Modeling of Vector Controlled Induction Motor in Different Reference Frames

Transcription

1 ISSN (Online) : ISSN (Pint) : Intenational Jounal of Innovative Reseah in Siene, Engineeing and Tehnology Volume 3, Speial Issue 3, Mah 4 4 Intenational Confeene on Innovations in Engineeing and Tehnology (ICIET 4) On st & nd Mah Oganized by K.L.N. College of Engineeing, Maduai, Tamil Nadu, India Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames P N H Phaninda kuma, D M Deshpande, Manisha Dubey 3 M.Teh Shola in Eletial Depatment, MANIT, Bhopal, India Pofesso in Eletial Depatment, MANIT, Bhopal, India 3 Pofesso in Eletial Depatment, MANIT, Bhopal, India ABSTRACT This pape desibes the vaious mathematial models of both squiel age and wound oto indution motos in diffeent efeene fames with diffeent state-spae vaiables. The wok suggests the d-q axis unified appoah fo both types of indution motos by using the state-spae analysis and it is a stong tool in the modeling of the symmetial indution motos. When an eletial moto is epesented as a mathematial model with inputs and outputs, it an be analyzed and desibed in many ways, onsideing diffeent efeene fames and state-spae vaiables. The appliations of eah model ae also disussed. Models ae simulated with MATLAB/SIMULINK softwae fo tansient esponse of the squiel age indution moto in tems of eletomagneti toque and oto angula veloity and esults ae disussed. KEYWORDS modeling of indution moto, senso less ontol, d-q axes model, and diffeent efeene fames. I. INTRODUCTION Due to advanes in ontol system, indution moto is used as vaiable speed dive. When an eletial moto is epesented as a mathematial model with inputs and outputs, it an be analyzed and desibed in many ways, onsideing diffeent efeene fames and state-spae vaiables. In thee-phase symmetial o two-phase unsymmetial vesion, the indution moto is employed with veto ontol stategy. Thus, indution moto an be analyzed as DC moto []. The dynami opeation of the indution moto dive system has an impotant ole in the oveall pefomane of the system and thee ae two fundamental methods fo the indution moto ontol: one is the Diet measuement of the mahine paametes, whih ae ompaed to the efeene signals though losed ontol loops and othe is the estimation of the mahine paametes in the senso less ontol shemes, with the following implementation methodologies: slip fequeny alulation method, speed estimation using state equation, estimation based on slot spae hamoni voltages, flux estimation and flux veto ontol, diet ontol of toque and flux, obseve-based speed senso less ontol with paamete adaptation, neual netwok based senso less ontol, fuzzy-logi based senso less ontol.[] The development of the peise system model is fundamental to eah stage in the design, analysis and ontol of all eletial mahines. The level of auay equied fo these models entielydepends on the design stage unde onsideation. In some ases, the mathematial desiption used in mahine design equies vey fine toleane levels as stated by Nabae and Muata [3], [4]. Howeve, in the development of suitable models fo ontol puposes, onsideetain assumptions that simplify the esulting mahine model. Additionally, sine moden eleti mahines ae ontinuously fed fom swithing powe onvesion stages, the developed moto models should be valid fo abitay applied voltage and uent wavefoms [5]. Geneally, the following assumptions ae made while implementing the indution moto models No magneti satuation. No salieny effets. Negligible spatial MMF hamonis. The effets of the stato slots may be negleted. Thee is no finging of the magneti iuit. The magneti field intensity is onstant quantity and dieted adiallyaoss the ai-gap. Hysteesis and eddy uent effets ae negligible. The goal of this pape is to establish the ommonly used d-q models in diffeent efeene fames. Matlab/Simulink softwae is used to simulate the Copyight to IJIRSET 7 M.R. Thansekha and N. Balaji (Eds.): ICIET 4

2 dynami models of squiel age indution moto. The pape has been oganized as follows: setion II biefly explains the measuement of moto paametes, setion III demonstate the mathematial model of the indution moto, setion IV desibes the d-q axis models, and the esults of implemented Matlab models ae shown in setion V. II. MEASUREMENT OF ROTOR PARAMETERS A. Stato Resistane The stato phase esistane is measued by applying a DC voltage and the esulting uent with the oto at standstill. This poedue gives only the DC esistane at a etain tempeatue, the AC esistane is alulated by onsideing the wie size, the stato fequeny and the opeating tempeatue. B. No-Load Test This test is pefomed by applying a balaned ated voltage on the stato windings at the ated fequeny and diven at synhonous speed by DC moto o synhonous moto, pefeably a DC moto. The no-load test povides infomation about exiting uent and otationallosses. C. Loked-Roto Test The oto of the indution moto is loked and a set of low thee phase voltages is applied to alulate ated stato uents. The input powe pe phase is measued along with the input voltage and stato uent. The loked oto test povides the infomation about leakage impedanes and oto esistane. [7] III. MODELING OF INDUCTION MOTOR A. Spae veto equations fo thee-phase indution moto Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames End and finging effets ae negleted In this appoah, all vaiables ae epesented by pola vetos indiating the magneti and angula position fo the otating sinusoidal distibution. Let V p Phase Voltage, V s Spae Veto Stato Voltage, V Spae Veto Roto Voltage, I s Spae Veto Stato Cuent, I Spae Veto Roto Voltage, I m Spae Veto Magnetisation Cuent, λ s Spae Veto Stato Flux, λ Spae Veto Roto Flux, f Supply Fequeny, ω e Synhonous Speed, ω Eletial Roto Angula Veloity, ω m Mehanial Roto Angula Veloity, R s Stato Resistane, R Roto Resistane, L s Stato Self-Indutane, L Roto Self-Indutane, L m Mutual Indutane, J Moment of Inetia, L s Stato Leakage Indutane, L Roto Leakage Indutane, K s Stato Coupling Fato, K Roto Coupling Fato, σ Leakage o-effiient, τ s Stato Time Constant, Roto Time Constant, τ s Tansient Stato Time Constant, Tansient Roto Time Constant, þ Deivative Opeato. Fom the Fig (), the stato voltage equation is V s 3. V as + αv bs + α V s V s 3. I as + αi bs + α I s.r s + þ 3. λ as + αλbs+αλs O in a ondensed fom V s R s I s + þλ s () Similaly, the oto equation is V R I + þλ () And stato and oto flux linkage-uent equations ae λ s L s I s + L m e jθ I (3) λ L I + L m e jθ I s (4) Whee θ is elative oto position angle Fo the modeling of thee-phase indution moto Vs, Is θ geneally two theoies ae used. Fist one is the two eal V, I axis efeene fame theoy initially developed by Pak fo the synhonous mahine [8]. Seond one is the spae omplex veto theoy elaboated by Kovas and Raz V [9]. Both theoies ae used to desibe the omplete equations system of ontinuous-time linea model of the indution moto with etain assumptions. Usually, the Vbs following assumptions ae made []: Vs Geometial and eletial mahine onfiguation is Vb symmetial. Fig () Model of the 3-ϕ indution moto in Spae Veto Notation Spae hamonis of the stato and oto magneti flux B. Thee-Phase to Two-Phase Tansfomation ae negligible. To develop models of the indution moto, theephase Infinitely pemeable ion. (a, b, ) to two-phase (d, q) tansfomation is Stato and oto windings ae sinusoidally distibuted needed. Fig () shows the thee-phase to two phase in spae and eplaed by an equivalent onentated tansfomation windings. Assuming that eah of the winding. thee-phase windings has T tuns pe phase and equal uent magnitudes, the two-phase windings will have Magneti satuation, anisotopy effet, oe loss and 3T / tuns pe phase fo MMF equality. Let the q-axis is skin effet ae negligible. assumed to be lagging the a-axis by θ. The elationship Windings esistane and eatane do not vay with between ab and dqo is as follows the tempeatue. Cuents and voltages ae sinusoidal tems. Copyight to IJIRSET 7 M.R. Thansekha and N. Balaji (Eds.): ICIET 4 Va Vas

3 V qs V ds V o 3 os θ os θ π 3 Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames os θ + π 3 V as V bs V s sin θ sin θ π 3 sin θ + π 3 V qds T ab V ab (5) T ab isalso valid fo uents, flux-linkages in a mahine a b q Fig () Thee-phase to Two-phase Tansfomation In stationay efeene fame θ, In oto efeene fame θ θ, In synhonous efeene fame θ θ e. C. Genealized Model in Abitay Refeene Fame The analysis of indution moto dive system is aied out by epesenting the stato and oto vaiables ae in a ommon efeene fame. By using the same spae veto notations, we an define an abitay efeene fame, whih otates with the angula veloity ω, and aoding to Fig (3), the following elation is valid x qd x qd. e j θ Whee θ is the time vaiable elative angle between the abitay efeene fame and the stationay efeene fame. The evese tansfomation elation is x qd x qd. e j θ In an abitay ommon efeene fame, the voltage and flux linkage equations () (4) beomes V s R s. I s + j. ω. λ s + þλ s (6) V R. I j. ω ω λ + þλ (7) λ s L s. I s + L m. I (8) λ L. I + L m. I s (9) Equations (6) to (9) epesent the mathematial model of the indution moto in a ommon abitay efeene fame. The main advantage of the abitay efeene fame is mutual indutane doesn t depend on the elative oto position. The magnetisation flux and uent in an abitay efeene fame beomes λ m L m I s + I () I m I s + I () q q θ Fig (3) Tansfomation into an abitay efeene Fame d d d D. Instantaneous Eletomagneti Toque The eletomagneti toque of the indution moto is the atio of the ai-gap powe by mehanial oto speed (ω m ) in ad/se. The indution moto eletomagneti toque an be witten as P. I d I ds. I q T e 3 L m I qs () Whee P is the numbe of poles and T e is the instantaneous eletomagneti toque. The eletomagneti toque an be expessed in many othe foms by substituting the equations (8), (9), () & (). Negleting mehanial damping, the toque and oto speed ae elated as Copyight to IJIRSET 73 dω dt P J T e T L (3) wheet L is the load toque. E. Modeling of indution moto in Diffeent Refeene Fames When the mathematial model of the indution moto is established, seveal efeene fames an be employed depending on the appliation and the hosen stategy ontol. Thee ae seveal main efeene fames: stationay efeene fame fixed to the stato, oto efeene fame fixed to the oto shaft, synhonous otating efeene fame evolving with an angula veloity equal to: the ai-gap flux, the oto flux, the stato voltage, the oto uent spae vetos. The signifiane of the index is as follows: s stationay efeene fame oto efeene fame e synhonous otating efeene fame a. Stationay Refeene Fame Model Equations The hoie of the efeene fame fo the dynami analysis of the indution moto, espeially when the stato iuits ae unbalaned o disontinuous and the oto-applied voltages ae balaned o zeo, is moe onvenient to be fixed to the stato fame. This stationay efeene fame was fist employed by Stanley []. Tansfomation fom the abitay efeene fame to the stationay efeene fame fixed to the stato is made by substituting ω and the indution moto equations system an be witten as V s qs R s. I s s qs + þλ qs (4) V s ds R s. I s s ds + þλ ds (5) V s q R. I s s s q ω. λ d + þλ q (6) V s s s s d R. I d + ω. λ q + þλ d (7) λ s L s. I s + L m. I λ L. I + L m. I s b. Roto Refeene Fame Model Equations The possibility of the efeene fame fo the dynami analysis of the indution moto, espeially when the oto iuits ae unbalaned, is moe onvenient to be fixed to the oto fame. This efeene fame is initially developed fo synhonous mahine and then applied to M.R. Thansekha and N. Balaji (Eds.): ICIET 4

4 Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames the indution moto by Beeton []. The method of efeing the mahine vaiables to a oto efeene fame is most useful fo field oiented ontol systems. Tansfomation fom the abitay efeene fame to the oto efeene fame is made by substituting ω ω and the indution moto equations system beomes V qs R s. I qs + ω. λ ds + þλ qs (8) V ds R s. I ds ω. λ qs + þλ ds (9) V q R. I q + þλ q () V d R. I d + þλ d () λ s L s. I s + L m. I λ L. I + L m. I s. Synhonous Refeene Fame Model Equations The synhonously otating efeene fame is suitable when inopoating the dynami haateistis of an indution moto into a digital ompute pogam used to study the dynamiandtansient stability of the system. The synhonous efeene fame may also be useful in vaiable fequeny appliations if we may assume that the stato voltages ae a sinusoidal balaned set. It was systematially developed by Kovas [9], Kause [] and Loenz [6]. Tansfomation fom the abitay efeene fame to the synhonous efeene fame is made by substituting ω ω e and the indution moto equations system beomes V e qs R s. I e e e qs + ω e. λ ds + þλ qs () V e ds R s. I e e e ds ω e. λ qs + þλ ds (3) V e q R. I e e e q + ω e ω. λ d + þλ q (4) V e d R. I d ω e ω. λ q + þλ d (5) λ s L s. I s + L m. I λ L. I + L m. I s IV. D-Q AXES MODELS The thee-phase indution moto an be modeled by using diffeent state-spae vaiables and keeping as inputs the stato voltages and the load toque, and as outputs the eletomagneti toque and the oto angula veloity. The possible set of uents and flux linkages pe seond spae vetos ae defined as x I s I I m λ s λ λ T m (6) The d-q axes ae othogonal and fixed to the stato, q axis oinide with the magneti axis of the as winding. As thee ae fou voltage equations, it is neessay to onside two of the spae vetos as state-vaiables in ode to obtain a solution fo the equations system. Let the seleted pai of state-spae vaiables ae denoted asx, x. The set of six state-spae vaiables will be expessed in tems of the two seleted state-spae vaiables: x I s I I m λ s λ λ T m a a a a a 3 a 3 a 4 a. x x T 4 a 5 a 5 a 6 a 6 Thee ae mainly thee types of d-q models: uent state-spae vaiables models, flux linkage state-spae vaiables models, mixed uents-flux linkage state-spae vaiables models. By using d-q model to obtain a omplete vesion of the thee-phase IM model, viewed as the key fo a motion ontol system. The geneal fom of d-q model equations witten in state vaiables system is given by: þx A. x + B. u(7) Whee x is the seleted set of state-vaiables and epesent also the output of the model, u is the input veto (stato voltage), A is the oeffiient matix of x, B is the oeffiient matix of u, and þ is the diffeential opeato ( d ). Flowhat fo the dynami simulation of the dt indution moto in d-q model is shown in Fig (4) and in this pape ommonly used state spae-vaiables models ae pesented below: L s L s L m, L L L m, K s L m L s, K L m L, σ K s. K, τ s L s R s, L R, τ s σ. τ s, σ. Stat Read moto paametes Initialize time and ead applied voltages and finite time Choose the efeene fame ab to dq tansfomation Choose the state spae vaiables Solve the moto diffeential equations Compute toque and speed Stoe the values of vaiables Is finite time eahed? Pint/display the time esponses End TimeTime+ t Fig (4) Flowhat fo dynami simulation of the IM A. I qs I q I d : In this mathematial d-q model, stato and oto spae veto uents ae seleted as state-spae vaiablesx I qs I q I d. The stato uent spae veto is onsideed geneally as the ight hoie, beause it oesponds to dietly measuable quantities. This model is deived by substituting equations (8) & (9) in the equations (6) & (7) and expessed in a matix fom as follows: Copyight to IJIRSET 74 M.R. Thansekha and N. Balaji (Eds.): ICIET 4

5 I qs I q I d τ s ω K s ω. K s ω τ s ω. K s K s K ω ω. K ω ω. K K ω ω B. I qs I qm I dm : L s V qs L + s V V q L V d L Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames ω ω I qs I I q I d In this mathematial d-q model, stato and magnetisation uents spae vetos ae seleted as statespae vaiables x I qs I qm I dm. By seleting the magnetisation uent spae veto among the statespae vaiables, it is possible to inlude the satuation effet in modeling the IM. Also, the stato uent spae veto is a measuable quantity, and detemines a peise and auate option fo implementing ontolles [3]. This model is deived by substituting equations (8), (9) & () in the equations (6) & (7) and expessed in a matix fom as follows: I qs I qm I dm R s L s ω L m L s ω R s L s + K ω ω. K ω ω. K L s V qs L + s V V q L V d L C. λ qs λ ds λ q λ d : ω. L m L s + K ω ω ω. L m L s L m L s ω ω In this mathematial d-q model, stato and oto flux linkages spae vetos ae seleted as state-spae vaiables x λ qs λ ds λ q λ d. When flux linkages spae vetos ae seleted as state-spae vaiables, the models ae less omplex than the uent state-spae vaiables models beause of it ontains infomation about two uent spae vetos omponents. Fom the equations (8) & (9) I s L.λ s Lm.λ L s.l L m (3) I L s.λ Lm.λ s L s.l L m (3) This model is deived by substituting equations (3) & (3) in the equations (6) & (7) and expessed in a matix fom as follows: λ qs λ ds λ q λ d K ω τ s τ s ω τ s M.R. Thansekha and N. Balaji (Eds.): ICIET 4 K s K s ω ω D. λ qs λ ds λ qm λ dm : K τ s ω ω λ qs λ + λ q λ d. V qs V ds V q V d In this mathematial d-q model, stato and ai-gap flux linkages spae vetos ae seleted as state-spae vaiables x λ qs λ ds λ qm λ dm. This hoie pesents the advantage of an easie satuation effet modeling, but the disadvantage of an ineased omputational buden. This easie satuation effet modeling imposes many patial solutions fo vetoontol shemes. This model is deived by substituting equations (3), (3) & () in the equations (6) & (7) and expessed in a matix fom as follows: λ qs λ ds λ qm λ dm τ s. K s ω K s τ + K s. K σ ω ω K s. K σ λ qs I qs λ + K. K s I λ qm σ I qm λ dm I dm E. λ qs λ ds I qs : ω τ s. K s τ s. K s ω ω K s. K σ τ K s τ + K s. K σ ω ω K. K s σ V qs V V q V d τ s. K s ω ω In this mathematial d-q model, stato flux linkage and stato uent spae vetos ae seleted as statespae vaiables x λ qs λ ds I qs. This mathematial model is seleted when stato flux oiented stategy is implemented and deived by substituting equations (9) & (3) in the equations (6) & (7) and expessed in a matix fom as follows: λ qs λ ds I qs ω R s ω R s L s τ + L s σ ω ω L s σ τ ω ω ω ω L s σ L s τ + L s σ ω ω τ V qs + σ V L m σ V q σ V d L m σ F. λ q λ d I q I d : In this mathematial d-q model, oto flux linkage and oto uent spae vetos ae seleted as state-spae vaiables x λ q λ d I q I d. This model is optimum solution fo oto flux oientation ontol stategy in a dive system. Howeve, as it is impossible to measue the oto uents if the mahine is equipped with age oto, thee ae limitations in using this model fo veto ontol stategies. This model is deived by Copyight to IJIRSET 75 λ qs λ I qs

6 Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames substituting equations (8) & (3) in the equations (6) & (7) and expessed in a matix fom as follows: I q I d λ q λ d ω τ + s L τ s L σ ω L σ I q ω ω τ s L σ L τ + s L σ I. d λ q R ω ω λ d R ω ω σ L m σ V qs + σ V L m σ V q V d G. λ qm λ dm I qs : In this mathematial d-q model, ai-gap flux linkage and stato uent spae vetos ae seleted as state-spae vaiables x λ qm λ dm I qs. It peseves infomation egading both stato and oto paametes. This hoie also pesents the advantage of an easie satuation effet modeling. This model is suitable hoie fo the ai-gap flux oientation ontol stategy and deived by substituting equations (8), (9), () & (3) in the equations (6) & (7) and expessed in a matix fom as follows: I qs λ qm λ dm R s ω L s L s ω R s L s L m + L m. K ω ω. L m. K ω L s ω ω. L m. K L m + L τ m. K ω ω I qs L s V qs I V + λ qm L s V q λ dm K V d K ω L s L s ω ω IV. SIMULATION RESULTS The simulation sheme fo the modeling of squiel age indution moto in diffeent fames is shown in Fig (5) and flowhat fo the dynami simulation of the squiel age indution moto in d-q model is shown in Fig (4). Fo squiel age indution moto, oto voltage is equal to zeo i.e. V q V d and the following indution moto paametes ae hosen fo the simulation studies: R s.78ω, R.5Ω, L s.434h, L.47H L m.4 H, f 5 Hz, J.95 kg m, P 4. At t, the moto is onneted to a 4 V, 5 Hz theephase supply. The load toque T L is applied at t se. Figues (6) to (6) shows the esults of ompute simulation using the MATLAB/SIMULINK models with T L 4 N-m. Fig (5) Simulation sheme of squiel age indution moto model I qs I q I d : Stationay Refeene Fame: Fig (6) Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: Fig (7) Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (8) Eletomagneti Toque, Load Toque, Roto Angula speed I qs I qm I dm : Stationay Refeene Fame: Fig (9) Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: Copyight to IJIRSET 76 M.R. Thansekha and N. Balaji (Eds.): ICIET 4

7 Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames Roto Refeene Fame: Fig () Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (6) Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig () Eletomagneti Toque, Load Toque, Roto Angula speed λ qs λ ds λ q λ d : Stationay Refeene Fame: Fig (7) Eletomagneti Toque, Load Toque, Roto Angula speed λ qs λ ds I qs : Stationay Refeene Fame: Fig () Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: Fig (8) Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: Fig (3) Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (9) Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (4) Eletomagneti Toque, Load Toque, Roto Angula speed λ qs λ ds λ qm λ dm : Stationay Refeene Fame: Fig () Eletomagneti Toque, Load Toque, Roto Angula speed λ q λ d I q I d : Stationay Refeene Fame: Fig (5) Eletomagneti Toque, Load Toque, Roto Angula speed Fig () Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: Copyight to IJIRSET 77 M.R. Thansekha and N. Balaji (Eds.): ICIET 4

8 Modeling of Veto Contolled Indution Moto in Diffeent Refeene Fames REFERENCES Fig () Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (3) Eletomagneti Toque, Load Toque, Roto Angula speed λ qm λ dm I qs : Stationay Refeene Fame: Fig (4) Eletomagneti Toque, Load Toque, Roto Angula speed Roto Refeene Fame: [] R. Saidu, S. Mekhilef, M. B. Ali, A. Safai, H. A. Mohammed, Appliations of vaiable speed dive (VSD) in eletial motos enegy savings, Renewable and Sustainable Enegy Reviews, vol. 6, no., pp , Januay. [] M. Ibahim, Alsofyani, N. R. N. Idis, A eview on sensoless tehniques fo sustainable eliablity and effiient vaiable fequeny dives of indution motos, Renewable and Sustainable Enegy Reviews, vol. 4, pp. -, August 3. [3] A. Nabae, O. Kenihi, U. Hioshi, R. Kuosawa, An appoah to flux ontol of indution motos opeated with vaiable-fequeny powe supply, IEEE Tans. Ind. Appl., vol. IA-6, no. 3, pp , 98. [4] T. Muata, T. Tsuhiya, I. Takeda, Veto ontol fo indution mahine on the appliation of optimal ontol theoy, IEEE Tans. Ind. Appl., vol. 37, no. 4, pp. 8-9, 99. [5] D. W. Novotny and T. A. Lipo, Veto ontol and dynamis of AC dives, Oxfod Univesity Pess, New Yok. [6] R. D. Loenz, T. A. Lipo, D. W. Novotny, Motion ontol with indution motos, Poeedings of the IEEE, vol. 8, no. 8, 5-4, 994. [7] R. Kishnan, Eleti moto dives modeling, analysis and ontol, st ed., Pentie-Hall Intenational, New Jesey. [8] R. H. Pak, Two-eation theoy of synhonous mahines genealised method of analysis pat, AIEE Tans., vol. 48, pp , 99. [9] P. K. Kovas, Tansient phenomena in eltial mahines, Elsevie Siene Publishes, Amstedam. [] P. C. Kause, O. Wasynzjk, Analysis Of Eletial Mahiney, IEEE Pess, New Yok. [] H. C. Stanley, An analysis of the indution motos, AIEE Tans., vol. 57, pp , 938. [] B. K. Bose, Powe eletonis and dives, Pentie-Hall, Englewood Cliffs, New Jesey. [3] W. Leonhad, Contol of eleti dives, Spinge Velag, New Yok. Fig (5) Eletomagneti Toque, Load Toque, Roto Angula speed Synhonous Refeene Fame: Fig (6) Eletomagneti Toque, Load Toque, Roto Angula speed V. CONCLUSIONS In this pape, vaious mathematial d-q models of both squiel age and wound oto indution motos in diffeent efeene fames ae pesented. This pape pesents the d-q axes unified appoah fo both types of indution motos. The appliations of eah model ae also disussed. Models eithe only with magnetisation uent spae veto o ai-gap flux spae veto, o both inludes satuation effet in modeling of indution moto. MATLAB/SIMULINK softwae was used to implement the dynami esponse of squiel age indution moto d-q models in diffeent efeene fames and these models ae analyzed in tems of toque and oto angula veloity. Copyight to IJIRSET 78 M.R. Thansekha and N. Balaji (Eds.): ICIET 4