Exam Electronic Power Conversion 4 February 2000 (selection)

Transcription

1 Exam Elecronic Power Conerion 4 February (elecion) (8) PROBEM Gien i a imple circui wih a generic wich a hown in he figure a. Bunle of exam Elecronic Power Conerion (E49) February January 7 Remark: In fron of eery queion he maximum raing ha can be obaine i inicae. Fir ole he problem for your elf on raf paper an make a nea erion ubequenly. Sar each problem on a eparae piece of paper. Alway how he formula ha you ue o make he calculaion. You can gie your anwer in Duch or in Englih. I i allowe o ue a (elf-mae) piece of paper (xa4) wih formula an figure from he exbook. Fig. he aa hee of he wich pecifie he following wiching ime correponing o he linear wiching characeriic a hown in he figure. ri 8 n ; f 8 n ; r n ; fi n Furher: V 3V ; I 4A. (). Skech he inananeou wiching lo a a funcion of ime (4). Calculae he wiching power lo a a funcion of he wiching frequency in a range 5 - khz, auming V 3V an I 4A. (3).3 Calculae an plo he oal loe a a funcion of he wiching frequency in a range 5 - khz in he wich when he on-ae olage i V on.5v a 4A an he uy raio of he wich i D.4 (aume on off ). oe: - he anwer in hi bunle are in hor from. A more elaborae anwer, howing meho an applie formula, i expece from you a he exam. - Pleae inform me abou (yping) error in hi bunle:.w.h.ehaan@uelf.nl Summary of anwer o exam Elecronic Power Conerion 4 February. E lo,w / I o V ( ri f ) / I o V ( r fi ) / 4.3( ri f r fi ) 88 µj P lo,w f. E lo,w 88 f µw.3 P lo,on V on. I on on / V on. I on D,4 W P lo,o, f W /46 /46

2 Exam Elecronic Power Conerion 7 April (9) PROBEM Gien conerer hown Fig., coni of a forwar conerer ha i connece o he gri (3V, 5Hz) ia a ioe recifier. he following i gien: f 8 khz (wiching frequency of he forwar conerer) 5 µh R o 4 Ω W :W :W 3 3:5: Boh C en C o are ufficienly large o juify he aumpion of u an u o being conan. he forwar conerer i lole an can operae in boh coninuou an iconinuou conucion moe. Fig. (). Calculae he olage u acro C. (). Decribe he funcion of wining w an ioe D 3. (3).3 Calculae he allowable conrol range of he uy raio D. (3).4 Wha alue can he oupu olage ake when he uy raio i arie oer he allowable conrol range. Conier boh coninuou an iconinuou conucion moe. (3).5 Calculae D for an oupu olage of 5V. (3).6 Skech he coure of i, i, i 3, i, u ce an u a a funcion of ime. Mark he graph wih alue. (3).7 Calculae he criical inucance c a a funcion of he uy raio D. (3).8 Skech he curren i hrough he ac upply an calculae he inpu power. () PROBEM Gien i a full-brige c-c conerer (H-brige) wih RC-loa a hown. For conrol of he wiche o calle bipolar olage wiching i applie, were he conrol ignal are obaine by comparing a conrol ignal conrol wih a riangular waeform ri. V S S D D S3 S4 he following i gien: m ( i he perio of riangular waeform) R5 Ohm D3 D4 C 3/46 I o R V o mh V 3V V V (Deire oupu olage) C i ufficienly large o aume he oupu olage o be conan. (5). Expre he oupu olage in V an conrol / ˆ ri. (5). Define he uy raio D an calculae he require uy raio o ge an oupu olage of V. (3).3 Skech he (), i () an he ource curren i. (3).4 Inicae in he kech wha wiche are conucing a wha ime. (3).5 Expre he ripple in he oupu olage V in, C, D an. (5) PROBEM 3 () 3. Define he wich uiliaion raio. (3) 3. Calculae he wich uiliaion raio for a ep-up an a ep-own conerer a a funcion of he uy raio D were inucor an capacior are ufficienly large o aume ha inucor curren are conan an capacior olage are conan. Summary of anwer o exam Elecronic Power Conerion 7 April. U 3 35 V (peak recificaion). Funcion of w: o ree he core an o aoi ha he magneiaion energy i iipae ino he wich a urn off. Funcion of D: aoi ha an increaing c-curren will ar o flow hrough w..3 > B up B own ; U D U (- D) w A w A o: < D < /3.4 Coninuou: U D 35 wih <D< Diconinuou: D. 35 <U <. 35 wih <D< So: < U o < 4, w3.5 Coninuou conucion moe: U D U w U 3 D. w3 U.6 See book.7 R c (- D) f U o 5.8 P in P ou ; Pou 6.5W R 4. conrol V o V ˆ ri. V ( D -)V conrol ( V ) ˆ ri conrol ri.4 ; D.7.3 ike Mohan fig (DD4), (SS4), (DD3), (SS3), (DD4),..., 4/46 w

3 Exam Elecronic Power Conerion 7 January (elecion) () PROBEM he conerer hown in Fig. 3 coni of a forwar conerer ha i connece o he gri (3V, 5Hz) ia a ioe recifier. he following i gien f 8 khz (wiching frequency of he forwar conerer) 5 µh R o 4 Ω W :W :W 3 3:5: Boh C en C o are ufficienly large o juify he aumpion of u an u o being conan. he forwar conerer i lole an can operae in boh coninuou an iconinuou conucion moe. Exam Elecronic Power Conerion (E 4-9) March (elecion) (6) PROBEM For applicaion uch a moor an ero conrol i i ofen require o conrol he moor curren. here are ariou way o obain wiching ignal for he wiche o conrol he inerer oupu curren. In Fig. 4a phae leg of a olage ource inerer i hown. Fig. 3 (). Calculae he olage u acro C. (). Decribe he funcion of wining w an ioe D 3. ().3 Calculae he allowable conrol range of he uy raio D. ().4 Calculae D for an oupu olage of 5V. (3).5 Skech he coure of i, i, i 3, i, u ce an u a a funcion of ime. Mark he graph wih alue. ().6 Skech he curren i hrough he ac upply an calculae he aerage inpu power..5 D (- D) V V 8 C f 3. See Mohan par. 7.8 an See Mohan par. 7.8 an Summary of anwer o exam Elecronic Power Conerion 6 January. U 3 35 V (peak recificaion becaue he capacior C i large).. Funcion of w: o ree he core an o aoi ha he mageiaion energy i iipae ino he wich a urn off. Funcion of D: aoi ha an increaing c-curren will ar o flow hrough w..3 > B up B own ; U D U (- D) w A w A o: < D < /3.5 Coninuou conucion moe: w3 U D U w w U 3 5 D.. 35 w3 U 35.6 See Mohan fig. - Fig. 4 (4). Decribe a yem o conrol he oupu curren i A of he inerer leg in Fig. 4. Gie a block iagram of he yem an kech he olage A, i A an he on/off ignal for he wiche. (). Wha parameer in he conrol yem eermine he magniue of he curren ripple an how can a mall curren ripple be obaine. (7) PROBEM 3 Gien i a flyback conerer a hown in Fig. 5b. he inpu olage V may ary an he oupu olage V houl be kep conan by aaping he uy raio D. Gien i: V 4 V V 48 V / 6 f khz R Ohm i i Fig. 5 () 3. Derie he olage ranfer funcion V /V - x in coninuou conucion moe (incomplee emagneiaion moe) a a funcion of he uy raio D an calculae he uy raio for V V. R 5/46 6/46

4 () 3. Calculae he minimum alue of he ranformer inucance m ha i require o obain coninuou conucion moe for all alue of V in he range 4V. Hin: Be aware ha a he bounary of he coninuou/iconinuou conucion moe he following hol: D i / I an I V P. () 3.3 Calculae he maximum olage acro he wich. () 3.4 Skech i, i, x an a a funcion of ime for V V. Summary of anwer o exam Elecronic Power Conerion March. See book of Mohan par fig 8-35 or Fig 8-35: he olerance ban Fig 8-36: he frequency of ri (Oher facor ouie he conrol yem: he upply olage, he back EMF an loa inucance). D 3. V V ; D.4; (A V 4 V he uy raio i D.36) D 3. he bounary i reache a he highe inpu olage V 4V wih D.36 A he bounary of coninuou conucion: D i / I wih I P o /V 3.4 /4 6.5 A V V I 6.5 Alo: i D or m D3 wih i 9. 7 A i D.36 m V So D 4 m µ H i V x V V 4 6 V 3.4 See Mohan fig -8 Aume all componen o be ieal excep for he preence of he ranformer magneizaion inucance. he wining 3 ere complee emagneizaion of he magneizaion inucance of he core. he conerer operae in coninuou conucion moe for all gien upply an loa coniion (5) 3. Calculae / if he urn raio i eire o be a mall a poible() 3. Calculae he minimum alue of he oupu filer inucance o guaranee coninuou conucion moe for all pecifie loa an upply coniion. (5) 3.3 Skech he waeform of x, i, i, i 3, i for V 43,V an P loa 5W an min (5) PROBEM 4 Gien i a bi-irecional ingle-phae c/ac conerer ha i connece o a gri wih olage e, a hown in Fig. 7. Fig. 7 he oupu olage of he inerer, ha conain a full-brige olage ource conerer, i obaine by bipolar olage wiching a hown infig. 8. Only linear moulaion i applie (no oermoulaion). Exam Elecronic Power Conerion 5 January (elecion) (3) PROBEM 3 A forwar conerer wih emagneiaion wining (wih 3 ) a hown in Fig. 6 i o be eigne wih he following pecificaion: V 48V ±% V 5V (regulae) f khz P loa 5-5W 3 I I 3 I x -- Fig. 6 Fig. 8 Gien i furher: V 35V e E inω wih E 3V an ω π5 5 mh he inerer i fe from a phooolaic array an he objecie i o upply power o he gri a uniy power facor. In he following queion he ripple ha i caue by he wiching can be neglece. (5) 4. Define he moulaion raio m a an gie he relaion beween V o, m a an V, where V o i he rm funamenal of he oupu olage. () 4. Skech a phaor iagram wih he phaor of e, an i. Calculae he moulaion raio m a uch ha kw i upplie o he gri a uniy power facor (pf) in e. () 4.3 Wha i he lowe alue of V where we can ill upply kw o he gri wih linear inuoial moulaion? 7/46 8/46

5 Summary of anwer o exam Elecronic Power Conerion 5 January 3. See problem.5 in Mohan book. V V D. he highe D will be ue a he lowe alue of V or V 43.V. o guaranee coninuou conucion for all loa an upply coniion: / >.3. (oe: when /.3 an V 5.8V, he uy raio can be reuce o.48 o obain 5V) 3. For a gien iconinuou moe will fir occur a ligh loa (P loa 5W) an D.5, which i alo he maximum allowable alue of D. ( V V ) A bounary (ee eq. 7.5 in Mohan): I loa, min on wih I loa,min 3A. he ripple min increae wih on, bu alo wih V, o check boh combinaion: V 43.V an D.5: min, 4.7µH V 5.8V an D.48 min, 4.93µH, o ue 4.93µH 4. m conrol a ; V m a V ri 4. I /3 4.35A V jωi j.5 V V E jωi V V m a V V V.5 ϕ arcan( ) arcan( ) 5.9 eg ( c leaing o e a ) E 3 a V V 36. V m 5, min a,max ().3 Gie a formula for V an P a a funcion of I, where V i he aerage of an P i he aerage of he oupu power p. (3) PROBEM In a ep-own conerer, conier all componen o be ieal. he oupu olage V i hel a 5V by conrolling he wich uy raio D. (5). Calculae he minimum inucance o keep he conerer operaing in a coninuou conucion moe uner all coniion V 4V, P 5W an f 5 khz. (5). Calculae he peak-o-peak ripple V if V.6 V an I ma, where f khz, mh an C47 µf. (4) PROBEM 3 In Fig. a a ingle-line iagram of a hree-phae gri i hown wih a uiliy ource (ahe block) an a power elecronic loa. he power elecronic loa repreen a large inurial hree-phae ioe recifier a hown in Fig. b. Exam Elecronic Power Conerion March (3) PROBEM Gien i a ingle-phae recifier a hown in Fig. 9 wih mh he upply olage i inuoial wih ampliue 3 V an frequency 5Hz. Fig. 9 (). Skech, an i a a funcion of ime for I A. (). Calculae he commuaion angle u a a funcion of I. Fig. he uiliy ource (ahe block) i hree phae gri wih inuoial olage ource in erie wih inucance. he nominal rm alue of he phae olage i V 3V (per phae) an i frequency i f 6 Hz. he loa of he recifier i repreene by a conan DC curren ource I. () 3. Skech i a an calculae he harmonic of he inpu curren ia a a funcion of I, where. Aume for hi queion only. () 3. Calculae he aerage recifier oupu olage V a a funcion of V, an I. For he nex queion 3mH. () 3.3 Decribe qualiaiely he effec of inea of on he inpu curren harmonic. Conier boh high-orer harmonic an low-orer harmonic. Accoring o local regulaion of he uiliy company, he maximum allowable fifh harmonic olage a PCC caue by any loa houl be le han 3% of he nominal olage ( 3 mh). 9/46 /46

6 You may aume for hi cae ha he rm alue of he fifh harmonic of he recifier curren i equal o I 5.5 I () 3.4 Calculae he maximum allowable alue of I. Summary of anwer o exam Elecronic Power Conerion March. See book fig 5.4. See book eq. 5-3 o See book eq. 5-9, 5- an 5-3 o he bounary i fir reache a he highe inpu olage (lowe D). A V 4V: D.5. D( V V ) See book fig. 7-6, eq. 7-5, 7-8 an 7-9; µ H f I. D( D) V See book 7- o 7-5 ; V 8Cf. mv 3. See book fig. 5-33, eq. 5-6 o See book eq oe ha he phae olage V S i gien an ha V 3 V S ; V 538-,8 I 3.3 All harmonic are more or le reuce, incluing he funamenal. Higher harmonic are aenuae more han he lower harmonic, becaue eep ege on curren are remoe. ower harmonic are only lighly affece. 3.4 See book eq. 8-; 5 ω.5 I <. 3 V or I < 8. 3A Exam Elecronic Power Conerion January 3 (5) PROBEM Conier he reiie wiching circui hown in Fig. wih V 3 V, f khz an R75 Ohm. he wich urn-on ime i on 5 n an he wich urn-off ime i off 3 n. Aume linear olage an curren wiching characeriic. R Fig. (b). (). Skech he waeform of i, i, S an. (). Calculae by approximaion he ime inan where relean olage inerecion occur in he kech. ().3 Calculae he aerage of curren i. (ifficul if θf i unknown) he olage ource V i replace by a large capacior in parallel wih a reior a hown in Fig. b. he capacior i o large ha he olage i conan (R loa C >> m). he alue of he loa reior houl be choen uch ha V 5V again. Aume R. (5).4 Calculae he alue of R loa. (5).5 o wha limi will V rie if R loa i graually increae. (35) PROBEM 3 For a cerain applicaion a c olage ha o be eppe up from a ource olage V o a higher loa olage V. he olage acro he loa houl be fairly conan. he circui a hown in Fig. 3 i aailable, howeer he circui i no complee ye an a lea an inucor ha o be ae. he inicae erminal are no necearily he erminal ha hae o be ue a inpu an oupu. i Source V i A V oa Fig. (). Skech he waeform of an i an he power p ha i iipae in he wich a a funcion of ime. (). Calculae an plo he aerage wiching power lo a a funcion of frequency in he frequency range 5 khz- khz. (5).3 Calculae he efficiency η of he power ranfer from he ource V o he loa R a khz an a uy raio D.5. (4) PROBEM he ingle-phae recifier circui a hown in Fig. a i connece o a inuoial upply olage wih V V a 6 Hz. Furher mh an V 5 V. Fig. 3 he following i pecifie: V 5V, V 4V, f khz an C C 47µF an P 5W. Inucor 6µH. () 3. Show by mean of a circui iagram how he eire conerion can be obaine by uing he circui from Fig. 3. Show where he inucor houl be ae an inclue he connecion o ource an loa. Decribe horly how he circui i operae. (5) 3. Expre V o in he uy raio D an V. Define an calculae he uy raio D. () 3.3 Calculae he aerage inucor curren. Skech for 4µH he erminal curren i A he ioe curren i D an he olage A or A () 3.4 Can i A hae zero croing? Calculae he minimum alue of he inucor ha will aure ha i A oe no hae zero croing for he gien coniion. /46 /46

7 Summary of anwer o exam Elecronic Power Conerion January 3. oe ha he waeform for he wiching of reiie loa are quie ifferen from he waeform for clampe inucie loa (Mohan Fig -6). Wih he circui from he exam an i are alway relae by: V V IR. During urn on: i I / on an V (-/ on ) ; p () i V I / on (-/ on ). Similar uring urn off. ia A D D i o R i P 9 W i A on off 3.33 A i P E on f khz on 3 V. Diipae energy uring urn on: I E on i V I, 3 on 3*4*/6*5 on 6 on n (J) Similar for urn off. V I Aerage power: P ( on off ) / * (53) * -9 * f. 6 PR P P DV I P η. 985 P P DV I 6. See Mohan Fig 5-6. V θ b arcin.83 ra ; θ p π θ b.57 ra V ϑ f f f θb ω.3 i ( V inω V ) ω ( 69.7 coω ω) ( V V inω) ω co θ.884 θ. 46 θ f.53 ra π θ 5 ; I i ω b π.64a ω ω.4 I.64A ; R V /I 56.8 Ohm.5 V,max 69.7 V 3. he circui houl be configure uch ha a boo conerer i obaine (Mohan ecion 7-4 an Fig 7-33). an D are he acie componen. oe ha he erminal pair {A,O} canno be ue a inpu a he noe canno aborb a DC curren. he capacior C, C- are in parallel o he loa a i require in a boo conerer. When i O he curren hrough increae an when i OFF he inucor curren i puhe in he oupu circui ia D. A V o 3. V V wih D on / where on i he on-ime of an /f ; D.375 D DS 3.3 I A 5/53.33A ; I 5/4.8A ; R5/.85 Ohm ; i A, pp V 4.7 A 3.4 I A can hae zero croing if i mall. In ha cae conuc uring he negaie par of I A. he coniion for no haing zero croing i imilar o he coniion for coninuou conucion DS DS moe wih up-conerer (ee Mohan eq. 7-8). min V V 4µH I A I A oe ha RC>>, o ha V i inee conan. Exam Elecronic Power Conerion June 3 () PROBEM A he erminal of a conerer he olage an curren are a hown in Fig. 4. u i δ δ A δ Fig. 4 he ampliue of he olage i 3 V. (5). Calculae he power a he erminal. (5). Calculae he rm alue of he curren i. (5).3 Define an calculae he power facor PF. (5).4 Define an calculae he Diorion Power Facor DPF. - A (4) PROBEM Gien i a full-brige c-c conerer (H-brige) wih c moor loa a hown (Fig. 5). he moor i moelle by he erie connecion of R a, a an e a. For conrol of he wiche o 3/46 4/46

8 calle bipolar olage wiching i applie, where he conrol ignal are obaine by comparing a conrol ignal conrol wih a riangular waeform ri. () 3. Show by mean of a circui iagram how he eire conerion can be obaine by uing he circui from Fig. 6. Show where he inucor houl be ae an inclue he connecion o ource an loa. Decribe horly how he circui i operae. (5) 3.3 Expre V o in he uy raio D an V. Define an calculae he uy raio D. () 3.4 Calculae he aerage inucor curren. Skech for 6µH he erminal curren i A, he ioe curren i D an he olage A or A () 3.5 Can i A hae zero croing? Calculae he minimum alue of he inucor ha will aure ha i A oe no hae zero croing for he gien coniion. Summary of anwer o exam Elecronic Power Conerion June 3 Fig. 5 he following i gien: m ( i he perio of riangular waeform) R a. Ohm a mh V 3V e a V For he calculaion of he curren waeform, he reiance R a can be neglece. (5). Expre he aerage alue of o in V an conrol / ˆ ri. (5). Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I A a e a V. (5).3 Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I -A a e a V. (5).4 Skech he (), i () an he ource curren i for I A a e a V. ().5 Inicae in hi kech which wiche are conucing a wha ime. (4) PROBEM 3 For a cerain applicaion a c olage ha o be eppe up from a ource olage V o a higher loa olage V. he olage acro he loa houl be fairly conan. he circui a hown in Fig. 6 i aailable, howeer he circui i no complee ye an a lea an inucor ha o be ae. he inicae erminal are no necearily he erminal ha hae o be ue a inpu an oupu. Source V i i A V oa 3. P ui coπδ 7 coπδ W π. I rm i A.3 P PF U rm I rm π coπδ.9 coπδ.4 I, rm π DPF. 9 (oe ha for a inuoial olage: PFDPF. coϕ) I rm. conrol V V ri. o ( ) R ( ) ( ) ea ( ) Afer aeraging: V I R - e a conrol conrol Or: 3 R o:. 43 ; (D.7) 3 conrol ri ^ V ri ri / o(a -B V o i o (A, B ) conrol V V i o Io ( A, B ) I A I ri ( V e ) D a poiie peak curren: 63/ 4.6 A negaie peak curren: - 63/ -.6 A 6 Fig. 6 he following i pecifie: V 5V, V 4V, f khz an C C 47µF an P 5W. Inucor 6µH. (5) 3. Wha ype of conerer woul you preferably ue for hi conerion? (DA D, D ), B ) (D A B i 5/46 6/46

9 .4 ike Mohan fig. 7-9e 3. Boo conerer (Mohan ecion 7-4 an Fig 7-33). 3. he circui houl be configure uch ha a boo conerer i obaine (Mohan ecion 7-4 an Fig 7-33). an D are he acie componen. oe ha he erminal pair {A,O} canno be ue a inpu a he noe canno aborb a DC curren. he capacior C, C- are in parallel o he loa a i require in a boo conerer. When i O he curren hrough increae an when i OFF he inucor curren i puhe in he oupu circui ia D. ia i A i A on off A D D i o 3.33 A V o 3.3 V V wih D on / where on i he on-ime of an /f ; D.375 D 3.4 I A 5/53.33A ; I 5/4.8A ; R5/.85 Ohm ; peak-o-peak alue of he DS curren: i A, pp V 4.7 A 3.5 I A can hae zero croing if i mall. In ha cae conuc uring he negaie par of I A. he coniion for no haing zero croing i imilar o he coniion for coninuou conucion DS DS moe wih up-conerer (ee Mohan eq. 7-8). min V V Iˆ I 4µH A A oe ha RC>>, o ha V i inee conan. Exam Elecronic Power Conerion 9 January 4 (elecion) R (3) PROBEM For a forwar conerer a ranformer i neee. For he ranformer wo pair of o-calle E- core wih ienical hape are aailable (Fig. 7a), bu hey are mae from ifferen maerial. he baic BH-loop of he repecie maerial are hown in Fig. 7b an c for he cae of maximum exciaion of he maerial. Only a par of he BH-loop will be ue. Boh he primary, he econary an he auxiliary emagneiing wining of he forwar conerer are woun aroun he cenral leg. he urn raio beween primary an emagneiaion wining i. Fig. 7 a: ouble E-core; b: normal BH-loop; c: fla BH-loop. For iagram a an b: B-cale:. per iiion; H-cale: 5 A/m per iiion he E-core hae he following aa: A c cm Core cro ecion of cenral leg l e 4 cm Equialen lengh of magneic pah of fiel line Oher relean maerial properie (B, B r, H c ) can be rea from he figure. For he forwar conerer he following i gien: f 75 khz (wiching frequency) V 3 V (upply olage) (). Wha ype of maerial (normal loop or fla loop) i mo uie for he applicaion an why. Wha o you chooe a he operaing range in he loop (more anwer are poible)? (). Calculae he minimum number of urn,min for he elece ype of maerial o aoi auraion. Rea relean aa from Fig. 7. Skech he flux eniy B a a funcion of ime for D.5 an inicae minimum an maximum alue. ().3 Eimae he magneizing inucance m for,min (% accuracy i ufficien here)..4 Calculae he peak alue of he curren in he auxiliary wining. (4) PROBEM 3 Gien i a ingle-phae H brige c/ac olage ource conerer ha i connece o a ingle phae inucion moor wih couner emf e, a hown in Fig. 8. i i Fig. 8 he oupu olage of he inerer i obaine by bipolar olage wiching imilar o Fig. 9. o obain a low iorion linear moulaion i applie (no oermoulaion; m a <). 7/46 8/46

10 Fig. 9 (acual wiching frequency i much higher han hown here) Gien i furher: V 35V (DC link olage) ω (funamenal frequency of o an e ) ω,nom π6 ra/ (nominal alue of ω ) V,nom 3 V (nominal rm alue of funamenal of ) e (couner emf which i inuoial) 3 mh (inucance of machine) f 7.5 khz (frequency of riangular carrier ri ) C mf (capaciance of inpu filer) A nominal pee an nominal olage he inpu power of he loae rie i kw a co φ.8 () 3. Skech equialen circui moel o calculae he funamenal componen of he curren i an he ripple componen of he curren i. Calculae an upper limi for he peak-o-peak curren ripple in i o ha i caue by he wiching. () 3. Calculae he rm alue of he funamenal of i when he machine run a rae pee an rae power. Skech a phaor iagram wih he phaor of e, an i. (5) 3.3 Define he moulaion raio m a an gie he relaion beween V o, m a an V, where V o i he rm alue of he funamenal of he oupu olage. Calculae he moulaion raio m a uch ha he machine run a nominal pee an nominal olage. () 3.4 Skech he inananeou power p () ha i ranmie by he funamenal curren i an olage (oe: inω in( ω φ) coφ co( ω φ) ) (5) 3.5 Calculae he low-frequency (< khz) peak-o-peak olage ripple V, auming ha he curren i i conan. Summary of anwer o exam Elecronic Power Conerion 9 January 4. For a gien core he ieal loop woul be ery eep wih a large ifference beween B an B r. On one han a eep loop reul in a mall magneiing curren reuling in le loe, alhough in general he loe caue by he magneiing curren i mall in comparion o he ranforme loa curren (/ i). On he oher han he number of urn epen on he aailable flux wing. For a forwar conerer he flux wing i B -B r becaue of he unipolar exciaion. he anwer i ha he fla core i preferre becaue of he much larger flux wing, reuling i le urn an le loe. Selec B max.4 o hae ome margin o auraion. B r. D DV. B Ac or f A ( B B ) 75 (.4.) c r.3 µ A c m (hi follow from eq. 3-6 an 3-8) where µ i obaine from he BH-loop: µ le B/H.5/.5; m 8 mh.4.4 Becaue 3, he peak alue of he curren in he auxiliary wining i equal o he peak alue of he magneiing curren. D ˆ 3.5 i m V 7.mA 3 3 c 75 8 Anoher way: ˆ ˆ ˆ ˆ Hl.5.4 Hl im or i m 7.4mA See Mohan fig. 8-8 b an c. Becaue he circui i linear, he funamenal an ripple componen can be reae eparaely: ripple an i i iripple. he (inuoial) funamenal componen follow from he phaor equaion: V E V E jω I. he ripple follow from: i, ripple( ), ripple( ς ) ς. he large ripple occur uring he zero croing of () (ee fig 8-9b). hen he ampliue of he ripple olage i V / an he uraion of he pule i /. he maximum ampliue of he curren equal: V / 35 / i.38a 3 3 f P VI coφ or I 5.43 A. (o ω I 6.4V). oe ha φ i he angle beween V o an I o. he phaor iagram i like fig m Io conrol a ; V m a V ri or m a p ( ) V inω I in( ω φ ) VI coφ VI co(ω φ). 3.5 For low frequencie: ( ) ( ) wih p ( ) V i (See Mohan fig 8-3) o V I VI i ( ) co co( ) co( φ ω φ ω 36.9 ) V V φ Vo Eo V Ampliue of (inuoial) low frequency ( Hz) curren ripple: V I iˆ A ripple V iˆ ; Vˆ ripple 3.57 ripple 4. 73V, 3 C ; ω π Peak-o-peak alue: V Vˆ, ripple 9. 46V 9/46 /46

11 Exam Elecronic Power Conerion 9 June 4 (4) PROBEM A forwar conerer wih emagneiaion wining a hown in Fig. i o be eigne wih he following pecificaion: V 5V an 3V V 5V (regulae) f khz P loa W µf C µf he conerer houl be able o operae a boh inpu olage. he conerer houl operae in coninuou conucion moe for all operaional coniion. he wining 3 ere complee emagneizaion of he magneizaion inucance of he core. he conerer houl be eigne o operae wih a maximum uy raio D max of.7. Aume all componen o be ieal excep for he preence of he magneiing inucance of he ranformer. I I 3 I x -- Fig. a Fig. b (). Skech, i an i a a funcion of ime. (5). Calculae he peak alue if i. (5).3 Calculae he aerage curren I an he aerage oupu power P. ().4 Wha i he range of V for iconinuou conucion of i. (3) PROBEM 3 Gien i a bi-irecional ingle-phae c/ac conerer ha i connece o a gri wih olage e, a hown in Fig.. o 6 o gri o 6 V o Fig. (). Calculae he wining raio 3 / uch ha D max <.7 (5). Calculae / if hi urn raio i eire o be a mall a poible. ().3 Skech x, i an for V 5V. Inicae alue in he kech of x an i. (5).4 Calculae he maximum olage ha i applie o he wich for any of he operaional coniion. ().5 Calculae he peak-o-peak alue of he ripple in he oupu olage for V 3V (3) PROBEM Gien i a ingle-phae recifier, a hown in Fig. a, ha i connece o a block hape upply olage (Fig. b) an a conan loa olage V : Gien i: V 4V V 3V (ampliue of a hown in Fig. b) f 5Hz (frequency of ) mh Fig. he oupu olage of he inerer, ha conain a full-brige olage ource conerer, i obaine by bipolar olage wiching a hown in Fig. 3. Only linear moulaion i applie (no oermoulaion). Fig. 3 (oe: acual wiching frequency i much higher han hown here) Gien i furher: V 35V /46 /46

12 e E inω wih E 3V an ω π5 5 mh f 7.5 khz (frequency of riangular carrier ri ) he inerer i fe from a phooolaic array an he objecie i o upply power o he gri a uniy power facor. In he following queion he ripple ha i caue by he wiching can be neglece. (5) 3. Skech equialen circui moel o calculae he funamenal componen of he curren i an he ripple componen of he curren i. (5) 3. Define he moulaion raio m a an gie he relaion beween V o, m a an V, where V o i he rm funamenal of he oupu olage. () 3.3 Calculae he moulaion raio m a uch ha kw i upplie o he gri a uniy power facor (pf) in e. Skech he aociae phaor iagram wih he phaor of e, an i. (5) 3.4 Wha i he lowe alue of V where we can ill upply kw o he gri wih linear inuoial moulaion? (5) 3.5 Calculae an upper limi for he peak-o-peak curren ripple in i o ha i caue by he wiching. Summary of anwer o exam Elecronic Power Conerion 9 June 4. V V 3 D upfluxownflux o D ( D) o.43 3 D. Vo 5 V DV wih D max.7 for V 5V; >.476 V,minDmax 5.7 oe: if you combine D max wih V max, (leaing o /.38) han he conerer canno be operae a 5V..3 See Mohan..4 Vw V V 3 (.43) 998V 3.5 Q i ( D) V Vpp wih i C C Vpp ( D) (.35).4; V 6 3 pp mv V 8 C 8 3. See Mohan fig 8-8 b an c. conrol 3. ma ; V m a V ri 3.3 I /3 4.35A V jωi j.5 V V E jωi V V m a V V V.5 ϕ arcan( ) arcan( ) 5.9 eg ( c leaing o e a ) E 3 a V V 36. V m 5, min a,max 3.5 he ripple follow from: i, ripple (), ripple( ς ) ς. he large ripple occur uring he zero croing of () (ee fig 8-9b). hen he ampliue of he ripple olage i V / an he uraion of he pule i /: / V / 35/ i V.78A 3 3 f Exam Elecronic Power Conerion January 5 () PROBEM Gien i a wich-moe DC-power upply, where he oupu olage o houl be regulae cloe o i nominal alue. For ha purpoe a negaie-feeback conrol yem i ue o reuce he effec of ariaion in he inpu olage an he loa.. V i i 6,67m I ( V V ) A peak o 5 /.3 I i o A; P V i V i kw 36.4 i,up i,own ; i houl be zero again before / o ( V V) 6.67m< V 3.33m or V > V (5). Skech a block iagram of he yem, an ecribe horly he funcion of he block. Inicae all relean ariable in he iagram. (). Decribe horly he ep ha are neee o obain he mall-ignal ranfer funcion () of he yem. Here i he oupu olage an i he uy () raio. oe ha you are no expece o calculae he ranfer funcion. (5).3 Obain an aerage ae-pace ecripion of an up-conerer (reul of ep ). (4) PROBEM Gien i a flyback conerer a hown in Fig. 4b. he loa reiance R may ary an he oupu olage V houl be kep conan by aaping he uy raio D. he conerer may operae boh in coninuou an iconinuou conucion moe. 3/46 4/46

13 i i ac moor - x R Fig. 4 Flyback conerer he following i gien: f khz (wiching frequency) R.5.. Ohm (range of loa reiance) m µh (magneizing inucance, een from econary ie) V 3V (upply olage) V 5V (require oupu olage) C µf (oupu filer capacior) / 8 (urn raio) (). Derie he olage ranfer funcion V /V in coninuou conucion moe (incomplee emagneiaion moe) a a funcion of he uy raio D an oher relean circui parameer. (). Wha i he range of he loa curren I for coninuou conucion moe (V 5V)? (Hin: Conier he coure of he curren i a he bounary of coninuou conucion moe an calculae î ). (5).3 Calculae he require uy raio D when I A (o R.5 Ohm). (V 5V). (5).4 Calculae he require uy raio D when I.5 A. (V 5V). (Hin: ˆ P f mi an P f ˆ m i ) ().5 Skech i, i, x an a a funcion of ime for R.5 Ohm an inicae relean alue. (4) PROBEM Gien i a full-brige c-ac conerer (H-brige) wih a ingle phae ac moor a hown (Fig. 5). he moor i moelle by he erie connecion of an inucance a an he couner emf e a. For conrol of he wiche o-calle bipolar olage wiching i applie, where he O/OFF ignal for he wiche are obaine by comparing a inuoial conrol ignal conrol wih a riangular waeform ri (Fig. 6). inear moulaion i applie o obain a low iorion (no oermoulaion; m a <). Fig. 5 Fig. 6 (oe: he acual wiching frequency i much higher han hown here) Gien i furher: V 35V (DC link olage) ω (funamenal frequency of he moor olage o an of he couner emf e ) ω,nom π6 ra/ (nominal alue of he funamenal frequency of he moor) V,nom 3 V (nominal rm alue of funamenal of ) e (couner emf which i inuoial) 3 mh (inucance of moor) f 7.5 khz (frequency of riangular carrier ri ) A nominal pee an nominal olage he inpu power of he loae rie i kw a co φ.8 (5) 3. Skech he equialen circui moel o calculae he funamenal componen of he curren i an he ripple componen of he curren i. (5) 3. During wha par of he oupu olage oe he maximum curren ripple occur? Calculae an upper limi for he peak-o-peak curren ripple in i ha i caue by he wiching. (5) 3.3 Calculae he rm alue of he funamenal of i when he machine run a rae pee an rae power. () 3.4 Define he moulaion raio m a an gie he relaion beween V o, m a an V, where V o i he rm alue of he funamenal of he oupu olage. Calculae he 5/46 6/46

14 moulaion raio m a uch ha he machine run a nominal pee an nominal olage. (5) 3.5 Skech he inananeou power p () ha i ranmie by he funamenal curren i an olage (oe: inω in( ω φ) coφ co( ω φ) ) (5) 3.6 Calculae he low-frequency (< khz) peak-o-peak olage ripple V, auming ha he curren i i conan. (5) 3.7 Wha will change in he anwer o problem 3. o 3.6 if unipolar wiching i ue inea of bipolar wiching? Summary of anwer o exam Elecronic Power Conerion January 5. See Mohan ecion -5. or imilar rawing. he block on he righ ie i he power age wih inpu uy raio an upply olage V. he PWM block coner he conrol ignal c o he ignal. he lef block i he conrol block ha compare he meaure oupu olage wih ome reference an generae he conrol ignal c.. See Mohan ecion -5- Sep Obain ae-pace equaion for ubequen ubcycle Sep : Aeraging; Obain aerage ecripion of he circui by aeraging he imeweighe ae marice: Sep 3: inearizaion; eparae he ariable in eay ae componen an mall perurburaion Sep 4 aplace ranformaion o -omain.3 Sae ariable are i an C i V i or i C i V for < < D c C c c RC R. A he bounary of coninuou an iconinuou conucion moe he anwer from. V i ali, o D.57 V V oe ha a he bounary he curren i i a riangle ha ju become zero a. From i when he wich i off : ˆ V i, bounary ( D).75A m iˆ From coure of i a he bounary i follow: I, Bounary ( D).3A So he region for coninuou conucion moe i I >.3A ( or R <.6 Ohm).3 he loa curren i larger han.3 A, o we hae coninuou conucion moe, o D.57.4 he loa curren i maller han.3a, o we hae iconinuou conucion moe P f ˆ mi or ˆ P 5.5 ˆ i 5A an ˆ i i A f m 8 Alo ˆ V i ˆ i D or m.65.8m D.66 wih m V 3 µ m m 8 µ H.8mH oe: i i more raighforwar o calculae î irecly from P f ˆ m i..5 Duraion of i : iˆ m 5 µ Di. V 5 µ i c V C c C i R or i i i V c c C RC for D < < Aerage: i ( D) i i V c ( D) c C RC V D. Coninuou conucion moe: V D 3. See Mohan fig 8-8 b an c. 3. he large ripple occur uring he zero croing of () (ee fig 8-9b). hen he ampliue of he ripple olage i V an he uraion of he pule i /: / V 35 i V.78A 3 3 f P V I coϕ or I P 5.43A V coϕ 3.8 7/46 8/46

15 ˆ conrol V 3 ma ; V ma V or ma.93 ˆ ri V 35 p () () i() V inω I in( ω φ) VI coφ VI co( ω φ) co( ω φ) 5 co( ω φ) wih φ arcco.8 37 he waeform i a inu wih ouble frequency an aerage alue W, op alue 5V, boom alue 5V an lagging φ/ behin he olage. 3.6 For low frequencie: p () p () wih p() V i (See Mohan fig 8-3) o V I VI i ( ) co co( ) co( φ ω φ ω 36.9 ) V V Ampliue of (inuoial) low frequency ( Hz) curren ripple: ˆ VI iˆ iripple 3.57A; Vˆ ripple 3.57 ripple 4. 73V V 35, 3 C ; ω π Peak-o-peak alue: V Vˆ, ripple 9. 46V 3.7 Only he anwer o 3. will change. he ripple will a lea be hale becaue of he ouble hf-frequency in. Exam Elecronic Power Conerion 5 June 5 () PROBEM Gien i a imple circui wih a generic wich a hown in he figure a I 6A. (5). Skech he inananeou wiching lo a a funcion of ime. (). Calculae he wiching power lo a a funcion of he wiching frequency in a range 5 - khz, auming V 5V an I 6A. (5).3 Calculae an plo he oal loe a a funcion of he wiching frequency in a range 5 - khz in he wich when he on-ae olage i V on.5v a 6A an he uy raio of he wich i D.6 (aume (on) (off) ). () PROBEM A he erminal of a conerer he olage an curren are a hown in Fig. 8. Fig. 8 he ampliue of he olage i 3 V. (5). Calculae he power a he erminal. (5). Calculae he rm alue of he curren i. (5).3 Define an calculae he power facor PF. (5).4 Define an calculae he Diorion Power Facor DPF. u i δ δ (3) PROBEM 3 Gien i a ingle-phae recifier ha i connece o a upply olage an a baery a hown in Fig. 9a. he baery i repreene by a DC loa olage V. he olage ha a block-like hape (Fig. 9b) ha i prouce by ome HF inerer (no hown). he recifier i inene o charge he baery. Depening on he charging ae of he baery he olage V may ary. Gien i: V,nom 4V (nominal olage of V ) V 3V (ampliue of a hown in Fig. 9b) 3µ (perio of olage ) f / 33.3 khz (frequency of ) µh A δ - A Fig. 7 he aa hee of he wich pecifie he following wiching ime correponing o he linear wiching characeriic a hown in he figure. ri 8 n ; f 8 n ; r n ; fi n Furher: V 5V ; Fig. 9a Fig. b () 3. Skech an i a a funcion of ime an inicae relean alue for V V,nom. 9/46 3/46

16 (5) 3. Calculae he peak alue of i, he aerage curren I an he aerage oupu power P for V V,nom. () 3.3 Wha i he range of V for iconinuou conucion of i in a eay ae. (5) 3.4 Wha will happen if V i ecreae below he lower limi of hi range? (3) PROBEM 4 Gien i a full-brige c-c conerer (H-brige) wih c moor loa a hown (Fig. 3). he moor i moelle by he erie connecion of R a, a an e a. For conrol of he wiche o calle bipolar olage wiching i applie, where he conrol ignal are obaine by comparing a conrol ignal conrol wih a riangular waeform ri. P.3 PF coπδ.9 coπδ U rm I rm π I, rm π.4 DPF. 9 (oe ha for a inuoial olage: PFDPF. coϕ) I rm 3. Fig. 3 he following i gien: m ( i he perio of riangular waeform) R a. Ohm a mh V 3V e a V For he calculaion of he curren waeform, he reiance R a can be neglece. (5) 4. Expre he aerage alue of o in V an conrol / ˆ ri. (5) 4. Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I A a e a V. (5) 4.3 Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I -A a e a V. (5) 4.4 Skech he (), i () an he ource curren i for I A a e a V. Summary of anwer o exam Elecronic Power Conerion 5 June 5. See book of Mohan,. E lo,w / I o V ( ri f ) / I o V ( r fi ) /. I o V ( ri f r fi ) / (48n) 7 µj P lo,w f. E lo,w 7 f µw.3 P lo,on V on. I on on / V on. I on D W P lo,o f W 3. P ui coπδ 7 coπδ W π. I rm i A 3. ˆ V V i µ 3A µ (3 4) on m µ V V follow from a, ( V V)µ V µ.5µ V / iˆ ' ( µ ) 3.5 I a, i.5a 5 Becaue V i conan we can wrie: P V I, 4.5 3W a 3.3 he ime will increae when V ecreae, becaue in eay ae he aerage inucor olage i zero: a ( V ), V on V or on V V on he bounary for coninuou conucion i reache when 5m on µ V V 3 V. Range: V >V. oe : for V >3V here µ 5µ on i no curren flowing a all. 4. V V ˆ conrol ri 4. ( ) ( ) ( ) e ( ) o R a Afer aeraging: V I R - e a conrol conrol Or: 3 R o:. 43 ; (D.7) 3 conrol ri ri ri 3/46 3/46

17 ^ V ri / o(a -B V o i o conrol V V i o Io I A ( V e ) D 3 3 I.7 3 a poiie peak curren: 63/ 4.6 A negaie peak curren: - 63/ -.6 A 63 (5). Calculae he minimum number of urn,min for he elece ype of maerial o aoi auraion. Rea relean aa from Fig. 3. Skech he flux eniy B a a funcion of ime for D.5 an inicae minimum an maximum alue. ().3 Eimae he magneizing inucance m for,min (% accuracy i ufficien here). (5).4 Calculae he peak alue of he curren in he auxiliary wining. (4) PROBEM Gien i a forwar conerer a hown in Fig. 3 (A, B ) ( A, B ) (DA D, D ), B ) (D A B I x I 3 I i 4.4 ike Mohan fig. 7-9e -- w -- Exam Elecronic Power Conerion January 6 (3) PROBEM For a forwar conerer a ranformer i neee. For he ranformer wo pair of o-calle E- core wih ienical hape are aailable (Fig. 3a), bu hey are mae from ifferen maerial. he baic BH-loop of he repecie maerial are hown in Fig. 3b an c for he cae of maximum exciaion of he maerial. Only a par of he BH-loop will be ue. Boh he primary, he econary an he auxiliary emagneiing wining of he forwar conerer are woun aroun he cenral leg. he urn raio beween primary an emagneiaion wining i. Fig. 3 a: ouble E-core; b: normal BH-loop; c: fla BH-loop. For iagram a an b: B-cale:. per iiion; H-cale: 5 A/m per iiion he E-core hae he following aa: A c cm (Core cro ecion of cenral leg) l e 4 cm (Equialen lengh of magneic pah of fiel line) Oher relean maerial properie (B, B r, H c ) can be rea from he figure. For he forwar conerer he following i gien: f 75 khz (wiching frequency) V 3 V (upply olage) Fig. 3 Gien i: V 3 V (nominal inpu olage, howeer he acual olage i ariable) V 6 V (nominal oupu olage) f khz (wiching frequency) : 3 (urn raio) m 5 mh (magneiing inucance of ranformer, een from primary ie) 5 µh (oupu filer inucance) he wining 3 ere complee emagneiaion of he core. (5). When D.4 an V 3V, calculae he urn raio : o ge V 6V (5). Aume : ha he alue ha i calculae in.. Wha i he lowe inpu olage allowe if V i o be kep equal o 6 V? In he following, D.4, V 3V, V 6V an I A. (5).3 Calculae he olage oer he ranior uring he off. (5).4 Calculae he maximum alue w, i an he magneiing curren of he ranformer i m. (5).5 Calculae I for he bounary of iconinuou conucion moe. (5).6 Skech, w, i, i, i 3 an i m. (3) PROBEM 3 Gien i a ingle-phae recifier ha i connece o a upply olage an a baery a hown in Fig. 33a. he baery i repreene by a DC olage V. he olage ha a blocklike hape a hown in Fig. 33b an ha i prouce by ome HF inerer (no hown). he circui i inene o charge he baery. Depening on he ae-of-charge of he baery he olage V may ary. Gien i: V,nom 4V (nominal baery olage) V 3V (ampliue of a hown in(fig. 33b) 3µ (perio of olage ) f / 33.3 khz (frequency of ) µh (). Wha ype of maerial (normal loop or fla loop) i mo uie for he applicaion an why. Skech a ypical loop ha applie in normal operaion of he forwar conerer. 33/46 34/46

18 .4 V,max 6V;.5 ˆ D V i 8mA ' m 3 m 5 6 ( DV ) iˆ I.36A m ( DV ) Ipp,.7A. oa curren on he bounary: I, B.36 I A Fig. 33a Fig. b () 3. Skech an i a a funcion of ime an inicae relean alue for V V,nom. () 3. Calculae he peak alue of i, he aerage curren I an he aerage oupu power P for V V,nom. () 3.3 Wha i he range of V for iconinuou conucion of i in a eay ae Summary of anwer o exam Elecronic Power Conerion January 6. For a gien core he ieal loop woul be ery eep wih a large ifference beween B an B r. On one han a eep loop reul in a mall magneiing curren reuling in le loe, alhough in general he loe caue by he magneiing curren i mall in comparion o he ranforme loa curren ( / i ). On he oher han he number of urn epen on he aailable flux wing. For a forwar conerer he flux wing i B -B r becaue of he unipolar exciaion. he anwer i ha he fla core i preferre becaue of he much larger flux wing, reuling i le urn an le loe. Selec B max.4 o hae ome margin o auraion. B r. D DV. B Ac or f A ( B B ) 75 (.4.).3 µ A c r c m (hi follow from eq. 3-6 an 3-8) where µ (µ µ r ) i obaine from he BH- le loop: µ B/H.5/.5; m 8 mh.4.4 Becaue 3, he peak alue of he curren in he auxiliary wining i equal o he peak alue of he magneiing curren. D ˆ 3.5 i m V 7.mA 3 3 c 75 8 Anoher way: ˆ ˆ ˆ ˆ Hl.5.4 Hl im or i m 7.4mA 67 DV.4 3. V D V V 6 V 6. V,min 4V. (oe: : 3 D max.5) Dmax.5.3 w V V 3 3 6V 3 3. µ ˆ V V (3 4) i 3 on A µ m µ H V V follow from a, ( V V)µ V µ.5µ V / iˆ ' ( µ ) 3.5 I a, i.5a 5 Becaue V i conan we can wrie: P V I, 4.5 3W a 3.3 he ime will inceae when V ecreae, becaue in eay ae he aerage inucor olage i zero: a ( V ), V on V or on V V on he bounary for coninuou conucion i reache when 5m µ V V 3 V. Range for iconinuou conucion: µ 5µ on V >V. oe: for V >3V here i no curren flowing a all. 3.4 When V <V he curren i coninuou. A inan k. / he curren will no be reuce o zero ye. Ju afer hee inan he curren i oppoe by he olage V V unil he curren ha a zero croing, afer which i i oppoe by V -V. 35/46 36/46

19 Exam Elecronic Power Conerion June 6 () PROBEM Conier he reiie wiching circui hown in Fig. 35 wih V 3 V, f khz an R75 Ohm. he wich urn-on ime i on 5 n an he wich urn-off ime i off 3 n. Aume linear olage an curren wiching characeriic. For a cerain applicaion a c olage ha o be eppe up from a ource olage V o a higher loa olage V. he olage acro he loa houl be fairly conan. he half-brige circui a hown in Fig. 36 i aailable, howeer he circui i no complee ye an a lea an inucor ha o be ae. On he oher han ome oher componen in he circui are uperfluou. he inicae erminal are no necearily he erminal ha hae o be ue a inpu an oupu. i Source V i A V oa Fig. 34 (5). Skech he waeform of an i an he power p ha i iipae in he wich a a funcion of ime. (). Calculae an plo he aerage wiching power lo a a funcion of frequency in he frequency range 5 khz- khz. (5).3 Calculae he efficiency η of he power ranfer from he ource V o he loa R a khz an a uy raio D.5. (4) PROBEM Gien i a forwar conerer a hown in Fig. 35 Fig. 35 Gien i: V 3 V (nominal inpu olage, howeer he acual olage i ariable) V 6 V (nominal oupu olage) f khz (wiching frequency) : 3 (urn raio) m 5 mh (magneiing inucance of ranformer, een from primary ie) 5 µh (oupu filer inucance) he wining 3 ere complee emagneiaion of he core. (5). When D.4 an V 3V, calculae he urn raio : o ge V 6V (5). Aume : ha he alue ha i calculae in.. Wha i he lowe inpu olage allowe if V i o be kep equal o 6 V? In he following, D.4, V 3V, V 6V an I A. (5).3 Calculae he olage oer he ranior uring he off. (5).4 Calculae he maximum alue w, i an i m. (5).5 Calculae I for he bounary of iconinuou conucion moe. (5).6 Skech x, w, i, i, i 3 an i m. (4) PROBEM 3 I I 3 x -- w -- I 37/46 Fig. 36 he following i pecifie: V 5V, V 4V, f khz an C C 47µF an P 5W. Inucor 6µH. (5) 3. Wha ype of conerer woul you preferably ue for hi conerion? () 3. Show by mean of a circui iagram how he eire conerion can be obaine by uing he circui from Fig. 36. Show where he inucor houl be ae an inclue he connecion o ource an loa. Decribe horly how he circui i operae. (5) 3.3 Expre V o in he uy raio D an V. Define an calculae he uy raio D. () 3.4 Calculae he aerage inucor curren. Skech for 6µH he erminal curren i A, he ioe curren i D an he olage A or A. () 3.5 Can i A hae zero croing? Calculae he minimum alue of he inucor ha guaranee ha, for he gien coniion, he inucor curren i alway poiie. Summary of anwer o exam Elecronic Power Conerion June 6.4 oe ha he waeform for he wiching of reiie loa are quie ifferen from he waeform for clampe inucie loa (Mohan Fig -6). Wih he circui from he exam an i are alway relae by: V ir During urn on: i I / on an V (-/ on ) ; p () i V I / on (-/ on ). Similar uring urn off. P E on i f khz on on 3 VI.5 Diipae energy uring urn on: Eon, i VI 3 on 6 on 3*4*/6*5 on n (J) Similar for urn off. VI ( on off ) Aerage power: P. (53). -9. f. 6 38/46 P 9 W

20 PR P P DV I P 6 9 η.985 P P DV I 6 DV.4 3. V D V V 6 V 6. V,min 4V. (oe: : 3 D max.5) Dmax.5.3 w V V 3 3 6V V,max 6V; ˆ DV.4 3 i' m 8mA 3 m 5 6 ˆ ( DV ) im I.36A 6 5 ( DV ) I.5 Ipp,.7A. oa curren on he bounary: I, B.36A 3. Boo conerer (Mohan ecion 7-4 an Fig 7-33). 3. he circui houl be configure uch ha a boo conerer i obaine (Mohan ecion 7-4 an Fig 7-33). an D are he acie componen. oe ha he erminal pair {A,O} canno be ue a inpu a he noe canno aborb a DC curren. he capacior C, C- are in parallel o he loa a i require in a boo conerer. When i O he curren hrough increae an when i OFF he inucor curren i puhe in he oupu circui ia D. ia i A i A on off A D D i o 3.33 A V o R 3.3 V V wih D on / where on i he on-ime of an /f ; D.375 D 3.4 I A 5/53.33A ; I 5/4.8A ; R5/.85 Ohm ; peak-o-peak alue of he DS curren: iapp, V a b 4.7 A 3.5 I A can hae zero croing if i mall. In ha cae conuc uring he negaie par of I A. he coniion for no haing zero croing i imilar o he coniion for coninuou conucion 6 DS DS moe wih up-conerer (ee Mohan eq. 7-8). min V V 5 Iˆ I A 3.33 A 4µH oe ha RC>>, o ha V i inee conan uring a wiching perio. Combine exam E365-D an E49 ; 9 January 7 () PROBEM Gien i a imple circui wih a generic wich a hown in Fig. 37. Fig. 37 he aa hee of he wich pecifie he following wiching ime correponing o he linear wiching characeriic a hown in he figure. ri 8 n ; f 8 n ; r n ; fi n Furher: V 5V ; I 6A. (5). Skech he inananeou wiching lo a a funcion of ime. (). Calculae he wiching power lo a a funcion of he wiching frequency in a range 5 - khz, auming V 5V an I 6A. (5).3 Calculae an plo he oal loe a a funcion of he wiching frequency in a range 5 - khz in he wich when he on-ae olage i V on.5v a 6A an he uy raio of he wich i D.6 (aume (on) (off) ). (4) PROBEM Gien i a ingle-phae recifier ha i connece o a upply olage an a baery a hown in Fig. 38a. he baery i repreene by a DC loa olage V. he olage ha a block-like hape (Fig. 38b) ha i prouce by ome HF inerer (no hown). he recifier i inene o charge he baery. Depening on he charging ae of he baery he olage V may ary. Gien i: V,nom 4V (nominal olage of V ) V 3V (ampliue of a hown in Fig. 38b) 3µ (perio of olage ) f / 33.3 khz (frequency of ) µh 39/46 4/46

21 Summary of anwer o exam E365-D an E49 7 Jan 7. See book of Mohan,. E lo,w / I o V ( ri f ) / I o V ( r fi ) /. I o V ( ri f r fi ) / (48n) 7 µj P lo,w f. E lo,w 7 f µw.3 P lo,on V on. I on on / V on. I on D W P lo,o f W. Fig. 38a Fig. b (). Skech an i a a funcion of ime an inicae relean alue for V V,nom. (). Calculae he peak alue of i, he aerage curren I an he aerage oupu power P for V V,nom. ().3 Wha i he range of V for iconinuou conucion of i in a eay ae. ().4 Wha will happen if V i ecreae below he lower limi of hi range? (4) PROBEM 3 Gien i a full-brige c-c conerer (H-brige) wih c moor loa a hown (Fig. 39). he moor i moelle by he erie connecion of R a, a an e a. For conrol of he wiche o calle bipolar olage wiching i applie, where he conrol ignal are obaine by comparing a conrol ignal conrol wih a riangular waeform ri. Fig. 39 he following i gien: m ( i he perio of riangular waeform) R a. Ohm a mh V 3V e a V For he calculaion of he curren waeform, he reiance R a can be neglece. () 3. Expre he aerage alue of o in V an conrol / ˆ ri. () 3. Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I A a e a V. (5) 3.3 Calculae he require raio of conrol / ˆ ri o mainain an aerage oupu curren of I -A a e a V. (5) 3.4 Skech he (), i () an he upply curren i () for I A a e a V.. µ ˆ V V (3 4) i 3 on A µ m µ H V V follow from a, ( V V)µ V µ.5µ V / iˆ ' ( µ ) 3.5 I a, i.5a 5 Becaue V i conan we can wrie: P V I, 4.5 3W a.3 he ime will inceae when V ecreae, becaue in eay ae he aerage inucor olage i zero: a ( V ), V on V or on V V on he bounary for coninuou conucion i reache when 5m µ V V 3 V. Range for iconinuou conucion: µ 5µ on V >V. oe: for V >3V here i no curren flowing a all..4 When V <V he curren i coninuou. A inan k. / he curren will no be reuce o zero ye. Ju afer hee inan he curren i oppoe by he olage V V unil he curren ha a zero croing, afer which i i oppoe by V -V. 3. conrol V V ˆ ri 3. o ( ) R ( ) ( ) ea ( ) Afer aeraging: V I R - e a 4/46 4/46

22 conrol conrol Or: 3 R o:. 43 ; (D.7) 3 conrol ri ri ri ^ V ri / o( A -B V o i o (A, B ) conrol V (DA D, D ), B ) (D A B i 3.4 ike Mohan fig. 7-9e V i o Io ( A, B ) Exam E49 an E365-D on June 7 I A ( V e ) D 3 3 I.7 3 a poiie peak curren: 63/ 4.6 A negaie peak curren: - 63/ -.6 A () PROBEM Conier he reiie wiching circui hown in Fig. wih V 3 V, f khz an R75 Ohm. he wich urn-on ime i on 5 n an he wich urn-off ime i off 3 n. Aume linear olage an curren wiching characeriic. 63 Fig. 4 Gien i: V 35 V (inpu olage range) V 5 V (nominal oupu olage) f 5 khz (wiching frequency) : 3 : (urn raio) m 5 mh (magneiing inucance of ranformer, een from primary ie) µh (oupu filer inucance) P...3 W (oupu power Boh he upply olage an he loa power P may ary beween he inicae alue. he wining 3 ere complee emagneiaion of he core. oe he unuual wining raio : 3. (5). Calculae he urn raio : o ge V 5V a a nominal inpu olage V 35V an D.4 (5). D houl be arie o mainain a conan oupu olage a ariable inpu olage. Wha i he maximum allowable alue of D o guaranee complee emagneiaion of he ranformer? ().3 Wha i he lowe allowable inpu olage V o aoi ranformer auraion? Check wheher he conrol range of D correpon o he inpu olage range. In he following, D.4, V 35V, V 5V an I 5A. (5).4 Calculae he maximum alue w, i an i m. (5).5 Calculae I for he bounary of iconinuou conucion moe. Check hi reul wih he gien minimum loa curren. ().6 Skech, w, i, i, i 3 an i m. Fig. 4 (4) PROBEM 3 In Fig. a a ingle-line iagram a power yem wih power elecronic loa i hown. he uiliy power ource (ahe block) i repreene by a inuoial olage ource in erie wih an inucance in each phae. he nominal rm alue of he phae-o-neural olage i V 3V an i funamenal frequency i f 6 Hz. he power elecronic loa i a large inurial hree-phae ioe recifier a hown in Fig. b. he loa of he recifier i repreene by a conan DC curren ource I. (). Skech he waeform of an i an he power p ha i iipae in he wich a a funcion of ime. (5). Calculae an plo he aerage wiching power lo a a funcion of frequency in he frequency range 5 khz- khz. (5).3 Calculae he efficiency η of he power ranfer from he ource V o he loa R a khz an a uy raio D.5. (4) PROBEM Gien i a forwar conerer a hown in Fig. 3 Fig. 4 43/46 44/46