FAKULTEIT INGENIEURSWESE FAULTY OF ENGINEERING Elektriese Aandryfstelsels 324 Electrical Drives Systems 324 Tutoriaal 11 Tutorial 11 15/16 Mei 2014 15/16 May 2014 Tydsduur: Duration: 2.5h Totaal: Total: 90 Vraag 1: [20] Question 1: Power Electronics & [20] n 110 V, 20 A permanente magneet GSservomotor het n motorkonstante, K m = 0,94, n ankerweerstand, = 0,48Ω, n ankerinduktansie, L A = 2,2 mh en word aan n tweekwadrant GS-GS omsetter gekoppel soos hieronder getoon. A 110 V, 20 A permanent magnet D servo motor has a motor constant, K m = 0,94, an armature resistance, = 0,48Ω, an armature inductance, L A = 2,2 mh and is connected to a twoquadrant D-D converter as shown below. V s = 110 V I A L A V A (a) Indien die skakelaars en diodes van die twee-kwadrant omsetter as ideaal beskou sodat die motor n konstante draaimoment las van 15 Nm teen 600 o.p.m. kan aandryf. (b) Vir die bedryfstoestand soos in (a) hierbo, bereken die maksimum riffel draaimoment wat deur die omsetter veroorsaak word indien die IGBT skakelaars van die tweekwadrant omsetter n AAN -spanning het van 2,2 V, teen 25 khz geskakel word en die diodes in anti-parallel met elke IGBT n AAN -spanning het gelyk aan 1,2 V. (c) Vir die bedryfstoestand soos in (a) hierbo, bereken die drywing deur die 110 V toevoer gelewer. (a) If the switches and diodes of the twoquadrant ideal, calculate the duty cycle necessary so that the motor kan drive a constant torque 15 Nm load at 600 rpm. (b) For the operating condition as in (a) above, calculate the maximum ripple torque produced by this converter if the IGBT switches of the four-quadrant converter have an ON -voltage of 2,2 V, are switched at 25 khz and the ON -voltage of the diodes in anti-parallel with each IGBT is equal to 1,2 V. [1] (c) For the operating condition as in (a) above, calculate the power delivered by the 110 V supply. [1] bladsy 1 van 5 page 1 of 5
(d) Vir die bedryfstoestand soos in (a) hierbo en deur van die gegewens in (b) gebruik te maak, bereken die geleidingsverliese in die omsetter. (e) Vir die bedryfstoestand soos in (a) hierbo en deur van die gegewens in (b) gebruik te maak, bereken die benuttingsgraad van die twee-kwadrant omsetter. (f) Vir die bedryfstoestand soos in (b) hierbo, bereken die werklike gemiddelde uittree spanning van die twee-kwadrant omsetter met die geleidingsverliese van die omsetter in ag geneem. (g) Vir die nuwe uittree spanning soos in (f) hierbo bereken, bereken die nuwe spoed waarteen die konstant draaimoment las van 15 Nm aangedryf sal word. (d) For the operating condition as in (a) above and by making use of the information given in (b), calculate the conduction losses in the converter. [1] (e) For the operating condition as in (a) above and by making use of the information given in (b), calculate the efficiency of the twoquadrant converter. (f) For the operating condition as in (b) above, calculate the actual average output voltage of the two-quadrant converter with the conduction losses of the converter taken into account. (g) For the new output voltage as calculated in (f) above, calculate the new speed at which the constant torque load of 15 Nm will be driven at. [1] Vraag 2: [25] Question 2: Power Electronics & [25] n 24 V, 5 A permanente magneet GS-motor het n motorkonstante, K m = 0,11, n ankerweerstand, R a = 1,0Ω, n ankerinduktansie, L A = 0,12 mh en word aan n tweekwadrant GS-GS omsetter gekoppel soos hieronder getoon. A 24 V, 5 A permanent magnet D motor has a motor constant, K m = 0,11, an armature resistance, = 1,0Ω, an armature inductance, L A = 0,12 mh and is connected to a twoquadrant D-D converter as shown below. V s = 24 V I A i LA A 1 L A v LA E A A 2 (a) Vir hierdie GS-motor, bereken: (a) For this D motor, calculate: i. die motor se kendraaimoment en [1] i. the motor s rated torque and [1] ii. die motor se kenspoed. ii. the motor s rated speed. (b) Indien die MOSFETs en diodes van die twee-kwadrant omsetter as ideaal beskou sodat die motor n las van 0,4 Nm teen 800 o.p.m. sal kan aandryf. (b) If the MOSFETs and diodes of the twoquadrant ideal, calculate the duty cycle necessary so that the motor will be able to drive a load of 0,4 Nm at 800 rpm. bladsy 2 van 5 page 2 of 5
Indien die MOSFETs van die twee-kwadrant omsetter n AAN -weerstand het van 0,05 Ω, teen 50 khz met n dienssiklus van 60 % geskakel word, die meganiese las wat aan die motor gekoppel is n konstante draaimoment las is van 0,4 Nm en die spanningsval oor elke borsel van die GS-motor 1 V: (c) Bereken die spoed waarteen die GS-motor nou sal loop. (d) Bereken en teken nou die: i. benaderde spanning, v LA, oor die induktor L A van die GS-motor en ii. benaderde stroom, i LA, deur die induktor L A van die GS-motor. L.W. Toon alle berekenings en dui die spanning- en stroomwaarde duidelik op die grafieke aan. If the MOSFETs of the two-quadrant converter have an ON -resistance of 0,05 Ω, are switched at 50 khz with a duty-cycle of 60 %, the mechanical load connected to the motor is a constant torque load of 0,4 Nm and the voltage drop across each brush of the D motor can be taken as 1 V: (c) alculate the speed at which the D motor will now be running. (d) alculate and draw the: i. approximate voltage, v LA, over the inductor L A of the D motor and ii. approximate current, i LA, through the inductor L A of the D motor. PS Show all calculation as well as all the voltage- and current values on the graph. Vraag 3: [25] Question 3: Power Electronics & [25] n 75 V, 5 A permanente magneet GSservomotor het n motorkonstante, K m = 0,23, n ankerweerstand, = 8,9Ω, n ankerinduktansie, L A = 6 mh en word aan n vierkwadrant GS-GS omsetter gekoppel met n GS busspanning van 48 V soos hieronder getoon. A 75 V, 5 A permanent magnet D servo motor has a motor constant, K m = 0,23, an armature resistance, = 8,9Ω, an armature inductance, L A = 0,3 mh and is connected to a fourquadrant D-D converter with a D bus voltage of 48 V as shown below. Q 3 D 3 V s = 48 V A 1 L E A A A 2 Q 4 D 4 (a) Vir hierdie GS-motor, bereken: (a) For this D motor, calculate: i. sy kendraaimoment en [1] i. its rated torque and [1] ii. sy kenspoed. ii. its rated speed. (b) Indien die skakelaars en diodes van die vier-kwadrant omsetter as ideaal beskou kan word, bewys dat die uittree spanning, E t, van die vier-kwadrant omsetter soos gemeet tussen terminale en, deur die volgende vergelyking gegee kan word. [3] (b) If the switches and diodes of the twoquadrant ideal, prove that the output voltage, E t, of the four quadrant converter as measured between terminals and, can be given by the following equation. [3] bladsy 3 van 5 page 3 of 5
E t = E s (2D 1) E t = E s (2D 1) (c) Indien die skakelaars en diodes van die vier-kwadrant omsetter as ideaal beskou kan word en die spanningsval oor die borsels van die GS-servomotor geïgnoreer sodat die motor n draaimoment van 1,0 Nm by stilstand sal kan ontwikkel. (d) Indien die IRFR120N MOSFETs van die vier-kwadrant omsetter n AAN - weerstand het van 0,21 Ω, die AAN - spanning van die parasitiese diodes in antiparallel met elke MOSFET gelyk is aan 2,06 V, die MOSFETs teen 20 khz met n dienssiklus van 20 % geskakel word, terwyl die as van die motor antikloksgewys roteer teen 500 o.p.m. en indien die spanningsval oor elke borsel van die GS-motor as 1,0 V geneem kan word: [4] (c) If the switches and diodes of the twoquadrant ideal and the voltage drop over the brushes of the D servo motor can be ignored1calculate the duty-cycle necessary so that the motor will be able to develop a torque of 1,0 Nm at standstill. (d) If the IRFR120N MOSFETs of the four-quadrant converter have an ON - resistance of 0,21 Ω, the parasitic diodes in anti-parallel with each MOSFET have an ON -voltage of 2,06 V, the MOSFETs are switched at 20 khz with a duty-cycle of 20 %, whilst the shaft of the motor is rotating anti clock wise at 500 r.p.m. and if the voltage drop over each brush of the D motor can be taken as 1,0 V: [4] L.W. Aanvaar dat die polariteit van die geïnduseerde ankerspanning is soos aangedui op die figuur met die motor wat antikloksgewys roteer. N.B. Assume that the polarity of the induced armature voltage is as indicated on the figure for a motor rotating anti clockwise. i. Bereken die gemiddelde ankerstroom. i. alculate the average armature current. ii. Bereken die rimpelstroom wat deur die omsetter veroorsaak word. iii. Skets die benaderde spanningsgolfvorm oor die ekwivalente anker induktansie van die GS motor vir een skakel periode, en dui die waarde van die spanning vir die D en die 1 D periodes duidelik op die skets aan. iv. Skets die benaderde stroomgolfvorm deur die ekwivalente anker induktansie van die GS motor vir een skakel periode, en dui die waarde van die stroom vir die D en die 1D periodes duidelik op die skets aan. [4] ii. alculate the ripple current caused by the converter. [3] iii. Sketch the approximate voltage waveform over the equivalent armature inductance of the D machine for one switching cycle, and show the values of the voltage for the D and the 1 D periods clearly on the sketch. iv. Sketch the approximate current waveform through the equivalent armature inductance of the D machine for one switching cycle, and show the values of the current for the D and the 1 D periods clearly on the sketch. [4] [3] bladsy 4 van 5 page 4 of 5
Vraag 4: [20] Question 4: Power Electronics & [20] n 110 V, 20 A permanente magneet GSservomotor het n motorkonstante, K m = 0,94, n ankerweerstand, = 0,48Ω, n ankerinduktansie, L A = 2,2 mh en word aan n vierkwadrant GS-GS omsetter gekoppel soos hieronder getoon. A 110 V, 20 A permanent magnet D servo motor has a motor constant, K m = 0,94, an armature resistance, = 0,48Ω, an armature inductance, L A = 2,2 mh and is connected to a fourquadrant D-D converter as shown below. Q 3 D 3 V s = 110 V L E A A Q 4 D 4 Indien (i) die vier-kwadrant omsetter teen 25 khz met n dienssiklus van 68 % geskakel word (i.e. vir Q1 & Q4 met Q2 & Q3 wat komplemenêr geskakel word), (ii) die IGBTs n AAN -spanning het van 2,2 V, (iii) die diodes in anti-parallel met elke IGBT n AAN -spanning het gelyk aan 1,2 V (iv) die borselspanning oor elke borsel van die GSservomotor is 1 V en (v) die motor teen n spoed van 500 o.p.m. roteer, bereken: (a) die gemiddelde draaimoment wat deur die GS-servomotor ontwikkel word (b) die rimpel draaimoment wat deur die omsetter veroorsaak word, en (c) die benuttingsgraad van die omsetter vir die bedryfstoestand. If (i) the four-quadrant converter is switched at 25 khz with a duty cycle of 68 % (i.e. that is for Q1 & Q4 with Q2 & Q3 swithing complementary), (ii) the IGBTs have an ON -voltage of 2,2 V, (iii) the diodes in anti-parallel with each IGBT have an ON -voltage of 1,2 V, (iv) the brush voltage over each brush of the D servo motor is 1 V and (v) the motor is turning at 500 r.p.m., calculate: [9] (a) the average torque developed by the D servo motor, (b) the ripple torque caused by the converter, and (c) the efficiency of the converter for the operating condition. [9] L.W. Aanvaar dat die polariteit van die geïnduseerde ankerspanning is soos aangedui op die boonste figuur met die motor wat teen 500 o.p.m. roteer en dat die wind en wrywingsverliese geïgnoreer kan word. N.B. Assume that the polarity of the induced armature voltage is as indicated on the above figure with the motor rotating at 500 r.p.m. and that the windage and friction losses may be ignored. bladsy 5 van 5 page 5 of 5