CHAPTER 6 VECTOR CONTROL ON DOUBLE OUTPUT INDUCTION GENERATOR FOR VARIABLE SPEED WIND ENERGY CONVERSION SYSTEMS

CHAPTER 6 VECTOR CONTROL ON DOUBLE OUTPUT INDUCTION GENERATOR FOR VARIABLE SPEED WIND ENERGY CONVERSION SYSTEMS 6.1 Intoucton Woun oto nucton machne ue n vaable pee WECS a hown n fgue 1.4 an 3.6 known a Double output nucton geneato (DOIG) becaue the output fe to the g fom both the tato an oto of the machne. The mplfe agam of the ytem hown n fgue 6.1. Fgue 6.1 Vaable pee g-connecte WECS ung oubly-fe woun oto nucton machne The oto e contol cheme fo woun oto nucton machne ntouce n chapte 1. Th aangement offe enomou flexblty ntem of contol of actve an eactve powe n vaable pee WECS. To enhance the pefomance of vaable pee WECS, contol cheme fo the DOIG ae expecte to acheve the followng goal: 120

(1) To ynamcally pove the eque pee output coepon to the maxmum powe captue fom pecbe toque-pee cuve of wn tubne. (2) To acheve the ee powe facto opeaton. A vecto contol appoach ung tato flux oentaton a popoe by Leonha [67] employe to ecouple the ynamc of the actve an eactve cuent loop n oe to contol the actve an eactve powe. Th contol of actve an eactve powe wll lea to acheve the above goal epectvely. In th chapte a mathematcal moel of the oubly-fe g-connecte woun oto nucton machne an the font en convete fomulate. A egn methoology evolve fo evelopng the cuent contolle. Smulaton eult ae peente to confm the egn an moelng. 6.2 Roto e contol: Moe of opeaton The opeatng egon of the ytem hown n the toque pee plane hown fgue 6.2 A tate eale, the oto e contol tategy avantageou wthn a lmte lp ange. Hence the opeatng egon pea out on both e of the ynchonou pee (W) mplyng both ub an upe ynchonou moe of opeaton. Moeove the machne can opeate n the motong an geneatng moe epectve of the pee. Thu fou tnct moe of opeaton can be acheve though oto e contol coeponng to the fou quaant n the toque pee plane. In fgue 6.2, moe 1 efe to potve toque an ub ynchonou pee an teme a ub ynchonou motong (.e nomal motong) opeaton. 121

Toque Moe 2 coepon to potve toque an upe ynchonou pee an calle upe ynchonou motong. Smlaly, moe 3 coepon to ub ynchonou geneatng an moe 4 to upe ynchonou geneaton. The followng ecton ecbe how thee ffeent moe of opeaton can be acheve though oto e contol. 0 MODE 1 MODE 3 MODE 2 MODE 4 Spee Fg 6.2 Fgue 6.2 Opeatng egon of the oubly fe nucton machne wth oto e contol L u L o Fgue 6.3 Appoxmate equvalent ccut wth oto cuent contol Moe 1: Sub ynchonou motong A mplfe equvalent ccut of the oubly fe woun oto nucton machne contolle fom the oto e hown n fgue 6.2. It aume that the oto cuent can be njecte at any ee phae, fequency an magntue. Theefoe, the oto ccut can be epeente by a contollable 122

cuent ouce. The equvalent ccut awn n the tato efeence fame hence the oto cuent epeente a. The teay-tate phao agam an powe flow fo the ub ynchonou motong moe of opeaton ae hown n fgue 6.4. Neglectng the tato etance, t may be aume that the tato flux ( ) eman contant n magntue an fequency nce the tato connecte to the powe g. ha two component; the tato leakage component an the magnetzng component. The fome ue to the tato cuent alone, whle the latte ue to both the tato an oto cuent. An equvalent cuent (I m ) can be efne n the tato efeence fame, whch eponble fo the tato flux. Th teme a the tato flux magnetzng cuent [67]. The ecton of (whch n phae wth m ) efne a the - ax an the ecton of the tato voltage, whch at quaatue of, teme a the q-ax. It poble to eolve an along an pepencula to m (The component of the cuent along the -ax ae epeente wth ubcpt, an thoe along the q-ax wth ubcpt q). 123

q ax q ax u q L o e u q L o e m ax m ax m m e q e q (a) (b) q ax A' q B' m ax P P B q A P m (c) Fg 6.4(c) Fgue 6.4 Phao agam an powe flow agam ung ubynchonou motong () 124

Snce contant, t mple the m alo contant an equal um of an. Wth cuent contol beng exece n the oto ccut, an njecton of potve wll natually eult n a lee value of beng awn fom the tato temnal. The tato powe facto theeby mpove. Th featue clealy epcte n fgue 6.4(b). Fgue 6.4 (a) how m beng fully upple fom the tato e, a n the cae of cage oto nucton machne, wheea n fgue 6.4(b) t patally upple fom the oto e an patly fom the tato e. It may be note hee that wll neve be mae negatve. Th woul mean that the tato ha to upply the magnetzng enegy of the machne a well a the eactve enegy eman of the oto ccut bngng own the tato powe facto to a vey low value. Along the q-ax, the magntue of the actve component of tato cuent( q ) ectly popotonal to q, but oppote n gn. In fact, the nucton machne can be looke upon a cuent tanfome a fa a the actve powe flow n the tato an oto ccut concene. Hence, to pouce a motong toque (.e. potve toque),, ha to be negatve. Th event fom fgue 6.4, a negatve nuce a potve I q, mplyng flow of actve powe nto the tato ccut. Below the ynchonou pee the oto fall behn the a-gap flux an the oto ntouce emf (e ) the lag the mutual flux ( m ) by 90 0 a hown n fgue 6.4 (a) an (b). The locu of an fo contant actve powe flow hown n fgue 6.4c. A the tp of the fo the oto cuent phao move fom B to A, the tato cuent phao move n the oppote ecton fom B to A. Fom th phao agam t may be appecate that ome amount powe 125

upple fom the oto e moe than the machne equement. Th, howeve poble when the actve loa eman low an thee aequate cuent magn n the oto col. In oe to utlze the coppe n the tato an oto ccut effectvely, t avable to ve the eactve powe eman between the two pot. Une the conton of ubynchonou motong the tato voltage phao (U ), lea the a-gap voltage e (-e ) une all conton of loa whch ncate powe flowng nto the tato. Alo the oto cuent ( ) make an angle le than 90 0 wth e, the oto-nclue emf, mplyng that actve powe beng extacte fom the oto ccut. Th oto powe, o the lp powe, ecovee fom the oto ccut an fe back to the man, theeby nceang the ytem effcency. The mechancal powe output oughly the ffeence between the tato an oto powe (fgue 6.4 ()). Moe 2 : Supeynchonou motong Wth q emanng negatve f the machne un above ynchonou pee, t ente the upeynchonou motong moe of opeaton. The oto now move ahea of the a-gap flux ( m ) an, theefoe, e lea ( m ) by 90 0. The phae elaton between the tato an oto cuent eman a n moe 1; only the ecton of oto powe evee a now make an angle moe than 90 0 wth e (fgue 6.5). 126

It may be note n th moe of opeaton, f the tato nput powe 1p.u. an the moto at a lp of p.u., the mechancal output that can be obtane (1) p.u. whch moe than the atng of the machne. q ax u q L o e = e m ax P P m q P m (a) (b) Fgue 6.5 Phao agam an powe flow agam ung upe ynchonou motong Moe 3: Sub ynchonou geneaton If a potve q njecte nto the oto ccut, q change ecton an become negatve. Theefoe, the actve powe flow nto the tato become negatve ncatng that the machne geneatng. Th can alo be appecate fom the fact that the tato temnal voltage vecto (u ) now lag the tatonclue emf. The phae angle between an e excee 90 0, mplyng that powe fe nto the oto ccut. The powe flow an phao agam ae gven n fgue 6.6. 127

q ax L o e q u m ax m P P q e P m (a) (b) Fg 6.6 Phao agam an powe flow agam ung ub ynchonou geneaton Moe 4: upe ynchonou geneaton Wth q emanng potve, the machne can go ove to the upe ynchonou geneatng moe. A fa a the tato ccut concene eveythng eman the ame a n moe 3; only the oto powe flow change t ecton. Wth the oto-nclue emf e leang the a-gap flux, the angle between an e become le than 90 0 ncatng powe flow out of the oto. It nteetng to note that n upe ynchonou geneaton moe the haft powe ecovee fom both the tato an the oto en. Theefoe, f 1 p.u. powe extacte fom the tato, whle the machne unnng at a lp, the total powe geneate wll be (1) p.u. Hence n the upe ynchonou geneaton moe t 128

actually poble to geneate powe that moe than the atng of the machne (fgue 6.7). q ax Lo u e = e q m ax m P P q P m (a) (b) Fg 6.7 Phao agam an powe flow agam ung upe ynchonou geneaton 6.3 Machne Moel n Fel Coonate In a oubly-fe woun oto nucton machne, contol exete on the oto e whle the tato eman connecte to a contant voltage contant fequency ouce. In oe to fomulate the ynamc moelng n the fel coonate, t aume that the oto e convete equppe wth fatactng cuent loop. Hence, gven a efeence * the oto cuent pace phao follow t wthn a fnte but extemely hot nteval of tme. the oto voltage equaton ue fo egnng the oto cuent contolle, a cue n a late ecton. Fo the peent, the oto e can be mply epeente by a 129

contollable cuent ouce [fgue 6.8] an the oto cuent phao can be taken a an nput to the machne moel. It the tato voltage equaton, whch etemne the ynamc behavo of the machne. Th equaton, n the tatonay efeence fame, funhe below. R j ( 1 ) Lo Lo ( e ) u R L o [(1 ) e j ] u (6.1) R L o u = mlo Lo Fgue 6.8 Equvalent ccut n tato efeence fame The magnetzng cuent vecto efne a m (1 ) e j ( 1 ) (6.2) = m the equvalent cuent vecto n the tato efeence fame eponble poucng the tato flux a epcte n the equvalent ccut of fgue 6.8. Hence t may be calle the tato flux magnetzng cuent. In tem of I m equn.6.1 can be wtten a 130

R Lo m u (6.3) Snce the quantty ove whch ect contol can be exece (an not ), Equn.6.3 nee to be expee ntem of the oto cuent. Subttutng fo n Equn.6.3, ung Equn.6.2 we get R [ m e 1 j ] L u o m o, (1 ) R j T u e (6.4) m m whee T L (1 ) R o the electcal tme-contant of the tato ccut. L R The above equaton Equn.(6.4) efne n the tato efeence fame. It can now be expee n tem of a coonate ytem fxe to the tato flux o equvalently to the cuent. In oe to o th ft expee n m m pola fom wth epect to tato coonate a = m j me (6.5) whee m the ntantaneou magntue of the cuent pace phao m an t ntantaneou poton wth epect to the tatonay ax. The vaou phae elatonhp ae hown n fgue 6.9. 131

Now Equn.(6.4) can be wtten a T ( m e j ) m e j 1 R u e j o, 1 R m j j j j T e T (j )e e u e (6.6) m m - m q Fel ax e Roto ax Stato ax Fgue 6.9 Angula elaton of cuent vecto fo oubly fe nucton machne The above equaton can be tanfome nto fel coonate by multplyng both e wth the opeato j e T m 1 j j( ) jtm m ue e (6.7) R In the fel coonate, the tato voltage an oto cuent pace phao can be epeente a u e j u ju q an e j( ) j q (6.8) ubttutng th n equn.6.7 an epaatng the eal an magnay pat yel the followng equaton. 132

T m 1 R u (6.9) m m 1 T m 1 [ R u q q ] (6.10) Equn.6.9 an 6.10 epeent the ynamc of the fel vecto magntue an angle epectvely. The tato voltage an oto cuent vecto ae the two nput to the ytem, of whch the fome not contollable (hence a tubance vaable) an the latte the contol vaable. The electomagnetc toque evelope can alo be expee n tem of the cuent vecto. In the tatonay coonate the toque equaton gven by m 2 p j Lo Im ( e )* (6.11) 3 2 Subttutng fo ung Equn.6.2, we get m 2 P ( ) m L Im * o 3 2 1 2 P Lo = Im * 3 2 1 2 P Lo j j = Im[ e j e *] m q 3 2 1 m 2 P L o m q (6.12) 3 2 1 The complete et of equaton that ecbe the machne ynamc n the fel coonate can be theefoe, wtten a 133

T m 1 R u (6.13 a) m m 1 T m 1 [ R u q q ] (6.13 b) J 2 P Lo 3 2 1 m q m l (6.13 c) p 2 e (6.13 ) The mulaton block agam of the oubly-fe woun oto nucton machne moele n the fel coonate gven n fgue 6.10. The nput to the ytem ae the tato voltage an the oto cuent. It aume that thee a contolle cuent ouce n the oto ccut whch capable of njectng cuent at appopate phae, fequency an magntue. The oto cuent ae ft tanfome to the tato efeence fame ung the opeato j e. Subequently the tato voltage an oto cuent (n the tato efeence fame) ae tanfome to the fel coonate by multplyng wth j e. The angle eve by olvng the q-ax equaton equn. (6.13b). The magntue of m compute ung the -ax equaton equn. (6.13a). It may be note that the altenatng quantte n the tatonay coonate, when tanfome to the fel coonate appea a c quantte. 134

u 1 u u 1 R u 2 3/2 e -j u 3 u u q 1 R 1 a q * * m 2 3/2 -j e 3 b m T S T S m - P 2 2 3 L 0 1 X m - 1 J P 2 w e - m l Fgue 6.10 Block agam of the oubly-fe woun oto nucton machne moel n the fel coonate 6.4 Fel Oente Contol The oto ccut cont of a thee phae voltage ouce nvete opeatng n the cuent-contolle moe. The tato connecte to a contant magntue, contant fequency ouce whch ha eally nfnte capacty fo oucng an nkng actve an eactve powe. It may alo be aume fo the tme beng that the c ouce fo the nvete can upply o nk the actve an eactve powe hanle by the oto wthout affectng the c bu voltage. (In pactce the FEC nteface the c bu wth the ac g, whch cue n the late ecton). The chematc block agam of th aangement hown n fgue 6.11. 135

3 Phae contant Voltage contant Fequency 3 Phae vaable Voltage vaable Fequency Feeback Sgnal * * q Contolle Fgue 6.11 Schematc block agam of the ytem aangement fo oubly-fe SRIM 6.4.1 Roto Equaton n Fel Coonate Fo egnng the oto cuent contolle the oto voltage equaton ha to be conee. Th equaton R L L o ( e j ) u (6.14) n the oto efeence fame an nee to be tanfome to the fel coonate fo fel-oente contol. Moeove, the equaton ha to be 136

expee only n tem of the vaable to be contolle, an, the fel m vaable. Fom equn. (6.2) m e 1 j (6.15) Subttutng fo ung equn.(6.15), equn.(6.14) may be expee a R L L o j me u 1 (6.16) Now, Lo 1 2 Lo L L L (1 ) L an m = e j m Theefoe, equn. (6.16) can be wtten a R L (1 )L [ m e j( ) ]e j( ) u (6.17) Wtng n tem of the ect an quaatue ax component of oto cuent an voltage vecto R ( j q )e j ( ) L [( j q )e j ( ) ] (1 )L [ m e j( ) ] (u ju q ) e j( ) j o, R ( j )e ( ) j( ) q L [( jq )e ] 137

( ) L j ( j q )e j( ) (1 )L m e j( ) (1 )L m ( ) j e j( ) = (u j( ) ju q ) e (6.18) In oe to tanfom th equaton to the fel-oente efeence fame, both e have to be multple by e j( ). Thee by the followng complex equaton can be eve. R ( j q ) L ( j q ) j( m ) L e ( j q ) m ( 1 )L j( m e )(1 )L = ( u ju ) (6.19) q m whee, ( ) m e the lp fequency (6.20) Fnally, the eal an the magnay pat ae epaate to get the -ax an q-ax equaton epectvely a gven below. m T ( ) T (1 )T (6.21) m e q R q q T ( ) T ( )(1 )T m e (6.22) m e m R Thee equaton epeent the ynamc of the oto cuent n the fel coonate ytem. It obeve that ue to the peence of the otatonal emf tem, thee ome amount of co-couplng between the an q axe. 138

Howeve, the cuent-loop ynamc n the two axe can be mae nepenent of each othe by compenatng fo thee co-couplng tem. It nteetng to note the connotaton of the tem unelne n thee two equaton. Multplyng thee tem wth R gve the coeponng voltage, whch can be ntepete a follow. (a) ) T xr ( e) L : Th the otatonal emf ( m e q m q nuce n the ax ue to the q ax oto cuent. Snce the elatve pee of the oto wth epect to the fel ax ), the fequency tem ( m e nvolve n th equaton coepon to the lp fequency. (b) ( 1 )T mxr (1 )L m : Th enote the tanfome nuce voltage n the -ax ue to the fel cuent. Obvouly th tem wll not appea n the q-ax. (c) ) T xr ( ) L : Th tem gve the otatonally ( m e m e nuce emf n the q-ax ue to the -ax cuent, mla to the ft tem. () )(1 )T x R ( )(1 )L : Th enote the ( m m m e m pee emf nuce n the q-ax ue to the fel. The fequency tem nvolve n th equaton agan the lp fequency. Due to the peence of thee tem, thee ext ome couplng between the two axe. Howeve, a the lp ange lmte, the contbuton of the tem (a) an (c) elatvty mall compae to the pee emf tem (). The tanfome emf tem (b) alo oe not ext afte the flux ha bult up, pove the tato voltage contant n magntue an fequency. Whle egnng the 139

oto cuent contolle t poble to compenate fo thee tem an make the loop ynamc n the two axe nepenent of each othe. Th cue n the followng ecton. 6.4.2 Degn of Roto Cuent Contolle n Fel Coonate It obvou that f the oto cuent nee to be contolle n the fel coonate, two nepenent contolle ae neee; one fo the -ax an the othe fo q-ax. The egn metho ame fo both; only the fee fowa tem ffe n each cae. Degn of a popotonal (p) contolle, an a popotonalntegal (PI) contolle ae peente hee. (a) Popotonal Contolle Let the ee cuent loop ynamc n the -ax be gven by T * (6.23) K Whee T the ee cuent-loop tme contant an K the cuent eno gan. The tak now to fn out the -ax component of the ntantaneou nvete temnal voltage eque to pouce the cuent ynamc gven by equn.(6.23). Subttutng fo fom equn.(6.23) n equn.(6.21) gve u L T K * m ( K ) R (1 )L ( ) L (6.24) m e q 140

The nvete can be moele a a gan block G. Fo ne-tangle moulaton the nvete gan epen on the c bu voltage u c an the peak of the tangle u t. u c G (6.25) 2.u t In oe to make the nvete gan contant, the peak of the cae tangula wavefom u t mae popotonal to u c. Theefoe the efeence fo the -ax component of oto voltage gven by * u u G L T K G ( * K R ) G (1 )L G m ( m G e ) L q (6.26) Aumng ame cuent loop ynamc fo the q-ax the efeence fo the q-ax component of the oto voltage can be expee a * u q u G v L T K G * = q q q ( K R ) G ( )(1 )L ( ) L G G m e m e m (6.27) If the mpee oto voltage ae n accoance wth equn. (6.26) an equn.(6.27), the fel an quaatue axe oto cuent can be contolle nepenently. The oto cuent contolle, theefoe, oe not contbute gnfcantly to the ynamc of the ytem. It only enue that the oto cuent 141

tack the efeence gnal pouce by the oute loop. It may be appecate that the cuent loop ynamc can be mae much fate than the oto tme contant. Howeve, a pactcal lmtaton to the banwh of the cuent contolle mpoe by the wtchng fequency. Snce the contolle egne n the fel coonate, all the quantte ae c an mplementaton of the contolle become mple. The mulaton block agam of the oto cuent contolle hown n fou pat. Fgue 6.12 how the computaton of the vecto an tanfomaton of the oto cuent to the fel coonate. Aumng that at t = 0, the oto an tato axe ae algne, the oto poton can be ectly obtane n the mulaton by ntegatng the haft pee. The oto cuent ae ft tanfome to the tatonay coonate wth th angle nfomaton. The angle, whch the fel ax make wth the tato coonate, a well a the magntue of m, can be calculate fom the tato an oto cuent a follow. In the tato coonate, m e j (1 )( a j ) ( a j b )(co jn ) = 1 ) co n ] [( a a b j[(1 ) a n b co] [ (1 ) co n (6.27) Theefoe m = 2 a a 2 ( 1 ) n co 1/ 2 a b ] b (6.28) (1 actan[ ) n co (1 ) co n ] a a a b b (6.29) 142

1 2 3 3/2 Eq:(6.28) Eq.(6.29) m - / / m - m e 1 2 3 3/2 a b e j -j e q Fgue 6.12 Flux computaton an oto cuent tanfomaton block Fg 6.5 The -ax contolle block agam along wth the plant gven n fgue 6.13(a). All the paamete neceay fo contuctng the fee fowa tem have aleay been compute n the pevou tage. Afte geneaton of the efeence voltage * * u an q u, they ae agan tanfome back to the oto efeence fame by multplyng wth the nvee tanfomaton opeato j( ) e. Howeve, fo the ake of mplfcaton, tanfomaton of * u fom the fel coonate to the oto efeence fame n the contolle, an the coeponng fowa tanfomaton n the machne moel fom th agam. It event fom the agam that the contolle jut a o ubtact the tubance nput to the machne moel eucng the plant to meely an ntegato. Hence, the cloe loop ytem behave lke a ft-oe lag ccut whoe tme-contant can be mofe by changng the popotonal gan of the ytem, a fgue 6.13(b) an 6.13(c). The q-ax cuent contolle can be mlaly moele; the compenatng 143

tem wll only be ffeent n th cae. In the contolle block agam the cuent eno gan K aume to be unty fo mplfyng the agam. ) L G m m e) L q R * - L G T - - G - 1 L 1 S R G m G e L q ) L m (a) * - L T 1 L 1 S (b) * 1 1 T (c) Fgue 6.13 Block agam of -ax popotonal oto cuent contolle (b) Popotonal Integal Contolle In the popotonal contolle, the teay-tate eo n the oto cuent wll epen on the accuacy of computaton of the feefowa tem. Any eo n the compenaton tem woul eult n lght mofcaton of the ynamc epone. In the pactcal mplementaton, t extemely ffcult to pefectly nullfy the tubance tem owng to meauement an computatonal eo. Theefoe a popotonal ntegal contolle nee to be ncopoate. Th patculaly mpotant when the machne un n the toque-contol moe wthout any oute pee loop. The flux computaton an tanfomaton hown n 144

fgue 6.12 eman entcal. The plant moele a a ft-oe lag ytem wth the two otatonal emf a tubance nput a hown n fgue 6.14(a). Thee two tem ae cancele though fee fowa compenaton a befoe. In the contolle, the PI-tme-contant mae equal to T, o that the ynamc of the ytem ece by the popotonal gan, a hown n fgue 6.14(b) an fgue 6.14(C). The choce of popotonal gan follow fom the equaton K = R, p T T whee T the ee effectve tme contant of the cuent loop. ) G L m m e) L q * - K p G T ) T - G - R 1 T ) m e) G (a) L q ) L m * K T ) 1 p T - R T ) (b) * 1 1 T (c) Fgue 6.14 Block agam of -ax popotonal-ntegal oto cuent contolle 145

6.5 Smulaton Reult-Roto Se Contol The ente ytem mulate on the MATLAB (6.0)-SIMULINK Platfom. The mulaton moel compe ffeent functonal moule o ubytem. Each of thee moule, n tun have eveal level of ubytem whch ae evelope ung the tana SIMULINK lbay. Va V Vb 3ph to 2ph Stato Se V Vc Va U Electcal Subytem Toque Convete Mechancal Subytem 7 W Vb Vc 3ph to 2ph Roto Se U Roto to Stato Pole Pa P/2 7 MI Sn E, Co E * we I2 I1 I3 Cuent Inpecton Block I1 I2 I2 Fgue 6.15 SIMULINK moel of the oubly-fe SRIM A an example, the moelng of the oubly-fe SRIM may be conee. The machne moel cont of the tanfomaton block, electcal ubytem, toque convete block an, the mechancal ubytem. Th hown n fgue 6.15. The tanfomaton block nclue 3 phae to 2 phae tanfomaton, oto coonate to tato coonate tanfomaton an, the coeponng nvee tanfomaton (ue n the cuent npecton block.). The electcal ubytem moele n the tatonay coonate ytem. The tate pace equaton 146

(equn.(a32)) to compute the tato an oto cuent n the tato efeence fame ae eve n Appenx A. The toque equaton, gven by equn.(a33), execute n the toque convete block. Fnally, the mechancal ubytem compute the machne pee fom the mechancal ynamc, a gven by equn.(a22). The poton of the oto wth epect to the tato obtane though ntegaton of the haft pee n the n, co block. Thee moule wth appopate nteconnecton ae goupe togethe to fom the SRIM block n the ytem mulaton moel of fgue 6.16. In a mla manne, the othe functonal moule of fgue 6.16 ae evelope. Va Vb Vc 3 Phae to 2 Phae Conveon V V Va Vb Vc 3 Phae to 2 Phae Conveon U U Roto Quantte to Stato Quantte Conveon ( x e j) Calculaton of tato an Roto Cuent n 2 phae Stato Quantte to oto quantte conveon & calculaton of m& m Toque Calculaton m = 2 3 x P 2 x Lo - ) m Spee Calculaton J. w w =m.m l m m q V c PWM Invete * V a V* b V* c Cuent Contolle q * * Spee Contolle * * * & q ae convete to U * & U * q ung P I contolle an convete to V * & V * Then Convete to Va *, V * b & Vc * Fgue 6.16 SIMULINK block agam of a pee-contolle ve ung oubly-fe SRIM 147

A pee contolle ve ung g-connecte oubly-fe SRIM mulate. Stato flux oentaton, a cue n the eale ecton, employe. The -ax an q-ax cuent contolle ae egne n the fel efeence fame. Fo the pee loop, a PI contolle employe whch geneate the q-ax / actve cuent efeence * q. The -ax efeence * et n open loop. The pee epone of the ve une no loa gven n fgue 6.17 (a). The moto aume to be tate DOL wth the oto hote. At t=0.25, the oto e contol eleae wth a pee efeence * 0. 75 p.u. At t=1.25, the pee efeence gven a tep change fom 0.75 p.u. to 1.25 p.u. The coeponng moto toque an q ae gven n fgue 6.17(b) an fgue 6.17(c) epectvely. The pee contolle tme contant et to 100 m. At t=1.75, *, gven a tep change to 0.75 p.u. Th eult n tanfe of the eactve powe fom the tato to the oto e. Howeve, a change n oe not affect, a q can be een fom thee plot. The ynamc epone of the cuent loop ae gven n fgue 6.18 an fgue 6.19. The q-ax cuent loop tme contant egne fo 1m an, the -ax loop tme contant egne fo 4m. (The -ax efeence not eque to be vae ynamcally; o the ynamc epone of nee not be vey fat). The actual tato cuent an, the oto cuent n the tato efeence fame ae alo hown. In fgue 6.18 zeo, o the tato upple the eactve powe an the oto powe facto unty. In fgue 6.19, the eactve powe tanfee fom the tato to the oto e, eultng n an mpovement n the tato powe facto. 144

Fgue 6.17(a) Smulate pee epone of the pee-contolle g-connecte SRIM ve Fgue 6.17(b) Smulate toque epone of the pee-contolle g-connecte SRIM ve 145

Fgue 6.17(c) Smulate q epone of the pee-contolle g-connecte SRIM ve Fgue 6.17() Smulate epone of the pee-contolle g-connecte SRIM ve 146

Fgue 6.18(a) Smulate tep epone of q fo the g-connecte SRIM Fgue 6.18(b) Coeponng mulate epone of fo the gconnecte SRIM 147

Fgue 6.18(c) Coeponng mulate epone of along wth u fo the g-connecte SRIM Fgue 6.18() Coeponng mulate epone of along wth u fo the g-connecte SRIM 148

Fgue 6.19(a) Smulate tep epone of fo the g-connecte SRIM Fgue 6.19(b) Coeponng mulate epone of q fo the gconnecte SRIM 149

Fgue 6.19(c) Coeponng mulate epone of along wth u fo the g-connecte SRIM Fgue 6.19() Coeponng mulate epone of along wth u fo the g-connecte SRIM 150

6.6 Font en Convete A conventonal phae-contolle ectfe ha eveal eou avantage. Ftly, wth the c bu polaty emanng contant, powe flow can be n one ecton only. Seconly, t aw eactve powe fom the lne, whch ubtantal at lage fng angle. Latly, the cuent awn fom the man fa fom nuoal. Obvouly, a fou-quaant ve o geneatng ytem cannot be mplemente wth a phae-contolle convete n the lne e. The font en convete employ a thee-phae nvete bge topology an contolle to enable powe flow n both ecton, keepng the c bu voltage wthn goo egulaton. It can be opeate at any ee powe facto, an hence, can even act a a eactve powe ouce a fa a the g concene. The convete opeate a a PWM voltage ouce nvete n the cuent-contolle moe; o, the hamonc n the lne cuent wavefom ae ubtantally euce. It unetoo that by employng tato voltage oentaton, the actve an eactve cuent at the nput of the font en convete can be contolle n the ynchonou efeence fame. The contol eentally ha the ame tuctue a the oto e contolle. The objectve of contol an, moelng of the powe an contol ccut ae ecbe n the followng ecton. 151

6.7 Sytem Decpton Tanfome Inucto Invete u 1 u ac1 fe1 u fe1 u 2 u ac2 fe2 u fe2 u c - c u 3 u ac3 u fe3 fe3 PWM Sgnal Feeback Sgnal fe1, fe2 u ac1, ac 2 u c l Dgtal Contolle u c * Fgue 6.20 Schematc block agam of the font en convete The chematc block agam of the font en convete hown n fgue 6.20. The tanfome n the nput e ue to match the voltage level between the c bu an the ac e. The oto e convete opeate wthn a lmte fequency ange. Hence, the c bu voltage equement le when compae to the tato e contol cheme of cage oto nucton machne. The avng n the convete atng n the oto e acheve ue to eucton n voltage atng of the powe evce. Wth a euce c bu voltage t, howeve, become neceay to ue a tanfome at the nput of the font en convete. Snce the oto e nee not be olate fom the ac g, an autotanfome can be ue ntea. Th euce the cot an weght of the equpment coneably. The PWM wtchng convete connecte to the econay e of the tanfome though ee choke. Thee nucto act a buffe between the 152

two voltage ouce. The choce of the value fo thee nucto epen on the wtchng fequency, allowable hamonc n the nput cuent wave an the eactve powe equement. The objectve fo the contol of the convete ae, ) Voltage egulaton of the c bu ) ) v) b-ectonal powe flow, opeaton at any ee powe facto, an low cuent hamonc. 6.8 Pncple of Opeaton an Contol The font en convete eque cloe-loop contol to meet the tate objectve. The bac tategy fo contol an eultng ccut behavo can be explane ealy by mean of the phao agam gven n fgue 6.21. fe x fe fe fe uac u ac u ac u fe fe x fe x fe fe a) AC e equvalent ccut b) Fowa powe flow at upf u fe u fe c)fowa powe flow at leang powe facto u fe fe u fe fe fe x fe fe x fe u ac u ac ) Revee Powe flow at upf e) Revee Powe flow at leang powe facto Fgue 6.21 Equvalent ccut an phao agam fo the font en convete 153

The pmay objectve of contol c bu voltage egulaton. A change n the c bu voltage can be attbute to an mbalance between the actve powe between the ac an c e. (The effect of eactve powe on the c bu to pouce pple n the voltage even though the aveage value eman the ame.) Hence, the voltage eo n the c e an ncaton of the actve powe eman n the ac e. If the eman potve, actve powe awn fom g nee to be nceae; f the eman negatve, t ha to be fe back to the g. Snce the convete ha bectonal wtche, cuent flow can be n ethe ecton an t poble to ouce o nk actve powe n the ac e. Fgue 6.21(a) how the ngle phae equvalent of the ac e of the font en convete. If the loa cuent n the c e fo a gven c bu voltage known, the cuent awn fom the ac e at any ee powe facto can be calculate applyng powe balance between the ac an c e. Conequently, ubtactng the eactve op fom the ouce voltage, the magntue an phae of the nvete temnal voltage wth epect to the ouce can be compute. The nvete, theefoe, act a a fxe fequency ouce wth contollable phae an magntue. Fgue 6.21(b) an 6.21() epeent teay-tate phao agam at unty powe facto opeaton when powe flowng fom ac to c e an vce vea. The coeponng phao agam fo leang powe facto opeaton ae llutate n fgue 6.21(c) an 6.21(e). It obeve that the magntue of the nvete temnal voltage nceae n th cae. The amount of eactve powe that can be njecte nto the g epen on the avalable c bu voltage an the value of pe unt nuctance n the ac e. 154

The temnal voltage of the nvete wll alo contan wtchng hamonc apat fom the funamental. A fa a the hamonc ae concene the ac ouce act a a hot-ccut an the effectve mpeance to the hamonc cuent nx fe. Fo hgh fequency wtchng (moe than 1kHz), the hamonc mpeance qute hgh eultng n vey low toton of the ac e cuent wavefom. Wth the above cheme of contol t poble to acheve the ee objectve a tate eale. The alent featue of the contol tategy can be umme up a the followng. Employ an oute voltage contol loop to egulate the c bu voltage an an nne cuent contol loop to contol the ac e nucto cuent. Oute voltage loop ece the value of nucto cuent to meet the actve powe balance between the two c an ac e. The cuent loop tack th efeence by ajutng the nvete temnal voltage o that pope phae elatonhp between the upply voltage an the nucto cuent mantane fo a gven powe facto opeaton. Employ cuent-contolle nuoal PWM fo cuent tackng. The cuent contolle egne n ynchonouly otatng efeence fame wth oentaton beng one wth epect to the upply voltage pace phao. Fgue 6.22 how the chematc block agam of the contol tuctue of the font en convete. The voltage contolle a popotonal-ntegal contolle wth fee-fowa of the loa cuent an geneate * feq o the efeence fo the 155

actve component of cuent. The efeence fo the eactve component of cuent * fe et n open loop; e.g. t et to zeo fo unty powe facto opeaton. The cuent contolle opeate n the ynchonou efeence fame an geneate * * u fe an u feq fo the nvete temnal voltage. Thee efeence ae ft tanfome back to the tatonay efeence fame, an then fom two phae to thee phae quantte. Fnally, the thee phae efeence ae compae wth a tangula cae to geneate the PWM gnal fo the nvete wtche. The moelng of the powe ccut an egn of the contolle ae cue n etal n the followng ecton. Sn Co uac1 uac2 uac3 u c * u c - fe * Voltage Contol - feq * feq - D-Ax Contol Q-Ax Contol Tanf, & PWM Gen. u fe1 u fe2 u fe3 Powe Ccut u c fe1 fe2 fe3 u c fe fe1 Tanf. fe2 fe3 Sn Co Unt Vecto Gen. u ac1 u ac2 u ac3 Fgue 6.22 Schematc block agam of the contol tuctue of the font-en convete 156

6.9 Moelng of the Powe Ccut In the tatonay efeence fame, the ac e voltage equaton fo the thee phae can be wtten a follow. u u u ac1 ac2 ac3 ufe1 Lfe (6.30) fe1 u fe 2 Lfe (6.31) fe 2 u fe 3 Lfe (6.32) fe 3 The above equaton can alo be epeente n tem of pace phao a u ac ufe Lfe (6.33) fe whee, u ac ufe L fe fe (6.34) u ac ufe Lfe (6.35) fe Stato Voltage pace Phao q Fg 6.17 Fgue 6.23 Statonay an ynchonou efeence fame 157

The tatonay efeence fame equaton ae tanfome to ynchonouly otatng efeence fame; the oentaton beng one wth epect to the upply voltage pace phao a ncate eale. The elatve oentaton of the tatonay an ynchonou efeence fame hown n fgue 6.23. To mantan compatblty wth the -ax an q-ax efnton ue n oto e contol, the upply voltage phao ax taken a the q-ax n th cae. The unt vecto co an n can be ectly obtane fom uac an u ac epectvely. In tem of the -ax an q-ax vaable equn.(6.34) an (6.35) can be ewtten a follow : u acq e j (u feq ju fe )e j L fe [( feq j fe )e j ] o, u acq e j (u feq ju fe )e j L fe [( feq j fe )] e j j j Lfe (feq j fe ) e (6.36) Equn.(6.36) ecbe the ytem ynamc n the tatonay coonate n tem of the ynchonou efeence fame vaable. Snce the oentaton one wth epect to the g voltage, u zeo. Tanfomng th to the ac otatng efeence fame by multplyng both e wth j e an epaatng the eal an magnay pat the followng -ax an q-ax equaton can be obtane. u fe Lfe fe Lfefeq 0 (6.37) 158

u feq Lfe feq Lfefe u (6.38) acq Due to the tanfomaton, otatonal emf tem appea n the voltage equaton n the ynchonou efeence fame, gvng e to co-couplng between the two axe. Thee otatonal emf tem ae eque to be compenate by appopate fee fowa gnal n oe to nepenently contol the actve an eactve component of cuent. c feq 2. 3 u acq u c c C l u c Fgue 6.24 DC Bu Moel DC BUS MODEL The ynamc of the c bu voltage can be moele by coneng the balance between the actve powe flow between the ac an the c e. If the ee nucto loel, 2 u 3 acq. feq u (6.39) c c whee the c bu cuent a ncate n fgue 6.24. Th cuent can be c wtten n tem of the capacto chagng cuent c an, the loa cuent l a u c c c l C (6.40) l 159

Subttutng fom equn.(6.40) n equn.(6.39) the followng equaton can be c eve. u C c 2 u 3 u acq. (6.41) feq l c Snce the c bu voltage egulate wthn a naow ban an, the ac e voltage nomnally contant, the facto u u acq c may be conee a a contant ato to tanfom the ynchonou efeence fame cuent to the c lnk cuent. The moel chematcally hown n fgue 6.24. 6.10 Font en convete contolle egn 6.10.1 Degn of the cuent contolle The egn of the cuent contolle mla to that cue n oto e contol. Two nepenent contolle ae ue fo contollng the -ax an q- ax cuent. Fo the ake of completene egn of popotonal contolle an popotonal-ntegal contolle ae cue n etal. a) Popotonal Contolle Let the ee cuent loop ynamc n the q-ax be gven by, T fe feq * feq (6.42) feq K fe whee T the ee cuent-loop tme contant fe an, K the cuent eno gan. fe 160

Subttutng feq fom equn.(6.42) n equn.(6.38) gve the q-ax component of the ntantaneou nvete temnal voltage eque to pouce the ee cuent ynamc. u feq L T K fe fe fe u L * K (6.43) acq fe fe feq fe feq The nvete can be moele a a contant gan block u 2.u t c G a fe explane n ecton 6.4.2(a). The efeence fo the q-ax component of oto voltage, theefoe, gven by u * feq u G feq fe u fe fe fe uaq fe fe fe * K (6.44) feq fe feq G fe L G fe T L K G The plant along wth the contolle fo the q-ax hown n fgue 6.25. The cuent eno gan K fe taken a unty to mplfy the agam. Aumng ame cuent loop ynamc fo the -ax, the efeence fo the -ax component of the oto voltage can be expee a the followng: u u * fe G fe fe L fe feq Lfe ( * K ) (6.45) fe fe fe G T K G fe fe fe fe 161

If the mpee nvete voltage ae n accoance wth equn.(6.44), the actve an eactve component of the ac e cuent can be contolle nepenently, uacq G fe L fe fe L fe * feq Tfe G fe - - G fe - 1 1 feq L fe S feq L fe fe G fe u acq (a) * feq - L 1 1 S fe T fe L fe feq (b) * feq 1 1 T fe feq (c) Fgue 6.25 Block agam of q-ax popotonal font en cuent contolle So fa t ha been aume that the etve op fo the nucto neglgble, whch n pactce a val aumpton. Howeve, f a popotonal contolle ue, the ncluon of the etve op a compenatng tem n (6.44) an (6.45) mnmze the teay-tate eo. 162

b) Popotonal Integal Contolle The egn of the popotonal-ntegal contolle mla to that cue n ecton 6.4.2(b). The etve op taken nto coneaton an the plant epeente by a ft-oe lag along wth the co-couplng an nput voltage tem. The q-ax plant an contolle ae gven n fgue 6.26. The PI tme-contant T mae equal to T ( L / R ) pfe an the popotonal fe fe fe gan fe K electe a R fe pfe T T fe, whee T the effectve cuent-loop tme fe contant. uacq G fe L fe fe feq * - K pfe T fe ) G fe S T fe - G fe - - 1 R T ) fe fe feq feq L fe fe G fe u acq (a) * feq - K pfe T fe) T fe 1 R fe T fe) feq (b) * feq 1 1 T fe feq (c) Fgue 6.26 Block agam of q-ax popotonal-ntegal font en cuent contolle 163

6.10.2 Degn of the voltage contolle Snce the pmay objectve of the contolle to egulate the c bu voltage wthn a naow ban, a popotonal ntegal contolle the obvou choce. It may be appecate that the epone of the voltage contolle nee not be vey fat. It, howeve, eable that the tanent unehoot o ovehoot n the c bu voltage ue to uen vaaton of loa n the c e lmte to a mnmum, nomally wthn 5%. Th acheve by ung the c-e loa cuent a a fee-fowa tem to the voltage contolle. The tuctue of the contolle, along wth the plant hown n fgue 6.27(a). It aume that the cuent contol loop much fate than the oute voltage loop. So the ynamc of the cuent loop can be neglecte whle egnng the voltage contolle. The fowa path tanfe functon of the ytem become, K CT pvfe vfe 1 T 2 vfe Fom the boe plot of the ytem, hown n fgue 6.27(b), t can be nfee that 1/T vfe ha to be electe lghtly lowe than the ee ban wh. The gan K then ajute to make the phae magn cloe to 90 o. pvfe l l u c * - K pvfe T ) vfe T vfe 3 2 u c u acq * feq 1 feq 2 uacq 3 u fe 1 C u c u c 2.21 (a) Stuctue of PI contolle Fgue 6.27(a) Stuctue of PI contolle B 164 1/Tvfe Fequency (Logcale)

u c * - K pvfe T ) vfe T vfe 3 2 u c u acq * feq 1 feq 2 uacq 3 u fe 1 C u c u c 2.21 (a) Stuctue of PI contolle B Fequency (Logcale) 1/Tvfe 0 Fequency (Logcale) -90-180 Fg 2.21 Magntue an phae plot of the voltage loop Fgue 6.27(b) Magntue an Phae plot of the voltage loop 6.11 Smulaton Reult Font en Convete The SIMULINK moel of the font en convete powe ccut hown n fgue 6.28. The thee phae nvete block geneate the nvete temnal voltage takng the gatng gnal a t nput. The ac e ynamc equaton n the tatonay efeence fame.e. equn.(6.30) though equn.(6.31) ae moele n the ubequent block. The output fom th block ae the nucto cuent, whch ae then multple wth the wtch tatu to fom the c e cuent n the emoulato block. Fnally, the ynamc of the capacto voltage, gven by equn.(6.41), moele to get the c bu voltage. The moelng of the ente ytem along wth the feeback an contolle gven n fgue 6.29. The nvual functonal moule can be entfe clealy fom th agam. 165

co U1* U fe1 U fe2 fe1 feq U2 * 3phae Invete U fe3 AC Se fe2 Demoulato DC Se Vc U3 * fe3 l1 V1 V2 V3 l3 l2 lloa Fgue 6.28 SIMULINK moel of the thee phae font en convete powe ccut V 1 3ph Souce V 2 V3 Uef Uef Voltage Contolle feq * AC Se V * feq V * fe PWM Geneato V 1 * V 2 * V 3 * Powe Ccut fe1 fe2 fe3 V c Loa n V c (v c) v c * feq fe e U acq Seno Fgue 6.29 SIMULINK ytem moel of the thee phae font en convete The mulaton eult fo the thee phae font en convete une vaou tanent conton ae gven n fgue 6.30 though fgue 6.34. The paamete fo the powe ccut an the contolle ue n th mulaton ae lte n a 166

MATLAB fle n Appenx B. The contolle moule moele n pe unt n oe to emulate the actual mplementaton of the contolle. In fgue 6.30(a), epone of feq an fe fo tep change n * feq fom 0 to 0.5 p.u. wth * fe = 0, ae hown. The egne cuent loop tme contant 2m. The coeponng epone of the ac e cuent gven n fgue 6.30 along wth the upply voltage. Snce * fe = 0, the nput powe facto obeve to be unty. The eveal of actve cuent fom 0.5 p.u. to -0.5 p.u. une unty powe facto opeaton hown n fgue 6.31. Cuent epone fo tep change n * fe fom 0 to 0.25 p.u. wth * feq =0.5 p.u. ae plotte n fgue 6.32. The nput cuent wavefom how that the font en opeate at a leang powe facto, theeby upplyng eactve powe to the ouce. Thee, of coue, a lmt to the eactve cuent that can be njecte. Th epen on the c bu voltage an the lne e nuctance value. Snce the eactve voltage op a to the lne voltage n the ame phae, the maxmum value of fe can be wtten by the followng equaton. uc mmax u 3 2 2 fe,max 2 (6.47) 2 L The ecouplng of the ynamc of the -ax an q-ax cuent loop clealy event fom thee plot. The ntal chagng of the c bu voltage an, tanent ue to applcaton of potve loa hown n fgue 6.33. The epone of the c bu voltage when 167

the loa evee plotte n fgue 6.34. The voltage loop tme contant aume to be 100m. Fgue 6.30(a) Repone of feq an fe Fgue 6.30(b) u ac an epone of fe 168

Fgue 6.31(a) Repone of feq an fe Fgue 6.31(b) u ac an epone of fe 169

Fgue 6.32(a) Repone of feq an fe 6.32(b) u an epone of fe Fgue 6.32 Smulaton eult fo tep change n * fe fom 0 to 0.25 p.u. wth * feq = 0.5 p.u. 170

Fgue 6.33(a) Repone of u c Fgue 6.33(b) Repone of feq Fgue 6.33 Smulaton eult of epone of c bu voltage when a potve loa of 0.75 p.u. uenly apple on the c e 171

Fgue 6.34(a) Repone of u c Fgue 6.34(b) Repone of feq Fgue 6.34 Smulaton eult of epone of c bu voltage when the c e loa evee fom 0.35 p.u. to -0.35 p.u. 172

6.12 Concluon A tato flux oente moel ha been eve fo the woun oto nucton machne. Cuent contolle egne n the fel efeence fame compe popotonal o popotonal-ntegal contolle wth ubequent aton o ubtacton of the compenatng tem. The egn metho mple a t ectly follow fom the oto voltage equaton. Smulaton eult how that the ynamc of the actve an eactve cuent loop ae ecouple a eque. The font en convete moele n the tato voltage efeence fame. The tuctue of the cuent loop mla to that fo the oto e contol. The font en convete ha been exhautvely mulate fo fowa an evee powe flow conton. It hown that leang powe facto opeaton poble upto a cetan lmt. The voltage contolle exhbt excellent tanent epone ung uen mpact of loa on the c bu. 173