Fuzzy Logic vs. Classical PI Voltage Controller for a Self-Excited Induction Generator

Transcription

1 Matheatical Application in Science and Mechanic Fuzzy Logic v. Claical PI Voltage Contolle fo a Self-Excited Induction Geneato MATEO BAŠIĆ, DINKO VUKADINOVIĆ, MILJENKO POLIĆ Faculty of Electical Engineeing, Mechanical Engineeing and Naval Achitectue Univeity of Split R. Boškovića 32, 2000 Split CROATIA abaic@feb.h, dvukad@feb.h, iljenko.polic2@gail.co Abtact: - Vecto contol algoith ae often ued fo contol of the elf-excited induction geneato (SEIG. Thi pape peent a copaative analyi of two diffeent appoache fo contol of the SEIG geneated voltage in a vecto contol yte. The claical appoach baed on the PI contol i fit conideed and then a fuzzy-logic-baed altenative i popoed. In paticula, two diffeent-type fuzzy logic (FL contolle, Madani and Sugeno, ae developed fo the pupoe. The analyi and copaion of the contolle pefoance i povided fo tep change in load and DC voltage efeence. The obtained iulation eult ae expeientally veified. Key-Wod: - Self-excited induction geneato, Vecto contol, Dynaic analyi, PI contolle, Fuzzy logic contolle Intoduction The capability of the quiel-cage induction geneato to excite without an extenal eactive powe ouce wa dicoveed in the 930 [], [2]. Thi capability allowed the application of quielcage induction geneato in tand-alone powe geneating yte, in which the eactive powe fo the gid i not available and which ae uually aociated with enewable enegy ouce [3]-[5]. Until ecently, howeve, the widepead application of elf-excited induction geneato (SEIG wa not poible due to the poble elated with the intability of the geneated voltage. Only with the advent of inulated-gate bipola tanito (IGBT and icocontolle thee poble could be uccefully ovecoe. Vecto contol algoith ae today doinantly applied in SEIG contol yte due to thei upeio contol featue. Mot of uch yte epoted in liteatue eploy claical PI contolle becaue of the iple deign and atifactoy pefoance [5]-[7]. Moe advanced appoache baed on fuzzy logic and atificial intelligence have alo been conideed [3], [8], but thoe ae uually adopted fo axiu powe point tacking while the voltage contol i alot excluively handled by ean of the PI contolle. In thi pape, the advanced fuzzy-logic-baed appoach to SEIG voltage contol i conideed. Unlike the claical PI contolle, the fuzzy logic (FL contolle doe not equie knowledge of a detailed atheatical odel of the contol yte. Alo, it ha the capability of handling uncetain and noiy ignal, and uually lead to bette eult copaed to the conventional contolle, in te of epone tie, ettling tie and obutne [9]. On the othe hand, thi i uually achieved at the expene of an inceae in the coputational equieent. It hould alo be noted that deigning of the FL contolle equie expet knowledge of the contol yte, and in the cae of vey coplex yte it ay pove to be vey tediou o even ipoible tak. Theefoe, the final deciion about which type of voltage contolle peent the bet oveall choice depend on vaiou paaete. In thi pape, two diffeent-type FL contolle ae developed fo contol of the SEIG voltage. Thei application in the SEIG vecto contol yte i popoed and oveall pefoance evaluated by copaion with the optially-tuned claical PI contolle. The analyi i caied out both on the iulation and expeiental level. 2 SEIG Vecto Contol Syte Baic configuation of the SEIG vecto contol yte unde conideation i hown in Fig.. A it can be een, an indiect oto-field-oiented (IRFO algoith i eployed fo contol of the SEIG geneated voltage. ISBN:

2 Matheatical Application in Science and Mechanic i i α β L L R i L α + L ω L i ( L R i α + L u ( L R i α α β + L u L ω L i α β + L ω L i β α β L ω L i L R i β β + (3 (4 Fig. Baic configuation of the SEIG vecto contol yte The ain coponent of the yte ae the induction geneato, the pie ove, the IGBT convete, the IRFO contolle and the DC link. The battey in the DC link povide the initial voltage aco the capacito C fo initial excitation of the induction geneato. The eitive load i connected in paallel with the capacito. The ain objective i to enue contant voltage aco the capacito, egadle of change in DC load and oto peed. Thi i achieved by adjuting the active and eactive powe flow in the yte though contol of the IGBT convete witching pule. Thee pule ae geneated at the output of the hyteei cuent contolle, a hown in Fig.3, while the efeence cuent ae calculated within the IRFO contol algoith, a explained in Section Modeling of the Contol Syte Coponent 2.. SEIG Model Application of vecto contol equie utilization of a dynaic SEIG odel. Such odel can be obtained by odification of the conventional dynaic odel of an induction achine, a decibed in [0]. Hee ae given only the final t ode diffeential equation of the conventional dynaic SEIG odel in the tationay efeence fae, expeed in the Laplace doain and uitable fo ue in MATLAB Siulink i α 2 ( L L + L R i α ω i β L u α L R i α α + L ω L i β + ( whee: u α and u β ae the α-axi and β-axi coponent of the tato voltage pace-vecto; i α and i β ae the α-axi and β-axi coponent of the tato cuent pace-vecto; i α and i β ae the α-axi and β-axi coponent of the oto cuent pace-vecto; R and R ae the tato and oto eitance, epectively; L, L and L ae the tato inductance, the oto inductance and the agnetizing inductance, epectively; ω i the oto angula peed; σ i the total leakage facto; K α and K β ae the α-axi and β-axi coponent of the initially induced voltage due to the eidual oto flux linkage. Fig.2 how the conventional SEIG equivalent cicuit decibed by Eq. (-(4. The agnetizing flux atuation i taken into account by expeing the agnetizing inductance a a function of the agnetizing cuent agnitude. The coeponding chaacteitic can be deteined fo the tandad no-load tet, a decibed in [4] and [0]. The agnetizing flux atuation i, in fact, andatoy fo build-up and tabilization of the SEIG geneated voltage. The ion loe of the SEIG ae neglected fo iplification pupoe. Thi i jutified by the fact that the ephai i not placed on the yte efficiency o detuning analyi but athe on deteining the adequate DC voltage contolle. The SEIG odel hown in Fig.2 i, a uch, applicable in cae when the capacito and eitive load ae connected in paallel and diectly to the induction achine tato teinal. i β L 2 ( L Riβ L L ω L i α L u β ω i α β + L R i β (2 Fig.2 Conventional SEIG equivalent cicuit in tationay efeence fae (α-axi ISBN:

3 Matheatical Application in Science and Mechanic Howeve, in the yte hown in Fig., the IGBT convete i placed between the induction achine and the DC link o the coeponding odel need to be deteined a well IGBT Convete and DC Link Model By auing ideal thee-phae IGBT convete, the tato phae voltage and the DC-link cuent can be expeed in te of the witching function a u u u a b c dc udc 2 3 udc 2 3 udc 2 3 a a ( S S S a ( S S S b b c c a ( S S S c b b a b c c (5 (6 (7 i S i + S i + S i (8 whee epeent the voltage aco the DC-link capacito, and i a, i b and i c epeent the tato phae cuent. The witching function, S a, S b and S c, ae deteined by the output of the hyteei cuent contolle in the coeponding phae. By conideing a eitive load, the DC link can be epeented by the following equation: t udc idc dt + udc0 C + 0 R (9 dc whee C i the DC-link capacito, R dc i the DC-link eitive load and 0 denote the initial voltage aco the capacito (i.e., the battey voltage. 2.2 Contol Algoith The IRFO contol algoith eployed fo contol of the DC-link voltage i hown in Fig.3. In Fig.3, the efeence d-axi coponent of the tato cuent pace vecto, i d, i eponible fo agnetization, while the coeponding q-axi coponent (heeinafte: q-axi tato cuent i eponible fo toque adjutent. The equation of the popoed contol algoith ae deived fo the conventional SEIG odel, condition of the indiect oto flux oientation and auption of ideal powe convete. The efeence oto flux linkage i calculated online a popotional to the atio of the efeence DC voltage and eaued oto peed. The input to the voltage contolle ae the efeence and the actual DC voltage, wheea the efeence q-axi tato cuent i the output vaiable. Howeve, the elationhip between the input and output vaiable of the contolle i not yet defined becaue the adequate contolle ha yet to be deteined. 3 PI and Fuzzy Logic Contolle 3. PI Contolle The claical PI contolle can be decibed by y( t K P ε ( t + K I ε ( t dt (0 t 0 whee ε(t epeent the input eo ignal, in thi cae ε ( t udc ( t udc ( t, and y(t epeent the output contol ignal, in thi cae y( t iq ( t. K P and K I ae the popotional and integal gain of the PI contolle, epectively. Thee gain ae tunable and thei optial value can be deteined by obeving the PI contolle epone to tep change in the efeence input ignal a well a to vaiou ditubance that ay occu in the yte, e.g. udden change in load. Such appoach wa adopted in thi pape. The following optial value wee finally obtained fo the PI contolle paaete: K P 0.02 A/V and K I 0.2 A/V. Fig.3 IRFO contolle cheatic diaga 3.2 Fuzzy Logic Contolle In thi ection, two diffeent-type FL voltage contolle, i.e. Madani and Sugeno, ae developed. Fig.4 how the ebehip function (MF of the Madani-type FL contolle. In Fig.4, N, P and Z tand fo negative, poitive and zeo, epectively, wheea S, M and B tand fo all, ediu and big, epectively. Hence, NS i intepeted a all negative. Vaiable e and ce epeent the input to the FL contolle, wheea ciq epeent the output vaiable. Naely, e i the ISBN:

4 Matheatical Application in Science and Mechanic eo ignal calculated a the diffeence between the efeence and the actual DC voltage, ce i the change in eo calculated a the diffeence between two conecutive value of the eo ignal e, and ciq i the adjutent ignal fo the efeence q-axi tato cuent. The univee of dicoue of the fuzzy vaiable i expeed in pe unit value, which equie caling of the input and output ignal. Thu, the caling facto equal to 0.005, 0.4 and 0. wee choen fo e, ce and ciq, epectively. The input MF of the Sugeno-type FL contolle ae the ae a thoe hown in Fig 4a and 4b. Howeve, the output MF ae diffeent than thoe hown in Fig.4c, which eflect the fact that diffeent algoith i ued fo calculation of the output vaiable copaed to the Madani-type FL contolle. A oppoed to the tiangula haped output MF of the Madani-type FL contolle, the Sugeno-type FL contolle ha ingleton output MF defined by the following contant value: NB -2, NM -, NS -0.5, Z 0, PS 0.5, PM and PB 2. A fo defuzzification, fo the Madanitype FL contolle the centoid ethod i choen, wheea fo the Sugeno-type FL contolle the weighted aveage ethod i choen. c Fig.4 Mebehip function of the developed Madani-type FL contolle The opeation of the FL contolle i govened by the et of IF-THEN ule uaized in Table. The ae et of ule applie to both FL contolle. Table Rule bae fo FL contolle e NB NM Z PM PB ce NB PB PB PM PS Z NM PB PM PS Z NS Z PM PS Z NS NM PM PS Z NS NM NB PB Z NS NM NB NB 4 Reult and Dicuion In thi ection, the pefoance of the optiallytuned claical PI contolle and the developed FL contolle ae evaluated and copaed baed on the eult obtained by iulation and expeient. 4. Siulation Reult The iulation odel of the SEIG contol yte unde conideation wa built in MATLAB Siulink envionent, baed on the equation given in Section 2.. To educe the coputational equieent, two diffeent apling tie wee ued: T /00 fo the induction geneato, the IGBT convete and the hyteei cuent contolle, and T 2 /4000 fo the et of the contol algoith. Paaete of the induction achine ued in the analyi ae given in Appendix. In the fit et of iulation (Fig.5, the load eitance wa changed at t 2, in a tep anne, fo R dc 0 2 Ω (no load to R dc 500 Ω, while both the oto peed and efeence DC voltage wee kept contant and equal to 200 p and V, epectively. In the econd et of iulation (Fig.6, the efeence DC voltage wa changed at t 2, in a tep anne, fo 250 Ω to Ω, while both the oto peed and load eitance wee kept contant and equal to 200 p and 220 Ω, epectively. In Fig.5a, it can be een that the FL contolle offe about fou tie fate DC voltage epone copaed to the optially-tuned PI contolle, with about twice a low undehoot value. Howeve, in Fig.5b, the undehoot value obtained fo the FL contolle ae highe copaed to that of the PI contolle. Still, at the expene of an inceae in the undehoot value the ettling tie wa deceaed fo about 0.2 copaed to the PI contolle. ISBN:

5 Matheatical Application in Science and Mechanic i q Fuzzy - Madani PI contolle 270 t [] Fuzzy - Madani - PI contolle t [] Fig.5 Siulation epone to tep change in load: actual DC voltage and efeence q-axi tato cuent i q Fuzzy - Madani PI contolle 240 t [] PI contolle Fuzzy - Madani -3 t [] Fig.6 Siulation epone to tep change in efeence DC voltage: actual DC voltage and efeence q-axi tato cuent In Fig.6a, the DC voltage epone obtained fo the FL contolle ae again notably fate copaed to the PI contolle, but again at the expene of lightly highe ovehoot value. Finally, in Fig.6b, it can be een that the peak value of the efeence q-axi tato cuent do not diffe ignificantly, egadle of the contolle ued. Howeve, fo the FL contolle, the q-axi tato cuent deivation i ignificantly lowe copaed to the PI contolle. High value of the q-axi tato cuent deivation can lead to dangeouly high induced voltage in the tato winding. The iulation eult ugget that the developed FL contolle offe iila pefoance. In addition, thei pefoance i ignificantly bette copaed to that of the PI contolle. A fo the coputational equieent, they ae oewhat highe fo the FL contolle, epecially fo the Madani-type. In paticula, when the Sugeno-type FL contolle i ued intead of the PI contolle, the iulation execution tie i extended fo about 5 %. Siilaly, when the Madani-type FL contolle i ued, the iulation execution tie i extended fo about 30 % copaed to the PI contolle. 4.2 Expeiental Reult An expeiental etup of the SEIG contol yte unde conideation wa built fo expeiental validation of the iulation eult. The IRFO contol algoith wa pogaed and executed in eal tie by uing MATLAB Siulink and DS04 R&D Contolle Boad, anufactued by dspace. The PI contolle i athe eaily ipleented in eal tie due to low coputational equieent. Fo the ae eaon, the Sugeno-type contolle i ipleented in eal tie oe eaily than the Madani-type contolle. In fact, the developed Madani-type contolle could not be uccefully ipleented in eal tie due to tak oveun iue, which could not be eolved by educing the nube of fuzzy ule o by inceaing the apling tie, while the C-code optiization wa not attepted. Conequently, only the Sugeno-type FL contolle wa ued in the expeiental analyi. It hould be ecalled, howeve, that in te of voltage contol both FL contolle delive iila eult anyway. In Fig 7 and 8, the expeiental eult obtained fo the opeating egie decibed in Section 4. ae hown. i q [A] PI contolle 270 t [] PI contolle t [] Fig.7 Expeiental epone to tep change in load: actual DC voltage and efeence q-axi tato cuent ISBN:

6 Matheatical Application in Science and Mechanic i q [A] PI contolle 240 t [] PI contolle -5 t [] Fig.8 Expeiental epone to tep change in efeence DC voltage: actual DC voltage and efeence q-axi tato cuent The eult hown in Fig 7 and 8 ae in good ageeent with the iulation eult hown in Fig 5 and 6, epectively. Maxiu deviation between the iulation and expeiental eult i noted in teady tate value of the efeence q-axi tato cuent. Thi i due to the fact that in the iulation odel cetain loe which exit in the actual yte ae neglected, eulting in lowe toque value and, conequently, in lowe value of the efeence q-axi tato cuent in iulation. Thee loe include echanical loe, ion loe and tay loe of the induction achine, a well a the powe convete loe. It hould be noted that thee deviation ae independent of the type of voltage contolle, while the analyi of the powe loe and elated phenoena i beyond the cope of thi pape. 5 Concluion In thi pape, two diffeent-type FL voltage contolle, Madani and Sugeno, ae developed and uccefully ipleented in the SEIG vecto contol yte. Thei pefoance i analyzed and copaed with that of the claical PI contolle. The obtained iulation and expeiental eult ugget that the FL contolle offe ignificantly bette pefoance copaed to the optially-tuned PI contolle, in te of epone tie, ettling tie and obutne. Howeve, thi i achieved at the expene of an inceae in the coputational equieent, epecially fo the Madani-type FL contolle. In futue wok, the pefoance of the developed contolle will be oe thooughly invetigated and evaluated by encopaing wide ange of oto peed, DC voltage and load. Appendix Induction achine paaete P n.5 kw, U n 380 V, p2, I n 3.8 A, n n 39 p, n L H, L σ H, L σ H, R Ω, R Ω (at 20 C, Ψ n Wb. Refeence: [] E. D. Baet, F. M. Potte, Capacitive Excitation fo Induction Geneato, AIEE Tanaction on Electical Engineeing, Vol.54, No.5, 935, pp [2] C. Wagne, Self-excitation of Induction Moto, AIEE Tanaction on Electical Engineeing, Vol.58, No.2, 939, pp [3] R. M. Hilloowala, A. M. Shaaf, A Rule-Baed Fuzzy Logic Contolle fo a PWM Invete in a Stand Alone Wind Enegy Conveion Schee, IEEE Tanaction on Induty Application, Vol.32, No., 996, pp [4] K. Idjdaene, D. Rekioua, T. Rekioua, A. Tounzi, Vecto Contol of Autonoou Induction Geneato Taking Satuation Effect Into Account, Enegy Conveion and Manageent, Vol.49, No.0, 2008, pp [5] E. Magato, J. Faia, M. J. Reende, J. Pala, A New Contol Stategy with Satuation Effect Copenation fo an Autonoou Induction Geneato Diven by Wide Speed Range Tubine, Enegy Conveion and Manageent, Vol.52, No.5, 20, pp [6] Y. W. Liao, E. Levi, Modelling and Siulation of a Stand-Alone Induction Geneato with Roto Flux Oiented Contol, Electic Powe Syte Reeach, Vol.46, No.2, 998, pp [7] R. Leidhold, G. Gacia, M. I. Valla, Field- Oiented Contolled Induction Geneato with Lo Miniization, IEEE Tanaction on Indutial Electonic, Vol.49, No., 2002, pp [8] D. Vukadinović, M. Bašić, A Stand-Alone Induction Geneato with Ipoved Stato Flux Oiented Contol, Jounal of Electical Engineeing, Vol.62, No.2, 20, pp [9] J. M. Zuada, R. J. Mak, C. J. Robinon, Coputational Intelligence Iitating Life, New Yok: IEEE Inc. Pe, 994. [0] M. Bašić, D. Vukadinović, G. Petović, Dynaic and Pole-Zeo Analyi of Self- Excited Induction Geneato Uing a Novel Model with Ion Loe, Intenational Jounal of Electical Powe & Enegy Syte, Vol.42, No., 202, pp ISBN: