Int ern at i onal  Journ al of  P ower E le ctr on i cs a n d  Drive  S ystem   (I J PE D S )   Vo l.   11 ,  No.   4 ,  Decem be r 202 0 , p p.   1670 ~ 1685   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v11.i 4 . pp 1670 - 1685       1670       Journ al h om e page :  http: // ij pe ds .i aescore.c om   Fundam ental   ele ments   of   constan t   volt/ hertz   ind uction   m oto r   dr i ves   bas ed   on   dSPACE   DS1104   contr oller       Siti   Nur syuh ada   M ah s ah ir u n 1 ,   Nik   R umzi   Nik   I dris 2 ,   Z ulki fli   Md.   Yusof 3 ,   Tole   Su tikno 4     1,3 Facul ty   of   Ma nufa ct ur ing   &   M ec ha troni c   Eng in ee ring   T ec hnolo gy,   Univer si ti   Mala ysi a   Pahan g,   Mala ysia   2 Pow er   El e ct ron i cs   &   Driv es   Res ea rch   Group,   Sc hool   of   Elec tr ica l   Eng ine er ing,   Univer siti   T eknologi   Mal aysia ,   M al aysi a   4 Depa rtment   of   El e ct ri ca l   Eng eeneri ng,   Univer si t as   Ahmad   D ahl a n,   Yogyak art a ,   I ndonesia   4 Em bedd ed   Sys t em   and   Pow er   E le c troni cs   R ese a rch   Group   ( ESP ERG),   Yogyak ar ta ,   Indone si a       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   Ja n   1 7 ,   20 20   Re vised   Ju l   18 ,   20 20   Accepte d   Aug   27 ,   20 20       An   induc t ion   mo tor   (IM)   h as   be e n   the   workhors e   of   the   industry   f or   decade s.   It   is   due   to   its   robustness,   sim ple   construction ,   r equi ring   l ess   ma intenan ce   and   ch ea p .   One   of   th e   most   wi del y   adopt ed   IM   drive   cont rol   sche m es   for   industri al   appl i c at ions   is   th e   op en - loop   consta n t   V/Hz .   In   thi s   pap er,   th e   im porta n t   elem e nts   of   an   open - loop   consta nt   V/Hz   driv es   ar e   pr ese nt ed.   The se   in cl ud e   t he   funda m ental   concept   of   a   consta nt   V/H z   sche me,   th e   volt ag e   source   i nver te r   (VS I)   an d   its   modu la t ion   sche m es.   T ec h nique s   th at   are   com mon ly   u sed   to   solve   prob le ms   of   low - spe ed   oper at ion   and   rotor   spe ed   reg ulation   a re   brie fly   d esc rib e d.   Simul at ions   using   MA TL AB/S im uli nk   pac kag e   ar e   use d   to   hel p   in   illus tra ti ng   the se   fun dam en ta l   concep ts.   Final ly ,   simpl e   la bor at or y - sca le   exp eri m e nts   are   condu cte d   to   im pl ement   t he   const ant   V/Hz   cont rol   sc hem e   on   a   ¼   hp   induc ti on   mot or .   The   consta n t   V/Hz   cont ro l   is   im p le m ent ed   using   th e   DS 1104   cont ro ller   boar d   with   th e   C   code s   aut om at i ca l ly   g ene ra te d   from   t he   Simu li nk   m odel .   A   cl oser   look   at   th e   cur ren t   wave for m   when   f ref =25   Hz   and   12   Hz   and   its   r espe c t ive   Fouri er   ana lysis   are   pre sente d.   Th e   r esult s   show   th at   t he   high - f req uen cy   ha rmoni c   cont en ts   aro und   the   sw itching   fre quenc y   can   be   o bserve d   for   both   ca s es ,   and   t he   vo ltage   wave form   pre s en ts   more   spik e   noises   in   c onstrast   to     cur ren t   wave for m .   Ke yw or d s :   Con sta nt   v olt /h ert z   Ind uction   m otor   dr ive s     Sp ace   vecto r   modu la ti on   V/ Hz   d rive   Vo lt age   s ource   inv e rter     This   is   an   open   acc ess   arti cl e   un der   the   CC   BY - SA   l ic ense .     Corres pond in g   Aut h or :   Sit i   Nursyu hada   M a hs a hir un ,   Faculty   of   M a nufactu rin g   &   M ec hatronic   E ng i neer i ng   Tec hnolog y   Un i ver sit i   M al aysia   Pa ha ng     26600   Pe kan,   Paha ng,   M al ay sia     Emai l:   ct _nur s yuha da@ymail .co m       1.   INTROD U CTION   Inver te r   based   inducti on   m oto r   (IM )   dr i ves   sy ste m   has   be en   widely   us e d   in   the   i ndus t ry   re placi ng   the   c onve ntio na l   direct - on - line   ( D OL),   t he   s ta r - delta   (Y - )   an d   oth er s   sta rter   meth ods   [1 – 4]   as   well   as   their   gear   inte gr at io n   ( gearb ox   tra ns missi on   s ys t em)   [5 – 7]   f or   var ia ble   s pee d   dri ve   ( VSD ) .   Fig ur e   1   sho ws   a   simple   il lustra ti on   of   t he   c onve ntio nal   ve r su s   powe r   el e ct ronics   in ver t er   IM   dr i v es.   This   te ch nolo gy   has   rap i dly   gro wn   since   the   era   of   powe r   el ect r onic s   wa s   born   in   the   mid   20 th   centu ry   unti l   nowa da ys   [8, 9] .   M a ny   eng i neer s   in   the   man uf act ur i ng   sect ors   a re   f or ce d   to   famil ia rize   an d   hav e   to   deci de   wh e ther   or   not   to   mer ge   the   te ch no l ogy   into   t heir   rea di ly   est ablishe d   conve ntion al   s ys te ms.   T he   m ai n   ad va ntage   of   t his   te ch nology   is   energ y   e ff ic ie ncy   w hic h   tra ns la te d   to   t he   li fe   long   opera ti on al   c os t   [1 0] .   A par t   from   that,   this   te ch no l ogy   comes   with   i mp le me ntati on   cost   an d   e nginee rs   nee d   to   make   sure   it   is   hig hly   reli able,   r obust ,   and   mana geab le   un der   their   ci rcumst ances.     Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Fu ndament al e le men ts  of c onstan t v olt/ hertz  inducti on  mo t or   dr iv es  …   ( Siti  Nursyuh ada Ma hs ahir un)   1671     (a)       (b)     Figure   1.   Ba sic   blo c k   diag ram   of   3 - ph a se   IM   dri veline   (a)   with   sta rter   a nd   gearb ox   ( b)   wi th   in ver te r       Simi la r   to   oth e r   el ect r on ic   de vices,   po wer   el ect ronics   in ve r te r   ca n   ca us e   s ign ific a nt   dow ns ide   to   the   ov e rall   s ys te m   par ti cula rly   w he n   operate d   in   a   ha rs h   a nd   unpr e dicta ble   e nvir onment   in   a   facto r y   due   to   heat,   humidit y,   vi brat ion ,   E MI,   a nd   oth er s   [ 11] .   Of te n   ti mes,   man uf act ur i ng   en gin eer s   do   not   necessa rily   ha ve   su f fici ent   kn owle dge   of   IM   dr i ves   that   would   finall y   tra deoff   dow ntim e   cost   [ 12] .   G et ti ng   the   knowle dge   thr ough   prop e r   c ourses   ca n   be   ti me - c ons umi ng   w hile   se lf - s yn t hesizi ng   the   knowle dg e   thr ough   nu mer ou s   journals   rea ding   with   diff e re nt   sta nd a rds   a nd   te rminolo gy   c ou l d   be   ov e r w helmin g   [13] .     In   this   pap e r,   t he   f undame nta l   el ements   of   t he   i nverter - ba s ed   IM   dri ves   method,   namel y   t he   co ns ta nt   V/Hz,   is   prese nted.   T he   pr oble ms   associat e d   with   the   low - sp ee d   ope rati on   s peed   re gula ti on   a re   discuss ed   a nd   p ossi ble   so l ution s   a re   sug ges te d.   This   pap e r   is   organ iz e d   in   t he   fo ll ow i ng   ma nn e r.   In   Sect ion   2,   imp or ta nt   con ce pts   of   c onsta nt   V/Hz   c on t ro l   a nd   maj or   c omp on e nts   that   are   ty pica ll y   us e d   in   IM   industria l   dri ve s   are   pr ese nted   a nd   exp la ine d.   T hi s   sect io n   will   a lso   pr e sent   the   pro blems   a ssoc ia te d   wit h   a   c on sta nt   V/Hz   c on t ro l   scheme   at   low - s pee d   opera ti on .   Sect io n   3   prese nts   t he   sim ulati on   a nd   ex per ime nta l   meth odol ogy   w hile   Sect ion   4   disc usse s   the   simula ti on   a nd   ex pe rimental   res ults.   Finall y,   Sect io n   5   pr ese nts   t he   co nclusi on.       2.   IND UCT ION   MOT OR   DRI VES   IM   is   one   of   the   hi gh l y   r obus t ,   high   tor que - to - i ner ti a   rati o   and   high   ef fici ent   ty pe   of   m ot or   [ 14 ,   15] .   On   t op   of   t hat,   IM   is   al so   known   for   its   simp le   con str uctio n,   easy   to   maint ai n   an d   relat iv el y   chea per   in   pr ic e.   It   has   bee n   a ppli ed   in   nume r ou s   a ppli cat ion s   in   ho us eh ol d   a ppli ances   a nd   in   var i ou s   i ndus tria l   sect ors.   In   gen e ral,   there   are   two   ty pes   of   co ntr ol   methods   f or   IM   dri ves:   scal a r   c on t ro l   a nd   vec tor   c ontr ol.   For   high - performa nce   a pp li cat io ns ,   ve ct or   c on tr ol   te chn i qu e s   su c h   as   fiel d - or ie nt ed   co ntr ol   (FOC)   [ 16]   a nd   direct   tor qu e   c on t ro l   (D TC )   [ 17]   are   no rmall y   em pl oy e d.   T hose   ap plica ti on s   that   requirin g   high - performa nce   to rque   con t ro l   s uc h   as   industrial   CN C   machi nes,   el evato rs,   a nd   re centl y   in   el ect r ic   veh ic le s   [18 ] .   F or   low   to   m edium   performa nce   a pp li cat io ns ,   s uc h   as   fa n,   bl ow e r,   pum p   and   c omp ress or,   scal ar   c ontrol   te ch nique s   are     normall y   prefe rr e d   [19] .   The   most   po pula r   s cal ar   c ontr ol   te ch niqu es,   known   as   const ant   V/Hz   ( or   co ns ta nt   V/F) ,   is   t he   simplest   mean s   to   ac hieve   li near   c on t ro l   of   I M’s   t orq ue   a nd   s pee d   [ 20,   21] .   T his   c ontr ol   me cha nism   ens ur es   the   operati on   of   the   IM   at   its   r at ed   flu x,   t hu s   pr e ve nts   the   r ot or   co re   ma gne ti zat ion   reachi ng   its   sat urat io n   an d   run   in   its   hyste resis   lo op.   T his   is   acc ompli sh ed   by   mai ntainin g   t he   rati o   betwee n   t he   ai r - gap   vo lt age   a nd   the   fr e qu e nc y   co nst ant   at   al l   sp eeds.   T he   op e n - l oop   ve rsion   of   this   c on t rol   scheme   is   the   mo st   wi dely   us ed   con t ro l   te ch niq ue   in   in dust rial   dri ves   due   to   its   sim plici ty,   c os t   eff ect ive ness   and   reli abili ty.   T he   impleme ntati on   of   a   c onsta nt   V/Hz   sc hem e   does   not   re quire   a   hi gh - pe rformance   pro cesso r,   an d   wi th   t he   op e n - lo op   op e r at ion ,   a   hi gh   pr eci sion   s peed   s ens or   is   not   ne eded.   The   pe rformance   of   t he   op e n - l oop   c onsta nt   V/Hz   dr i ves,   howe ve r,   deteri or at es   at   low - s peed   re gion   be cause   the   te rmi nal   volt age   no   longer   a ppr oximat es   the   bac k - EMF   due   to   the   si gnific ant   vo lt ag e   dro p   acr os s   t he   sta tor   impe dan ce ,   he nce   mainta inin g   c onsta nt   V/Hz   will   not   exactl y   resu lt   a   co ns ta nt   ai r - ga p   flu x.     A   t yp ic al   ope n - lo op   c on sta nt   V/Hz   IM   dri ve   syst em   is   s hown   in   Fi gure   2 .   In   this   co nfi gurati on,   the   input   powe r   is   obta ine d   from   the   3 - ph ase   powe r   sup ply ,   wh ic h   is   recti f ie d   by   the   3 - phase   di od e   rec ti fier   to   pro du ce   a   DC   vo lt age .   To   ob t ai n   a   sti ff   DC   vo lt age ,   a   la rg e   el ect ro lyti c   ca pacit or   is   nor m al ly   co nn ect e d   to   the   ou t pu t   of   t he   r ect ifie r.   It   co nsi sts   of   a   3 - ph a se   volt age   sou r ce   inv e rter   ( V SI )   with   in put   DC   volt age   ac qu i red   from   a   3 - ph as e   diode   recti fi er   ci rcu it .   T he   s witc hing   sig nals   f or   the   3 - ph a se   VSI   is   ge ner at e d   by   the   pu lse   width   mod ulator   base d   on   t he   fr e qu e nc y   a nd   volt age   mag nitud e   i nputs.   The   c on sta nt   V/Hz   blo c k   produces   the   ma gnit ud e   of   the   vo lt age   refe re nce   ( V re f ) ,   base d   on   the   freq ue ncy   re fer e nce   ( f ref ) .   If   a   diode   recti fier   is   us e d   as   t he   fro nt - e nd   co nvert er,   br a king   po wer   can not   be   fed   bac k   to   the   util it y,   instea d,   it   will   be   du mp e d   to       Evaluation Warning : The document was created with Spire.PDF for Python.
            IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  D ri   S ys t,   V ol .  11 , N o.   4 ,  D ecembe r  2020   :   1670   –   1 685   1672   the   DC   link   ca pacit or,   C.   T he refor e ,   a   cr owba r   ci rcu it   is   ty pical ly   a dd e d   to   t he   DC   li nk   ci rc uit   to   a vo i d   t he   capaci tor   volt age   f rom   e xcee ding   its   ma ximu m   al lowa bl e   value   duri ng   dyna mic   brak ing .   This   is   done   by   discha rg i ng   t he   acce ss   cha rge   via   the   re sist or.   The   f ollowi ng   sect io ns   di scuss   t he   f unda mental   co nce pt   an d   main   el eme nts   of   the   c ontrol   s cheme.           Figure   2.   O pe n - lo op   co ns ta nt   V/Hz   dri ve       2.1.   Constan t   V/H z   contr oller   The   t orqu e   of   t he   IM   can   be   wr it te n   in   te r m s   of   the   r otor   c urren t   a nd   ai r - gap   fl ux   as     = ′     (1)     wh e re   K   is   a   const ant,   a nd     is   the   a ngle   be tween   ′   an d   .   Figure   3( a )   s hows   the   pe r - phase   e quivale nt   ci rcu it   of   an   IM   a nd   its   co rresp onding   ph a so r   dia gr am .   F or   small   sli p   operati on,     is   cl os e   to   90 o   (i.e.   ≈ 0 )   and   he nce   ( 1 )   c an   be   wr it te n   as     = ′    (2)     Wh e n   t he   ro t or   is   r unning   at   s mall   sli p,   ′ ≫ 2  ′  ,   he nc e   com bin i ng   ( 1)   an d   (2),   we   can   wr it e     = ′  2    (3)     Ther e f or e,   to   maximize   the   tor qu e   ca pa bili ty,   the   ai r - ga p   fl ux   has   to   be   ma ximize d,   and   t he   ma xi mu m   po s sible   value   without   sat ur at ion   w ou l d   be   t he   r at ed   value .   The   ma gn et iz ing   cu rr e nt   of   an   IM   is   res ponsi ble   for   pro duci ng   the   ai r - gap   flu x.   F rom   the   pe r - ph a se   eq uiva le nt   ci rcu it   of   the   IM   s hown   in   Fig ur e   3 ,   the   mag netiz ing   c urren t   I m   is   the   current   that   fl ow s   t hro ugh   the   mag netiz ing   inducta nce   Lm.   Th us ,   from   t he   per - ph a se   ste ad y - s ta te   equ ivale nt   ci rcu it   point   of   view ,   in   orde r   to   mainta in   the   rated   a ir - ga p   flu x   at   any   fr e qu e nc y,   it   is   necess ar y   to   ens ur e   t hat   I m   is   at   its   rated   value   at   al l   fr e qu e ncies.   As   c an   be   see n   fro m   the   equ i valent   ci rc uit,   the   ma gn et iz ing   c urren t   I m   can   be   wr it te n   as   sho wn   in   ( 4).     = 2  ➔ ,  = ,   2     (4)     Accor ding   to   ( 4),   t he   mag nit ud e   of   the   ma gn et iz in g   cu rr e nt   ca n   be   mai nt ai ned   co ns ta nt   at   its   rated   by   mainta ini ng   the   rati o   of   the   back   e mf ,   E g ,   to   the   f re qu e ncy,   f   ( E g /f ),   e qu al s   to   the   rat io   at   the   rated   values ,   i.e.   E g,rated /f rated ,   at   al l   fr e qu e nc ie s.   If   the   fr e quenc y   is   re du c ed,   E g   has   to   be   reduce d   pro portio nally   to   m ai ntain   const ant   I m,rated .   At   high   s pee d,   E g   is   la r ge   a nd   the   volt age   dro p   ac ro s s   the   sta tor   le a kage   inducta nce   L ls   and   sta tor   resist anc e   R s   is   relat ive ly   s mall ;   un de r   t his   c onditi on,   E g / f   is   mai nt ai ned   co ns ta nt   by   mai ntainin g   V s / f   const ant.   In   ot her   w ords,   we   can   ass um e         Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Fu ndament al e le men ts  of c onstan t v olt/ hertz  inducti on  mo t or   dr iv es  …   ( Siti  Nursyuh ada Ma hs ahir un)   1673   ≃ = ,       (5)     Fo r   a   gi ven   fr e qu e nc y,   f ,   t he   mag nitud e   of   t he   sta t or   volt age,   the refor e ,   c an   be   dete rmine d   from   (5).   At   l ow   fr e qu e ncy,   the   ap pro ximati on   in   (5)   can no t   be   jus ti fied   since   the   mag nitud es   of   E g   and   V s   are   small   hen ce   the   vo lt age   dro p   ac r oss   sta tor   im pedance   bec om es   sign ific a nt.   To   overc ome   this ,   a   boost   vo lt a ge   is   add e d   to   c omp ensate   for   t he   vo lt age   drop   at   low   f reque nc ie s.   As   the   f re qu e nc y   i ncr eas es,   the   boos t   volt age   gr a dual ly   re du ced.   The re   a re   seve ral   possi ble   wa ys   of   boos ti ng   t he   volt age,   the   one s   that   are   sho wn   in     Figure   4   are   ba sed   o n   t he   non - li near   boos t   as   show n   in   Fig ur e   4 (a )   an d   li near   boos t   as   s how n   in   Fi gur e   4 ( b).   In   ei t her   cas e,   the   am ount   of   vo lt age   bo os t   is   a   f unct ion   of   fr e quenc y.   F or   insta nce,   us in g   a   li nea r   boost ,   we   can   de rive   the   e xpressio n   of   the   boos t   vol ta ge   by   ta king   the   diff e re nc es   betwee n   the   vo lt age - f requen c y   relat ion s hip s   with   an d   without   the   boos t.   Fro m   Fig ure   3(b),     Without   boos t:   1 ( ) =           With   boos t:   2 ( ) =     −   +     Ther e f or e,   the   amo un t   of   vo lt age   boos t   nee de d   is        ( ) =   2 ( ) − 1 ( ) = −     (6)     To   fe d   t he   des ired   3 - phase   V   an d   f   to   the   I M ,   a   3 - phase   vo lt age   s ource   in ver te r   (VSI )   is   use d   a nd   t his   is   discusse d   ne xt.             (a)   (b)     Figure   3.   IM   pe r - ph a se   T - f orm   ste ad y   sta te   equ i valent   ci rc uit   model   a nd   ph a sor   diag ra m   [ 22]           (a )     (b)     Figure   4 .   Bo ost   vo lt age   f or   c onsta nt   V/Hz   co ntr ol   (a )   Non - li near   bo os t;   ( b)   Linear   boost         Evaluation Warning : The document was created with Spire.PDF for Python.
            IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  D ri   S ys t,   V ol .  11 , N o.   4 ,  D ecembe r  2020   :   1670   –   1 685   1674   2.2.   Thre e - ph as e  inver ter   A   th ree - phase   vo lt age   s ource   inv e rter   (VSI )   is   one   of   t he   t ypes   of   po wer   e le ct ro nics   co nv erter   th at   is   us e d   to   c onve r t   a   DC   i nput   to   an   AC   ou t put.   As   s how n   in   Fig ure   5 ,   a   V SI   co ntains   6   powe r   se mico nducto r   dev ic es   ( with   anti - pa rall el   di od e s),   2   for   e ach   le g.   In   po wer   co nverte r   app li cat io ns ,   powe r   semic on du ct or   dev ic es   (for   e xa mp le   po wer   I GBTs   or   po we r   MOSF ETs)   a re   operate d   as   powe r   s witc he s .   Th ey   are   operate d   in   ei the r   c ut - off   reg i on   (tu rn - off   sta te )   or   sa turati on   re gion   (t urn - on   sta te ) ,   this   is   al so   know n   as   t he   s witc h - mode   op e rati on.   The   sta tus   of   the   up per   an d   lowe r   powe r   s witc hes   of   a   le g   in   a   VSI   m ust   al way s   be   op po sit e   to   av oid   s hoot - thr ough   or   s hort   ci rcu it .   In   ot her   w ords,   if   an   up per   s witc h   is   turned   on,   a   lowe r   switc h   has   to   be   tu r ned   off .   Fo r   pr act ic al   impleme ntati on,   a   so - cal le d   bl ank in g   ti me   ha s   to   be   i nclu ded   be f or e   the   oth e r   switc h   is   t urne d   on.   T his   is   be cause   a   po we r   s witc h   will   not   imme diate ly   be   t urne d   off   wh e n   a   tu rn - off   sig nal   is   ap plied   at   its   gate.   T he   durati on   of   the   bl ank in g   ti me   de pends   on   the   typ e   of   po wer   switc hes   an d   c an   be   determi ned   fro m   t he   data   sh e et s   of   the   s witc hes   [ 23,   24] .   Ther e   a re   va riou s   te c hn i qu e s   that   can   be   use d   to   con t ro l   t he   s witc hes   to   pro duc e   sinusoi dal   ou tpu t   vo lt age ,   howe ve r,   t he   m os t   wi dely   a do pted   te c hn i que   would   be   the   pu lse   width   mod ulati on   ( PWM )   te chn i qu e   [ 13] .   Using   P W M ,   the   outp ut   volt age   m ag nitu de   and   fr e qu e nc y   can   be   co ntr olled   simult ane ou sl y.   One   of   t he   mo st   po pu la r   PWM   meth ods   that   is   com monly   ta rg et ed   in   i ndus tria l   dri ves   is   know n   as   t he   sp ace   vecto r   P W M   ( SV - P W M )   [ 25,   26]   .           Figure   5.   A   3 - ph a se   vo lt age   s ource   i nv e rter       2.3.   SV - PW M   Sp ace   vecto r   P W M   ( SV - P W M )   [ 27]   is   a   m odulati on   te ch nique   that   is   w idely   a dopted   f or   AC - mo t or   dr i ves   c ompa r ed   to   oth e r   te chn i qu e s,   su c h   as   s in us oi dal   P WM   (S P W M )   [ 28] ,   beca us e   of   its   e xc el le nt   com patibil it y   with   di gital   im plementat io n.   In   oth e r   w ords ,   us in g   a   micr opr ocess or   or   microc ontrolle r,   SV - PWM   gi ves   le ss   c ompu ta ti on al   bur de n   a nd   easi er   to   im ple ment.   F ur t hermo re,   with   SV - P WM,   a   bette r   DC   vo lt age   util iz at ion   ca n   be   a chieve d   [29,   30] .   In   c on t rast   to   SP W M ,   w hich   tr eat s   the   3 - phase   quan ti ti es   separ at el y,   in   SV - PWM ,   the   3 - ph ase   quantit ie s   are   t reated   us in g   a   sing le   e qu at ion ,   know n   as   sp ace     vecto r   e qu at io ns .     In   a   th ree   3 - phase   VSI   with   three   le gs ,   as   show n   in   Fi gure   4,   there   are   2 3 = 8   possi ble   s witc h   config ur at io ns,   hen ce   ei ght   possible   vo lt ag e   vecto rs   that   c an   be   ge ner at e d   or   ob ta ine d.   The   po s sible   s witc h   config ur at io ns   f or   the   th ree   le gs   a nd   t he   r especti ve   volt age   vecto rs   are   de picte d   in   F igure   6 .   T he   volt ag e   vecto rs   a re   la be le d   as   v 1   to   v 7 ;   6   of   the m   are   act ive   vecto rs   ( v 1 - v 6 )   a nd   2   of   them   ( v 0   an d   v 7 )   are   zer o   vo lt ag e   vecto rs.   Stat us   ‘ 1’   i ndic at es   that   the   up per   s witc h   of   a   le g   is   ‘ON ’,   a nd   t he   lo we r   s witc h   is   ‘OFF ’   a nd   vice   ver sa .   F or   i ns ta nce,   [1   0   1]   means   t hat   the   uppe r   switc he s   of   le gs   A   an d   C,   an d   the   lo w er   switc h   of   le g   B   are   tur ned   on.   SV - P WM   util iz es   these   avail abl e   volt age   vect or s   to   synthe siz e   the   ref e re nc e   volt age   within   a   samplin g   per i od.   The   sp ace   ve ct or   of   the   out pu t   f or   a   3 - ph a se   VSI   is   gi ven   by     = 2 3  ( + + 2 )   (7)     wh e re   V dc   is   the   DC   link   volt age,   S a ,   S b,   an d   S c   a re   t he   swit chin g   f un ct io ns   for   le gs   res pe ct ively,   w hich   equ al s   ‘1’   if   the   uppe r   switc hes   are   ‘ ON’   a nd   ‘ 0’   if   the   lo wer   switc hes   a re   ‘OFF’.     The   re fer e nce   sign al s   to   the   SV - P W M   can   be   in   the   f orm   of   the   d - q   co mpon e nts   or   of   a mp li tud e   a nd   ang le   of   t he   volt age   ve ct or.   In   orde r   to   tr anslat e   the   3 - ph a se   volt ages   to   d - q   or   am plit ud e   a ngle   form,   coor din at e   tra ns f ormat io n   is   us e d.   T hese   t ran s f or mati on   is   well   know n   as   Cl ark e   ( )   [31 ]   an d   Pa rk   ( dq)   trans formati on s   [32 ] .   T he   re f eren ce   volt age   is   sy nt hesized ,   within   a   sam pling   pe rio d,   by   sel ect ing   t he   two   adjace nt   volt age   vecto rs   an d   zer o   volt age   vecto rs   t hu s   mainta inin g   t he   switc hi ng   frequ e nc y   c onst ant.   For   Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Fu ndament al e le men ts  of c onstan t v olt/ hertz  inducti on  mo t or   dr iv es  …   ( Siti  Nursyuh ada Ma hs ahir un)   1675   exam ple,   if   the   ref ere nce   vo lt age   vect or,   v ref ,   is   locat ed   in   s ect or   1,   volt ag e   vectors   v 1 ,   v 2 ,   v 0   an d   v 7   w ould   be   sel ect ed   an d   a ppli ed   within   a   s amplin g   per i od.   T his   is   il lustr at ed   in   Fig ur e   7 .     It   can   be   sho w n   that,   the   val ue s   of   T 1   an d   T 2   within   a   sam pl ing   pe rio d   T   ar e   as:     1 = 3 2 ∙ ∙  (  − 1 √ 3  )   (8 a )   2 = √ 3 ∙ ∙     (8b)       Figure   6 .   A vaila ble   volt age   spa ce   vect or   f or   a   3 - phase,   2 - le vel,   VSI             Figure   7 .   S witc hing   patte rn   of   the   3 - ph ase   V S I   in   Sect or   1       In   8( a )   a nd   8( b) ,   v ref   is   the   mag nitud e   of   the   refe re nce   vecto r   an d     is   the   an gle   be tween   t he   ref e ren ce   vo lt a ge   a nd   t he   adja cent   vecto r   (to   the   rig ht   of   the   re fer e nce   volt age).   T he   inter val   for   zer o   vo lt age   vecto r   is   giv e n   by:       + 7 = − ( 1 + 2 )   (9)     The   rati o   bet ween   T 0   an d   T 7   essenti al ly   con t ro ls   the   a moun t   of   t ripl en   ha rm onic   [ 33]   c ompone nt s   in   the   fun dame ntal   phase   volt age.     2.4.   Impro ved   ope n - lo op   co nsta nt   V/Hz   sc he me   Un li ke   s ynch r onous   mo t or   wh ic h   ro ta te s   at   a   s yn c hro no us   sp ee d   eve n   with   l oad   var i at ion s,   in   I M ,   the   r oto r   sp ee d   diff e rs   from   t he   s yn c hro nous   sp ee d   by   t he   sli p   sp ee d.   To   make   matt ers   worse,   t he   sli p   sp ee d   var ie s   with   lo ad.   To   ove rcome   this   in   an   op e n - lo op   c on sta nt   V/Hz   dr i ve,   the   sli p   spe ed   is   est imat ed   an d   su bse que ntly   a dd e d   to   the   re fer e nce   sp ee d   so   t hat   the   ro t or   s peed   will   be   more   or   le s s   eq ual   to   ref e ren ce   sp ee d.   T he   sli p   sp ee d   can   be   e sti mate d   by   est imat ing   the   ai r - ga p   power,    ,   wh ic h   is   obta in ed   by   s ubtract ing   the   input   po w er   to   the   VSI   with   the   lo sses   in   the   V SI   a nd   sta tor   c oppe r   an d   c or e   lo ss es.   O nce   the   a ir - ga p   powe r,   is   obta ined ,   the   to rque   can   be   e sti mate d   as ,   Evaluation Warning : The document was created with Spire.PDF for Python.
            IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  D ri   S ys t,   V ol .  11 , N o.   4 ,  D ecembe r  2020   :   1670   –   1 685   1676   =    (10)     Kno wing   the   tor qu e   T e ,   an d   since   the   ai r gap   flu x   is   ke pt   co ns ta nt   at   the   rated   value,   the   sli p   fr e qu e nc y   ca n   be   est imat ed   from   ( 3) .   T he   blo c k   dia gram   of   t he   open - loop   co nst ant   V/Hz   with   sli p   com pensat ion   scheme   is   sho wn   in   Fi gure   8 .   To   im pleme nt   this   sc heme ,   we   nee d   to   measu re   t he   DC   li nk   vo lt age ,   V dc ,   a nd   the   in pu t   DC   curre nt   to   the   VSI,   I dc .   In   order   to   li mit   the   rate   of   c ha ng e   of   t he   ref e ren ce   fr e qu e nc y,   a   ra te   li mit er   is   a dded .   T his   will   ens ur e   that   t he   ro t or   can   cat ch   up   with   the   r ot at ing   ma gnet ic   fiel d   so   that   the   sli p   fr e qu e nc y   can   be   ke pt   small .   The   fi gure   al so   s hows   the   i nject ion   of   bo os t   vo lt age ,   V boost ,   to   t he   amplit ude   of   t he   ref e re nce   volt age,   to   c ompen sat e   for   t he   sta tor   im pe da nce   dro p   at   l ow - s pee d   operat ion s .   As   sh ow n   by   ( 6),   t he   am ount   of   boos t   volt age   ne eded   is   a   functi on   of   t he   f re quency.         Figure   8 .   O pe n - lo op   co ns ta nt   V/Hz   with   sli p   com pensat ion   and   volt age   bo os t       3.   RESEA R CH   METHO D   3.1.   Simul at i on     To   st udy   t he   be hav i or   an d   c ha racteri sti cs   of   a   co ns ta nt   V/ Hz   c on t ro l   IM   dr i ve,   simulat ion s   us i ng   M A TLAB/Si m ulink   (R 2016b)   w ere   c onduct ed.   The   Sim ulink   bl ock   dia gram   of   t he   dr i v e   sy ste m   is   as   sh ow n   in   Fig ur e   9 (a ).   The   switc hi ng   f reque ncy   is   set   to   2   kHz   and   t he   pa ram et ers   of   a   4 - po le ,   50   Hz,   190V   with   powe r   rati ng   of   186   W   IM   ar e   giv e n   in   Ta bl e   1.   T he   same   IM   is   al s o   use d   in   the   ex per i ment,   wh ic h   will   be   discusse d   in   the   subseq ue nt   s ect ion .   Inste ad   of   us in g   a   diod e   recti fier   to   obta in   the   DC   volt age   to   fe d   to   the   3 - ph a se   VSI,   a   DC   vo lt ag e   s ource   is   us e d.   In   orde r   to   pro du ce   the   rate d   li ne   volt age   of   190   V   (rms) ,   wh ic h   is   equ i valent   to   a   phase   vo lt ag e   amplit ude   of   190 √ 3 √ 2 = 155   ,   a   DC   vo lt age   of   269   V   at   the   input   to   t he   V SI   is   require d   (w it hout   over - m odul at ion ).   T his   is   beca us e   us i ng   SV - P W M ,   t he   maxi mum   am plit ud e   of   the   ph a se   vo lt age   that   ca n   be   obta ine d   without   ov e r - modu la ti on   is    √ 3   .   H oweve r,   in   the   ex pe r imen t,   a   DC   vo lt ag e   of   155   V   is   us e d   (due   to   the   av a il able   volt age   s ource   a nd   sa fety   reasons ).   Th eref or e ,   in   the   simulat ion,   the   same   DC   volt age   of   155   V   will   be   us e d.   T his   mea ns   t hat   the   ma ximum   fr e que ncy   to   mainta i n   c onsta nt   V/H z   rati o   will   be   le ss   t ha n   the   rate d   f re quenc y   of   50   Hz .   i.e.    = 50 155 269 = 29   Hz .   The   m oto r   is   r un   based   on   t he   fr e quenc y   prof il e   ( Hz)   (c on st ru ct e d   us i ng   Signa l   buil der   bloc k   as   sh ow n   in   Fig ure   9(b) ).   In   or de r   to   li mit   the   sl ip   to   within   s m al l   value,   a   rate   li mit er   is   inserted   a fter   the   sta tor   fr e qu e nc y   re fe ren ce .   With out   the   rate   li mit er,   a   ste p - c ha ng e   in   a   fr e quenc y   will   res ult   in   a   sig nif ic ant   os ci ll at ion   in   the   s pee d   a nd   tor que   befor e   the   ste ad y - sta te   s peed   an d   t orq ue   is   reac hed.             Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Fu ndament al e le men ts  of c onstan t v olt/ hertz  inducti on  mo t or   dr iv es  …   ( Siti  Nursyuh ada Ma hs ahir un)   1677   Table   1 .   Ind uct ion   mo t or   rati ngs   a nd   par amet ers   Para m eters   rate   Po wer,   Vo ltag e   186   W,   190   V   Frequ en cy ,   p o les   50   Hz,   4   R S   1 0 .35     R r   6 .17     L s   0 .27 5 2   H   L r   0 .27 5 2   H   L m   0 .25 8 3   H   I   0 .00 1 4   kg   -   m 2   B   0 .00 2   Nm /rad/s         (a)     (b)     Figure   9 .   Sim ul at ion   of   c onst ant   V/ Hz   c on t r ol   of   IM   (a )   Power   sy ste m - si mu li nk    (b)   F re qu e nc y   ref e ren ce   pro fi le         3.2.   Ha rd w are   im plem ent at i on     In   orde r   to   ev al uate   the   vo lt age   a nd   cu rr e nt   of   the   IM   dri ve n   by   c onst ant   V/ Hz,   a   re al   hardware   exp e rime nt   has   been   co nducte d.   T he   blo c k   di agr am   of   the   exp e rime ntal   set up   is   s how n   in   Fig ur e   10   a nd   t he   act ual   hard ware   set up   is   s hown   in   Fig ur e   1 1 .   T he   ex pe riment   util iz ed   of   a   3 - phase   V SI   with   gate   dr ivers,   a   DC   powe r   sup ply ,   a   ¼   hp   3 - ph a se   i nductio n   m oto r   a nd   a   dSP ACE   D S1104   c on tr oller   bo a r d.   T he   c onsta nt   V/Hz   c on t ro l   is   impleme nted   us in g   the   DS110 4   co ntr oller   boar d   with   t he   C   co des   a ut om at ic al ly   ge ner at e d   from   the   Sim ul ink   m odel .   Th e   3 - phase   V SI   is   con st ru ct e d   us in g   th ree   (3)   un it s   of   2 - le ve ls   IG BTs   with   their   ded ic at e d   f ree wh eel in g.         Figure   10 .   E xp erimental   set up     Evaluation Warning : The document was created with Spire.PDF for Python.
            IS S N :   2088 - 8 694   In t J   P ow  Ele c  &  D ri   S ys t,   V ol .  11 , N o.   4 ,  D ecembe r  2020   :   1670   –   1 685   1678   Fo r   m on it ori ng   pur poses,   t wo   (2)   c urren t   se nsors   are   us e d   to   meas ure   the   ph a se   cu rr e nts.   The   rati ng s   and   par a mete rs   of   the   m oto r   a re   simi la r   to   the   one   use d   in   t he   simulat io n,   wh ic h   a re   as   li ste d   in   Ta ble   1.   As   mentio ned   earl ie r   in   the   pr e vi ou s   sect ion,   due   to   the   li mit at i on   on   the   a vaila bili ty   of   t he   DC   power   sup ply   an d   safety   reas on s ,   a   DC   vo lt a ge   of   up   to   only   155   V   is   us e d   (which   is   simi la r   to   t he   sim ul at ion   set ti ng).   Using   SV - PWM ,   the   maxim um   rm s   li ne - li ne   vo lt ag e   that   ca n   be   a chieve d   is       − ,  = 155 √ 3 √ 3 √ 2 = 109 . 6   Vrms     Fo r   c on sta nt   V /Hz   imple ment at ion ,   maxi mum   f reque ncy   is   there fore ,      = 50 190 109 . 6 ≈ 29   Hz         (i)   IM   un der   te st   (ii)   I GBTs   bri dge   (iii )   DS1 104   C ontrolle r   (iv)   Us er   i nterfac e   ( v)   DC   po wer   sup ply     Figure   11.   E xp erimental   set up         4.   RESU LT S   A ND   DI SCUS S ION   4.1.   Simul at i on     The   simulat io n   res ults   of   t he   sta tor   li ne   volt age,   sta to r   pha se   c urren t,   m ot or   to rque   a nd   r otor   s pee d   without   a nd   with   a   rat e   li mit er   ar e   s how n   in   Fi gure   12(a )   an d   12 ( b)   res pecti vely .   In   the   sim ulati on,   the   rate   li mit er   is   set   to   100   Hz/s.   A   sig nificant   s urge   in   t he   sta to r   c urre nt   (a mpl it ud e   of   beyo nd   2   A),   as   w el l   as   a   la rg e   os ci ll at ion   in   the   t orque   respo ns e   ca n   be   ob se r ved   in   the   wa ve forms   of   Fi gure   12 (a).   To rque   os cci ll at io n   influ e nce   pow er   ef fici enc y   and   s peed   pe r forma nce.   In   industrial   a pp l ic at ion   w he re   te ns   to   th ou san ds   horse powe r   I M s   a re   util iz ed ,   this   t orq ue   re sp onse   ca n   ca use   sev ere   pow e r   disruptio n   an d   dama ge   to   t he   dri ve   sy ste m.   With   the   li mit er,   fr e quenc y   is   grad ua ll y   increa sed   thu s   ens uri ng   s mall   sli p   ope ra ti on .   The   am plit ud e   of   the   c urre nt   grad ually   i ncr ea ses   an d   la rg e   osc il la ti on   in   to r qu e   is   re move d.     In   ord er   to   ob serv e   the   tra nsi ent - sta te   be ha vior   of   the   tor que   a nd   s pe ed   when   the   f reque ncy   is   increase d   from   0   Hz   to   18   Hz   an d   to   25   H z,   a nd   re duced   to   12   Hz,   the   tor que - s pee d   dynamic   sim ulati on   resu lt s   are   s uperim posed   onto   the   ste ad y - sta te   t orq ue - sp ee d   c har a ct erist ic   of   t he   m otor   at   the se   th ree   fr e qu e ncies;   t he se   are   s how n   in   Fi gure   1 3 (a )   with out   the   ra te   li mit er,   a nd   Figure   1 3 (b)   with   the   rate   li mit er.   As   ca n   be   se en   that   with   t he   inse rtio n   of   the   rate   li m it er,   a   sig nific ant   re duct ion   in   the   t orqu e - sp ee d   os ci ll at ion   is   obta ined .     Using   M A TL AB/Si mu li nk   it   is   al so   possi ble   to   perf orm   FFT   in   ord er   to   view   the   fr e quenc y   sp ect r um   of   the   wa veform   a nd   anal yze   the   harmo nics   c onte nts.   Fig ur e   13(a)   an d   (b)   sh ows   the   fr e quenc y   sp ect r um   of   the   li ne - li ne   volt age   an d   phase   current   of   the   IM,   res pecti vel y,   at   t he   f unda mental   fr e quen cy   of   25   Hz .   T he   fig ur e   cl early   dis plays   the   ha rm on ic s   co ntents   of   the   wa veforms   at   the   m ulti ples   of   t he   s wi tc hin g   fr e qu e nc y,   w hich   is   at   2000   Hz.   From   the   plo t,   t he   t otal   harmo nic   disto rtion s   in   Fig ure   14,   t he   c urre nt   a n d   vo lt age   hom on ic   con te nt   obta ined   as   TH D I = 5.39%   an d   T H D V = 52. 41%   re sp ect ively .   In   com par is on   wi th   the   work   pr e sente d   in   [ 13] ,   wit h   si mil ar   P W M   te c hniq ue   (S V PWM )   a ppli ed   to   1hp   IM   ( dif fer e nt   mo to r   par a mete rs),   t he   T H D I =2 0.14%   a nd   T H D V = 64. 78%.   Althou gh   bo t h   im pleme nted   simi la r   m odulati o n   te chn iq ue,   both   prese nted   va riat ion   in   power   qu al it y.   Othe r   than   due   to   mo to r   pa rameter   var ia ti on s ,   the     Evaluation Warning : The document was created with Spire.PDF for Python.
In t J  P ow Elec   & Dri S ys t   IS S N: 20 88 - 8 694       Fu ndament al e le men ts  of c onstan t v olt/ hertz  inducti on  mo t or   dr iv es  …   ( Siti  Nursyuh ada Ma hs ahir un)   1679   resu lt s   are   al so   de pe nd i ng   on   the   sa mp li ng   ti me,   wa vefo rm   al igh nme nt   ( S VPWM   ge ner a ti on   te c hniq ue),   type   of   switc he s   a nd   the   in ver te r   bri dge   to polo gy,   dc - li nk   an d   ot her s .           (a)       (b)     Figure   12 .   Sim ulati on   res ults   of   li ne   vo lt age ,   phase   c urre nt,   tor qu e ,   a nd   r oto r   sp ee d   w her e   the   red   li ne   refe rs   to   re fer e nce   s pe ed   (a)   with ou t   rate   li mit er   (b)   with   rate   li mit er   Evaluation Warning : The document was created with Spire.PDF for Python.