COMPARISON OF SCALAR AND VECTOR CONTROL STRATEGIES OF INDUCTION MOTORS

Transcription

1 HUNGARIAN JOURNAL OF INDUSTRIAL CHEMISTRY VESZPRÉM Vol. 9() pp (0) COMPARISON OF SCALAR AND VECTOR CONTROL STRATEGIES OF INDUCTION MOTORS G. KOHLRUSZ, D. FODOR Univeity of Pannonia, Faculty of Engineeing, Intitute of Mechanical Engineeing, Automotive Sytem Engineeing Goup, H-800, Vezpem, Egyetem t. 0., HUNGARY Cuently the ue of thee-phae induction machine i widepead in indutial application due to eveal method available to contol the peed and toque of the moto. Many application equie that the ame toque be available at all evolution up to the nominal value. In thi pape two contol method ae compaed: cala contol and vecto contol. Scala contol i a elatively imple method. The pupoe of the technique i to contol the magnitude of the choen contol quantitie. At the induction moto the technique i ued a Volt/Hetz contant contol. Vecto contol i a moe complex contol technique, the evolution of which wa inevitable, too, ince cala contol cannot be applied fo contolling ytem with dynamic behaviou. The vecto contol technique wo with vecto quantitie, contolling the deied value by uing pace phao which contain all the thee phae quantitie in one phao. It i alo nown a field-oiented contol becaue in the coue of implementation the identification of the field flux of the moto i equied. Thi pape epot on the changing poibilitie of the evolution toque chaacteitic cuve, and demontate the eult of the two contol method with imulation. The imulation and the applied equivalent cicuit paamete ae baed on eal meauement done with no load, with diect cuent and with loced-oto. Keywod: peed-toque chaacteitic, cala contol, vecto contol, Volt/Hetz contant contol, field-oiented contol. Intoduction The contol method fo induction moto can be divided into two pat: vecto contol and cala contol tategie. In thi eeach on thee phae uiel-cage induction moto the cloed loop Volt/Hetz voltage-fed invete dive a cala contol technique and the oto flux oiented contol with voltage-fed invete dive a vecto contol technique wee compaed. Howeve, thi i not the bet olution, becaue the impedance inceae and the cuent deceae with gowing fequency. Speed changing oppotunitie of induction moto Many application equie that the peed of the moto be vaiable without changing the toque. The peed of induction moto can be changed in thee diffeent way []: changing the numbe of pole pai, vay the magnitude of upplied voltage o vay the fequency of the upplied voltage. Changing the numbe of pole pai caue huge cuve hifting, and vaying the magnitude of upplied voltage give olution only in a mall ange. The mot pomiing poibility to change the peed of the moto i the vaying of the fequency (Fig. ). Figue : Speed v. toque cuve a function of fequency Cuent can alo be contolled by voltage. Thi offe a poibility of contol though both the voltage and the fequency changing. Thi idea wa the bai of the evolution of a contol method which i capable of contolling both peed and toque of induction moto, the o-called Volt/Hetz contant method.

2 66 Baic of cala contol The cala contol method i baed on vaying two paamete imultaneouly. The peed can be vaied by inceaing o deceaing the upply fequency, but thi eult in change of impedance. The change of impedance eventuate the inceae o deceae of cuent. If the cuent i mall, the toque of moto deceae. If the fequency deceae o the voltage inceae, the coil can be buned o atuation can occu in the ion of coil. To avoid thee poblem, it i neceay to vay the fequency and the voltage at the ame time. In thi way, the occuing diadvantage of changing fequency and voltage can be compenated. Accoding to the equation of induced voltage the V/Hz contant contol give contant flux in the tato (Eq. ). V e,rms f = 4.44 N ξ () whee V e,rms the induced voltage in the tato, f the fequency of the upplied voltage, N the numbe of tun, Ψ magnetic flux-linage in the tato, ξ contant of coil. The toque peed equation of induction moto (Eq. ) can be ued to detemine the voltage toque and fequency toque function []. T ai gap = ω m I R whee T ai-gap the toque of the moto in the ai-gap, ω m the mechanical angula peed, I the oto cuent, R the eitance of oto, the lip. () It can be een fom equation () that the elationhip between toque and fequency i invee, while voltage i diectly popotional to toque. Toque peed contol can be olved by the linea vaiaton of the two paamete (Eq. ). T ω V π f ~ ~ V f () With thi contol method the toque i acceible in all opeating point up to the nominal value of peed and the moto can opeate ove the nominal peed (Fig. ). In the ovepeed ange, the toque of the moto will deceae in invee popotion to the inceaing fequency becaue voltage cannot be highe than the value at which the dive electonic i able to opeate []. Figue : Toque-peed cuve with V/Hz contant contol Open-loop cala contol The open-loop Volt/Hetz contol of induction moto i widely ued in induty (Fig. ). Fo thi tategy, feedbac ignal ae not equied. Thi type of moto contol ha ome advantage: low cot, implicity and immunity to eo of feedbac ignal. Figue : Open-loop V/Hz contant contol Cloed-loop cala contol The cloed-loop method offe a moe pecie olution to contolling the peed than the open-loop method. Futhemoe, the cloed-loop technique contol the toque, too. A majo diadvantage of the open-loop contol method i that thi technique doe not contol the toque, o the deied toque i only acceible at the nominal opeating point. If the load toque change, the peed of the moto will change, too [4]. The cloed-loop method contain a lip contol loop, becaue the lip i popotional to the toque. The peed feedbac ignal fom the tachogeneato i compaed to the deied peed value. The diffeence i deceaed to zeo by the PI contolle, o the moto will each the deied peed.

3 67 Typical application of thi method ae in the winde dive [5]. A diadvantage of the method i uncontolled magnetic flux. Figue 4: Cloed-loop V/Hz contant contol Thee ae ome method which ue cuent contol. Cuent contolling olve the poblem of uncontolled flux, but thee method ae moe complex, e.g. in the cae of cuent egulated voltage-fed invete dive. Vecto contol method Field oiented contol i one of the vecto contol method. Thee ae othe well-nown method lie diect toque contol and diect elf-contol that wo with vecto, a well. The field oiented contol enue good and obut contol in cae of tanient. Field oiented contol i baed on a mathematical abtaction. Thi eult in an eaie model confomation which coepond the tuctue of well-contollable DC machine. The pinciple of field oiented contol wo with otating vecto (o phao) in a complex coodinate ytem. The magnitude and the phae of the contolled cuent change. With thi technique, it i poible to uncouple the field component. Uncoupling etablihe two independent and ingle contolled cuent: the flux- poducing cuent and the toque-poducing cuent. Uing thee cuent, the flux and toque can be independently contolled. Moeove, a 90 electic angle i enued between the uncoupled contol cuent. A a eult, the model of the induction moto loe it complexity, and a highpefomance dive can be ealized [6]. Field oiented contol can be caied out by ytemand coodinate tanfomation of the baic equation of the moto. Afte applying the tanfomation the altenating and inuoidal quantitie become nonaltenating quantitie. Due to uncoupling, the cuent can be contolled, and then, afte bac-tanfomation it i poible to modify the output of the invete with thee-phae quantitie. In thi way the magnitude and phae of upplied voltage o cuent can be modified. The quantitie of the moto ae decibed with a pace phao o a Pa-vecto (Eq. 4) in a thee-phae coodinate ytem [7]. u = ( u + au + a u ) a b c (4) The equation which ae valid intantenouly can be decibed fom the geneal voltage and flux phao of the moto (Eq. 5,6,7, 8). It i poible to divide the equation into two pat. The tato equation ae valid in the coodinate ytem fixed to the tato, and the oto equation ae valid in the coodinate ytem fixed to the oto [8, 9]. v = i R + (5) v = i R + (6) jθ = i L + i e L (7) m jθ = i L + i e L (8) m whee v, v the upplied voltage in oto and in tato, i, i the cuent in oto and in tato, R eitance of tato and oto coil, Ψ, Ψ magnetic flux-linage in oto and in tato, L, L, L m inductance of tato coil, of oto coil and of the ai-gap. It i neceay to detemine the electomagnetic toque to get the equation-of-motion of the moto (Eq. 9) [7]. in T e = i ϕ = whee T e the electomagnetic toque of moto, Ψ the magnetic flux-linage in oto, i the cuent in oto. i (9) The pupoe i the conveion into a two-phae coodinate ytem. Afte thi, both the tato and oto quantitie need to be tanfomed into a common coodinate ytem. Then, calculation become executable and o the contol ignal (e.g. cuent) ae geneated (Fig. 5). The ytem tanfomation can be pefomed by the tanfomation matix. Thi calculation eult in a eal and an imaginay pat of the pace-phao. Afte tanfomation the equation (5)-(8) become two-phae quantitie and need to be handled in a two-phae, complex α-β coodinate ytem [9, 0]. u u α β = 0 u a ub uc It i expedient to tanfom the complex, two-phae quantitie into a common coodinate ytem, which i expediently the ynchonouly otating d-q coodinate ytem. A a eult of thi tanfomation, the inuoidal quantitie become non-altenating quantitie. u u d q co ρ = in ρ in ρ uα co ρ u β

4 68 Afte tanfomation the quantitie have to be handled uncoupled to thei d and q component. It i deiable to contol the toque and peed. To achieve oto flux oientation it i neceay to oient the oto flux vecto to the d axi of the d-q ynchonou otating coodinate ytem (Fig. 5). Then the d diectional component of cuent can contol the oto flux, while the q diectional component contol the toque. dω p = J d i ml J B ω J (5) whee i d, i d and q component of tato cuent, L σ inductance of tato without mutual inductance, u d, u d and q component of tato voltage, ω, ω the ynchonou and the oto angula velocity, Ψ d d component of oto magnetic flux-linage, R, R eitance of oto and tato, τ oto time contant, J inetia of oto, p pole pai of moto, T l haft load of moto, B fiction contant. The bloc diagam of oto flux-oiented contol can be een in Fig. 7. Figue 5: Sytem and coodinate tanfomation The equation of toque get alo tanfomed (Eq. 0). T = p d i (0) The eduction of the oto quantitie to the tato give a imple model, which i the gamma-model (Fig. 6). Due to thi model, the equivalent cicuit diagam of the moto can be ceated []. Figue 7: Roto flux-oiented contol without flux calculation (Indiect field-oiented contol) Self-commiioning Figue 6: Gamma-model with educted value Fom the uncoupling to d-q component of equation (5)-(8) and fom the equation of toque (Eq. 0) it i poible to decibe the equation of the moto baed on the gamma-model (Eq. -5). di di d d = u d id R + ω Lσ σ ( u i R ω d ) id = ω L i () () d d + τ = Lm i () d ω R i ω = ω = (4) d To ceate the moto model it i neceay to detemine the unnown paamete of the moto by meauing the phae cuent and phae voltage. Moeove, it i neceay to meaue the phae diffeence between voltage and cuent. Fo detemining the paamete, thee diffeent meauement ae needed (Table -) [] : diect cuent tet, no-load tet, loced-oto tet. The eactance can be calculated fom the impedance which ae nown if the phae diffeence between the voltage and the cuent o the powe i nown. Table : Reult of the meauement with diect cuent VDC [V] IDC [A]

5 69 Fom the meaued data the tato eitance can be detemined. In cae of meauing with diect cuent the eactance ae zeo, o the meauement of two phae give only the eitance of the two phae. VDC, avg R = I DC, avg = 4Ω Table : Reult of the no-load tet V RMS [V] I RMS [A] P [W] coθ Modelling and imulation The model of the cloed-loop V/Hz and the oto fluxoiented contol wee implemented in MatLab/Simulin. Duing the imulation the model wee teted with changing peed and toque efeence. The epone can be een below. The eult in cae of peed change ae the following: In cae of no-load tet the lip i vey mall, hence the eitance of the oto i huge. The eult ae efeing to the tato becaue of the mall input cuent into the oto. VRMS Z nl = = X + X m = Ω I RMS Table : Reult of the loced-oto tet V RMS [V] I RMS [A] P [W] coθ The loced-oto tet wa implemented by locing the oto, which i allowed fo a hot time, only. In thi cae the lip i equal to one. The impedance and eitance can be meaued both fo the tato and the oto. If the phae diffeence i nown, the emaining paamete can alo be detemined. VRMS,avg Z l = = Ω I θ = acco RMS,avg P = 4.75 V t I l X l = Z l inθ = 47.9 Ω X l X = X = =.64 Ω X m = Z nl X = 4.0 Ω R l = Z l coθ = 5.6 Ω R = R l R = 7.6 Ω The unnown inductance can be detemined fom the paamete calculated fo modelling. L m = X m ω = L = L = X ω = Figue 8: Cloed-loop V/f=contant contol Figue 9: Roto flux-oiented contol Fom the eult it can be een that Volt/Hetz contol i a luggih method becaue it i baed on contolling the amplitude of voltage and fequency, intead of cuent. The oto flux-oiented method contol the amplitude and phae of cuent and fequency. Moeove, the contolled cuent ae decoupled, a it wa mentioned ealie. In thi way, contol can be apid and vey obut. The eult in cae of toque changing ae hown in Fig. 0-. Figue 0: Cloed-loop V/f=contant contol

6 70 ACKNOWLEDGEMENT The financial and infatuctual uppot of the State of Hungay and the Euopean Union in the fame of the TAMOP-4../B-09//KONV (Mobility and Envionment) poject i gatefully acnowledged. REFERENCES Figue : Roto flux-oiented contol The epone of the model to changing the toque i imila to that in the cae of changing the peed efeence. The V/Hz contant model contol the toque lowly. The field-oiented contol povide contant toque epone. Concluion Both contol method have advantage and diadvantage. Scala contol i a cheap, well-implementable method. Becaue of thee advantage and it implicity, many application opeate with thi contol technique in the induty. On the othe hand, it i not atifactoy fo the contol of dive with dynamic behaviou, ince it give low epone to tanient. Thi i becaue the V/Hz contant method contol the magnitude of voltage and fequency intead of contolling the phae and magnitude of cuent. It i a low-pefomance, but table contol technique. The field oiented contol method contol the cuent o it opeate with fat epone. Thi method atifie the equiement of dynamic dive, whee fat epone i neceay. It i an excellent contol method to handle tanient. It diadvantage i complexity, and the high pice of the dive cicuit. Nevethele, it i a high-pefomance contol technique. Both technique ae applicable ove the nominal peed at the expene of toque.. Z. HÁMORI: Villamo gépe, Tanönyvmete Kiadó, (00), pp S. HALÁSZ: Villamo hajtáo, BME Egyetemi Tanönyv, (99), pp M. A. LAUGHTON, D. F. WARNE: Electical enginee efeence boo, Newne, (00), p. 9/6 4. A. HUGHES: Electic moto and dive: fundamental, type, and application, Newne, (005), pp A. M. TRZYNADLOWSKI: Contol of induction moto, Academic Pe, (00), pp J. M. D. MURPHY, F. G. TURNBULL: Powe Electonic Contol of AC Moto, Pegamon Pe, (988), pp K. P. KOVÁCS, I. RÁCZ: Váltaozóáamú gépe tanzien folyamatai, Aadémiai Kiadó, (954), pp. 40 4, Á. KELEMEN, M. IMECS: Vecto Contol of AC Dive, Volume : Vecto Contol of Induction Machine Dive, OMIKK Publihe, (99), pp GY. RETTER: Villamoenegia-átalaító,. ötet, Azimmetiu é tanzien üzem, Műzai Könyviadó, (987), pp G. J. RETTER, K. NÉMETH: Matix and pace-phao theoy of electical machine, Aadémiai Kiadó, (987), pp I. SCHMIDT, GY.-NÉ VINCZE, K. VESZPRÉMI: Villamo zevo- é obothajtáo, Műegyetemi Kiadó, (999), p. 74. S. J. CHAPMAN: Electic Machiney Fundamental, McGaw-Hill, (998), pp