S-81.211 Power Electronics Exam 12.12.213 Answer all five questions (in English, Finnish, Swedish). Questions in Finnish are on the reverse side. 1. The current i c shown below is a typical waveform in a Buck converter. Explain the waveform based on the operation of the converter. The inductor of the converter is 5 H and the capacitor is 1 F. Calculate and draw the inductor voltage waveform when the peak value of the inductor current is 4 A. Calculate the peak-to-peak voltage change in the output capacitor due to i c. 2. A full-bridge single-phase diode rectifier is connected to a sinusoidal 5 Hz 23 V (rms) utility voltage. The ac-side inductance is 3 mh. The load of the rectifier is a very large inductance in series with a 2 resistance. What are the dc-side current and the average dc-side voltage? 3. The input voltage of a boost converter V in = 1 V and the output voltage V o = 25 V. Assume the converter to be lossless and omit the ripple in the output voltage. The inductance is,1 mh, the output power P o = 3 W, and the switching frequency f s = 1 khz. a) Draw the circuit diagram of the converter, when the switching power-pole is implemented with an IGBT and a diode. b) Calculate the IGBT duty ratio, the average input current, and the minimum and maximum values of the input current. c) Draw the waveforms of the inductor voltage, the input current, and the current of the diode below each other s. 4. A three phase voltage-sourced dc-ac converter is supplying a balanced three-phase load. a) Draw the circuit diagram of the converter in which individual power semiconductor devices can be recognized. b) Derive equations for the phase and line-to-line voltages as function of pole voltages. c) The converter operates in square-wave (six-step) mode. Draw the waveforms of pole, line-to-line and phase voltages. 5. Operating of power electronics is based on power semiconductor devices. What are the basic characteristics required by them? What are the main differences of the used power semiconductor devices when they are grouped in three categories? Fourier-series 1 f ( t) a ahcos h t bhsin h t 2 h 1 ah ( )cos,,, ( )sin, π f t h t d t h b h f t n t d t π h 1,,
S-81.211 Power Electronics Exam 12.12.213 Vastaa kaikkiin viiteen kysymykseen joko suomeksi, englanniksi, ruotsiksi. Kysymykset löytyvät englanniksi paperin toiselta puolelta. 1. Alla oleva virta i c on tyypillinen käyrämuoto jännitettä laskevassa katkojassa (Buck). Perustele käyrämuoto katkojan toiminnan perusteella. Katkojassa käytettävä induktanssi on 5 H ja kondensaattori 1 F. Laske ja piirrä induktanssin jännitteen käyrämuoto kun induktanssin virran huippuarvo on 4 A. Laske kondensaattorin jännitteen huipusta huippuun vaihtelu. 2. Yksivaiheinen diodisilta on kytketty 5 Hz ja 23 V (rms) vaihtojänniteverkkoon. Syöttöjärjestelmän induktanssi on 3 mh. Tasasuuntaajan kuormana on hyvin suuren induktanssin ja 2 resistanssin sarjaankytkentä. Kuinka suuria tasavirta ja tasajännite ovat? 3. Jännitettä nostavan katkojan (boost) syöttöjännite V in = 1 V ja lähtöjännite V o = 25 V. Katkoja on häviötön ja lähtöjännite on täysin tasainen. Katkojassa käytettävä induktanssi on,1 mh, lähtöteho P o = 3 W ja kytkemistaajuus f s = 1 khz. a) Piirrä kytkennän piirikaavio, b) laske kytkimen suhteellinen johtoaika, tulovirran keskiarvo ja sen minimi- ja maksimiarvot, c) piirrä induktanssin jännitteen, tulovirran ja diodivirran käyrämuodot allekkain. 4. Kolmivaiheinen jännitevälipiirillien dc-ac suuntaaja syöttää symmetristä kolmivaiheista kuormaa. a) Piirrä suuntaajan kytkentä, jossa näkyvät myös tehopuolijohdekomponentit. b) Johda yhtälöt pää- ja vaihejännitteille vaihtokytkimien (pole) jännitteiden avulla. c) Suuntaaja toimii täydellä ohjauksella (square-wave, six-step). Piirrä vaihtokytkimien sekä pää- ja vaihejännitteiden käyrämuodot. 5. Tehoelektroniikan toiminta perustuu tehopuolijohdekomponentteihin. Mitä komponenttien perusvaatimukset ovat? Mitä ovat käytettyjen komponenttien toiminnan periaatteelliset erot kun ne jaotellaan kolmeen eri ryhmään? Fourier-sarja 1 f ( t) a ahcos h t bhsin h t 2 h 1 ah ( )cos,,, ( )sin, π f t h t d t h b h f t n t d t π h 1,,
S-81.211 Power Electronics Solutions, Exam 12.12.213 Question 1, See example 3-1 and 3-2 in the text book The waveform of the capacitor current is the same as for the inductor current except the missing dc-component. Many had thought that the capacitor chargers at the same time as the inductor current and that the capacitor discharges as the current decreases. This is not the case. It is good to remember that which means that the voltage of the capacitor is an integral of the capacitor current. This means that there is a 9 degrees phase lag in the voltage. This can be seen in the right-hand figure below. Capacitor voltage increases when the capacitor current is positive. Voltage over the inductor can be calculated based on the given current waveform. During the on-time of the switch the inductor current rises from 3 A to 4 A, i.e. the increase is 1 A and the voltage over the inductance is v L di 1A L 5μH 16,67V dt 3μs During off-time of the switch we have negative voltage over the inductor and current decreases. The voltage over the inductance is di 1A vl L 5μH 25V dt 2μs The capacitor current and capacitor voltage waveforms are shown in the right hand figure above. Capacitor voltage increases with positive current and the peak-to-peak change can be calculated as with the help of the charge Q highlighted in the figure. 1,5A 2,5μs Q V 2 p p μs 6,25mV C 1μF
Question 2 The ideal dc-voltage, when the effect of the ac-side inductance L s is not taken into account is obtained by the integral Some has not taken the ac-side inductance into account. Without the ac-inductance the dcvoltage is 27 V and the dc-current 1.4 A. This answer gives in maximum 9 points out of 15.
Question 3 Question 4 a) Three switching poles as shown below (left) and each pole consist of two turn-on turn-off devices (IGBT) and two diodes (right) b)
c)
Question 5 The figure below gives an answer to some part of the question. However, this figure was not required for full points. Characteristics required by power semiconductor devices. They need to withstand high voltages when not conducting and high currents when conducting, i.e. power rating (VA) is high as shown in the figure. At the same time conduction losses and switching losses should not be high as high efficiency is important. Also, losses generate heat and increase the temperature of the device. Switching speed is also important and it needs to be fitted with the converter type and power semiconductor type concerned. Size and price of the components is also an issue. Power semiconductor devices can be grouped into three categories: diodes, thyristors and switches. Diodes conduct automatically when there is a positive anode-cathode voltage and they cannot be turned off. Thyristor turn-on can be delayed when there is positive anode-cathode voltage. They are turned on with gate pulse but they cannot be turned off, i.e. thyristor conducts as long as there is positive current through it. Switches (IGCT, IGBT, MOSFET in the figure above) can be turned on and off with gate control. The type of the used power semiconductor has a fundamental effect on the operating principle of the converter and on the way how it can be controlled.