Above Flux Estimation Issues in Induction Generators with Application at Energy Conversion Systems

Transcription

1 Acta Polytechnica Hungaica Vol. 3, No. 3, 2006 Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem Ioif Szeidet, Octavian Potean, Ioan Filip, Vaa Citian Depatment of Automation and Applied Infomatic Faculty of Automation and Compute Science Politehnica Univeity fom Timioaa Av. V. Pavan, No.2, , Timioaa, Romania Phone: (0040) , Fax: (0040) , Abtact: The pape peent iue egading the flux etimation of induction machine. The electical machine vaiable etimation epeent a majo poblem in the actual context of moden contol appoache, epecially of enole contol tategie. Thee ae conideed eveal implementation of induction machine flux etimato by uing the Matlab-Simulink envionment and thee ae dawn the affeent concluion. Keywod: flux etimato, obeve, induction machine, imulation, Matlab-Simulink envionment 1 Intoduction The iue of the tate etimation epeent a majo poblem in the actual tend of moden electical machine contol. The tate etimation mut be olved epecially in the cae when thoe vaiable ae not meauable o the tanduce ae expenive (uch a toque, o flux tanduce) and the pice cot of a contol ytem inceae due to thi fact. Theefoe, appea the neceity of uing of contol cheme and method without the uage of ome pecific tanduce/eno. Thi cae i the one of the enole contol method. [1] The etimato implementation ae baed on the uage of contol plant model, thei aim being to etimate the value of non-meauable vaiable by uing othe meauable vaiable. Baically thee ae two majo type of etimato: [1] - Etimato without coection (without feedback). 137

2 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem - Aymptotic etimato o obeve (with feedback), that peent a pedictive coection in ode to aue a fate convegence and a bette obutne of etimation at the etimated plant paamete vaiation and at exogenou petubation. In the context of electical machine the mot commonly ued etimato ae: - Flux and toque etimato ae ued in the FOC (field oiented contol) and the diect toque and flux vecto contol. - Speed and acceleation etimato baed on meaued poition ae ued in poition/peed contolle, tate contolle, liding mode contolle, etc. - Poition and peed etimato baed on meaued tato vaiable (cuent and voltage) ued in the enole contol (without poition eno/tanduce). - Petubation etimato ued in equivalent petubation compenato. In ode to fulfill the equiement of a fate and accuate contol (educed epone peiod) of the induction machine, the value of the flux vaiable mut be known. Thi vaiable value can be etimated on the bai of voltage, cuent and otation peed meauement. Thee ae eveal contol tategie and method fo the induction machine. In technical liteatue, ae epecially ued the contol baed on tato flux and the one baed on the oto flux. [2] [3]. The pape decibe ome etimato tuctue implemented in the Matlab- Simulink imulation envionment. The pape tudie thoe etimato tuctue having in view the poibility of thei implementation in unconventional enegetic conveion ytem, epecially of WECS (wind enegy conveion ytem). Thee ae tudied thee induction machine flux etimato: baed on voltage model, baed on cuent model and baed on the tato cuent etimation and a flux obeve. 2 Induction Machine Flux Etimato 2.1 Flux Etimato baed on Voltage-model Thi type of etimato (flux etimato baed on voltage model) can be yntheized by uing the voltage-baed model, a depicted in elation (1): Ψ ˆ = ( u R i (1) e ) Whee: ˆ epeent the etimated value, e epeent the etimato paamete, 138

3 Acta Polytechnica Hungaica Vol. 3, No. 3, 2006 Ψˆ the tato flux etimated value, u S tato voltage, R SE the tato eitance etimato paamete, i S tato cuent. Thee i conideed only the eal pat of the equation and epectively a zeo value oto cuent (without load toque), the obtained eult ae valid alo in the cae of the imaginay axi (with load toque). The etimato i defined by the elation (2), fo the x-axi: Ψ ˆ = ( u R i (2) e ) The elation (2) implementation in Matlab-Simulink i epeented in Figue 1. INDUCTION MACHINE ESTIMATOR Figue 1 Induction machine flux etimato baed on the voltage model (Matlab-Simulink implementation) The input vaiable in the etimato ae the machine cuent and voltage. In the cae that the value of the etimato paamete tato eitance R SE i identical to the electical machine tato eitance R S and the cuent and voltage ae meaued without eo (due to noie o offet) then the etimato can be ued when the oto cuent i not zeo. Thi fact can be noticed in elation (1) whee the oto cuent doen t occu. Howeve, in the cae of a lightly diffeent value of the R SE paamete thi would lead to eo in the etimato pefomance epecially in the cae of low otation peed. In Figue 2 i epeented the etimato eo in the cae when the eitance value i diffeent with a 5% egading the eal value of the eitance (the epone at a tep ignal the u voltage value). It can be noticed, that initially the etimate follow the flux evolution, but futhe it ha a deviation to infinite o to the integato atuation. 139

4 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem Figue 2 Simulation eult (etimato eo) In Figue 3 thee can be noticed that the etimate follow coectly the flux vaiable, even in the cae of a 5 Hz fequency (the eitance eo being alo 5%). Thee can be concluded that the influence of the eitance paamete eo educe with the fequency inceae. Alo, the offet in the cuent meauement conduct to eo in the flux etimation at any fequency value. Taking in conideation that thi etimation method peent difficultie in implementation (epecially al low otation peed), pactically it i not ued in application. Figue 3 Simulation eult (etimato eo at f=5 Hz) 140

5 Acta Polytechnica Hungaica Vol. 3, No. 3, Flux Etimato baed on Cuent-model In ode to impove to pefomance of the peviou etimato thee i ued the elation (3). Ψ = i + i ) (3) M ( Whee: M magnetization inductance, i tato cuent, i oto cuent, Ψ tato flux Thee i conideed the oto cuent to be zeo, and fom the elation (3) eult the following elation (4): Ψˆ = i (4) me Whee: me the magnetization inductance etimato paamete. Theefoe, only the tato cuent epeent the input of the etimato tuctue. In Figue 4, thee i epeented the Matlab-Simulink implementation of induction machine flux etimato baed on cuent-model. INDUCTION MACHINE ESTIMATOR Figue 4 Induction machine flux etimato baed on the cuent model (Matlab-Simulink implementation) One of the main diadvantage of thi etimato implementation baed on the cuent-model i the fact that a coect etimation of flux equie a vey pecie value of the magnetization inductance M. Anothe poblem i the fact that due to the magnetic atuation phenomenon that occu in the electical machine, thi paamete ( M ) i not contant. Thi paamete vaie fact that lead to a difficult obtaining of the me paamete. In Figue 5 thee ae epeented the imulation eult the evolution of the flux etimate in the condition of a 5% eo in the magnetizing inductance value. Anothe diadvantage of thi etimato type i the fact that the eo ae ignificant in the cae that the oto cuent i not zeo. In 141

6 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem ode to compenate the oto cuent effect, it i neceay to meaue the otation peed becaue the oto cuent uually cannot be meaued. Figue 5 Simulation eult (etimato eo) The peviou etimato, baed on the voltage-model peent the advantage of being independent to the otation peed and to the oto cuent. Fom elation (5) and elation (3) and (4) thee i obtained the elation (6). Ψ = Ψ + i (5) Whee: i leakage inductance. Ψ = ) M ( i + Ψ (6) + M In ode to calculate the oto flux, fom elation (5), (4), (3) and (7) thee i obtained the elation (8). dψ = jz pω Ψ Ri (7) whee: z p numbe of pole pai, dψ ω oto otation peed, R oto eitance. = i R M + M R Ψ ( jz p ω) + M (8) 142

7 Acta Polytechnica Hungaica Vol. 3, No. 3, 2006 Thee eult the etimato defined by the elation (9) and (10): ˆ = ( ei + Ψˆ (9) e + Ψ ) dψˆ = i Re + e Ψˆ ( e R e + jz pω) (10) Thi etimato ha a input the oto otation peed and the tato cuent, a it can be noticed in Figue 6. Figue 6 Flux etimato baed on cuent-model The flux etimato baed on cuent-model peent good pefomance in the cae of low fequencie, but i enible to the paamete eo at high fequencie. 2.3 Flux Etimato baed on the Stato Cuent Etimation In ode to olve the poblem of the etimato baed on voltage-model eo, thee i ued the etimate of the tato cuent intead of the meaued value of the tato cuent vaiable. dψ = u R i (11) Fom elation (11) and (3), conideing the oto cuent to be zeo, thee eult the etimato decibed by elation (12) and (13), epeented in Figue 7. ˆ (12) Ψ = ( u Reiˆ ) Ψ = ˆ iˆ (13) 143

8 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem INDUCTION MACHINE ESTIMATOR Figue 7 Induction machine flux etimato baed on tato cuent etimation. (Matlab-Simulink implementation) Thi flux etimato i pincipally a imulation model in open loop, becaue thee ae no feedback though ome meauement. In Figue 8, thee can be noticed the educed value of the etimato eo. Howeve, thee i peent a teady tate egime eo in the flux etimate due to the eo in the eitance o inductance eo. Figue 8 Simulation eult (etimato eo) 144

9 Acta Polytechnica Hungaica Vol. 3, No. 3, Induction Machine Flux Obeve 3.1 Induction Geneato Flux Obeve Anothe poibility i the combination of the thee etimato type aleady conideed by uing the obeve theoy. The Kalman filte tuctue can be alo applied in the cae of the induction machine. Conideing the tate epeentation of a ytem (decibed by elation (14), (15)), dx = Ax + Bu (14) y = Cu whee: x epeent the etimated tate, u epeent the ytem input, y epeent the ytem output decibed by elation (16): dxˆ = A ˆ e x + Beu + K( y Ce xˆ) (16) whee: K epeent the gain coefficient (Atom, 1976), and Ae, Be, Ce - the model paamete. In the cae of a Kalman filte, the model paamete ae A=A e, B=B e and C=C e, obtaining the identity obeve that follow the entie tate vecto, in compaion with a educed et obeve that follow only a ubet of the tate vecto (uenbege, 1979). Thee can be obtained a flux obeve tuctue of the induction geneato (conideing the cae when the oto cuent i zeo) by uing the following notation (17), (18), (19), (20), (21), (22), (23): (15) x = Ψ (17) xˆ = Ψ ˆ (18) y = i (19) u = u (20) A R e e = (21) 145

10 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem B =1 (22) C e e 1 = (23) The obeve equation i (24): dψˆ = u R e Ψˆ + K( i 1 Ψˆ The chooe of the gain coefficient epeent a high enitive tak. The liteatue ecommend the tudy of the pole-zeoe epeentation. [2] [3] The poblem that occu in the cae of the complete ode obeve (the oto cuent i not zeo) i that the pole depend by the otation peed if the K coefficient i contant. Anothe method i epeented by the QG (inea Quadatic Gauian) deign, in the cae that the K gain coefficient minimize the etimate eo. Thi method peent limitation due to the vaiation of the machine paamete in the functioning egime. The equation (16) can be efomulated a depicted in elation (25): dψˆ Whee: R e = u R e Ψˆ + kr e ( i iˆ ) ) (24) (25) K k = (26) iˆ = CeΨˆ 1 = Ψˆ (27) In Figue 9 i peented the conideed flux obeve, decibed by elation (17) - (23) Figue 9 Induction Machine Flux Obeve (Simulink implementation) 146

11 Acta Polytechnica Hungaica Vol. 3, No. 3, 2006 Conideing the peented Simulink diagam and the equation (17) - (23) and (25), thee eult: dψˆ = u R e Ψˆ ( (1 + k) ki ) = u R e ((1 + k)ˆ i ki The obtained obeve i a combination between the flux etimato baed on voltage model (Figue 1) and the etimato baed on tato cuent etimation (Figue 7). Thee can be noticed in Figue 10 and 11, that a chooe of an unitay K coefficient educe the teady tate egime eo of the etimato baed on tato cuent etimation and the deviation of the etimato baed on voltage model. The obeve pole i the oot of the chaacteitic equation, a depicted in elation (29): [( A KC ) ] = 0 e e R 1 kr e = 0 ) (28) Re = ( 1 + k (29) e ) If the K=-1 then the obeve become the etimato baed on voltage model, and epectively if K=0 then the obeve i pactically the etimato baed on tato cuent etimation. Figue 10 Step epone of the obeve (K=0) Figue 11 Step epone of the obeve (K=1) The eult obtained by thi obeve ae good, in the cae of an +/- 10% vaiation of the induction geneato paamete, thi ange coveing the iue egading the machine paamete vaiation (due to the tempeatue, magnetic coupling, etc). Concluion Thee can be concluded that the olution of uing the induction machine magnetic flux etimation i impoed becaue thi vaiable mut be known in the context of the contol tuctue, epecially in the cae of FOC tuctue and due to the fact that thi vaiable cannot be diectly meaued. 147

12 I. Szeidet et al. Above Flux Etimation Iue in Induction Geneato with Application at Enegy Conveion Sytem The thee etimato tuctue and the obeve peented in the pape peent both advantage and limitation that mut be conideed and tudied fo each type of application. The poblem that mut be olved i the deign of a flux etimato tuctue that peent good pefomance in the cae of entie fequency ange pectum. The fit peented etimato baed on voltage-model peent a bette epone in the cae of highe fequency ange; meanwhile the flux etimato baed on cuent-model peent a bette epone in the ange of low fequencie. In [1] [4], thee i decibed an efficient modality of a combination of thoe two etimato in ode to obtain a etimato with good pefomance both in cae of low fequency ange and of high fequency ange. The idea that lead to uch etimato i to ue a low fequency pa filte to elect the etimato baed on the cuent-model at low fequency ange and of coue, a high fequency pa filte to elect the etimato baed on voltage-model at high fequency ange. Anothe appoach modality that can be ued i the obeve theoy, uch a the Kalman filteing that can be applied alo in the cae of the induction geneato. [5] [6] The above expoed flux etimato and obeve peent a geat ignificance in the actual tend of the enole contol tuctue of the moden windmill baed on induction geneato. In ode to tudy the windmill contol tuctue pefomance thee i mandatoy a detailed analyi of the dynamic behavio of all main component of the wind enegy conveion line: wind tubine, electical geneato, convete, gid and othe additional element). Refeence [1] H. Siegfied: Gid Integation of Wind Enegy Conveion Sytem, Publihe: John Wiley & Son, ISBN X, 1998 [2] K. D. Hut, T. G. Habetle, G. Giva, F. Pofumo: Speed Senole Field- Oiented Contol of Induction Machine Uing Cuent Hamonic Spectal Etimation, Poc. IAS 94, 29 th Annual eting, Denve Coloado, 1994, pp [3] Z. Kzeminki: Speed and Roto Reitance Etimation in Obeve Sytem of Induction Moto, Poc. EPE 91, Fienze, Italy, 1991, pp [4] T. Umeno, Y. Hoi, H. Suzuki: Deign of the Flux-Obeve-Baed Vecto Contol Sytem of Induction Machine Taking into Conideation Robut Stability, Electical Engineeing in Japan, Vol. 110, No. 6, 1990, pp [5] G. C. Veghee, S. R. Sande: Obeve fo Flux Etimation in Induction Machine IEEE Tanaction on Indutial Electonic, Vol. 35, No. 1, Febuay 1988, pp [6] J. Holtz, J. Quan: Dift and Paamete Compenated Flux Etimato fo Peitent Zeo Stato Fequency Opeation of Senole Contolled Induction Moto. IEEE Tanaction on Induty Application, Vol. 39, No. 4, July/Aug. 2003, pp