Five-level fuzzy logic direct torque control of double star synchronous machine

Transcription

1 Fe-leel uzzy logc rect torue control o ouble tar ynchronou machne Elakhar Benyoue, Abelkaer erouel an a Barkat Abtract Th paper eal wth the rect torue control o the alent-pole ouble tar ynchronou machne re e by two eleel oe-clampe nerter. Th approach combne the wellknown aantage o the multleel nerter wth thoe o a rect torue control. The propoe approach cont to replace the hytere controller by one uzzy controller an the output ector o the uzzy controller le to a multleel wtchng table to ece whch reerence ector houl be apple to control the two threeleel nerter. mulaton reult how ome mproement regarng n the reucton o torue an lux rpple. Keywor Double tar ynchronou achne, ult-leel Inerter, Drect Torue Control, Fuzzy Logc Control. I. INTRODUCTION OR many year, electrcal re are oune on the Ftratonal three-phae machne. Howeer, when enhancng power capablte o the re conere, multphae machne re are potentally recommene. In act, multphae re are ueul or large ytem uch a naal electrc propulon ytem, locomote tracton an electrcal ehcle applcaton []. ultphae re are oten conere a a able oluton when reucton o the nerter per phae ratng reure ue to the hgh motor power. Furthermore, th category o re ha many aantage oer conentonal re uch a reucng the ampltue o torue pulaton, lowerng the DC lnk current harmonc, hgher relablty an ecreang the current tre o wtchng ece []. The multphae machne ue n electrcal re ytem are n prncple the ame a ther three-phae counterpart. Thee nclue aynchronou an ynchronou multphae machne. ynchronou multphae machne may be wth permanent magnet exctaton or wth el wnng exctaton [], among thee type o machne; the alent-pole ouble tar ynchronou machne (D) one o the mot ueul o multphae machne. Th kn o machne contan ouble tator place by egree; the rotor mlar to the rotor o a mple ynchronou machne an t excte by contant E. Benyoue wth the Intellgent Control & Electrcal Power ytem laboratory, Djllal Labe Unerty, Bel Abbe, Algera. (E-mal: lakharbenyoue@yahoo.com). A. erouel wth the Intellgent Control & Electrcal Power ytem laboratory, Djllal Labe Unerty, Bel Abbe, Algera. (E-mal: amerouel@yahoo.r).. Barkat wth the Faculty o cence an Engneerng, Department o Electrcal Engneerng, la Unerty, Ichbla treet, la 8, Algera. (E-mal: a_barkat@yahoo.r). current ource. The eeng o th type o machne generally aure by two two-leel nerter. Howeer, or the hgh power; multleel nerter are oten reure. nce the aantage o multleel nerter an multphae machne complement each other, t appear to be logcal to try to combne them by realzng a multleel multphae re. eeral topologe o multleel nerter hae been propoe n the techncal lterature [4], [5]. The oe clampe nerter () repreent one o the mot nteretng oluton, to ncreae oltage an power leel an to achee hgh ualty oltage waeorm [6]. Th make the an attracte oluton to hgh power re ytem. In orer to enure an eecte control o D, eeral metho hae been propoe [7]. Complexty an parameter entty are the weakne o thee metho. An alternate oluton the ue o rect torue control (DTC) trategy [8]. Drect torue control metho characterze by t mple mplementaton an a at ynamc repone [9]. Conerable reearch eort tll beng eote to the elmnaton o t nherent aantage. One more gncant aantage o conentonal DTC rpple, whch ext n the torue an lux arable. Recently, eeral technue hae been eelope [], [] to mproe the torue perormance. In th context, a FLDTC cheme apple on e-leel propoe n th paper. Then, an approprate oltage ector electe. mulaton are then carre out to ery the perormance o the propoe trategy. The mulaton reult obtane wth the optmzaton n the rule number how goo perormance. The remaner o th paper tructure a ollow: n ecton II the moel o the D preente, a utable tranormaton matrx ue to eelop a mple ynamc moel. The propoe e-leel nerter brely preente n ecton III. In ecton IV, the DTC trategy apple to get ecouple control o the lux an torue. In orer to mproe the tatc an ynamc control perormance o the D, the hytere controller ue n DTC are ubttute by a uzzy controller n ecton V. Fnally, the aantage o the propoe control ytem are hown by mulaton nolng 5 kw D n ecton VI. II. ODELLING OF THE DOUBLAR YNCHRONOU ACHINE In orer to etablh a moel o D, the uual aumpton are aopte: the F n ar-gap ha a nuoal repartton IN: -5 9

2 an the aturaton o magnetc crcut neglecte [7]. The tator an rotor oltage euaton are gen by: = R t φ () φ : tator oltage ector. : tator current ector. : tator lux ector. The orgnal x menonal ytem o the machne can be ecompoe nto three orthogonal ubpace ( α, ), ( z, z ) an ( z, z 4) [], ung the ollowng tranormaton. [ ][ ] T z z z z 4 X α X X X X X = A X (), : - ax tator oltage., : - ax tator current. φ, φ : - ax tator lux., : DC oltage an current o rotor exctaton. φ R R ω The lux euaton φ = L φ = L φ = L : Flux o rotor exctaton. : tator retance. : Rotor retance. : Rotatng pee o rotor lux lnkage. (6) T X = X X = X a X b X c X a X b X c Where: X repreent tator current ( ), tator lux ( φ ), an tator oltage ( ). [ ] [ ] [ ] The matrx A gen by: [ A ] π 4π π 4π co( ) co co co( γ) co γ co γ π 4π π 4π n ( ) n n n( γ) n γ n γ 4π π π 5π = co ( ) co co co ( π γ) co γ co γ 4π π π 5π n ( ) n n n ( π γ) n γ n γ To expre the tator an rotor euaton n the ame tatonary reerence rame, the ollowng rotaton tranormaton aopte co( ) n( ) P ( ) = n( ) co( ) Wth th tranormaton, the component o the α- plane can be expree n the - plane a: The electrcal euaton φ = R ωφ t φ t φ = R t = R ωφ () (4) (5) T L, L : - tator nuctance. L : ax rotor nuctance. : utual nuctance between ax or each tator an rotor. The mechancal euaton J = Tem TL r (7) t Tem, T L : Electromagnetc an loa torue. : Rotor pee. J : oment nerta. : Frcton coecent. r The electromagnetc torue euaton gen by: T = p( φ φ ) (8) em p the pole par number. III. TRUCTURE OF FIVE-LEVEL INVERTER The man crcut o the e-leel hown n gure. The DC bu capactor plt nto our, prong a three neutral-pont. Each arm o the nerter mae up o eght IGBT (Inulate Gate Bpolar Trantor) ece, an x clampng oe connecte to the neutral-pont. The aantage o the nerter that crcut topology mple, the output connecte wth the machne rectly, no tranormer neee. The oltage tre o wtchng ece only uarter o the DC bu oltage; t eay to exten the capacty o nerter. IN: -5

3 c 4 k 4 ak bk ck For each wtchng ece xk (k=,, = 8, x=a, b or c), a Boolean uncton F xk ene by: c 4 k ak bk ck F xk xk ON = (9) OFF xk c c ak bk ck The complementarte between upper an lower wtchng ece o each leg mpoe the ollowng euaton: c c ok k c ak 4 ak 5 bk 4 bk 5 ck 4 a b c ck 5 Fxk = Fxk ( 4) () For each leg o the nerter, e connecton uncton are ene a ollow: c k c k ak 6 ak 7 ak 8 bk 6 bk 7 bk 8 ck 6 ck 7 ck 8 F = F F F F F = F F F F F = F F F F F = F F F F F = F F F F Cxk xk xk xk xk 4 Cxk xk xk xk 4 xk 5 Cxk xk xk 4 xk 5 xk 6 Cxk 4 xk 4 xk 5 xk 6 xk 7 Cxk 5 xk 5 xk 6 xk 7 xk 8 () ak n Fg. tructure o e-leel oe-clampe nerter (k= or rt nerter an k= or econ nerter). nce e kn o wtchng tate ext n each phae, a e-leel nerter ha 5 wtchng tate an there are 6 eecte ector (gure ). bk ck The phae oltage ak, bk, ck can be wrtten a: c ak FCak FCak FCak FCak 4 FCak 5 c 4 = F F F F F bk Cbk Cbk Cbk Cbk 4 Cbk 5 ck FCck FCck FCck FCck 4 F Cck 5 c 4 c () = = L = = L 4L =4 L 5L 4L =5 L L (,) L = 9 6L 5L = 8 L 9L (6,7) L 8L 7L 8 9 = 7 8L = 6 6L 5L (8,9) L 7L 6L (6,7) (8,9) (,) (,) (4,5) (6,7) (,) (4,5) (,) (,4) (8,9) (,) = 5 (4,5) L L 4 9L (,) L = 4 4L L L (,4) L L =6 = 7L 9L L 8L L = 7 = 8 = 9 = L L = L L = = = L α 4L = = 4 IV. DIRECT TORQUE CONTROL TRATEGY The well-known DTC trategy bae on lux an torue control ung hytere comparator. Thee controller ue the etmate error o the control arable at each amplng tme o operaton. The conere lux an torue controller enure the eparate control o thee two arable, a or the DC re. When the leel o torue or tator lux pae to the hgh or low hytere lmt, a utable oltage ector apple to brng back each arable n t correponng ban [8]. The tator oltage etmator gen by: ˆ α ˆ = [ ] ˆ A ˆ Where ˆ an ˆ are compute ung E (). () The tator lux ector component an t ampltue can be ealuate rom the etmate tator oltage euaton a ollow Fg. pace oltage ector or a e-leel. IN: -5

4 t ˆ φ ( ˆ ) ˆ α = α R α τ φα() t ˆ φ ( ˆ R ) ˆ = τ φ() (4) ˆ ˆ ˆ φ = φα φ The tator lux angle calculate by: ˆ = tan ˆ ˆ φ α φ (5) The DTC block agram o D upple by e-leel n each tar repreente by gure. φ φˆ Tˆem Φ τ Zone() wtchng table x j x j Voltage etmaton Frt 5-leel econ 5-leel c D The electromagnetc torue can be etmate by: Tˆ = p( ˆ φ ˆ φ ) (6) em α α Table an preent the output oltage ector whch are electe to change the torue angle. tator lux an torue etmator ˆ α α ˆ α ˆ abc, Table. wtchng table ue n the DTC o rt tar or the D. Φ τ Zone() Φ τ Zone() Φ τ Zone() Fg. Fe-leel DTC cheme or D. 4 ( 4) L 4 ( 6) L 4 ( 8) L V. 4BFUZZY LOGIC DIRECT TORQUE CONTROL TRATEGY ( 4) L ( 4) ( 4) ( ) ( ) ( ) L 4 ( ) L Table. wtchng table ue n the DTC o econ tar or the D Φ τ Zone() Φ ( 6) L ( 6) ( 6) ( 8) ( 8) ( 8 ) L 4 ( 8) L τ Zone() Φ ( 8) L ( 8) ( 8) ( 6) ( 6) ( 6 ) L 4 ( 6) L τ Zone() The prncple o uzzy logc rect torue control mlar to tratonal DTC. Howeer, the hytere controller are replace by uzzy controller an the output ector o the uzzy controller le to a wtchng table to ece whch ector houl be apple. Th metho bae on uzzy clacaton ha the aantage o mplcty an eay mplementaton [7, 9]. Fgure 4 ge the memberhp uncton or nput arable, an ˆ. For th purpoe t aume that the tator lux lnkage pace ector can be locate n any o twele ector preente n gure 4. µ ET NL NL N N NP NP ZE PP PP P P P L P L 4 ( ) L 4 ( 4) L 4 ( 6) L ( ) L ( ) ( 4) L ( 4) ( 6) L ( 6) (a) Nm ( ) ( 8) ( 4) ( 6) ( 6) ( 4) µ N Z P ˆ ˆ ( 8) ( ) 4 ( ) 8 L 8 L ( 6) ( ) 4 ( ) 6 L 6 L ( 4) ( ) 4 ( ) 4 L 4 L Wb π (b) (c) Fg. 4 emberhp uncton o nput arable: a). Torue error, b). tator lux error, c). tator lux angle. The uzzy control rule bae, eelope ung aman metho, hown n table an 4. IN: -5

5 Table. Rule o uzzy control or rt tar. 4 PL 5L 6 9L PL 6L 6 L P 7L 6 L P 4L 8L P L 7L P 4 8 ZE NL 6 NL L 4 8L N L 8 6L N L 6 9L N L 8L 8L N L 6L 7L PL 5L 6 9L PL 8L 6 L P 7L 6 L P 4L 8L P 6L L P 4 8 ZE NL 6 NL L 4 9L N L 8 6L N L 6 9L N 4L 9L L N L 6L 7L PL 9L L PL L 4L P L 5L P 8L 6 L P 7L 6 L P 8 6 ZE NL NL L 8 L N L L N L L N L L L N L L L PL 9L L PL L 6L P L 5L P 8L 6 L P L 6 4L P 8 6 ZE NL NL L 8 L N L L N L L N 4L L 4L N L L L PL PL P 5 V L 4 7L 4L 4 8L 5L 4 9L PL PL P 6 V L 4 7L 6L 4 L 5L 4 9L PL PL P 7 V 7L 8 8L 8 L 9L 8 L L PL PL P 8 V 7L 8 L L 8 4L 9L 8 L P L 6L P L 5L P 6 ZE NL 4 NL 6L L N 4L L N 7L L N 6L L L N 5L L L P L 6L P 4L 8L P 6 ZE NL 4 NL 7L L N 4L L N 7L L N 8L L 4L N 5L L L P 6L 4 L P 5L 4 9L P 6 4 ZE NL 8 4 NL L 6L N 8L 6 4L N L 4 7L N L 6L 6L N 9L 4L 5L P 6L 4 L P 8L 4 L P 6 4 ZE NL 8 4 NL L 7L N 8L 6 4L N L 4 7L N L 7L 8L N 9L 4L 5L 9 PL L L PL L L PL L L PL 4L L PL L 5L PL L 6L PL L 5L PL 4L 8L P L L P L 8 L P 9L 8 L P 8 ZE NL 8 NL 4L 6 L N L 8L N 5L 8 L N 4L L L N L 8L 9L P L 4L P L 8 L P L 8 L P 8 ZE NL 8 NL 5L 6 L N L 8L N 5L 8 L N 6L L L N L 8L 9L tar... tar P L 7L P L 4L P L L P 4 ZE NL 6 NL 8L 4L N 6L 4 L N 9L 5L N 8L 4L 4L N 7L L L Table 4. Rule o uzzy control or econ tar. ˆ ˆ ˆ ˆ 4 ˆ 5 ˆ 6 ˆ 7 ˆ 8 ˆ 9 ˆ ˆ ˆ ˆ ˆ ˆ 4 ˆ 5 ˆ 6 ˆ 7 ˆ 8 ˆ 9 ˆ P L 7L P L 4L P L 6L P 4 ZE NL 6 NL 9L 4L N 6L 4 L N 9L 5L N L 5L 4L N 7L L L IN: -5

6 The general tructure o the e-leel FLDTC or D repreente by gure 5. φ φˆ Tˆem tator lux an torue etmator Fuzzy Logc Control ˆ α α x j x j Voltage etmaton ˆ α ˆ abc, Frt 5-leel econ 5-leel c D Fg. 5 Fe-leel FLDTC cheme or D Tme (),5 Electromagnetc torue (Nm).6.6 tator lux (Wb).6.8 VI. COPARATIVUDY To ery the alty o the propoe controller, the ytem wa mulate ung the D parameter gen n Appenx. The DC e o the nerter upple by a contant DC ource c =6V. The am o th ecton to compare the e-leel DTC or D wth the e-leel FLDTC or D. The obtane reult are preente n gure 6 or the eleel DTC an gure 7 or the e-leel FLDTC. The D accelerate rom tantll to reerence pee ra/. the ytem mulate wth loa torue (T L = N.m), aterwar t tep araton on the rate loa (T L = N.m) at tme t=. An then a uen reeron n the pee comman rom ra/ to - ra/ wa ntrouce at.5. In gure 6, the pee ollow t reerence alue whle the electromagnetc torue reache lowly t reerence alue. Elmnaton o the loa torue caue a lght araton n pee repone. The pee controller nterene to ace th araton an enure the ytem ollow t utable reerence pee pee (ra/) Tme (),5.5.5 Tme () Fg. 6 Dynamc repone e-leel DTC or D. Fgure 7 llutrate that the ytem ha a uck an mooth tartng proce an the comman reject eectely the turbance. The excellent ynamc perormance o electromagnetc torue an lux control eent. It mut be ponte out that the e-leel FLDTC ecreae conerably the torue rpple. The mulaton reult how that the e-leel FLDTC an eecte oluton or D re. In act, th control enure goo ecouplng between tator lux lnkage an electromagnetc torue. Alo, t can ecreae the torue rpple n comparon to the e-leel DTC wth goo ynamc perormance pee (ra/) Tme () IN: -5 4

7 - Electromagnetc torue (Nm) Tme (),5.6.6 tator lux (Wb) Tme () Fg. 7 Dynamc repone o e-leel FLDTC or D. VII. CONCLUION.6.8 In th paper, a multleel DTC metho apple on D e by two e-leel nerter preente an t mert oer the conentonal DTC approach are conrme by mulaton reult. mulaton reult that hae been preente n teay-tate an tranent operatng conton ugget that the propoe cheme capable o gng atactory teay tate an ynamc perormance. Inee, the re operate wth low rpple o motor arable an the ecouplng between the tator lux an the electromagnetc torue mantane, conrm the goo perormance o the eelope re ytem. oreoer, by mean the e-leel nerter e DTC re, t poble to reuce the tre o the wtchng ece o the oltage ource nerter an lowerng the wtchng power loe, oten emane reurement n hgh power applcaton. VIII. APPENDIX: D PARAETER p n =5 kw, n =V, p=, R=.5, R =., L =.8H, L =.H, L =5H, =.46H, J=.5Nm /ra, r =.Nm/ra, =A. [] K. arouan, F. Khoucha, A. Kheloul, L. Baghl, an D. Haouche, tuy an mulaton o rect torue control o ouble tar nucton motor re, IEEE, Internatonal Power Electronc an oton Control Conerence, ay, pp. -8. [] D. Bouana, L. Nezl, A. Tlemçan, an. ahmou, DTC o ouble tar ynchronou machne re ung backteppng concept wth xe wtchng reuency, Internatonal ympoum on Enronment Frenly Energe n Electrcal Applcaton, Algera,, pp. -6. [4] P. Thongprar, A 5-leel three-phae cacae hybr multleel nerter, Internatonal Journal o Computer an Electrcal Engneerng, Vol., No. 6,, pp [5] B. ngh, N. ttal, D. Verma, D. ngh,. ngh, R. Dxt,. ngh, an A. Baranwal, ult-leel nerter: a lterature urey on topologe an control tratege, Internatonal Journal o Reew n Computng, Vol.,, pp. -6. [6] C. Balamurugan,. Natarajan, an R. Benraj, Inetgaton on three phae e-leel oe clampe multleel nerter, Internatonal Journal o oern Engneerng Reearch, Vol., No.,, pp [7] D. Bouana, L. Nezl, T. ohan, O. ahmou, an. Tajne, Robut DTC bae on aapte uzzy control o ouble tar ynchronou machne re wth xe wtchng reuency, Journal o Electrcal Engneerng," Vol. 6, No.,, pp. -4. [8] B. Naa, A. aoum, an B. Naa. A oe rect torue control x-ector o a ouble tar permanent magnet ynchronou machne bae on uzzy logc, Internatonal Conerence on Power Electronc an Electrcal Dre, Oran, Algera, December. [9] E. Benyoue, A. erouel, an. Barkat, Drect torue control ung uzzy logc controller or ouble tar ynchronou machne, Internatonal Conerence on Power Electronc an Electrcal Dre, Oran, Algera, December. [] W. Xuezh, an L. Huang, Drect torue control o three-leel nerter ung neural network a wtchng ector elector, IEEE, Annual eetng,. [] R. Zammene, E. Berkouk, an R. Duke, A noel DTC cheme or a e-leel oltage ource nerter wth GTO thyrtor, Thr Internatonal Conerence on ytem, gnal & Dece, 5. E. Benyoue wa born n 'la (Algera) n 985. He recee the Eng. Degree n Electrcal Engneerng rom ohamme Boua Unerty o 'la n 9 an the egree rom the Electrcal Engneerng Inttute o Bel Abbe Unerty n. He a member o ICEP (Intellgent Control Electrcal Power ytem) Laboratory. H reearch nteret are n moelng an robut control o ual three phae ynchronou motor an conerter. A. erouel wa born n Bel Abbe (Algera) n 954. He recee h B egree n electrcal engneerng rom the UT Oran (Algera) n 98, the egree rom the ame Unerty (UTO) n 99 an the PhD egree rom the Electrcal Engneerng Inttute o Unerty o Bel Abbe (Algera) n 4. He currently Proeor o electrcal engneerng n th Unerty. He a member o ICEP (Intellgent Control Electrcal Power ytem) Laboratory. H reearch nteret are n robut control o electrcal machne, Harmonc analy metho an mproement o PFC, Non-lnear control o electrcal re, Power electronc. He an author an co-author o more than centc artcle.. Barkat recee h Engneer, agter an Doctorate egree, all n Electrcal Engneerng, rom the Polytechnc Natonal Inttute o Alger n 994, 997 an 8 repectely. In, he jone the Department o Electrcal Engneerng, Unerty o la. H current reearch nteret are n the el o power electronc, renewable energe, multphae re, an aance control theory an applcaton. IX. REFERENCE [] B. Naa, L. Nezl,. ahmou, an. Elbar, Drect torue control bae three-leel nerter e ouble tar permanent magnet ynchronou machne, Energy Procea, Vol. 8,, pp IN: -5 5