Tutorial 5 - Isolated DC-DC Converters and Inverters

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1 University of New South Wales School of Electrical Engineering and Telecommunications Tutorial 5 - Isolated DC-DC Converters and Inverters Flyback Converter N A dc-dc flyback converter has a turns ratio. The dc supply voltage V d to the N1 2 converter is at 10 V. The required output voltage V o is 24 V. The switching frequency of the converter, f s = 100 khz. The maximum load upto which the converter transformer core is required to demagnetise completely in each switching period is 120 W. Find the duty cycle D for the maximum load power of 120W. [D = 0.615] Find the maximum leakage inductance L m the transformer can have. [L m = 1.58 H] (iii) Find the capacitance C to keep the peak-peak output voltage ripple V o within 1% of V o. [C = 128 F] 2. The load resistance of the flyback converter of Question 1 increases to 12 when the output power drops. Find the output voltage V o of the converter if the duty cycle remains unchanged. [V o = 37.9 V] Find the required duty cycle if the output voltage is to be restored to 24 V. [D = 0.389] (iii) Find the output power when the output voltage is restored to 24 V. [P o = 48 W] Forward Converter 3. A dc-dc forward converter is to be designed with the following specifications: V d = 48 10%, V o = 5 V (regulated), f s = 100 khz, P o = W. For the demagnetising winding, a turns ratio of conduction mode of operation. N N is chosen. Assuming continuous N2 Calculate the smallest turns ratio N which is possible. [ N2 N ] 1 Calculate the minimum value of the filter inductance. [L = 4.93 H] (iii) If the demagnetising winding is to operate with a maximum duty cycle of D max = 0.7, calculate the voltage rating of the transistor in terms of the input voltage V d. [V sw, max = 3.33V d ] Tutorial 5 - Isolated DC-DC Converters 1 F. Rahman/May 2009

2 4. A forward converter has the following parameters: V d = 48 V, L = 0.4 mh, C = 100 F, R = 10, f s = 35 khz N 1 /N 2 = 1.5, N 1 /N 3 = 1, D = 0.4, L m = 5 mh Calculate the output voltage V o. [V o = 12.8 V] (iii) Calculate the average, maximum and minimun currents in the inductor L. [I L = 1.28 A, i Lmax = 1.56 A, i Lmin = 1.01 A] (iv) Calculate the output voltage ripple V o. [V o = 19.6 mv] (v) Calculate the peak current in the transformer primary. Assume that the transformer magnetising inductance L m is 5 mh. [I 1max = 1.15] (v) Verify that the transformer core is demagnetised (reset) during each switching period. [time for i L to fall to zero = 22.8 s < T s (28.6 s); thus, the core resets] Inverter 5. A single-phase, full-bridge, voltage source inverter as shown in figure Q5 supplies squarewave output to an R-L load. The transistor switching scheme is complementary bipolar. D1 D3 V d A R i L L B D2 v o D4 Figure Q5 Obtain expressions for the rms values of fundamental, and higher order harmonic output voltages. If the fundamental ac output voltage is 240V, what is the required dc input voltage for the inverter? [266.4V] (iii) Obtain expressions for the load current waveform. (iv) Calculate the output power when the load is 9 + j9 at 50 Hz. Tutorial 5 - Isolated DC-DC Converters 2 F. Rahman/May 2009

3 6. A single-phase, full-bridge transistor inverter, as shown in figure Q5 supplies a load of 10 in series with an inductance of 31.8 mh. The inverter is supplied from a 380 volts dc source. Calculate the rms value of the fundamental (i.e., V 1 ) output voltage and obtain expressions for the load current waveform for a squarewave output. [342.34V] Calculate the rms value of the fundamental (i.e., V 1 ) output voltage and obtain expressions for the load current waveform for a quasi-squarewave output of 50% ON time in each half cycle. [242V] (iii) Calculate the phase-shift angle between the two legs of the inverter when the output voltage is 200 V rms. [108.5] (iv) Calculate rms values of the output voltage and current for the two lowest order harmonics for phase shift angle of (iii). [V3 = V, V5 = 1.49V] 7. For a quasi-square output as shown in figure Q7(a), show that the harmonic components (in rms values) in the output voltage are given by 4Vd n Vn sin cosn t 2 n 2 ( - )/2 t = 0 t = t = 2 Figure Q7(a) When the above output waveform is displaced from the t = 0 reference by an arbitrary angle, as indicated in figure Q7(b), the harmonic components may be represented as phasors V n 4Vd n sin cos n 2 n 2 j sin n ( - )/2 t = t = 0 Figure 7(b) Tutorial 5 - Isolated DC-DC Converters 3 F. Rahman/May 2009

4 where the quantity in the square bracket represents angular displacements of the harmonics with respect to the t = 0 reference. [Note that this representation simplifies calculation, otherwise both a n and b n coefficients of the Fourier representation for the displaced waveform would have to be computed]. 1 2 t = 0 t = Figure Q7(c) Using the above results, develop expressions for the switching angles 1 and 2, as defined in the SPWM waveform of figure Q7(c), so that the fundamental output voltage is 0.8Vd, and that the third harmonic output voltage is zero. 8. For a single-phase unipolar switched SPWM inverter the output voltage waveform consists of five output voltage pulses per half cycle (i.e., k = 5). The dc supply voltage to the inverter is 200 V dc and the load consists of a resistance of 10 in series with and inductance of 20 mh. The fundamental output voltage is 100 V rms. Using impulse functions, show that output voltage harmonics of order lower than 2k1 are zero. Find the required depth of modulation, m. [0.707] (iii) Calculate the rms values of the two lowest order harmonic voltages in the output. [V 9 = 70.7V, V 11 = 70.7V] (iv) Calculate the total rms current due to the two lowest order harmonic voltages in the output. [1.59A] (v) Neglecting all other harmonics except the two lowest order, calculate the total harmonic distortion (THD) of the output current waveform. If the THD of the output current is not lower than 5% what measures would you suggest? 9. The four transistors - in the single-phase full-bridge bridge inverter of figure Q5 are switched as indicated in figure Q9. Draw one cycle of the output voltage waveform. Obtain an expression for the n-th order output voltage harmonic and hence show that the third harmonic in the output voltage is zero. (iii) Calculate the THD of the output voltage. [71.7%] Tutorial 5 - Isolated DC-DC Converters 4 F. Rahman/May 2009

5 Figure Q9 10. A three-phase transistor voltage-source inverter supplies a 3-phase load, as shown in figure Q10. The load consists of star connected resistance of 10 in each phase. The inverter supply voltage is 200 V dc and each inverter switch conducts for 180. Sketch the switching signals for the six transistors. Sketch the line-line voltage for one complete cycle of the output voltage (iii) Sketch the line-line voltage for one complete cycle of the output voltage (iv) Calculate the rms values of the first five harmonics in the line-line output voltage, including the fundamental. [V 1(l-l) = 156V, V 5(l-l) = V, V 7(l-l) = 22.29V, V 11(l-l) = V, V 13(l-l) = 12V, V 17(l-l) = 9.18V] (v) Calculate the rms values of the first five harmonics in the line-neutral output voltage, including the fundamental. [V 1(l-n) = 90V, V 5(l-n) = V, V 7(l-n) = 13.22V, V 11(l-n) = -8.19V, V 13(l-n) = 6.93V, V 17(l-n) = 5.3V] D1 D3 T5 D5 V d A B C D4 T6 D6 D2 Figure Q10 Tutorial 5 - Isolated DC-DC Converters 5 F. Rahman/May 2009

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