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 ,  N o.   4 ,  Decem be r 202 0 , p p.   1785 ~ 1798   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v11.i 4 . pp 1785 - 1798       1785       Journ al h om e page :  http: // ij pe ds .i aescore.c om   Modulat ion   ind ex   effect   on   i nverter   based   i nducti on   mot or   dr i ve       Ak hil esh   Sh ar ma 1 ,   Anan dh   N. 2 ,   Sa r sing   G ao 3   1,3   El e ct ri ca l   Eng ine er ing   Dep artme nt ,   North   Ea ste rn   Re gional   In sti tute   of   Sci ence   &   Tec hnol ogy,   Nirj uli,   Arunachal   Pr a des h,   India   2   Depa rtment   of   El e ct ri ca l   and   E l ec tron ic s   Eng ineeri ng,   Manip al   I nstit ute   of   Techn ology,   Man ipa l   Aca dem y   of   Hig her   Educ a ti on,   Mani pal ,   Karna ta k a,   I ndia       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   Ja n   23 ,   20 20   Re vised   A pr   26 ,   20 20   Accepte d   M a y   3 1 ,   20 20       Due   to   a   subs tantia l   in crease   in   the   use   of   inv e rte r   for   num ero us   el e ct ri cal   appl i anc es   starti ng   from   dome st ic s   to   industr ia l   drive s ,   an   inverter   may   be   dire c tl y   conn ec t ed   to   the   power   grid   sys tem.   Th e   dep ende n cy   on   an   inve rt er   has   bee n   in creased   over   th e   y ea r s.   Henc e,   the   pr oper   and   eff icie nt   design   of   the   inv erter   will   lead   to   high er   ef fic i enc y.   One   of   the   ma jor   challenges   is   the   gene ra ti on   of   sui ta bl e   ga te   pu lses   for   power   sw itc hing   device s,   wh ic h   in   turn   depe nds   on   the   modul ation   index.   Th e   se le c ti on   of   prope r   modu la ti on   ind ex   will   h el p   in   th e   produc ti on   of   th e   ra te d   voltage .   If   the   modulati o n   inde x   is   le ss ,   the   dur atio n   of   on - ti m e   p ulses   will   be   les s   and   henc e ,   t he   device 's   conduc t ion   ti m e   is   al so   l ess,   th ere by   th e   ou tpu t   vo lt ag e   of   the   inv ert er   is   red uce d .   A   r edu ce d   vo lt ag e,   when   app li ed   to   an   induc t ion   mo to r   will   h ave   lower   spe ed   an d   eve n   i ts   per fo rma nc e   wi ll   be   sluggish.   Th e   s pee d   of   th e   mot or   i mprove s   when   it   is   oper a t ed   in   a   c losed - lo op   for   the   same   modul ation   inde x.   Thi s   rese a rch   pape r   tries   to   bring   out   the   eff ec t   of   modul a ti o n   inde x   on   spee d   con trol   of   an   induc t ion   m otor   base d   on   an   inve r te r   for   b oth   open   as   well   as   c losed - loop   oper ation.   The   simu la t ed   result s   indicate   th at   th e   modul ation   index   in   the   vi ci ni ty   to   un it y   wil l   p r ovide   ra te d   vol t age   for   th e   smooth   oper at io n   of   th e   mot or .   Ke yw or d s :   Ind uction   Mot or   M od ulati on   I ndex   Neural   Netw ork   Sp ace   Vecto r   PWM     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 :   Akhile sh   S harma,     Ele ct rical   Eng i neer i ng   De par t ment,   North   East er n   Re gional   I ns ti tute   of   Scie nce   &   Tec hnolog y,   Nirjuli,   Papum   Pare ,   Arun ac ha l   Pr a desh   79 1109,   I ndia .   Emai l:   as@n e r ist .ac.in       1.   INTROD U CTION   Fr e qu e nt   fau lt   on   the   power   sy ste m,   un a vai la bili ty   of   pow er   to   rem ote   l ocati on   a nd   a va il abili ty   of   so la r   e ne rgy   at   su ch   locat io ns   ha ve   in creas ed   the   util it y   of   i nverter ,   as   they   ser ve   as   a   sta ndby   ac   powe r   su ppli es   f rom   a   DC   source   [ 1]   to   meet   the   load   dema nd.   Eve n,   in ver te rs   are   ap plied   for   the   in dustria l   dr ive   durin g   s hu t   do wn   or   powe r   f ai lure   due   to   f ault.   He nce,   the   op e rati on   of   inv e rter   pla ys   an   imp or ta nt   r ole   in   su c h   a pp li cat io ns .   T he   in ve rter   ci rc uit   c on sis ts   of   ma ny   s wi tc hin g   dev ic es .   To   tu rn   on   th ese   de vices,   prop e r   trigg e rin g   pulse s   are   esse ntial .   The   du rati on   of   these   pul ses   de pe nds   on   the   s witc hing   fr e qu e nc y   a nd   its   modu la ti on   i ndex   (MI)   [2 - 7].   MI   sel ect ion   be comes   imp ort ant   pr ov i ded   the   switc hi ng   f re qu e nc y   is   c ons ta nt.     With   the   a dva nceme nt   in   the   desig n   of   in ve rter,   the y   a re   c apab le   of   pro vi ding   the   powe r   need e d   for   industrial   dri ve s.   Mostl y,   the se   dr i ves   c onsist   of   i nductio n   mo to rs   (IM )   because   the y   ha ve   s pecial   fea tures   li ke   sim ple,   rugg e d   in   co ns tr uction   with   minimu m   mainte nan ce   need,   et c.   M ost   im port antly,   the y   ca n   oper at e   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   :   1785   –   1798   1786   at   an y   en vir onmental   c onditi on s .   The se   mot or s   are   pr e ferred   for   c onsta nt   s pee d   opera ti on .   T he   c ha nge   in   sp ee d   f r om   no   loa d   to   f ull   lo ad   is   small .   H ence   t hese   mo t or s   are   wi dely   us e d   in   i ndus t ries.   Motors   use d   in   industries   nee d   co ntin uous   e le ct rical   po w er .   Disr upti on   in   the   el ect rical   powe r   le ads   to   the   co mp le te   sh ut   dow n   of   the   i ndus t ries   as   el ec tric al   energy   c onve rsion   is   m os tl y   based   on   the   co nventio na l   so urces   of   e nerg y.   The   dr i ve   sto pp a ge   may   be   av oid e d,   pro vi ded   t he   m otor   dri ves   sy ste ms   are   base d   on   both   i nv e rt er   an d   conve ntion al   powe r   plants .   T he   i nv e rter - bas ed   dr i ves   may   be   a ble   to   provi de   the   rate d   volt age   nee ded   for   the   dr i ves.   The   in ver te r   ou t pu t   volt age   de pends   on   t he   s witc hi ng   pulse s   [ 8],   wh ic h   in   tu rn   is   relat ed   to   MI.   S o,   there   is   a   ne ed   for   a   pro per   sel ect ion   of   MI.   Fo r   a   pa rtic ula r   MI,   t he   trig ge rin g   pulse s   ar e   gen e rated   t ha t   are   us e d   for   switc hing   the   dev ic es .   Th e   ou t pu t   volt age   of   a   t hr ee - ph as e   inv e rter   is   a ppli ed   to   a   t hr e e - phase   i nduct ion   mo t or   (IM ),   whose   par a mete rs   are   giv e n   in   T able   1 ,   in   an   open   as   well   as   cl os e d - l oop   c onditi on.   In   the   cl os e d - l oop   op e rati on   [10 ],   ma ny   con t ro ll ers   like   P ID ,   fu zz y - log ic   [ 11]   or   ne ural   netw ork   co uld   be   em ployed .   In   t his   pa per ,   a   NN     con t ro ll er   [ 12 - 18]   has   bee n   employe d   to   c on t ro l   t he   e rro r   in   the   sp e ed   of   the   m otor,   ge ner at e d   fro m   the   diff e re nce   of   r efere nce   sp e ed   a nd   m otor   s pe ed.   T hus,   co nt ro ll ing   the   m otor   to   f ollow   the   ref e rence   s peed,   wh il e,   in   ope n - loop   c ontrol ,   t he   s pee d   of   IM   is   in dep e nd ent   of   re fer e nc e   sp ee d.   In   this   pa per,   an   at te mp t   has   been   mad e   to   fin d   the   e ff ect   of   MI   on   the   s peed   of   an   IM   and   t he   re su lt s   are   obta ine d.   The   re su lt s   in dicat e   that   the   mod ulati on   in dex,   ne ar   the   unit y,   ge ner at es   the   tri ggeri ng   pu lse s   of   suffici ent   width   to   pro du ce   rate d   vo lt age   for   t he   m otor.   B ut   w hen   the   MI   is   l ess   tha n   0.8   or   m or e   tha n   1.2 5,   the   wi dth   of   the   switc hi ng   pu lse s   so   produce d   is   le ss   an d   he nce   the   in ver te r   ou tpu t   vo lt age   re du ce s.   T her e f ore,   the   m oto r   ta kes   a   l onger   ti me   to   pick   up   the   re f eren ce   sp ee d.       Table   1.   Para m et ers   of   i nduction m otor   Nu m b er   of   Po les     4   Per   Ph ase   Stato r   &   Ro to r   Res istan ce   0 .90   Ω;   0 .66   Ω   Per   Ph ase   Stato r   &   Ro to r   Ind u ctan ce   0 .00 4 5 7   H   each   Moment   of   in ertia   0 .13 8 4   Kg - m 2   Frequ en cy   50   Hz   Load   Torq u e   10   N - m   DC   so u rce   Vo ltag e   540   V       2.   MO DU L ATI ON   I N DEX   Con si der   two   s ign al s,   a   tria ng ular   wa ve   an d   a   DC   sig nal,   a ct ing   as   a   car ri er   a nd   mod ulati ng   sig nals   resp ect ivel y   as   show n   in   Fig ur e   1   (i).   W he n   the   t rian gu la r   sig nal   [ 19]   is   com par e d   with   the   DC   si gnal   su c h   that,   the   ma gnit ud e   of   t he   tria ngular   be co me s   eq ual   to   t hat   of   DC   sig nal,   then   the   ou t pu t   will   be   co ns ta nt   unti l   it   beco mes   le ss   than   the   DC   si gn al   as   s how n   in   Fig ur e   1   (ii)   and   (iii )   res pe ct ively,   act in g   as   trigg e rin g   pulse s   for   c ontr olled   powe r   el ect r on ic   de vices   T 1   and   T 2   as   s hown   in   Fig ur e   2.   T he   wi dth   of   the   pulse s   dep e nds   upon   t he   mag ni tud e   of   t he   DC   sig nal.   The   width   of   the   pulse   for   T 1   dec reases   as   t he   mag nitud e   of   t he   DC   so urce   in creas es.   At   the   sam e   ti me,   the   pul se   widt h   f or   T 2   increases   t hereby   i ncr ea sin g   the   co nductio n   per i od   of   T 2 .   The   high   an d   low   dura ti on   pulse s   bec om e   e qu al   pro vid e d   the   m od ulati ng   si gn al   has   zer o   ma gn it ud es.   Sin ce   t he   a m plit ud e   of   the   m odulate d   si gn al   deci des   the   widt h   of   t he   pulse s,   he nce,   this   sche me   of   modu la ti on   is   cal le d   as   a mp li tud e   m odulati on   [20].   Th us ,   t his   is   de fine d   as   the   rati o   of   the   am plit ud e   of   the   modu la ti ng   si gnal ,   (V m )   to   t ha t   of   the   a mp li tu de   of   the   ca rr ie r   w ave ,   (V c ),   i. e.      =   (1)     If   T c   is   the   ti me   pe rio d   of   t he   tria ngular   wa ve ,   the n   c onduct ion   pe rio ds   for   T 1   an d   T 2   a re   e xpresse d   as ,     ℎ = 2 ( 1 − )   ( 2)   = 2 ( 1 + )   (3)     Wh e re   t h   a nd   t l   are   t he   c onduc ti on   ti me   of   T 1   and   T 2   resp ect i vely.   Con si der   an   in ver te r ,   as   s how n   in   Fi gure   2.   The   ou t pu t   vo l ta ge   betwee n   node s   A   a nd   B   will   hav e   a   mag nitud e   of   e it her   ± 0. 5   V dc   or   0,   de pendin g   on   the   DC   m odulati ng   sig nal .   This   volt age   has   been   re ferr ed   to   as   pole   vo lt age ,   V AO   as   in dicat ed   in   Fig ur e   2.   The   DC   c omp on e nt   of   this   volt age   is   e valu at ed   as,     = 0 . 5    (4)   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       Mo du l ation i ndex ef fe ct  on i nv ert er base d  in du ct io n m oto r   dr iv e ( Akhil es h S ha r m a)   1787   =    (5)     Eq uations   ( 2)   a nd   ( 3)   can   be   e xpresse d   in   te r ms   of   mod ulati on   in dex   ( MI),   as     ℎ = 2 ( 1 −  )   (6)   = 2 ( 1 +  )   ( 7)     As   ca n   be   see n   f r om   e xpres sion   ( 4) ,   the   mean   volt age   becomes   ze ro,   w hen   the   ma gn it ude   of   the   modu la ti ng   sig nal   bec om es   ze ro   i.e .   the   pu ls e   width   of   both   low   a nd   high   s ign al s   are   eq ua l   and   hen c e   the   are a   unde r   both   hal ves   are   e qu al ,   making   the   a ve rag e   value   of   the   DC   c omp onent   to   be   ze r o.   Along   with   the   DC   com pone nt,   the   outp ut   will   al so   ha ve   harmo nics   of   inte gr al   m ulti ples   of   t he   car rier   fr e qu e nc y,   while   the   fr e qu e nc y   of   lo wer   orde r   harmo nics   becom es   eq ual   to   the   carrier   f reque nc y.       A m p l i t u d e   o f   C a r r i e r   S i g n a l A m p l i t u d e   o f   M o d u l a t i n g   S i g n a l M o d u l a t i n g   S i g n a l C a r r i e r   S i g n a l A m p l i t u d e   o f   S i g n a l s T i m e G a t e   P u l s e   f o r   T 1 A m p l i t u d e T i m e T c 0 . 5 V dc 0 . 5 V dc T i m e T h T l A m p l i t u d e   G a t e   P u l s e   f o r   T 2 T i m e V AO ( i )  M o d u l a t i n g   a n d   C a r r i e r   S i g n a l s ( ii )  G a t e   P u l s e   f o r   T 1 ( iii )  G a t e   P u l s e   f o r   T 2 ( iv )  O u t p u t   V o l t a g e ,  V ao     Fig ure   1 .   Ge ne rati on   of   m odul at ing   an d   car rier   sig nals,   gate   pulse s   a nd   pol e   volt age       The   DC   mod ul at ing   si gn al   may   be   re plac ed   by   a   sin usoidall y   va r ying   si gn al   [ 21]   with   a   certai n   amplit ude,   ph a se   an d   f reque nc y.   T he   f re qu e ncy   of   this   sig nal   is   quit e   le ss   than   t he   car r ie r   fr e quenc y.   This   makes   the   modu la ti ng   sig nal   vi rtuall y   c on s ta nt   ov e r   the   high   car rier   f r equ e nc y,   ma ki ng   the   a ve rage   pole   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   :   1785   –   1798   1788   vo lt age   to   de pe nd   on   the   ma gn it ude   of   t he   modu la ti ng   si gnal .   T hus,   the   po le   volt age   w avefor m   will   ha ve   a   low - f reque ncy   c ompone nt   w ho s e   i ns ta nta ne ous   mag nitu de   is   pro portio na l   to   the   modul at ing   signa l.   It   will   al so   hav e   a   higher   f reque ncy   harmo nic   vo lt a ge.   If   DC   is   us ed   as   a   m odulati ng   sig nal,   t her e   will   be   ha rm on ic   fr e qu e ncies.   These   fr e que nc ie s   will   be   an   i nteg ral   m ul ti ple   of   the   c arr ie r   f re qu e nc y.   But   t his   does   not   ha pp e n,   if   DC   is   re pl aced   by   si nus oid al ly   varyin g   si gn al   w her e   pulse   width   de pe nds   on   the   f requ ency   of   m odul at ing   sig nal.   This   is   visible   from   equ at io ns   ( 2)   a nd   ( 3)   res pecti vely.   D ue   to   t hi s,   there   will   be   harmo nics   in   the   pole   volt a ges   a nd   t her e   e xists   a   band   of   f reque ncies   in   t he   vicinit y   to   a   c ar rier   an d   its   m ulti ple   f reque ncies .   The   ba nd   f re qu e ncies   a re   f orme d   by   an   i ntegr al   mu lt iple   of   the   f reque ncy   of   modu la ti ng   sig nals.   It   is   usual   to   ha ve   mod ulati ng   fr e quenc y   quit e   le ss   in   co mp a r ison   with   the   c arr ie r   fr e quenc y,   hen ce   the   frequ e nc y   of   the   domina nt   ha r monics   will   be   in   the   cl os e   vicinit y   of   car rier   fr e que ncy   an d   its   i ntegr al   mu lt iple.           Figure   2 .   A   simpli fied   in ver t er   to polo gy       3.   SPACE   VEC TOR   P ULSE   WIDTH   M O DU L ATIO N   ( SV PW M )   This   is   a   vecto r   te c hn i qu e   t ha t   is   a pp li e d   for   pulse   wi dth   m odulati on   (PW M )   for   3 - Φ   in ve rters.   T his   scheme   is   wi de ly   use d   f or   ge ner at in g   gatin g   si gn al s   f or   hi gh   volt age   with   low   harmo ni c   distor ti on,   s uitable   for   var ia ble   f r equ e nc y   in dust rial   dr i ves   s uc h   as   in du ct io n   mo t or.   T his   t echn i qu e   ca n   be   e xp la in ed   with   the   help   of   Fi gure   3.   T he   ci rc uit   will   produce   t wo   volt age   le ve ls.   It   co ns ist s   of   si x   co n tr olled   switc hes,   S 1   to   S 6   and   a   DC   s our ce   vo lt age   of   “V s ”.   T her e   ar e   ei ght   possibl e   s witc hing   ve ct or s   [ 22] ,   as   dep ic te d   in   Fi gure   4.   The   sta te s   V 0   [ 000]   a nd   V 7   [ 111]   a re   nu ll   ve ct or s   w hile   V 1 - V 6   a re   act ive   vect or s .   T he   nu ll   vecto r   pro du ce s   zero   volt age   w hile   an   act ive   vecto r   pr oduce s   non - zer o   volt age.   T he   sp ace   vecto r   [23 - 25]   volt age   gen e r at ion ,   oth e r   tha n   t he se   sta te s,   is   s how n   in   Fig ur e   5.   T he   re qu ired   volt age   ve ct or s   c ould   be   obta ined   ba s ed   on   equ at io ns   ( 8)   a nd   ( 9)   w hich   c ou l d   be   e xten de d   to   3 - dim ens ion al   s pace   ve ct or   [26]   as   we ll .   This   est a blishes   a   ro ta ti ng   vect or   [27]   a nd   it   is   simi la r   to   a   ro ta ti ng   fl ux   de velo ped   in   the   sta tor   of   an   i nductio n   m otor.   T he   ro ta ti ng   flu x   pa sses   th r ough   t he   ai r   ga p   to   t he   r oto r   si de.   This   te c hn i que   co uld   be   e xte nd e d   to   a   mu lt i - le vel   inv e rter   as   wel l.       V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B M o t o r     Figure   3:   I nver te r   base d   mo t or   loa d   represe nt at ion     V dc 0 . 5 V dc 0 . 5 V dc + + - - O A T 1 T 2 V AO 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       Mo du l ation i ndex ef fe ct  on i nv ert er base d  in du ct io n m oto r   dr iv e ( Akhil es h S ha r m a)   1789   Fr om   Fig ure   5,   the   ref e re nce   vo lt age ,    ̅ ̅ ̅ ̅ ̅ ,   is   exp ress ed   as ,   in   equ at io n   ( 8).   T he   co rr es pondi ng   li ne   vo lt age s   are   ta bu la te d   in   Tabl e   2 .        ̅ ̅ ̅ ̅ ̅ = 1 ( 1 ⁄ ) + 2 ( 2 ⁄ ) + 3 ( 3 ⁄ )   (8)   1 ⁄ + 2 ⁄ + 3 ⁄ = 1   (9)     Her e   T 1 ,   T 2   an d   T 3   a re   t he   pe rio ds   th r ough   ve ct or s   V 1 ,   V 2   a nd   V 3   res pecti vely,   T s   is   sa m pling   pe rio d.       V 1 =[ 1 0 0 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( ii )  S t a t e   2 V 2 =[ 1 1 0 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( i i i )  S t a t e   3 V 3 =[ 0 1 0 ] Vs S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( iv )  S t a t e   4 Vo =[ 1 1 1 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( i )  S t a t e   1 V 5 =[ 0 0 1 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( ii )  S t a t e   6 V 6 =[ 1 0 1 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( i i i )  S t a t e   7 V 7 =[ 0 0 0 ] Vs S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( iv )  S t a t e   8 V 4 =[ 0 1 1 ] V s S 1 S 3 S 5 S 4 S 6 S 2 R Y B ( i )  S t a t e   5   1    i n d i c a t e s   O N   s t a t e s   o f   u p p e r   s w i t c h e s   S 1 ,  S 3   o r   S 5   w h i l e     0 "  s h o w s   O N   s t a t u s   o f   l o w e r   s w i t c h e s   S 2 ,  S 4   o r   S 6 ,  V o -   V 7   r e p r e s e n t   o u t p u t   v o l t a g e s ;  V o   a n d   V 7   r e p r e s e n t   z e r o   v e c t o r s ;  V 1 -   V 7   r e p r e s e n t   a c t i v e   v e c t o r s     Figure   4 .   S witc hing   sta te s   of   the   two - le vel   in ver te r       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   :   1785   –   1798   1790   Table  2.   V oltage  vecto r wit h i ts resp ect ive  li ne vo lt age   Vo ltag e  Vector   Switch in g  Vector   Line Vo ltag es   a   b   c   V RY   V YB   V BR   V o   0   0   0   0   0   0   V 1   1   0   0   Vs   0   - Vs   V 2   1   1   0   0   Vs   -   Vs   V 3   0   1   0   -   Vs   Vs   0   V 4   0   1   1   -   Vs   0   Vs   V 5   0   0   1   0   -   Vs   Vs   V 6   1   0   1   Vs   -   Vs   0   V 7   1   1   1   0   0   0         Figure  5. S pac e v ect or  repres entat ion       4.   DYN AM I C   M ODELL IN G   OF   I NDU CTI ON   MOT OR   An   in duct ion   mo to r   (IM )   po ssesses   man y   s pecial   feat ur es   li ke   r obus t   in   c on st ru ct io n,   hig h   to rque   to   inerti a   rati o,   a ble   to   be   util iz ed   in   a ny   en vi ronme nt.   Hen c e,   m os t   of   the   industrial   dri ve s   us e   an   in du ct io n   mo to r.   T he   sta tor   of   the   in du c ti on   mo t or   r eq uires   a   t hr ee - phase   sup ply .   T his   will   est abli sh   MMF   in   the   sta to r   wh ic h   in   tu rn   pa sses   th rou gh   the   ai r   ga p,   li nked   with   the   r ot or   ci rcu it .   Th us,   an   em f   is   in duced   in   t he   ro t or   a nd   it   is   simi la r   to   a   tran sf ormer.   Hen ce ,   t he   e quivale nt   m odel   of   the   tran sf ormer,   with   sli gh t   modific at io n,   co uld   be   us e d   f or   IM.   To   dra w,   eq ui valent   ci rcu it   di agr am   of   IM,   t he   a ssumpti ons   [ 27, 28]   ma de   are ;   (i)   T he re ex ist s   un i form   ai r   ga p,  (ii)   Si nu s oi dal  fl ux  distr ibu ti on   is  un i f orm,   (iii )   Ef fe ct   of  c ha nge  in  t he  parame te r  is   neg le ct e d,   (iv ) Effect  of satu r at ion  is  ne glect ed.   The   perf or ma nc e   of   the   IM   c ou l d   be   easi ly   ob ta ine d   base d   on   its   eq ui valent   ci rc uit   model   w hich   is   sh ow n   in   Fig ure   6.   T his   help s   to   stu dy   t he   ste ady - sta te   c ha racteri sti cs,   ne glect ing   the   t ran sie nt   sta te   wh ic h   occurs   due   to   change   in   t he   load   or   e ven   c hange   in   fr e qu ency,   espe ci al ly   in   va riable   s peed   dr i ves.   M ost ly,   these   dr i ves   a r e   base d   on   co nv e rter   ci rc uits.   T he   c onve rte rs   a re   fe d   t hro ugh   de finite   s ource   volt age .   Hen ce ,   there   is   a   ce rtai n   li mit   to   draw   t he   outp ut   po wer   from   t hem.   More ove r,   filt e rs   of   de finite   siz e   ma y   be   connecte d   to   s hap e   the   outp ut   vo lt ag e   of   t he   co nv e rters .   T hi s   li mit s   them   to   s uppl y   la r ge   transient   pow e r   a nd   makes   esse ntial   to   stu dy   the   dyna mic   m odel li ng   of   s uch   dri ves.       0  s e q u e n c e   e q u i v a l e n t   c i r c u i t Q -   a x i s   e q u i v a l e n t   c i r c u i t - + - + R s ω e Ψ qs L ls L l r ( ω e -   ω r ) Ψ qr V ds I ds L m I dr R r + - V dr I dr V o r + L l r - V o s I o s - R s L ls + Rr V q s V q s D -   a x i s   e q u i v a l e n t   c i r c u i t + + - R s L ls L m L l r R r ( ω e -   ω r ) Ψ dr + - + - - I q s I qr ω e Ψ ds     Figure   6:   A   dq0   e qu i valent   ci rcu it   of   an   I nduction   M ot or     d -   a x i s q -   a x i s V 1   =[ 1 0 0 ] V 2   =[ 1 0 0 ] V 3   =[ 1 0 0 ] V 4   =[ 1 0 0 ] V 5   =[ 1 0 0 ] V 6   =[ 1 0 0 ] V 0   =[ 1 1 1 ] V 7   =[ 0 0 0 ] T 1 T 2 V ref 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       Mo du l ation i ndex ef fe ct  on i nv ert er base d  in du ct io n m oto r   dr iv e ( Akhil es h S ha r m a)   1791   4.1   Equi va le nt   ci r cuit   of   in duc tion   m otor   The   dynamic   beh a vior   of   t he   mo to r   is   due   to   the   ti me - de pende ncy   of   vo lt age   an d   to rque.   He nce,   they   ca n   be   e xpress ed   in   differentia l   eq uations.   B ut,   this   will   increase   s ys te m   c omplex it y.   Fig ure   6   in dicat e s   dq0   eq ui valen t   ci rcu it   dia gram   of   an   I M .   T he   dyna mic   eq uatio ns   of   the   mo t or   are   de vel op e d   f r om   its   equ i valent   ci rc uit   [ 9,   11,   24,   27,   29 ].     4.2   Arbitr ary   refe rence fr ame   This   helps   in   r epr ese ntin g   a   s inu s oid al ly   va r ying   qu a ntit y   i nto   its   DC   eq ui valent.   If   t his   con ce pt   is   us e d   in   I M ,   t he   con tr ol   of   the   mo to r   bec ome s   easy ,   simi la r   to   a   DC   m otor.   U nder   t his   fr ame ,   it   is   assume d   that   the   an gu l ar   sp ee d   of   the   mo to r   is   r otate d   at   the   an gu la r   sp ee d   of   the   ref e re nce   fr ame .   U nder   this   ci rcu msta nce,   t he   di ff e ren ce   in   an gula r   s pee d   bec om e s   zer o   an d   th us   a   si nu s oi d   sig nal   looks   li ke   DC   s ign al .   This   m akes   ea sy   to   dev el op   small - sig nal   e qu at io n   out   of   the   non - li near   eq uatio n,   des cribin g   t he   op erati ng   po i nt   by   DC   va lues   on l y.     The   eq uiv al e nc e   bet wee n   t w o   a nd   t he   thr ee - phase   mac hine   co uld   be   ach ie ved   pr ov i ded   their   MMF   pro du ce d   a re   equ al .   If   t her e   are   N p   num be r   of   wi nd i ng s   pe r   ph a se,   for   ide ntica l   MMF,   the   two   windin g   machine s   nee d   3Np/2   t urns   pe r   phase.   The   MMF   of   th ree - phase   c ou l d   be   conve rted   into   two - ph ase   whos e   axes   a re   d   a nd   q   re sp ect ivel y.   Con si der i ng   α   and   β   as   t he   a xi s   of   the   a rb it ra ry   ref e re nce   f r ame,   the   th ree - ph a s e   vo lt age   is   e xpr essed   a s:     [ ] = 2 3 [ 1 1 2 ⁄ − 1 2 ⁄ 0 √ 3 2 ⁄ − √ 3 2 ⁄ ] [ ]     ( 10)     The   direct   a nd   qu a drat ur e   axis   volt ages   a re   e xpresse d   as ,     [ ] = [   −   ] [ ]     (11)     The   i ns ta nta ne ou s   r otor   a nd   s ta tor   c urren t   e quat ions   are ,     [ ] = [  −    ] [   ]   (12)   [ ] = − 2 3 [ 1 2 ⁄ √ 3 2 ⁄ 1 2 ⁄ √ 3 2 ⁄ ] [ ]     (13)     Wh e re,   V R ,   V Y   a nd   V B   are   t he   sta to r   volt ages ,   V d   a nd   V q   are   the   direct   an d   qu a drat ur e   a xi s   vo lt age s.   i rd   and   i rq   are   t he   insta ntane ous   dq   r otor   cu r ren ts,   V α   an d   V β   are   a r bitrar y   re fer e nce   fr a me   volt ages   wi th   i α   an d   i β   as   their   insta ntane ous   cu rre nts,   wh il e   i R ,   i Y   and   i B   be   the   instanta neous   st at or   c urre nts.   The   e quat ion s   (10)   to   (13)   re pr e sents   the   ass ociat io n   of   cu rr e nts   a nd   volt ages   in   diff e re nt   f rame s.     The   dyna mic   model   of   IM   may   be   ac hiev ed   by   est a blish ing   an   e qu i valence   betwee n   3 - Φ   a nd   2 - Φ   machine s.   T hi s   is   base d   on   t he   ma gnit ud e   of   MMF   c reat ed   in   windin gs   of   both   mach ines   w he n   the   equ a l   mag nitud e   of   c urren ts   is   al lo wed   to   fl ow   t hro ugh   t hese   wi nd i ngs.   S o,   N p   of   3 - Φ   will   pro du ce   t he   same   MMF,   pro vid e d   two   windin g   mac hi nes   hav e   3N p /2   num ber   of   tur ns   per   phase.   T he   direct   ( d)   a nd   qua dr at ur e   (q)   axe s   MMF   are   fou nd   by   res olv i ng   M MF   of   the   t hr ee - phase   al ong   t hese   axes .   The   eq uatio n,   thu s   dev el op e d,   will   hav e   s om e   c ommo n   facto r   t hat   c ou l d   be   e li minate d,   e xc ept   c urren ts   in   windin gs.   F r om   Fig ure   6,   the   dq0   sta tor   a nd   ro t or   vo lt age s,   unde r   balance d   c onditi ons,   can   be   ex pr e ssed   ea sil y   [ 27,   31 ].   Fr om   t he   e quivale nt   ci rcu it ,   the   volt age   e qu at i on s   are,      =  +   +    (14)    =  +   −      ( 15)    =  +   + ( − )      ( 16)      =  +   − ( − )      ( 17)    =  +       ( 18)    =  +       ( 19)   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   :   1785   –   1798   1792   Wh e re,    =  + (  +  )   (20)    =   + (  +  )   (21)    =   + (  +  )   (22)      =   + (  +  )   (23)    =     (24)    =     (25)        and      are   the   zer o - se quence   fl ux   li nkage s.   Wh e re,     and     are   ar bitrar y   a ngular   a nd   sta to r   angular   f reque ncy   res pecti vel y.   The   el ect r om a gn et ic   to r qu e   is   ex pr e ssed   as,     = 3 2 2 (   −   )     ( 26)     Also ,     = + 2      ( 27)     T l   an d   J   re pr es ent   loa d   to r qu e   an d   m om e nt   of   ine rtia   res pec ti vely.       5.   CLOSE D - LO OP   CONTRO L   The   cl os ed - loop   op e rati on   usual ly   pro vid es   more   acc urat e   res ults   at   the   cost   of   inc re asi ng   ci rcu it   com plexity .   I ndus t rial   dri ves   empl oy   diff e r ent   ty pes   of   mo to rs   by   varyi ng   ac   sup ply .   The   s peed   of   thes e   dr i ves   c hanges ,   due   to   facto r s   li ke   cha nge   in   the   s uppl y   vo lt age   or   c ha ng e   in   loa d   t orq ues.   U nd e r   t hese   var ia ti ons,   the   dr i ve   sp ee d   vari es.   this   le ads   to   de velo pm e nt   of   s pee d   co ntr ol   by   ma ny   me thod,   no ta ble,   direct   tor qu e   of   V/ F   methods   [ 30,31].   T her e   a re   c ertai n   a pp li cat ion s ,   wh e re   t he   sp ee d   of   t he   in du st rial   dr i ves   sh oul d   be   co ns ta nt   un der   a ny   ci rc umst ances.   Unde r   su c h   a   sit uation,   the   e ff ect   of   a ny   of   the   pa rameters   sho ul d   not   reduce   t he   s pe ed   of   s uch   dri ves.   This   is   possible   onl y   if   the   dr i ve   s ys te m   is   op e rated   in   a   cl os ed - lo op.   The   cl os ed - lo op   op erati on   will   ha ve   no   ef fect   of   change   in   par a mete rs   on   the   industrial   dr i ve s.   A   simple   dia gram   of   a   cl os e d - lo op   s ys te m   is   s how n   in   Fi gure   7.   As   see n   from   t he   Fig ur e ,   t hat   an   error   si gn al ,   E( s),   is   gen e rated   by   subtract in g   plant   out pu t,   Y( s ),   from   t he   ref e ren ce   si gna l,   R(s).   A   c on t r oller   of   gain ,   G c (s ),   mu st   be   a ble   to   co ntr ol   the   error.   If   G p (s )   is   the   gai n   of   the   pla nt,   the n   the   ov e rall   tr ansf e r   functi on   is   e xpresse d   in   ( 30).           Fig ure   7 .   Cl os e d - l oop   represe ntati on   of   a   s yst em       ( ) = ( ) − ( )     ( 28)   ( ) = ( ) ∗ ( ) ∗ ( )     ( 29)     The   overall   tra ns fe r   functi on,   TF,   is   e xpres se d   as ,      = ( ) ( ) = ( ) ∗ ( ) 1 + ( ) ∗ ( )     (30)     5.1   Neur al   ne two rk  ( NN)   archi tectu re   It   is   base d   on   t he   interce ptio n   of   a   ne uron,   a   basic   unit   of   the   nerv ou s   sy st em,   on   wh ic h   t he   messa ge   is   trans mit te d   from   t he   brai n   to   dif fer e nt   pa rts   of   t he   hum an   body   a nd   ba ck   to   the   br ai n.   Each   neuron   has   a   transmitt er   a nd   a   receive r   thr ough   wh ic h   these   mes sag es   are   tra ns mi tt ed   an d   recei ved.   T his   sc he me   of     R ( s ) G p ( s ) G c ( s ) Y ( s ) + - E ( s ) 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       Mo du l ation i ndex ef fe ct  on i nv ert er base d  in du ct io n m oto r   dr iv e ( Akhil es h S ha r m a)   1793   transmitt in g   an d   recei ving   ca n   al so   be   ap plied   to   so l ve   rea l - li fe   series   pro blems   base d   on   certai n   set   of   ru le s .   Hen ce ,   it   can   be   sai d   that   an   NN   has   a   se qu e nce   of   set   of   r ules   that   is   pro fici ent   to   i den ti f y   fun da mental   associat ions   in   a   set   of   inf or mati on   in   s uch   a   man ne r   t hat   is   simi la r   to   t he   huma n   brai n.   An   NN   c ou ld   be   natu ral   li ke   m essage   tra ns mi ssion   a nd   recei ving   in   human   bein gs   or   a rtific ia l   to   so lve   r eal - li fe   pro blems   by   human   bein gs .   It   has   a   f eat ure   to   a da pt   it sel f   with   t he   c hange   in   in puts   i.e .   the   net wor k   c an   pro du ce   the   m ost   su it able   re su lt   without   c hangi ng   its   str uctur e .     Neural   netw orks   le ar n   it sel f   from   the   prel oad   ta sk   by   a nalyzin g   trai ni ng   sam ples   from   t he   ta s k   wh ic h   ha ve   be en   pre - lo ade d.   F or   e xam ple,   an   obje ct   rec ogniti on   sy ste m   ma y   co ntain   thousa nds   of   la bele d   images   of   thin gs   li ke   glass ,   t ables,   et c.   It   w ou l d   fin d   gr a phic al   patte r ns   of   t he   ima ges   that   are   c onsis te ntl y   correla te d   with   s pecific   la bels .   In   ge ner al ,   an   NN   c on ta in s   t hous a nds   or   ev en   m or e   sim ple   processin g   node s.   These   nodes   a r e   cl os el y   li nke d.   T hese   nets   a re   orde re d   into   strat a   of   no de s,   na mely,   i nput,   hi dden   a nd   ou t pu t   nodes .   T he   net s   co ul d   be   “fe ed - for ward,”   or   “ feed - backw ard ” .   In   feed - f orward   arc hitec ture,   the   data   move s   on l y   in   the   for ward   di recti on.   A   sin gle   node   may   recei ve   and   tra nsmi t   data   from   se ve ral   nodes   in   a   la yer   unde rn eat h   an d   ab ove   it.   W hile,   in   fee d - ba ckw a r d,   s ome   portio n   of   the   outp ut   is   f ed - bac k   to   tra in   the   netw ork.   In   the   ne tw ork,   eac h   node   has   a   s pecific   weig ht,   in dicat ed   by   “W i ”.   W he n   the   net wor k   is   li ve ,   t he   node   acce pts   a lt ered   data   t ha t   gets   mu lt ipli ed   by   its   weig ht   “W i ”,   sum med   up   with   bi as   “b”   res ulti ng   in   a   sing le   numb e r.   If   the   num ber   is   le ss   than   a   t hr es hold   value,   the   node   does   not   pass   a ny   da ta   to   the   subs equ e nt   la yer .   B ut,   if   t he   num ber   is   gr eat er   t han   the   th reshol d   va lue,   t he   no de   t ran s mit s   the   num ber.   A   sim plifie d   mu lt i - la ye r   NN   struct ur e   [ 32]   is   show n   in   Fi gure   8.           Figure   8 .   A   simpli fied   m ulti - la yer   NN   str uc ture         In it ia ll y,   weig hts   an d   t hr es holds   f un ct io n   a re   ra ndoml y   c on si der e d,   the n,   t he   trai ni ng   of   NN   sta rts.   The   data   to   be   trai ne d   is   f ed   t hro ugh   in pu t   la ye rs,   th en,   it   passes   t hro ugh   su c ces sive   la yer s .   At   each   su ccessi ve   la ye r,   it   gets   m ulti plied   to   it s   weig hts.   Th e   res ultant   ge ts   ad de d   t og e ther   unti l   ra di cal ly   trans forme d   da ta   is   avail able   at   the   outp ut   la yer.   T rainin g   is   co ntin ued   by   co ntinuo us ly   adjustin g   t he   weig hts   and   th reshold s   un ti l   co ns ist e nt   res ults   are   obta ined   at   t he   outpu t.   A   blo c k   dia gr a m   re prese ntati on   of   in ver te r   connecte d   to   a   mo to r   loa d   has   bee n   sho wn   in   Fig ur e   9.   In   this   case,   the   dynamic   loa d   consi der e d   is   an   I M .   The   m otor   s pee d   is   measu red   a nd   it   is   co nv e rted   into   its   equ i valent   fr e quenc y.   E ven,   t he   ref e ren ce   s peed   in   r pm   ha s   bee n   c on vert ed   to   its   f requ ency   domain.   The n,   the   fr e que ncy   error   is   m easu r ed.   T hese   valu es   are   sto re d   to   tun e   t he   NN   c on t ro ll er.   I niti al ly,   the   weig hts   ha ve   been   rand om ly   ass um e d.   A   sigm oid   has   bee n   us e d   as   an   ac ti vation   f unct ion.   The   c ontro ll er   tu nes   up   the   er r or   so   that   it   is   mi nimize d.   T he   ou t pu t   of   the   c on t ro ll er,   t hu s   ob ta ine d,   is   a   f reque ncy   si gn a l.   T his   si gn al ,   al ong   with   a   par ti c ular   mod ulati on   ind e x,   is   us e d   to   generate   gat e   pulse s   for   t he   in ver te r   w hich   c ontr ols   t he   RMS   ou t pu t   volt age   app li ed   to   t he   I M .           Figure   9.   Cl os e d   loop   of   in du c ti on   m otor       O ut put ,  Y I N P U T S X 1 X 2 W 1 W 2 W n B i a s ,  b S i gm oi d A c t i va t i on F unc t i on W e i gh t s ,  W i 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   :   1785   –   1798   1794     6.   RESEA R CH   METHO D     Ba sed   on   t he   s ect ion s,   disc usse d   a bove,   Simuli nk   m odel s   hav e   bee n   de velo ped   in   MATL AB   16a.   The   im pleme nt ed   m od el   is   de picte d   in   Fig ur e   10.   F or   a   par ti cula r   MI,   the   switc hi ng   pu lse s   f or   an   i nv e rter   us in g   s pace   ve ct or   m odulati on   ha ve   been   ge ner at e d   by   c onsiderin g   the   sinu s oi dal   wa ve   of   50Hz   as   refe ren ce   sign al .   A   tria ngula r   wa ve,   use d   as   a   ca rr ie r   sign al ,   has   a   carrier   fr e quen cy   of   720   Hz.   The   c omparis on   of   these   two   sig na ls   is   us ed   to   ge ner at e   tri gg e ring   pulse s   f or   t he   po wer   el ect ronic   co ntr olled   switc hes,   pro du ci ng   a   ste p   al te rn at ing   volt age.   T hi s   al te rn at ing   volt age   has   bee n   sh a pe d   into   a   sinu s oid al ly   varyin g   volt ag e   us in g   a   low   pass   filt er   (LPF).   It   is ,   the n,   a ppli ed   to   the   sta to r   of   a   th ree - ph a se   in duct ion   mo to r,   m odel le d   in   a   sta ti on ar y   ref e ren ce   frame   w ho s e   pa ramete rs   are   gi ven   in   Table   1 .   This   pro vid es   an   op en - l oop   operat ion   of   the   in ver te r - ba sed   c ontrol   of   i nductio n   m ot or.   In   the   cl os e d - l oop,   f or   a   known   MI,   meas ured   sp e ed   of   IM   is   co nverte d   into   its   f reque ncy   do main.   This   is   c ompar ed   with   the   eq uiv al ent   freq ue ncy   of   t he   re fe ren ce   sp ee d.   T he   e rror   th us   ge ner at e d   is   min imi zed   with   a   fee d - forw a rd   ne ural   ne twork   ( NN)   with   15   la ye rs ,   one   i nput,   one   ou t pu t   an d   a   sig mo i d   act ivati on   functi on.   T he   NN   t un es   t he   error   si gn al   so   that   it   beco me s   zero,   pro vid i ng   an   ou t pu t   f r equ e nc y   eq ual   to   the   ref e ren ce   f re quenc y.   T his   frequ e nc y   is   us e d   f or   ge ne rati ng   a   sin usoida l   ref e re nce   si gnal ,   w hile   the   carrier   fr e qu e nc y   r em ai ns   unc hange d.   C omparisio n   of   t he   two   s ign al s   pro du ce s   trig ger in g   pu lse s   us in g   SVPW M   te chn iq ues ,   whose   width   of   t he   pu lse s   de pe nd   up on   the   re fer e nce   fr e qu e ncy,   th us   c ontr olli ng   t he   on   ti me   of   the   s witc hes.   T his   est ablis hes   a   cl os e d - loop   operati on.           Figure   10:   Cl ose d - l oop   simul ink   model   of   in du ct io n   mo t or       7.   RESU LT S   A ND   DI SCUS S ION   The   var i ou s   re su lt s   obta ine d   are   de picte d   in   Fig ur e   11   to   Figure   13   f or   bo t h   op e n - l oop   a nd   cl os e d - loop   co ntr ol.   Figure   11   i nd i cat es   the   li ne   vo lt age   of   one   ph as e   with   it s   corres pondin g   RMS   val ue.   These   values   a re   35 9.9   V,   38 8.8   V,   415.6   V,   427.8   V,   406.9   V,   a nd   384.1   V   r es pecti vely   for   MI   va riat ion s   f rom   0.6   to   1.5.   The   de viati on   in   the   RMS   volt age   is   due   to   the   w idth   of   the   pu l ses.   For   l ow e r   MI,   the   wi dth   of   t he   pu lse s   for   uppe r   powe r   s witc hes   dec reases   wh il e   t he   widt h   of   the   pulse s   f or   lo wer   s witc h   i ncr eases   th ereb y   pro du ci ng   lo w er   R M S   volt ag es.   Under   this   case,   it   is   te r m ed   as   un der - m odulati on.   As   t he   m odulati on   ind e x   reaches   unit y,   the   maxi mum   RMS   vo lt age   of   427.8 V   is   ob ta ine d.   At   t his   m odulati on   ind e x,   the   wi dth   of   pu lse s   for   bo t h   lower   a nd   up pe r   switc hes   a re   equ al .   T he   reverse   occ urs,   w hen   MI   is   gr e at er   tha n   unit y.   Unde r   this   case,   it   is   te rmed   as   over - m odulati on.   T her e fore,   the   RMS   vo lt age   r edu ce s   to   38 4.1   V   for   1.5   MI.   T he   per ce ntage   dro p   in   volt age   f r om   un it y   MI   to   1.5   MI   is   a   10. 22%.   F or   dif fer e nt   MI,   li ne   vo lt age s   are   ta bu la te d   in   Ta ble   3 .   Figure  12  in di cat es  an  open - loop  s pee d  c ontr ol  of  the   I M   with  differe nt  MI.   It  is  vis ible  from   the  Figure  that  th e  maxim um   s pee d  of  IM   is  1476  r pm   w hich  is   achieve d  at   a  un it y  MI  f or  a  load  t orqu e  of  10   N - m.  The   s pee d  decr ease s  with   e it her  a n  inc re ase  or  a   dec rea se  in   M I   from   un it y.   I n  t he   unde r - mod ulati on,  t he   per ce ntage   s pe ed  va riat ion  is   2.3 7  %   w hile  in   ove r - m odul at ion ,  t his  va r ia ti on   is   1.0 1% .  T his   is  du e   to   le ss   Evaluation Warning : The document was created with Spire.PDF for Python.