Int ern at i onal  Journ al of  P ower E le ctr on i cs a n d  Drive  S ystem s   ( IJ PEDS )   Vo l.   12 ,  No.   3 ,  Septem be r 2021 , pp.  1304 ~ 1314   IS S N:  20 88 - 8694 ,  DOI: 10 .11 591/ ij peds . v12.i 3 . pp 1304 - 1314          1304       Journ al h om e page :  http: // ij pe ds .i aescore.c om   A   com parative   s t udy   for   t he   pe rfo rman ce   operatio n   of   electric   machi ne   bas ed   on   conven tional   and   D - Q   theori es       Sa n ab el   M.   AL - H ajzber ,   A hmed   J.   Ali,   Alya   H.   AL - Rif aie,   Ab d ull ah   K.   S hansh al   Depa rtment   of   E le c tri c al   Pow er   Te chn ique s   E ngi nee ring ,  Engi ne e ring   t ec hni cal   c o ll eg e ,  Mos ul   Northe rn   T ec hn i ca l   Univer sity ,   Ir aq       Art ic le   In f o     ABSTR A CT   Art ic le   hist or y:   Re cei ved   Dec  12, 202 0   Re vised   Jun   17 , 202 1   Accepte d   J ul   8 , 202 1       Induc ti on   mo tors   ar e   used   wid el y   in   industrial   app lications,   tha nks   to   th ei r   high   eff icienc y   and   r e li abilit y   which   n omi nates   it   as   a   g ood   machin e   use d   in   var ious   appl i ca t ion.   Bas ed   on   the   appl i c at ion   and   accur ac y,   mode l ing   p roc esses   of   el e ct ri c   ma ch ines   are   carrie d   out   using   diff ere n t   ma th em a ti c al   m et hods.   The   most   co mm on   me thod   for   mod el ing   elec tri c al   ma ch ine s   is   bas ed   on   soluti on   of   diff ere nt ia l   e quat ions   of   vol t age s   as   wel l   as   ca l cul a ti ng   the   t im e   var y ing   self - inductances   and   the   mut u al   i nduct an ce s   base d   on   the   roto r   an gle .   One   of   the   most   i mportant   fe at ure s   of   t his   m et hod   is   th at   the   induc t ance   is   no   long   depe nd   on   th e   time   var y ing   voltage,   whi ch   is   th e   major   problem   fac ing   the   conve nt iona l   mo del .   But   the   D - Q   mode l ing   app roa ch   h as   seve r a l   probl em s,   the   gr eate st   of   w hic h   is   th at   th e   v olt ag e   appl i ed   on   stat or   must   be   bal an ce d   in   addi ti on   to   th e   f ac t   that   the   win ding   ar e   sinusoi dal   d istri but ed   f orm.   H ere in   thi s   rese arc h   is   f ocuse d   on   buil d   two   models   of   a   3 - Φ   induction   mot or   (IM)   base d   on   the   t wo   analytica l   a pproa che s   and   com par e   them   to   c la ri fy   the   diffe ren ce.   The   result s   h ave   b een   show n   tha t   th e   conve n ti ona l   mode l   giv es   more   a cc ur at e   r esponse   when   it   is   appl i ed   in   both   nor ma l   an d   upnorm al   oper ation.   MA T LAB/Sim uli nk   softar e   is   used   to   construct   th e   D - Q   and   cl assic al   abc   IM   mode ls.   Ke yw or d s :   Diff e re ntial   eq uations     D - Q   m odel   Eq uiv al ent   ma gn et ic   ci rc uit   Finit e   e le ment   method     Ind uction   m otors     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 :   Ahmed   J.   Ali   Dep a rtme nt   of   Ele ct rical   Pow er   Tec hnolog y   En gin eeri ng     En gin eeri ng   T echn ic al  C ollege /M osul   Northe rn   Tec hnic al   U niv e rsity ,   Ir a q   Emai l:   ahme d. j .ali @n tu .edu.i q       1.   INTROD U CTION   Ind uction   mac hin e   with   mu lt i   ph a ses   hav e   man y   feature s   com par e d   with   cl assic al   typ e ,   it   has   a   low   tor qu e   rip ple,   f ew   har m onic s   com pone nts,   l ow   val ue   of   st at or   c urre nts   at   same   le vel   of   phase   vo lt age ,   fau lt   tolerant   a bili ty   is   great er   an d   m or e   reli able.   In   a dd it io n,   it   has   the   abili ty   to   sta rt   if   ther e   is   an   op e n   or   short   ci rcu it   at   one   of   the   sta to r   phases.   N ow a da ys   in du ct io n   machine s   ha ve   been   e xtensi ve ly   us e d   in du s tria l   app li cat io ns   due   to   the   sim ple   struct ur e,   reli abili ty,   hi gh   e ff i ci ency   with   ac cepted   powe r   f act or   in   ad diti on   to   its   low   pri ce   com par e d   wit h   permane nt   ma gn et   a nd   s ynch ron ou s   machi ne s.   D ue   to   me nt ion ed   featu res   it   as   a   good   machi ne   us e d   in   va rio us   ap plica ti on   Also   it   can   be   us e d   in   unpre dicta ble   or   hug   ope r at ing   co ndit ions   a nd   did   not   af fected   by   co rrosio n   and   t her e   are   no   sp a rk   l os ses   due   to   a bs e nce   of   br us he s   in   cage   ty pe   r oto r s.    T he   gen e rated   el ec trom a gnet ic   to rque   is   cal c ulate d   base d   on   t he   de rivati ve   of   the   sto re d   mag netic   e nergy   a nd   relat ive   to   the   angular   locat io n   of   the   r ot or .   In   a ddit ion ,   it   is   po s sible   to   eval uate   the   t orq ue   base d   on   t he   relat ion s hip   be tween   the   c urre nts   an d   in du ct a nces.   T his   ap pr oach   is   cal le d   t he   el ect romag ne ti c   cou ple d   ci r cuits   [1 ] - [ 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       A com pa r ative   stud y  for  t he p erf or m ance  operatio n of ele ct ric  mach i ne  …   ( Sa nabel M.  A L - H ajz ber )   1305   Diff e re nt   ap proach e s   ha d   be en   use d   to   si mu la te s   the   dyna mic   an d   st eady   sta te   performa nce   of   el ect rical   mach ines.   One   of   t he   widel y   a pproaches   us e d   to   c on st ru ct   t he   operati on   of   el ect ric   mac hin es   unde r   healt hy   a nd   fa ulty   c onditi ons   is   the   fi nite   el ement   met hod   [5 ] - [ 8].   T his   method   is   a pp l ie d   to   sim ulate s   the   el ect rical   an d   mecha nical   pa rts   base d   on   the   geomet rical   dimensi ons   an d   t ype   of   mate rial s   us ed   to   buil d   the   machine .   It   is   a lso   us e d   to   cal c ulate   the   el ect ri cal   pa rameter s   of   el ect ric   mac hin es   acc ur at e   by   s olv i ng   nonl inear   diff e re ntial   equ at ions   on   a   s pecified   reg i on   [9].   M ore ov e r ,   modeli ng   me thod   us i ng   t he   equ i valent   ma gn et ic   ci rcu it   is   al so   ut il iz ed,   wh ic h   dep e nds   on   the   cal culat ion   of   reluctance s   f or   po s sible   ma gn et ic   flux   pat hs   within   the   el ect rical   machine.   B ut   this   method   has   s ever al   dr a wb ac ks   li ke   ti me   co ns um ption   in   s olu ti on   the   differentia l   equ at io ns   a nd   require d   an   ac cur at e   in f orma ti on   a bout   the   el ect ric   machi nes,   w hich   ma ke   it   us i ng   in   desig n   appr oach es .     The   cl assic al   ( abc)   ap proac h   wh ic h   is   us e d   to   sim ulate   the   dynamic   pe rfo rma nce   a nd   ca lc ulate s   the   main   var ia bles   directl y   with ou t   af fect   by   the   as ymmet r y   of   c urren ts ,   volt ages   a nd   i nducta nces   [ 10] .   T he   dynamic   res pons e   of   t he   in du ct ion   mac hin e s   unde r   un sta ble   an d   fa ults   ope rati on   a re   sim ul at ed   easi ly   usi ng   D - Q   tra nsfo rmati on   the ory ,   wh e re   t his   a pproac h   is   use d   to   m od el   an d   sim ulate s   the   two - phase   an d   short   ci rcu it   conditi on   on   st at or   windin g   ba sed   on   t he   sa me   set   of   eq uat ion s   de velo ped   for   no rmal   ope rati on   [ 11].   A   gen e ral   pur po se   m od el   is   intr oduce d   to   sim ulate   the   ste ady   sta te ,   tr ansient   a nd   unbalance d   t wo - ph a se   op e rati on   of   the   machine s   [12 ] ,   [ 13 ] .   In   ad diti on,   the   D - Q   m od el   is   us e d   as   a   com pute r   ai de d   desig n   to   simulat e   an d   rea li ze   the   performa nce   operati on   durin g   sta rt   up,   br ea ki ng ,   re gen e rati on   a nd   al so   at   op e n   ci rc uit   an d   bl oc ked   ro t or   te st   of   inducti on   mac hin e.   F or   best   unde rstan ding   the   ope rati on   of   el ect ric   mac hi nes,   it   is   nece ssary   to   c onsid er   the   eff ect   of   sat ura ti on .    D ue   to   the   ma gnet iz ing   inducta nce   is   not   int rod uced   in   most   a nalytic al   meth ods,   the refor e   the   co mp a rison   betwee n   pra ct ic al   and   sim ulate d   r esults   has   a   big   dif fe ren ce .   T hu s ,   in   orde r   to   c onstruct   an   accurate   m ode l,   it   is   imp ort ant   to   i ntr oduc e   al l   the   non - li near   c har act erist ic s   of   ma gn et ic   mate ria ls   [ 14 ].   Ca lc ulati on   of   va r ying   in du c ta nce   with   ti m e   is   the   dra wback   of   this   ap proac h   w hich   le ads   to   incr ea se   the   inv est igati on   ba sed   on   D - Q   th eory.   T his   a ppr oach   re moves   t he   e ff ect   of   ti me   varyin g   as   well   as   sim ulat es   the   machine s   unde r   diff e ren t   oper at ing   c onditi on s.   T he   D - Q   me thod   is   us e d   to   model   the   m oto r   w her e   bo t h   sta tor   current   a nd   m agn et ic   fl ux   ha s   a   co ns ta nt   m agn it ude   a nd   it   is   easy   to   t rac k   their   ref e re nc e   values   [1 5 ].   D - Q   trans formati on   ref e ren ce   t he ory   ha s   the   a dvanta ges   of   re du ce d   the   num ber   of   paramet ers   w hich   re duce   the   com plexity   acc ompanie d   with   the   us e   of   tra di ti on al   meth od s   to   sim ulate   the   mu lt i - ph a se   machine   [16 ] - [ 19].   Ind uction   mo t or s   (I.Ms.)   a re   us e d   wi dely   in   industr y   f or   up   to   10MW   in   siz e.   D ur in g   st art - up,   I.Ms .   dr a w   la r ge   c urr ent,   pro du ce   hi gh   volt age,   to r qu e   osc il la ti on   as   well   as   ge ne rate   ha rm on ic s .   Va rio us   mode ls   are   dev el op e d   to   s tudy   the   ste a dy   sta te ,   tra ns ie nt,   healt hy   a nd   fa ulty   op e rat ing   c onditi ons   of   I . Ms .   [ 20].   The n   models   are   te ste d   to   be   reli abl e   an d   acc ur at e.     Usu al l y,   the   ch aracte risti cs   of   the   th ree   phase   in du ct i on   mac hin e   s uch   as   the   cu rr e nt,   in du ced   volt ag e   and   li nk a ge   flu x   ar e   de scri bed   base d   on   the   di ff e ren ti al   eq uat ion s   in   wh ic h   c oeffici ents   ar e   ti me   va ry i ng   (e xcept   the   sta nd   sti ll   conditi on   of   the   r otor),   the   m at hemati cal   m od el   of   s uc h   c har act erist ic s   is   ve r y   c omple x   due   to   the   co ntin uous   changin g   of   the   curre nt,   in duc ed   vo lt age   an d   li nk age   fl ux   va lues   as   t he   el ec tric   ci rcu it   in   re la ti ve   mo ti on.   T her e f or e ,   f or   this   ty pe   of   mac hin e s   to   so lve   t he   equ at io ns   t hat   con ta in   ti me   de pendin g   qu a nt it ie s,   a   model   base d   on   mathemat ic a l   trans f or mati ons   a re   usual ly   utli zed   to   dec ouple   pa ramete r s   by   re ferrin g   it   to   a   commo n   ref e r ence   fr ame   s uc h   as   us i ng   Pa rk   a nd   Cl ar ke   trans formati on   meth ods   [ 21].   The   quantit ie s   of   the   three   ph a se   in du ct io n   mo t or   (IM)   su c h   as   c urren t,   in du ce d   volt age   a nd   li nk a ge   flu x   a re   represe nted   as   two - ph a se,   quad ra ture,   bala nced   sta ti on a ry   s ys te m   of   var i ables   ( al pha - be ta   axes )   a nd   base d   o n   C la rk e   trans formati on   meth od.   The   t wo - phase   balanced   sta ti onar y   syst em   of   qu a ntit ie s   of   the   c urren t   an d   volt age   a re   then   re pr ese nt ed   or   c onver te d   to   balance d   two - phase   ort hogo nal   r otati ng   ref e ren ce   s yst em   ba sed   on   Par k   trans formati on   method   as   sho wn   in   Fig ure   1   [21].   (α’,   β ’)   re pr ese nts   t he   t w o - phase   quad ra ture   r otati ng   syst em   of   the   r otor.   W hile   ( α,   β)   repr esents   t he   t wo - ph a se   quad ratu re   s ys te m   of   sta tor.   Wh e re   t he   r otor   a xes   ( α ’,   β’ )   ro ta te s   by   sp e e d   ( ωr)   a nd   by   a ng le   (θ r)   ref e rri ng   to   the   sta to r   re fer e nces   fra me.   T he   s ynch ron ou s   f rame   (D - Q)   axes   of   bo t h   sta tor   a nd   r oto r   r otate s   at   s pee d   (ω e )   with   sh i f t   an gle   ( θe)   re f err in g   to   the   sta tor   ref e re nce   fr ame .   (θsl)   is   the   a ng le   betwee n   t he   sy nc hro nous   f r ame   an d   r oto r   f rame   [22 ].   The   rest   of   t his   pap e r   is   org ni zed   as   f ollo ws,   Sect ion   2   pres ents   the   m od el   of   3 - phase   in duct ion   mo t or   in   a bc   a nd   D - Q   form ulas.   S ect ion   3   pro vi des   t he   res ults   of   IM   under   di ff ere nt   op e rati ng   c onditi on s .   In   sam   sect ion ,   a   co m par isi ons   of   the   dy namic   res pons e   f or   the   t wo   s uggeste d   IM   m odel s   ha ve   bee n   im pe mentd.   Finall y,   t he   c oncl us i on   an d   t he   most   imp or ta nt   di ff e ren ces   betwee n   the   two   m odel s   is   pr e sent   in   sect io n   4.   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 .  12 , N o.   3 ,  Se ptembe r  2021   :    13 04   –   13 14   1306       Figure   1 .   Stat or   fiel d   ori entat ion   (SFO )   tr ans formati on   ref e r ence   fr am e       2.   MO DELIN G   OF   I NDU CTI ON   MOT OR   Ba sed   on   Cl ar ke   tra nsfo rm,   t he   3 - phase   s up ply   volt age   of   the   I.Ms.   is   re presented   an d   t ra ns f orme d   to   (α,   β)   a xis,   as   s how n   in   Fig ure   1   a nd   e xpresse d   in   the   ( 1 ) - ( 4 )   [ 23]:     =   (  )     ( 1)     =   (  − 2 3 )   (2)     =   (  + 2 3 )   (3)     [   ] = 2 3 [  1   0  1 2  √ 3 2  − 1 2  − √ 3 2 ] [    ]     ( 4)     Wh e re   ( V a,   V b,   V c )   represe nt   the   thr ee   pha se   volt ages   of   the   bala nced   sy ste m,   (V α,   V β )   are   t he   two - ph a se   qu a drat ing   sta ti on a ry   bala nce d   s ys te m.     Ba sed   on   Pa rk   trans formati on   meth od   the   t w o - phase   sta ti on ary   sy ste m   (V α ,   V β )   a re   tra ns f ormed   into   two - phase   r otati ng   s ynch r onous   ref e rence s   frame   as   il lust rate   in   Fig ur e   ( 2)   and   gi ve n   by   the   ( 5 ),   ( 6 )   [2 0 ] ,   [ 23].       [   ] = [   −   ] [   ]     ( 5)     [   ] = [  −    ] [   ]     ( 6)             Figure   2 .   D - Q   axes   a ppli ed   on   a   t hr ee   phase   IM   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       A com pa r ative   stud y  for  t he p erf or m ance  operatio n of ele ct ric  mach i ne  …   ( Sa nabel M.  A L - H ajz ber )   1307   Figure   3   s how s   the   ge ner al   th r ee   windin gs   m od el   of   the   t hr e e   ph ase   ca ge   I M .   It   is   can   be   represe nted   by   set   of   ( 7 ) - ( 15 )   w hich   ex pr e ss   the   el ect r oma gn et ic   c ouplin g   betwee n   sta t or   an d   ro t or   [24 ] - [ 26].           Figure   3 .   Th re e - phase   c omp onent   sta tor   a nd   ro t or   IM        =  +       (7)      =  +       ( 8)     Wh e re   (v abcs ,   v abcr ,   ψ abcs,   ψ ab cr,   i abcs,   i abcr ,   R s ,   R r )   are   the   t hr ee   ph a se   vol ta ges,   li nkage   flu x,   cu rr e nt,   ph a se   resist ance   of   the   sta tor   a nd   ro t or   res pecti vely .         [     ] ≡ [   (  )    ] [     ]     ( 9)     = [          − 1 2  − 1 2  − 1 2   − 1 2  − 1 2  − 1 2   ]             (10)     = [          − 1 2  − 1 2  − 1 2   − 1 2  − 1 2  − 1 2   ]             (11)     Wh e re,    =  +    ,    =  +    a re   t he   sel f - i nducta nce   of   the   sta to r   a nd   ro t or ,   ( L l s,   L ms ,   L 1 r ,   L mr )   are   the   li nk a ge   an d   mag netiz in g   i nductance   of   st at or   a nd   r otor   windin g   resp ec ti vely.        =  [           ( + 2  3 )  ( − 2  3 )  ( − 2  3 )   ( + 2  3 )  ( + 2  3 )  ( − 2  3 )  ]             (12)      =      (13)     Wh e re   ( L sr ,   L mr )   are   the   mu t ua l   inducta nces   betwee n   sta to r   and   r otor   wind ing .   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 .  12 , N o.   3 ,  Se ptembe r  2021   :    13 04   –   13 14   1308    ′ =      =  [           ( + 2  3 )  ( − 2  3 )  ( −  3 )   ( + 2  3 )  ( +  3 )  ( − 2  3 )  ]             (14)       [     ′ ] = [ +   ′  (  ′ )  ′ + ′  ] [     ′ ]     (15)     Wh e re:   (  ′ )   is   the   mu tual   in duc ta nce   ref e r   to   s ta tor   side,   ( ′ , ′ )   is   the   sel f - i nduc ta nce   an d   resi sta nce   of   the   ro t or   windin g   r efer   to   sta to r   si de   resp ect iv el y.   T he   el ect r oma gn et ic   t orqu e   in   ( N.m.)   is   de scribe d   as   sho wn   in   (16)   an d   ( 17)   r especti vely .     = ( 2 ) (  ) [  ′ ]  ′     (16)     = − ( 2 )  { [  (  − 1 2  − 1 2  ) +  (  − 1 2  − 1 2  ) +  (  − 1 2  − 1 2  ) ]    + √ 3 2 [  (  −  ) +  (  −  ) +  (  −  ) ]  }     (17)       The   ro ta ti ng   s pe ed   of   the   ro t or   (ω r)   a nd   to r que   are   ro ta te d   as   show n   in   (18 ).     = ( 2 ) +     (18)     Wh e re   ( J )   is   the   m om e nt   of   i ner ti a   c offici en t   of   the   r otor   ( kg.m 2 ),   T L   is   t he   a ppli ed   s ha ft   to rque   of   I . M .   D - Q   axes   wit h   zer o   seq uen ce   c ompone nt   is   us e d   to   ha nd le   the   unbala nce   volt a ge   an d   c urren t   and   to   re verse   park  ҆ s   trans formati on,   by   tra ns f orm   t he   c onve ntial   ABC   r otor   paramet ers   int o   D - Q   a xes .   T he   li nk a ge   flu x   e qu at ion s   in   te rms   of   D - Q   a xes   c oils   ar e   giv e n   belo w   [13] :       = [  −  + 1 (  −  ) ]     (19)       = [  +  + 1 (  −  ) ]     (20)       = [  − ( − )  + 1 (  −  ) ]     (21)       = [  + ( − )  + 1 (  −  ) ]     (22)      = 1 [  1 +  1 ]     (23)      = 1 [  1 +  1 ]     (24)     1 = 1 ( 1 + 1 1 + 1 1 )     (25)     The   (D - Q)   a xe s   val ues   of   the   current   a re   i nvest igate d   as   gi ven   in   ( 26 ) - ( 29 ).        = 1 1 (  −  )     (26)      = 1 1 (  −  )     (27)      = 1 1 (  −  )     (28)   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       A com pa r ative   stud y  for  t he p erf or m ance  operatio n of ele ct ric  mach i ne  …   ( Sa nabel M.  A L - H ajz ber )   1309    = 1 1 (  −  )     (29)     The   value   of   t he   tor que   a nd   r ot or   s pee d   ca n   be   deter mine d   as   f ollow s:     = 3 2 ( 2 ) 1 (   −   )     ( 30)     = ∫ 2 ( − )     (31)     Wh e re   P   re pre sents   num ber   of   po le s;( ω b )   ba se   sp ee d.   Si nc e   the   ro t or   ca ge   ba rs   of   the   sq ui rr el   ca ge   I .M .   is   sh ort ed .   T he   rot or   volt age s   ( v q r,   v dr )   a re   s et   to   zero   in   t he   li nk age   flu x   e qu at i on s .       3.   SIMULATI O N   RESU LT S   AND   DISC USSION   Figure   4   de picts   the   wa veform   of   the   el ect romag netic   tor qu e   (Te )   gen e rate d   base d   on   AB C   (or   act ual)   trans formati on   model,   it   is   observ e d   that   a   hi gh   os ci ll at ion   with   va riat ion   of   the   value   of   (Te)   at   the   tra ns ie nt   reg i on   till   (tim e   =   0.5   sec )   t he reafter ,   a   ste a dy   sta te   value   can   be   ac hieve d.   T he   e ff ect   of   l oad   to r qu e   (T L )   on   the   r otati on   s pe ed   is   il lustrat ed   in   Fig ur e s   5   (a)   a nd   5   (b) ,   in   a no t her   w ord,   as   the   loa d   t orque   in cre ase   the   ro ta ti on   s pee d   of   the   I .M   dec rease   to   reac h   a   minim um   va lue   of   17 50r.p. m   at   maxim um   loa d   to rque   of   (12   N. m ).   Alte r nativel y,   t he   el ect romag netic   tor qu e   inc reases   as   sho wn   in   Fi gure s   6   ( a )   an d   6   ( b)   a nd   Ta ble   1   resp ect ivel y .       Table   1 .   Re la ti on s hi p   betwee n   s pee d,   TL   &   Te   of   IM     Tim e   ( sec )   Total   Sp eed     Load   to rqu e(N.m)     Dev elo p ed   to rqu e   ( N. m )     Po wer   ( w)   0   1800   0   0 .00 0 1 0 2 2   0   2   1783   4   3 .98 4   7 4 4 .5   4   1787   8   7 .98 2   1496   6   1750   12   1 1 .98   2 1 9 8 .9   8   1787   8   7 .98 4   1496   10   1783   4   3 .98 4   7 4 4 .5   12   1800   0   0 .00 0 1 0 2 2   0         Figure   4 .   Ele ct romag netic   to r qu e   ba sed   on   a ct ual   trans f orm at ion         (a)     (b)     Figure   5.   Rotat ing   sp ee d   var ia ti on   at   differe nt   load   c onditi on,   (a)   ap plied   l oad   to rque,   ( b)   sp ee d   of   m otor   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 .  12 , N o.   3 ,  Se ptembe r  2021   :    13 04   –   13 14   1310     (a)       (b)       Figure   5 .   Va riat ion   of   el ect romag netic   tor qu e   at   dif fer e nt   lo ad,   (a)   ap plied   load   t orq ue,   (b)   dev e ople d   t orqu e   of   m oto r       Figure   7   co mpa res   t he   wa veforms   of   the   ge ner at e d   (or   pro du ce d)   t orqu e   base d   on   ABC   and   D - Q   a xes   trans formati on   of   mac hin es   models,   at   different   oper at ing   co ndit ion .   Due   to   the   na ture   of   D - Q   m odel   w hic h   consi ders   t he   s inu s oid al   va r yin g   of   the   tra nsf ormat ion   mat rix,   the   el ect rom agn et ic   tor que   (T e )   ba sed   D - Q   axis   trans formati on   has   le ss   trans ie nt   ti me   end i ng   at   ab out   (0.25sec)   t hen   go   to   ste ad y   sta te   reg io n.   Where   the   transient   ti me   of   the   (T e )   base d   on   act ual   t ra ns f ormat io n   m od el   is   more   th en   ( 0.5sec) .   Th eref or e ,   t he   ge ner at e d   tor qu e   base d   on   D - Q   m odel .           Figure   6 .   el ect r om a gn et ic   t orq ue   wav e f or m   ( Te)       Figure   8   s how s   the   va riat ion   of   l oad   tor qu e   at   diff e re nt   r otati on   s pee d.   It   can   be   s hown   t hat   (T L )   pr e dicte d   ba se d   D - Q   tra ns f or mati on   m odel   has   low   os ci ll at ion   till   1000r.p.m .   t hen   i ncrea sed   as   t he   r ot at ion   sp ee d   inc rease   to   a rr i ve   its   m aximum   value   at   sp ee d   a bout   1500 r.p.m .   In   con t ract   the   osc il la ti on   of   the   (T L )   pr e dicte d   base d   on   t he   act ua l   transfo rmati on   m odel   is   ve r y   high   at   the   wh e n   t he   mac hin e   sta rts   r ot at e   till   1000r .p.m.   a nd   t hen   reduce d   grad ually   till   the   rated   s peed   1800r .p. m.   C ompa rin g   with   ABC   ( act ual)   trans formati on   model,   a   ste a dy   sta te   r otati on   s pee d   with   s hort   tra ns ie nt   t ime   can   be   ac hieve d   base d   on   D - Q   axis   m od el   as   sh ow n   in   Fig ure   9,   in   wh ic h   a   ste ady   sta te   r at ed   sp ee d   of   1800r .p.m   is   obta ined   at   sim ulati on   ti me   of   a bout   ( 0.25   sec) .   Alte rn at ivel y,   a   high   tra ns ie nt   ti m e   with   m ore   th an   ( 0.5   sec )   is   pr e dicte d   at   No - L oa d   conditi on.   Re fer ri ng   to   Fi gure s   10   (a )   a nd   10   ( b),   the   w avefor m   of   t he   sta tor   a nd   r otor   cu rr e nt   as   we ll   as   id   an d   iq   are   il lustrate d.   As   me ntioned   a bove   t he   D - Q   a xes   t ran s formati on   mod el   plays   an   im portant   ro le   to   get   an   accurate   val ue   of   the   c urren t   with   t ran sie nt   t ime   an d   osc il la ti on .   Re su lt in g   a   high   el ect romag netic   to rqu e   an d   then   high   outp ut   powe r   as   show n   in   Fi gure s   11   (a )   a nd   11   ( b).   T he   sp e ci f ic at ion s   of   the   pro po se d   th ree   ph ase   inducti on   m otor   are   detai le d   in   Ta ble   2   a nd   the   a dopted   m odel ing   ste ps   ca n   be   sta te d   as   s how n   in   Fig ure   12.         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       A com pa r ative   stud y  for  t he p erf or m ance  operatio n of ele ct ric  mach i ne  …   ( Sa nabel M.  A L - H ajz ber )   1311       Figure   7 .   va riat ion   of   loa d   t orqu e   at   di ff e ren t   ro ta ti on   s pee d       Figure   8 .   Rotat ion   sp ee d   of   IM   at   No - L oa d         (a)     (b)     Figure   9 .   Stat or   a nd   r otor   c urr ent   of   IM   at   c onsta nt   ro ta ti on   sp ee d ,   (a)   b ase d   on   co nventio nal   m od el ,     ( b)   b ase d   on   D - Q   m odel         (a)     (b)     Figure   10 .   O utp ut   powe r   of   IM ,   (a )   b ased   on   c onve ntional   model ,   ( b)   b as ed   on   D - Q   m odel       Table   2 .   S peci f ic at ion s   of   t he   three   phases   I M   Variable   Sp eed   (r p m )   Load   v o ltag e   (VL )   220   V   Rated   sp eed   (r .p. m )   1710   r. p .m   No .   Of   p o les   ( P )   4   Rated   fr eq u en cy   ( F)   60   Hz   Rated   p o wer   ( Ho rse   p o wer)   3   HP   Stato r   resistan ce   (R s )   0 .43 5   Ω   Stato r   re actance   (X ls )   0 .75 4   Ω   Ro to r   resistan ce   (R r )   0 .81 6   Ω   Ro to r   reac tan ce   (X lr )   0 .75 4   Ω   Magn etizin g   reac t an ce   (X m )   2 6 .13   Ω   Inertia   of   th e   roto r   ( J )   0 .89   k g .m 2     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 .  12 , N o.   3 ,  Se ptembe r  2021   :    13 04   –   13 14   1312       Figure   12 .   Flo w   c har t   for   t he   simulat ion   m odel   of   IM       4.   CONCL US I O N   In   c urre nt   w ork ,   an   in   ste p   by   s te p   ma nn e r   to   buil t   a   dyna mic   modeli ng   of   th r ee - phase   i nduc ti on   m otor   us in g   M A TLA B / Simuli nk   a r e   ob ta ine d.   Th e   Tw o   m od el s   are   ap plied   to   inducti on   m oto r   in   this   rese arch   a   const ru ct io n   of   two   models   of   a   3 - Φ   in du ct i on   mo t or   based   on   the   two   a nalytic al   ap proac he s   a nd   c ompare   them   to   cl arif y   the   diff e re nce   in   t heir   dynamic   performa nce.   Tw o   anal ytica l   appr oach es   (D - Q   a xes   an d   Actual   appr oach es )   of   a   t hr ee - ph ase s   in duct ion   m otor   a re   re pr es ented   a nd   in ve sti gated.   Co mp a rin g   to   D - Q   a xes   appr oach es ,   the   Actual   m od e l   is   mo re   c onve nient   to   be   use d   in   normal   a nd   a bnormal   c onditi ons,   s uch   as   the   un s ymmet rical   supp l y   vo lt ag e .   In   c on t rast   the   D - Q   a xes   m odel   is   s uitable   in   normal   c ondi ti on s   a nd   is   si mp le r   and   faster,   tha n   act ual   m odel   to   be   us ed   as   in   on   Li ne.    T he   two   sti m ulate d   machi nes   show   a dequate   re sp onse   in   te rms   of   dya mic   pa rameters   cha racteri sti cs   (torq ue   a nd   s pe ed).   Bot h   met hods    pr ov i de   the   al te red   res ults.   The   ob ta ine d   res ults   pro ve   t hat   MATL AB / Simul ink   is   de pe nd a ble   an d   a   sop hi sti cat ed   ap proa ch   ca n   be   util i zed   to   analyze   a nd   pr edict   the   be ha vior   of   I .M s .   T hro ugh   this   work,   a   three - ph a se   inducti on   m otors   m od el e d   us in g   conve ntion al   a nd   D - Q   meth ods.   B oth   a re   si mu la te d   to   m onit or   t he   dyna mic   be hav i or.   Ba sed   on   t he   obta ined   resu lt s,   it   can   be   seen   that   the r e   is   a   div er ge nc e   in   the   pe rfo r mance   of   the   va riables   of   bot h   m odel s.   C ons iderin g   the   tor que   obta ined   from   a   D - Q   m od el ,   it   is   possible   to   noti ce   that   there   is   a   var ia ti on   in   the   value   of   t he   tor qu e   associat ed   with   c hange   of   Id   an d   Iq   c urre nts.   H oweve r,   a    simi la r   va riat ion   in   the   ro t or   s peed   co mp a re d   with   the   c onve ntio na l   model.   Due   to   natu re   of   D - Q   c urre nts,   it   is   diff ic ult   to   obser ve   an d   rec ognize   t he   be ha vior   of   the   el ect ric   ma chine   durin g   t he   sudd e n   vary   of   t hese   c urre nt s.   W her e   t he   main   ai m   on   w hich   t he   D - Q   t heor y   is   bu il t   by   obta ini ng   co ns ta nt - val ue   c urren ts ,   a nd   th us   ti me - de pende nt   in duct or s   an d   t orq ue.   In   a dd it io n,   th ere   is   a   dif ficu lt y   in   ide ntify i ng   cases   of   unbalance   c onditi on   that   occ ur   thr ough   t he   op e rati on   of   the   el ect rical   machine   wh e n   it   s ub je ct s   to   short   ci rcu it   in   the   s ta tor   an d   the   r ot or   windin g.   A mong   the   f aults   t hat   occur   it   has   be en   fou nd   that   40%   of   the   el e ct rical   machi ne s   fa ults   is   the   ai r   ga p   ecce nt rici ty,   wh ic h   is   disco ver e d   by   the   ha rm on ic s   that   a re   injec te d   int o   the   sta tor   cu rrent.   Th us,   due   to   the   fact   that   one   of   the   c onditi ons   for   modeli ng   t he   el ect ric   mac hin es   usi ng   the   D - Q   met hod   is   that   t he   ai r   ga p   a rou nd   of   the   r otor   par t   is   unif orm ,   this   model   ca nnot   be   us e d   to   detect   this   t ype   of   fa ults.   D ue   to   the   co ntinuo us   de velo pme nt   arises   in   po we r   el ect r on ic s   dri ves   sy ste ms   t hat   are   wi dely   us e d   to   c ontr ol   the   sp e ed   a nd   to rque   of   el ect rical   machine s   le ads   to   an   i ncr eas e d   ne ed   for   int r oducin g   model   capa ble   of   ta ki ng   i nto   c onsid erati on   t he   ef f ect   of   harmo nics   a ss ociat ed   with   the   volt age   s uppl ie d   by   th os e   ty pes   of   el ect ric   powe r   s ources .   D ue   to   ba dly   eff ect s   of   these   harmo nics,   the   dy na mic   pa ramete r s   of   the   el ect ric   mac hin es   vary   from   its   act ua l   valu es   a nd   pro duce   inco rr ect   performa nce.   Since   the   the ory   of   the   D - Q   m odel   dep e nds   mainl y   on   the   c onsi der at io n   of   sin us oi dal   distrib utio n   of   windin g   of   the   sta tor   par t. ,   Th eref or e ,   it   will   not   be   ap pro pr i at e   to   c hec k   the   pe rforman ce   of   the   mo to rs   f or   non -   sin usoidal   powe r   s upplie s.   Ba se d   on   t he   a bo ve   men ti on ed ,   it   can   be   c oncl ude d   that   the   modeli ng   of   el ect rical   machi nes   base d   on   D - Q   the ory   is   su it able   f or   ma chines   operate s   in   an   ideal   operati on   Evaluation Warning : The document was created with Spire.PDF for Python.
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