Optimizing Voltage-Frequency Control Strategy for Single-Phase Induction Motor Drives

Transcription

1 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) Optiizing Voltage-Fequency Contol Stategy fo Single-Phae Inuction Moto Dive N. NAEWNGERNDEE, C. SUKCHAROEN &. KUWORAWANICHPONG School of Electical Engineeing, Intitute of Engineeing Suanaee Univeity of echnology 111 Univeity Avenue, Suanaee Ditict, Nahon Ratchaia HAIAND 3 Abtact: - Single-phae inuction oto ae wiely ue in houehol electic oto application. Although ot electic appliance equie a few aount of ilo-watt input, iniizing powe loe uing thei opeation give a geat benefit eulting in nationwie electic enegy ue by houehole. In thi pape, a oel-bae iulation fo lo iniization uing the pace-phao theoy i popoe. Intea of a fixe 22 V, 5 Hz AC powe ouce, a vaiable-voltage,vaiable-fequency (VVVF) contol chee i aue to function the AC upply. By foulating an olving a containe optiization of ingle-phae inuction oto ive with VVVF, opeation of the ingle-phae inuction oto with iniu powe loe can be attaine. o evaluate thi contol tategy, tet cae of a ingle-phae inuction oto ive with vaiable echanical loa ae ituate to evaluate it pefoance. Key-Wo: - ingle-phae inuction oto, optiization, vaiable-voltage-vaiable-fequency contol, equential quaatic pogaing, lo iniization, pace-phao theoy 1 Intouction o ate, thee-phae inuction oto have been inceaingly ipotant fo inutial electic oto application. It houl note that thee till exit DC oto in oe liite application, e.g. oto fo vehicle. Apat fo a lage-ize electic oto ive, ingle-phae inuction oto ae wiely ue in houehol electic oto application. hi application typically conue powe of a factional hoe powe up to aoun ten hoe powe. Although ot electic appliance equie a few aount of ilo-watt input, iniizing powe loe uing thei opeation give a geat benefit eulting in nationwie electic enegy ue by houehole. In geneal, ingle-phae oto ae contolle by a thyito-phae contolle o a vaiable eito. hi i quite iple, but it i not efficient in te of enegy conuption. o achieve thi goal, coplex contol tategy cannot be avoi a long a ac achine ae involve. One of wiely-ue contol chee i vaiable-voltage, vaiable-fequency (VVVF) [1,2]. It can be applie fo oto contol in any fo. Fo exaple, the contant volt-pe-hetz chee i one of the ot popula etho ue fo pactical ipleentation. Howeve, following thi contol tategy oe not guaantee iniu lo opeation. heefoe, ajutable fequency an voltage of the powe upply i oe flexible an can lea to oe econoical opeation of houehol electic appliance. In thi pape, the contol chee of VVVF in oe to iniize total powe loe in a ingle-phae inuction oto. hee ae five ain ection to illutate the popoe tategy. Section 2 i Moeling of Single-phae Inuction Moto, Section 3 i Poble Foulation, Section 4 i Siulation Reult an Section 5, the lat ection, i Concluion. 2 Moeling of Single-phae Inuction Moto Fig. 1 wining alignent of a ingle-phae oto Single-phae inuction oto can be chaacteize by eveal iffeent oel. he pace-phao appoach [2,3] i the etho ue in thi pape. With thi oel, oto cuent, toque an pee can be

2 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) obevable. he pace-phao oel i vey coplicate an nee oe pace fo explanation. Howeve, in thi pape only a bief eciption i peente a follow. Figue 1 ecibe wining alignent of a ingle-phae inuction oto coniting of ain an auxiliay wining with thei inuce voltage an cuent. A hown in the figue, a tationay efeence fae which i along the axi of the ain tato wining i efine an ue fo atheatical analyi thoughout thi pape. It i eential to info that all quantitie epecially on the oto nee to be tanfee to the tato axi. hi can be pefoe by uing the following tanfo atix. V V q co θ = inθ inθ v θ co v q (1) he upecipt an inicate the efeence axi in which the vaiable belong to. Biefly, the inuce voltage on the tato an oto wining ae uaize in Equation 2 an 3, epectively V V V V q q q + pqq = pq qq + q q + p = pq qq + q qq q q p + p i p i i p i q q p + p q q i i q i i q (2) (3) By uing the tanfo atix entione above, all tate vaiable can be tanfoe into the tato iect axi a follow. whee, A t [] i [ A][] i + [ B][ v] = (4) 1 [ ] = [ D ] [ E ] [B] = [D] [] i = [ i q, i, i q, i ] [] v = [ v, v, v, v ] q -1 q q = ω inθ ω coθ lq + = D co θ in θ [ E] [ ] ω inθ ω coθ co in ω θ ω θ ω co θ ω inθ q co θ in θ ( l + ) in θ co θ in θ + q q co θ ( ) l q ( + ) whee, q i tato eitance of the ain wining i tato eitance of auxiliay wining l i leaage inuctance of the ain wining ls i leaage inuctance of the auxiliay wining q i utual inuctance on the tato q-axi i oto eitance l i leaage inuctance of the oto q-axi A can be een, the two echanical quantitie, ω an θ, caue the nee fo aitional two equation which can be obtaine fo Newton econ law of otion a hown in Equation 5. ω t = θ t B J 1 ω θ P + 2J l e q [ ] (5) Cobine Equation 4 an 5, Equation 6 i foe. [ i] 4x1 [ A] [] i ω t 4x4 B M 4x1 = ω J θ θ t M 1 (6) t [ B] 4x4 [] v M + P 4x 2J e 1 M whee, J i oto oent of inetia B i aping coefficient Applying a nueical tie-tepping etho to olve a et of iffeential equation, oto cuent, angula pee an poition can be calculate nueically. 3 Poble Foulation o iniize powe loe uing the opeation of a ingle-phae inuction oto ive, a containe nonlinea optiization poble ut be foulate an then olve fo a local iniu. Befoe

3 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) icuion of the optiization faewo, the powe loe eulting fo any opeating point can be expee by Equation 7 an 8. whee, P lo =P cu + P ot (7) P cu = q i q + i + i q + i (8) P cu enote oto coppe loe P ot enote otational loe of the oto It note that in thi calculation the otational lo i aue to be contant an iply equal to no-loa loe. In oe to iniize the powe loe, VVVF contol tategy i ue. hi give two contol vaiable, fequency (f) an voltage (V). By ajuting thee paaete inepenently, a et of optial value fo fequency an voltage upply to the oto at any paticula loa i achieve via an appopiate optiization technique. Without poviion of optiization technique, a geneal fo of lo iniization fo a poble of ingle-phae inuction oto ive i uaize a follow. Miniize Subject to P f V lo in in ( f,v ) = F f f V V o olve the optiization poble, a equential quaatic pogaing (SQP) [4] i ecoene. If tool fo copute iulation ae popt to be ue, the optiization faewo with the SQP can be ecibe tep-by-tep a follow. ax ax SAR Step : All input ata ae loae. All vaiable ae initial. x = [f V ] Set counte Step 1: If any topping citeion ha not been et hen go to tep 2, othewie tep 3 Step 2: Appoxiate the nonlinea optiization poble by uing quaatic ub-poble epeenting by gaient an Heian of the objective function a follow Miniize 1 2 H + f whee, i a ecent each iection f i the gaient of the objective function H i the Heian atix Subequently, the appoxiate quaatic poble i olve fo an optial each iection at each iteation, conecutively. Upate fo a olution of the next iteation by x +1 = x + Retun to tep 1 Step 3: Diplay eult SOP 4 Siulation Reult In thi ection, eontation by iulation i illutate. A ingle-phae inuction oto i aue to be opeate with an ajutable AC powe upply ouce. he voltage agnitue an fequency of the upply ae both ajutable (5 25 V, an 1 1 Hz). Alo, it i an ieal inuoial voltage ouce. Fo the tet oto, paaete [5] ae given below. P = 4 pole q = 1.3 Ω = 2.6 Ω = 2.1 Ω q =.2785 H l =.74 H lq =.53 H l =.74 H J =.1 B =.5 In thi pape, MAAB optiization toolbox i ue a an optiize to ee an optial opeating point in aociation with echanical loa toque. Fou loa conition ae ituate fo eontation a given below. oa 1: oa 2: oa 3: oa 4: 4 N 8 N 12 N 16 N hee loa ae contant toque an aue to be applie on the oto haft at t = 1. econ afte tat. et f = 5 Hz an V = 22 V be the initial olution fo all loa cenaio. he optial olution obtaine

4 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) by the SQP optiize of MAAB toolbox (fincon function) fo each loa cenaio ae hown in able 1. able 1 Optial olution fo each loa conition Powe Optial olution oa Iteation loe Voltage Fequency (N.) ue (W) (V) (Hz) Powe lo (W) Powe lo at oque loa 8 N. Fo claification, copaion between the bae cae (22 V, 5 Hz powe upply) againt the optial opeating point peente in able 1 i in able 2. able 2 Copaion between the bae cae an the optial opeating point oa (N.) Bae cae o Miniu powe lo Powe lo euction W W 17.37% W W 4.52% W W 6.71% W W 3.77% It i the fact that ot oto ae typically eigne to have the axiu efficiency at it full-loa conition. he eae can obeve that the tet oto alo behave in thi anne. he full-loa toque of thi oto i 16. N, a a eult thi opeating point i cloe to the optiu (only 3.77% of the powe loe can be euce). In aition, Fig 1 4 how convegence fo each tet cae. hee gaph illutate a equence of olution oveent, iteation-by-iteation, until the local iniu ha been eache Powe lo at toque loa 4 N. Powe lo (W) Powe lo (W) Iteation Fig. 2 Convegence fo 8 N loa conition Powe lo at oqu loa 12 N Iteation Fig. 3 Convegence fo 12 N loa conition Powe lo at oque loa 14 N. Powe lo (W) Iteation Fig. 1 Convegence fo 4 N loa conition Iteation Fig. 4 Convegence fo 16 N loa conition o obeve oto chaacteitic, copaion between bae-cae opeation an optial opeation i pefoe. Stato wining cuent, echanical toque an pee epone of the tet oto une both upply conition ae epicte in Fig Fig 5 7 peent the epone of the bae cae while Fig 8 1 illutate thoe of the optial opeation. Futheoe, Fig. 11 i the copaion

5 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) between the upply cuent of the bae cae an the optial opeation. Fig. 5 Wining cuent of the bae cae Fig. 8 Wining cuent of the optial Fig. 6 Spee of the bae cae Fig. 9 Spee of the optial Fig. 7 oque of the bae cae Fig. 1 oque of the optial

6 Poceeing of the 5th WSEAS Intenational Confeence on Application of Electical Engineeing, Pague, Czech Republic, Mach 12-14, 26 (pp84-89) Fig. 11 Supply cuent of both upply conition he eult can confi that with caeful eign of the upply ouce ingle-phae inuction oto ive ae lo-iniize in oe to cut-off electic enegy ue by conue loa in eiential ection, office o all-ize factoy. Futheoe, the popoe contol chee give a geat avantage when the oto ive eve a patial loa. hi can guaantee the opeation with iniu powe loe. Refeence: [1] A.S. Ba-thunya, R. Khopa, K. Wei & H.A. oliyat, Single phae inuction oto ive-a liteatue uvey, IEEE Int. Conf. on Electic Machine an Dive (IEMDC21), 17 2 June 21, Cabige, Maachuett, USA, pp [2] P.C. Kaue, Analyi of Electic Machine, McGaw-Hill, 1987 [3] M.B. Coea, C.B. Jacobina, E.R.C. a Silva & A.M.N. ia, Vecto contol tategie fo ingle-phae inuction oto ive yte, IEEE an. on Inutial Electonic, Vol. 51, Iue 5, pp , 24 [4] S.G. Nah & A. Sofe, inea an nonlinea pogaing, McGaw-Hill, 1996 [5] N. Abel-Rahi & A. Shaltout, Opeation of ingle-phae inuction oto a two-phae oto, IEEE 28 th Annual Conf. on Inutial Electonic Society (IECON2), Vol. 2, 5 8 Novebe 22, pp Concluion an Futue Wo hi pape peent a voltage-fequency contol tategy though a containe optiization in oe to iniize powe loe of a ingle-phae inuction oto ive. By ajuting the upply voltage an fequency, thi chee i able to povie the upply conition uitable fo any paticula loa toque. Not only the full-loa opeation but alo any patial loa of the yte, the enegy loe ae iniize effectively. With MAAB optiization toolbox, elevant containe optiization poble can be olve eaily. hi wo eveal that thee exit at leat one opeating point which i ai to be a local iniu fo lo iniization poble. hi point give iniu powe lo fo a ingle-phae inuction oto ive. Howeve, to geneate the inuoial powe upply with optial voltage an fequency accoing to any pecifie loa i too expenive an ipactical. o enhance thi eeach an to bing thi contol tategy fo pactical ipleentation, a quae-wave invete i alteative. Howeve, ue to haonic enichent, an optial olution of the quae wave powe upply ay be hifte fo the optial olution of the inuoial one. hi nee caeful tuy an obevation of chaacteitic fo a ingle-phae inuction oto fe by quae wave invete in oe to iniize powe loe at each paticula loa conition.