CHAPTER 7 THREE-PHASE THREE-LEG THREE-LEVEL NEUTRAL POINT CLAMPED RECTIFIER. 7.1 Introduction
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1 CAPTE 7 TEE-PASE TEE-EG TEE-EE NEUTA PONT CAMPED ECTFE 7. ntrouton Mny nhrnt nft of multll onrtr h l to thr nr ntrt mongt nutry utlt. At rnt, th two mot ommonly u multll toolog r th thr-ll nutrl-ont-lm NPC [4-6] n toolog. Multll onrtr h n ttrtng ttnton for mum-oltg n hgh-owr lton. Th ntg of th NPC onrtr r mrong th wform ulty n rung oltg tr on th owr. Th torlm onrtr n ltrnt trutur to otn th multll wform on th trmnl. Th oltg tr on th on owr ontrn y lmng tor. Sr onnton of full rg onrtr w n ltrnt mtho to h multll wform u of thr moulrty n mlty of ontrol. owr, f th oltg ll r mor thn thr ll, th ontrol trtgy omlt to mlmnt. Mot thr-h rtfr u o rg rut n ul torg tor ut t h oor owr ftor n hgh ulton ln urrnt. P tor n nutor h n u to form C fltr for lmntng urrnt hrmon n mrong th ytm owr ftor. Th rw of th two-ll onrtr r th hgh oltg tr ro th, lrg omonnt n 9
2 hn u to th nhrnt ntg of th thr-ll NPC onrtr wr roo to rw th nuol ln urrnt n h wth mn oltg [57-65]. Ojt of th Control Shm: To otn ontnt DC u oltg. To ln th tor oltg. Brtonl owr flow. ow hrmon torton of ln urrnt. To rw nuol urrnt wth unty owr ftor. To gnrt thr oltg ll on th AC trmnl oltg,,. 7. Crut Confgurton Th roo rut onfgurton on th thr-h, thr-lg nutrl ont lm onrtr hown n Fgur 7.. Th onrtr ont of oot nutor on th, to fltr th nut hrmon urrnt n h nuol urrnt wform. th r ulnt rtor. Twl wthng wth rtng / n x lmng o wth th rtng of / r u. Th o r u to lm th -oltg. Th onrtr lo ont of two tor on th trmnl.,, rrnt th h oltg of th thr-h AC ytm. n Fgur 7. S, S, S n, S n r th four wthng for h A n mlrly h B n C h four wthng., D, D, D, D D r th x lmng o., r th nut rtn D, 9
3 n th oot nutor, th lo rtn onnt ro th two tor. C,C r th outut DC tor to hol th outut oltg.,, r th thr nut uly oltg,,, r th nut h urrnt, n, r th thr outut no urrnt whh hrg th tor., S S S S S S D D D C O A D D D D C S n S n S n S n S n S n Fgur 7.: Crut onfgurton of Thr-Ph Thr-ll Thr-g tfr. 94
4 7. Mo of Orton From Chtr, n th orton of th multll onrtr omnton of wth r u to otn t wform, whh lo to nuol wform. Th followng notton r u for rtn omnton of S S S S S S 7. S S, S S whr,,. n n of thr-ll onrtr thr wll thr l ortng mo for h h of th onrtr hown n Fgur Conr Ph A xml. Orton mo S S : Fgur 7. how th orton mo. n th mo of orton, th trmnl oltg ul to / umng tht. Th oot nutor oltg / < umng th oltg ro ro th rtor to nglgl. Thrfor th ln urrnt r n th o urrnt lo t { / / }. Th ln urrnt wll hrg or hrg th u tor C f th ytm oltg ot or ngt, rtly. 95
5 C o o O A D C Fgur 7.: Ortonl mo of th rtfr: Orton Mo. Orton mo S S : Fgur 7. how th orton mo. Th trmnl oltg ul to zro umng tht o. Th oot nutor oltg. Thrfor th ln urrnt nr or r urng th ot or ngt yl of th nut uly oltg, rtly. Th ln urrnt wll not hrg or hrg th u tor n th mo of orton. C o O A D C Fgur 7.: Ortonl mo of th rtfr: Orton Mo. 96
6 Orton mo S S : Fgur 7.4 how th orton mo. n th mo of orton, th trmnl oltg ul to oltg o /. Th oot nutor / >. Thrfor th ln urrnt nr n th urrnt lo / t { } /. Th ln urrnt wll hrg or hrg th u tor f th ytm oltg ot or ngt hlf yl of th uly C oltg, rtly. C o O A D C Fgur 7.4: Ortonl mo of th rtfr: Mo orton. 97
7 7.4 Mthmtl Mol of th Crut Alyng rhoff oltg lw for th nut, th uly oltg n wrttn th um of th oltg ro ro th nut mn n 7. o 7. o. 7.4 o Th ot no oltg r t ont whn th ur two wthng omnton our.., whn S, S r on. n th fft oltg tht r t ont n yl. Smlrly th othr two no oltg r whn th othr wthng omnton our.., n. n th oltg gn y th um of th thr fft oltg o 7.5 o o 7.6 o. 7.7 From Chtr 4, mlr to th thr-ll nrtr, th wthng ontrnt to o th hortng of th outut tor;.., t ny ntnt of tm only on omnton of houl on. Th l to th onton n E Conr h ; 98
8 . By uttutng th o uton n outut oltg E. 7.7 o whr th oltg twn th nutrl of th uly to th ommon ont of th two tor. Smlrly for th othr two h o 7. o 7. o. 7. By uttutng th xron n E nto E n unr ln onton, [ ]. From Chtr 4, th nul wthng funton r otn,,
9 Th wthng funton of th n roxmt ung th Fourr r. Sn th wthng ul r ro funton of tm n thy rt ftr ry yl of moulton gnl n hn th ro gnl n rrnt ung th Fourr r um of omonnt n n n on tm ryng trm. M 7.8 M 7.9 M 7. whr M, M, M r ll th moulton gnl. By utng th wthng funton n E. 7.8 M. n th moulton gnl for th to M. 7. Smlrly for th othr, th moulton gnl otn M n M. 7. From E. 7. n 7. M M. 7. whr th moulton gnl. Suttutng th moulton gnl n E
10 Th no urrnt r gn y Wrtng th rhoff Currnt w C t no ;.., th urrnt flowng through th tor C ul to th ffrn of th no urrnt n th lo urrnt. Th urrnt flowng through th tor gn y th C t no. C C 7. [ C ] Molng of th Conrtr Wrtng E n th mtrx form. Trnformng th o uton to ynhronou rfrn frm y ung trnformton mtrx θ T, whr
11 o θ o θ β o θ β T θ n θ n θ β n θ β π β θ t θ ; θ - ntl rfrn ngl. Th uton r otn whr C [ ] 7.5 [ ] 7.6 C [ o θ o θ β o θ ] β [ n θ n θ β n θ ] β [ ]. Smlrly [ o θ o θ β o θ ] β [ n θ n θ β n θ ] β
12 [ ]. Aumng α α ; β β ;. By uttutng th o xron n E α β α β [ ] C α [ β ]. C From th ty tt nly ung E. 7.9 n 7.4 t n hown tht α β. Suttutng th o onton n E [ ] C [ ]. C
13 7.6 Sty-Stt Anly Th t n rt owr for thr-h ytm gn y P 7.45 Q For unty owr ftor, th rt owr zro. Th onton for unty owr otn y utng th rt owr to zro. n ynhronou rfrn frm, hoo ntl rfrn ngl uh tht n. By uttutng th oltg n E. 7.46, Q. But n hn. Th ty tt nly on for unty owr ftor onton;.., th -x omonnt of th nut urrnt zro n lo n th ty tt nly th rt trm r m zro. n y lyng th o onton to E , th ty tt uton r otn α
14 β. 7.5 By utng th o two uton, t or tht β α. By uttutng th o onton n olng for unnown,, [ ] [ ] 6 8, 6 8 / / [ ] [ ] 6 8 6, / / [ ] [ ] 6 8, 6 8 / /. 5
15 Fgur 7.5: Plot of -x moulton gnt -x moulton for rou oltg for unty owr ftor orton. 6
16 Fgur 7.6: Plot of moulton nx gnt of th h urrnt for rou oltg for unty owr ftor orton. Fgur 7.5 n 7.6 r otn ung th ty tt nly. Th lot r otn y ung th xron for,,. By ryng th oltg from 7 to 7 n h ont of oltg nrmnt, th xron r lut n lott. Fgur 7.5 how th lot of rton of th -x moulton nx gnt th -x moulton nx. Fgur 7.6 how th lot of th moulton nx gnt th of th h urrnt. Th lot r for unty owr ftor orton. 7
17 7.7 On-loo Smulton of th tfr From th ty-tt nly, hoo rtulr lu of moulton nx from th lot for, nx, th onrtr mult.. Ung th rut rmtr gn low n ung th moulton 7.7. Crut Prmtr nut ln rtn nut ln nutn. Ω m nut Suly oltg 8o t 8o t 8 o t Outut -tn C C µ F o rtn 75Ω n th multon, frtly th moulton gnl r trnform to rfrn frm n th moulton gnl r omr wth th two trngl to otn th wthng; th PWM hm xln n Chtr n ung th uton mnton o, th moulton hm mlmnt for unty owr ftor onton n for two ffrnt lu of th oltg. 8
18 , S Fgur 7.7: On loo multon of th rtfr: Ortng Conton :. n-ln oltg nut h oltg n nut h urrnt howng th unty owr ftor orton, Outut Ctor oltg,. 9
19 n-n oltg Ph oltg & Ph Currnt Ur Ctor oltg owr Ctor oltg S Fgur 7.8: On-loo multon of th rtfr: Ortng Conton :. n-ln oltg nut h oltg n nut h urrnt howng th unty owr ftor orton, Outut Ctor oltg,.
20 Fgur 7.7 n Fgur 7.8 how th on loo multon rult for unty owr ftor orton for two ortng onton. Fgur 7.7 how th multon rult for n ortng oltg of. Fgur 7.7 how th ln-to-ln oltg n t how th t n th oltg wform. Fgur 7.7 how th unty owr ftor orton. Fgur 7.7 n how th two tor oltg n n n tht th nutrl ont oltg ry low, n th rng of. Fgur 7.8 g th multon rult for othr ortng onton of. 7.8 Control of Thr-g Thr Ph Thr-l tfr Th mn ojt of ny ontrol hm to rgult th tul untty wth th rfrn untty. Th roo ontrol hm ntn to h th -ln oltg ontnt, n to otn unty owr ftor t th nut. Any untty of th ytm n t th outut of th ontrollr ro rlton to how th ontroll untty fft th rl tn th outut n gn, ut th uully tou jo. n th ontrol of th rtfr two mtho h n roo. Both th ontrol hm r ntn for th m ojt ut th roh n th ontrollr u r ffrnt n th two Control Shm A n th rtulr hm, th nly n th ontrol on n rfrn frm;.., ll th untt uh th oltg, urrnt, t., r trnform to
21 nothr rfrn frm o to m th tm ryng untt to tm nrnt untt. Controllng th tm nrnt untt ml n n h ung P, PD, or PD ontrollr. n th followng ontrol hm ontrol trutur ng u,.., th outut of on ontrollr u to lult th rfrn of th othr ontrollr. n th tm ron of th ontrollr om mn rtron n gnng th ontrol rmtr. From th nly, E. 7.4 n wrttn. Aumng σ σ. 7.5 Smlrly. Aumng σ σ. 7.5 Ang th two tor uton E. 7.4 n E [ ] [ ] C o o o o. Unr ln onton. Wrtng E. 7.5 n mor mlf form o [ ] 7.5 C. 7.54
22 From E th xron for moulton gnl n n otn σ 7.55 σ Suttutng th xron n th tor uton C σ σ [ ]. C σ σ Aumng C δ. Now rrngng th trm n th o uton n mlfyng [ ] [ ] σ σ δ whr [ ] P. n [ P σ σ ] δ 7.57 whr P th rur owr to mt th lo. For unty owr ftor orton, rt owr zro,.., Q ; Th t n rt owr for thr-h ln ytm P 7.58 Q By olng P n for n Q
23 [ P Q ] 7.6 [ P Q ] 7.6 whr P Q. Fgur 7.9 how th hmt of th ontrol hm A. Th oltg ontrol ll th outr ontrol loo n th urrnt ontrollr r th nnr ontrol loo. n th tm ron of th urrnt ontrollr h to ftr thn tht th oltg ontrollr y t lt tm. n th ontrol hm th ur of th tul oltg omr wth th rfrn oltg. Th rror gnl through P ontrollr who trutur xln n th nxt ton. Th outut of th ontrollr um σ. Ung xron 7.6 n 7.6 th rfrn urrnt n n lult. Th rfrn urrnt r omr wth th tul urrnt. Th rror r through th two urrnt ontrollr n. Th outut of th ontrollr r um σ n σ. Ung xron 7.55 n 7.56 th moulton gnl n otn. Th gnl n trnform to th rfrn frm to otn th tul moulton gnl. Th rrr PWM u to otn th gtng gnl for th xln n Chtr. Th moulton gnl whn omr wth th two trngl, th wthng funton for th n otn. 4
24 - P,Q - Clulton Of Moulton Sgnl - Fgur 7.9 Blo grm of th ontrol hm A / Thrll rtfr / 5
25 7.8. Controllr Strutur n Dgn t lr from th nly tht th ontrolll untt r gnl. To ontrol untty ml P, PD, or PD n u. n th rnt P ontrol trutur ng u oltg Controllr From Fgur 7. C C C. C Aumng th trutur of th ontrollr th o trnfr funton n y uttutng th n to - σ Fgur 7.: Strutur of th oltg ontrollr. 6
26 C C. On mtho of otnng th ontrollr rmtr y omrng th nomntor of th trnfr funton wth Buttr-Worth olynoml. Th orr of th olynoml m th orr of th ytm. Th Buttr-worth mtho lot th Egn lu of th trnfr funton unformly n th lft hlf of th -ln, on rl of ru, wth t ntr t th orgn. n n th rnt th trnfr funton of on orr ytm n hn th nomntor omr wth th on orr Buttrworth olynoml. Th on orr Buttr Worth olynoml gn y. 7.6 n y omrng th offnt of m xonntl C n C Currnt Controllr follow: Ung mlr nly th trnfr funton of th -x urrnt n otn 7
27 - σ Fgur 7.: Strutur of th urrnt ontrollr Agn th ontrollr rmtr n otn y omrng th nomntor wth th Buttrworth olynoml n A xln o th of th ontrollr n on. of urrnt ontrollr houl t lt tn tm grtr thn tht of th oltg ontrollr. Th - x urrnt ontrollr h th mlr n of trutur. Th trnfr funton of th -x urrnt
28 , Fgur 7.: Smulton rult of ontrol hm A: tfr mo of orton wth lo rtn of 75Ω. : n-ln oltg nut h oltg n nut h urrnt howng th unty owr ftor orton, Outut Ctor oltg,. 9
29 , 5 o hng Tm Fgur 7.: Moulton gnl urng th trnton from rtfr mo of orton to nrtr mo of orton. Ph moulton gnl Ph moulton gnl n Ph moulton gnl. Plot howng hng n lo.., from th rtfr mo of orton to nrtr mo of orton t t.6.
30 , Fgur 7.4: Smulton rult of ontrol hm A: nrtr mo of orton,, lo hng t tm t.6. n-ln oltg nut h oltg n nut h urrnt howng th unty owr ftor orton, Outut Ctor oltg,.
31 , Fgur 7.5: Control hm A: frn oltg n th tul oltg. &, Fgur 7.6: Control hm A: frn -x urrnt n th tul -x urrnt
32 , Fgur 7.7: Control hm A: frn -x urrnt n th tul -x urrnt. Fgur 7. to 7.7 how th multon rult for ontrol hm A. Fgur 7. how th ty tt lot ftr th tor oltg h ttl. Th rfrn tor oltg n th rnt tn n hn th ty tt lu of th tor houl h. Fgur 7. how th ln-ln oltg ; Fgur 7. how th unty owr ftor orton; Fgur 7. n how th two tor oltg n n n tht th oltg ttl to th rfrn oltg. Fgur 7. how th hng of lo;.., hng of orton from rtfr to nrtr mo. Fgur 7. how th moulton gnl urng th hng of lo. Fgur 7.4 how th ty tt lot n th nrtr mo of orton. Th lo hng from 75 Ω to Ω. Ngt lo nt nrtr mo of orton;..,
33 th owr f to th uly. A n from th rult, th ontrol hm wor fftly n n th nrtr mo of orton t h th tor oltg ontrol n lo th unty owr ftor orton n n th nrtr mo. Fgur 7.5 how th trng of th tor oltg. t n n tht thr r om u of th lo hng n lo ntlly t too om tm to ttl to th rfrn oltg. Fgur 7.6 how th trng of th -x urrnt. For unty owr ftor orton -x omonnt h to zro n t lr from th lot tht -x urrnt tr wll. Fgur 7.7 how th trng t omonnt of th urrnt or th - x urrnt Control Shm B n th rou ontrol hm A, th nly n rfrn frm;.., ll th untt r trnform to ynhronou rfrn frm o to m th untt tm nrnt. Th ontrol trutur ml n of th untt, ut whn t om to mlmntton t om omlx. Bu ll th untt houl trnform to ynhronou rfrn frm n ftr tht gn th moulton gnl h to trnform to rfrn. n nw ontrol hm ng formult ung th nturl rl;.., ontrol th tul gnl wthout ny trnformton. n th ontrol om ml
34 For ln, By uttutng n E To lmnt th trm, utrt E. 7.67, 7.69 n E. 7.67, Solng for n. rrngng th trm n mlfyng. Aumng n σ. σ. 7.7 Smlrly σ. 7.7 From th o E. 7.7 n 7.7, olng for, σ σ 7.74 σ σ
35 Th tor uton C Agn uttutng for C By uttutng th xron for, from E σ σ σ σ C By mlfyng th uton n wrtng n trm of th h oltg C σ 4 σ σ 4 σ For unty owr ftor orton n. n uttutng th o onton n E n mlfyng C 6 [ 6 σ σ ]. Aumng C σ n olng for lu of σ 6 whr [ 6 σ σ ] n th rfrn frm urrnt n lult. 6
36 - Clulton Of Clulton Of frn Currnt - Clulton Of Moulton Sgnl - Fgur 7.8: Blo grm of th ontrol hm B Thr-l tfr 7
37 Fgur 7.8 how th hmt of th ontrol hm B. Smlr to ontrol hm A, hm B lo h th oltg ontrol ll th outr ontrol loo n th urrnt ontrollr th nnr ontrol loo. n th tm ron of th urrnt ontrollr h to ftr thn th oltg ontrollr t lt y tm. n th ontrol hm th ur of th tul oltg omr wth th rfrn oltg. Th rror gnl through P ontrollr who trutur xln n th nxt ton. Th outut of th ontrollr um σ. Ung xron 7.8 th lu of lult n thry th rfrn urrnt n n lult. Th rfrn urrnt r omr wth th tul urrnt. Th rror r through th two urrnt ontrollr n. Th outut of th ontrollr um σ n σ. Ung xron 7.74 n 7.75 th moulton gnl n otn Controllr Strutur n Dgn t lr tht th ontrolll untt r gnl n of oltg n gnl n of urrnt. n n th ontrol of untty ml P, PD, or PD nnot u. n nw ontrollr ll nturl rfrn frm ontrollr ng u. 8
38 Controllr G S AC - θ j x n n j y θ j x θ n j y θ n Fgur 7.9: Strutur of th ontrollr Nturl frn Frm Controllr Th lo grm of th ontrollr outln n Fgur 7.9. n th hm urrnt r ng ontroll n hn th nrtr urrnt r u th f gnl. Th urrnt, r tn from th nrtr n r omr wth th rfrn urrnt gnl,. Th rror of th urrnt r frtly trnform to ot n ngt ynhronou rfrn frm;.., θ x n lo θ. n th outut of th trnformton x θ x 7.67 n θ x 7.68 θ x whr θ x t θ x; - ntl rfrn ngl. 9
39 Aftr trnformton th outut gnl r untt. Th gnl r through th ontrollr who trnfr funton gn y n n. n th outut of th rgultor 7.69 θ x n n θ x. 7.7 Now th gnl r gn trnform to th rfrn frm wth om ly ngl ;..,, θ θ θ θ x y x y t t. n th rultng gnl from th trnformton lo r. 7.7 θ θ j y x. 7.7 θ θ j n n y x t θ θ y x ; thn 7.7 j j n n. 7.7 Now t th um of th two gnl, n to gt th outut of th ontrollr, whh ul to. ] [ j j j j n n By mlfyng th o uton th trnfr funton of th ytm otn j j j j n n. 7.74
40 n th rtulr um th ontrollr to P ontrollr who trnfr funton gn. n n n 7.75 n, y uttutng th o trnfr funton n 7.67 n mlfyng,. ] [ ] [ ] [ ] [ n n n n j j j j j j j j For mlty, f n n ;, thn [ ]. n o ] o [ o n o o o Smlr nly n on for th h B urrnt n trnfr funton otn [ ]. n o ] o [ o n o o o n gnng th rmtr of th ontrollr, omr th nomntor of th trnfr funton wth Buttrworth Polynoml. Th Buttr-worth olynoml for th thr orr follow: w w w n y omrng th nomntor of th trnfr funton wth o olynoml o 7.77
41 o 7.78 o n n y olng th o thr uton for th thr unnown,, n y ryng th ly ngl th ontrollr rmtr n lult oltg Controllr Th oltg ontrol trutur m u n ontrol hm A. n th trnfr funton of th ontrollr follow:. C Th on orr Buttr Worth olynoml gn y. 7.8 n y omrng th offnt of m xonntl C n C σ Fgur 7.: Strutur of th oltg ontrollr
42 n th lu n on th lu of whh otn from th urrnt ontrollr. Th lu of th oltg ontrollr h to t lt tm lr thn tht of th urrnt ontrollr o to m th ron tm of th oltg ontrollr lowr thn tht of th urrnt ontrollr. Fgur 7.: rton of th ontrol rmtr of th urrnt ontrollr wth th rton of th ly ngl.,,.
43 Fgur 7. how th rton of th ontrol rmtr of th urrnt n th oltg ontrollr wth th rton of th ly ngl. Th ly ngl r from / to / n th xron,, otn y olng th xron r lut n lott gnt th ly ngl. Aftr gttng from th urrnt ontrollr th oltg ontrol rmtr r otn ung xron Smulton ult Fgur 7. to 7.4 how th multon rult for ontrol hm B. A n from th lot tht n th ontrol hm B wor fftly. En hm B mult for oth th rtfr n nrtr mo of orton. Th rfrn tor oltg n th rnt tn n hn th ty tt lu of th tor houl h. Fgur 7. how th ty tt lot ftr th tor oltg h ttl n th rtfr mo of orton.., th owr ng f to th lo from th our. Fgur 7. llutrt th moulton gnl urng th rtfr mo of orton. Fgur 7. n how th tor oltg n t n n tht th tor oltg h ttl to th rfrn lu of h wth rl of.7. Fgur 7. how th ln-ln oltg n how th unty owr ftor onton. Aftr th tor h ttl n whn th ytm n ty tt, th fftn of th ontrollr h y ortng th rtfr n th rgnrt mo.., th owr now f to th our from th lo for xml, n of motor whn th motor run n th rr rton. Th hng m t tm t.. Fgur 7. how th ynm of th ytm urng th trnton. Fgur 7. 4
44 how th moulton gnl, th tor oltg n n th tor oltg r ttl to th rfrn oltg. Fgur 7. th ln-to-ln oltg n gn th unty owr ftor onton ng mntn n n th rgnrt mo. n th rult how th lty n th fftn of th ontrol hm.,,, Tm Fgur 7.: Smulton rult of ontrol hm B: tfr mo of orton wth lo rtn of 75Ω. Moulton gnl ur tor oltg ottom tor oltg n-ln our oltg, nut h oltg n our h urrnt. 5
45 ,,, Fgur 7.: Smulton rult of ontrol hm B: nrtr mo of rgnrt orton, lo hng t tm t. Moulton gnl,, ur tor oltg ottom tor oltg n-ln oltg, h oltg n h urrnt. 6
46 , Fgur 7.4: Trng of th h urrnt. frn h urrnt n th tul h urrnt. 7
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