicating the commutation overlaps. [6 marks] (v) Discuss briefly how commutation overlap affects the performance of a converter. See over for Question 4 ELEC4240/9240 Power Electronics 4
QUESTION 4 The output DC voltage V o of a boost or step-up converter (see Figure Q4) is maintained at 24 V by controlling the duty cycle D of the transistor T. The input dc voltage to the converter varies in the range of 8-18 V. The switching frequency f s of the converter is 25 khz. The minimum load of the converter is 12 W. Assume ideal devices and componenents. i d L i L D i D + v L i c + I o T C V o R (Load) Figure Q4 Develop an expression of inequality from which the maximum or minimum value of inductance L may be determined for operation of the converter in the continuous or discontinuous conduction modes. (ii) Find the maximum and minimum values of the inductance L if the converter is required to operate in the (a) continuous conduction mode or (b) discontinuous conduction mode. (iii) In normal operation, the above boost converter operates with discontinuous inductor current when the input DC voltage is Vd = 12 V. With the inductance L selected from the results in (ii) for operation in discontinuous conduction mode, determine whether the inductor current be continuous when the load current is 1A. [6 marks] (iv) For the operating condition of (iii) find the filter capacitance C required to keep the Vo output voltage ripple 1%. V o (v) Find the RMS ripple current in C for the operating condition of part (iii). Note that the capacitor ripple current is the same as the diode ripple current. See over for Question 5 ELEC4240/9240 Power Electronics 5
QUESTION 5 N2 The transformer of the flyback converter of Figure Q5 has a turns ratio of = 3. The dc N 1 supply voltage to the converter is 12 V and the output dc voltage V o is maintained at 24 V. The converter switching frequency is 100 khz. The converter must be operated with complete de-magnetisation of the transformer core (or core reset) in each switching cycle. i d N 1 :N 2 D i D T v 1 + v T v 2 + v D i c C + V o i o R (Load) Figure Q5 Sketch the transistor (T) switching signals, i d, i m, v 2, i D and v D waveforms, and describe the operation of the converter with the help of these sketches. Here i m is the magnetising current of the transformer. Assume linear transitions of current. (ii) Show that the maximum value of the magnetising inductance L m of the transformer for delivering a maximum load current of I o while operating with discontinuous conduction is given by L m(max) ( ) 2 2 1 D Vo N1 = 2fs Io N2 Vo where Io =, and R is the minimum load resistance (for maximum load) and D R is the operating duty cycle. Assume that core reset occurs up to the maximum value of the load current I o. ELEC4240/9240 Power Electronics 6 [6 marks] (iii) Find the maximum magnetising inductance L m allowable when the converter delivers its maximum output power of 120 W with just discontinuous conduction. What is the duty cycle D of the converter for this condition of operation? [7 marks] (iv) Find the capacitance C required to keep the output voltage ripple, V o, within 1% of V o. [7 marks] See over for Question 6
QUESTION 6 The voltage waveform of Figure Q6(b) typically occurs across the load terminals of the voltage- source SPWM single-phase bridge inverter of Figure Q6(a). The number of output voltage pulses per half cycle of the output voltage waveform is k. The width of each voltage pulse is proportional to value of the sinusoidal modulating signal at the centre of each pulse. Using an apprixamate analysis with the help of the unit impulse function, d(t), and taking k = 5, develop a general expression for the output voltage, including its harmonic components. [8 marks] T1 D1 T3 D3 A i L Load B T4 D4 v o T2 D2 Figure Q6(a) +c c Figure Q6(b) The DC supply to the inverter of Figure Q6a) is 380V. The inverter fundamental output frequency is 50 Hz. The load resistance and inductance are: R = 10 W and L = 25 mh. For k = 5, (ii) find the depth of modulation, m, when the fundamental output voltage of the inverter is 240V, RMS; (iii) calculate the RMS fundamental output voltage when m = 1. Question 6 continued on page 7 ELEC4240/9240 Power Electronics 7
(iv) (v) What is the switching frequency of the inverter? Will it be possible to limit the THD of the output current for the lowest order output harmonic voltage to 10% of the fundamental load current? If not, what remedy would you suggest? END OF PAPER ELEC4240/9240 Power Electronics 8
Notice for the Examinations section: these figures should be on a separate page to enable students to submit with their answer books Voltage waveforms in three-phase systems Degrees Three-phase line-neutral voltages v an, v bn v cn, and so on. Degrees Three-phase line-line voltages v ab,v bc, v ca and so on. Degrees Three-phase ine-line voltages v ab, v bc, v ca and so on. ELEC4240/9240 Power Electronics 9