A Generalized Dynamic Model of Induction Motor using Simulink

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1 A Generalzed Dynac Model of Inducton Motor ung Sulnk P. M. Palpankar, R. U. Ghanare & *N. Makade D.B.A.C.E.R, Nagpur *Y.C.C.E, Nagpur E-al : prach_bd@yahoo.co, ghanare.rahul@gal.co, nluakde@gal.co Abtract - Th paper decrbe a generalzed odel of the three-phae nducton otor and t coputer ulaton ung MATAB/SIMUINK hang adantage that t doe not requre the coplaton. Contructonal detal of arou ub-odel for the nducton otor are gen and ther pleentaton n SIMUINK outlned. For th purpoe, the releant equaton are tated at the begnnng, and then a generalzed odel of a three-phae nducton otor deeloped. Th approach could be extended to other engneerng yte. Index Ter echancal ub odel, odelng, peed, torque ub odel. I. INTRODUCTION In the cae of Matlab, the proper tate equaton hould be obtaned n order to decrbe the power coneron crcut. Wth the tate equaton, the crcut can be ealy odeled by ung the functonal block, whch are upported n Matlab Sulnk. In partcular, n Matlab, the arou kn of control algorth can be ealy pleented wthout ung actual analog coponent. Howeer, obtanng the tate equaton accordng to the crcut confguraton a cuberoe and te-conung job. Wheneer there a nor change n the crcut confguraton, new tate equaton hould be obtaned for decrbng the new crcut. Therefore, a ple ethod to odel the power coneron crcut hghly derable, whch not baed on the tate equaton. Thu the SIMUINK oftware of MATAB for the dynac odelng of the nducton otor ued here. The an adantage of SIMUINK oer other prograng oftware that, ntead of coplaton of progra code, the ulaton odel bult up yteatcally by ean of bac functon block. Through a conenent graphcal uer nterface (GUI), the functon block can be created, lnked and edted ealy ung enu coan. A et of achne dfferental equaton can thu be odeled by nterconnecton of approprate functon block, each of whch perforng a pecfc atheatcal operaton. Prograng effort are atcally reduced and the debuggng of error eay. Snce SIMUINK a odel operaton prograer, the ulaton odel can be ealy deeloped by addton of new ub-odel to cater for arou control functon. A a ub-odel the nducton otor could be ncorporated n a coplete electrc otor e yte. II. ANAYSIS METHOD The tator oltage of three phae are phae hfted by 1 each and are gen by the equaton a b c n( t) n( t / 3) n( t / 3) where the apltude of the ternal oltage, the upply frequency and θ the ntal phae angle. Due to the oltage op n the upply cable, the ternal oltage gen by Equaton: E R c c ISSN (PRINT) : , olue -1, Iue -5,

2 ITSI Tranacton on Electrcal and Electronc Engneerng (ITSI-TEEE) Fg. Three-phae tator oltage The three-phae to two-ax oltage tranforaton ean the coneron of coordnate fro the threephae tatonary coordnate yte to the dq rotatng coordnate yte. Th tranforaton ade n two tep: 1) a tranforaton fro the three-phae tatonary coordnate yte to the two-phae, o-called αβ, tatonary coordnate yte and ) a tranforaton fro the αβ tatonary coordnate yte to the dq rotatng coordnate yte. The three-phae to two-ax oltage tranforaton can be acheed ung the followng Equaton 1 ( / 3) 1/ 3 / 1/ 3 / a b c [A] where a, b, and c are the three-phae tator oltage, whle and are the two-ax coponent of the tator oltage ector. Fg.4 abc-qd coneron In the two-ax tator reference frae, the current equaton of an nducton otor can be wrtten a the dfferentaton operator, d/dt, whle l, lr and are the tator and rotor leakage nductance and the agnetzng nductance, repectely The u of the tator leakage nductance and agnetzng nductance called the tator nductance and denoted by Analogouly, the rotor nductance, r defned a the u of the rotor leakage nductance and agnetzng nductance. Thu, r l lr The dynac odel allow deraton of the oltagecurrent equaton of the nducton otor. Ung pace ector, the equaton can be wrtten a where d dt A B A B T T r In the two-ax tator reference frae, the current equaton of an nducton otor can be wrtten a Fg.3 Two-ax coponent of the tator oltage t r 1 R r P P R Rr P r P r dt R r [B] [C] 119 ISSN (PRINT) : , olue -1, Iue -5, 13

3 ITSI Tranacton on Electrcal and Electronc Engneerng (ITSI-TEEE) Matrx [A] n Equaton (1) and atrx [B] can be pleented by the Matrx Gan block of SIMUINK, whle atrx [C] can be pleented by four Fcn block of SIMUINK. In the electrcal odel, the three-phae oltage [a, b, c] the nput and the current ector [,,, ] the output ector. The rotor oltage ector norally zero becaue of the hortcrcuted cage rotor wndng,.e. = and =. Stator current output ub-odel The tator current output ub-odel ued to calculate the tator current apltude accordng to the followng equaton 3 Fg.8 Stator current output ub-odel Fg.5 Matrx [B] pleented ung 4 functon block Torque ub-odel of nducton otor In the two-ax tator reference frae, the electroagnetc T gen by T 3P 4 III. PROPOSED MODE OF INDUCTION MOTOR Fg.6 Torque ub-odel Mechancal ub-odel of nducton otor Fro the torque balance equaton and neglectng cou frcton, the rotor peed w ay be obtaned a t T T J where J the oent of nerta of the rotor and load and T the load torque. dt Fg.7 Rotor peed odel Fg.9 Propoed oerall odel for Inducton otor I. SIMUATION RESUT AND DISCUSSION The nducton otor choen for the ulaton tude ha the followng paraeter: Type: three-phae, 3hp, 38 4-pole, wye-connected, qurrel-cage nducton otor R=3.5 oh l=6.973h lr= J=.4 kg Rr=3.16oh =.6674H J=.4 kg Rc=. To llutrate the tranent operaton of the nducton otor, a ulaton tudy deontrated. At t=, the otor, preouly de-energzed and at tantll, connected to a 38, 5 Hz three-phae upply through a cable. The load torque, T, contant at 11.9N.. 1 ISSN (PRINT) : , olue -1, Iue -5, 13

The reult are lar to thoe obtaned ung the

1 Sulaton oltage waefor of Inducton otor Fg

4 ITSI Tranacton on Electrcal and Electronc Engneerng (ITSI-TEEE) Fg. how the reult of coputer ulaton ung the SIMUINK odel. The reult are lar to thoe obtaned ung the tradtonal ulaton ethod nolng dfferental equaton. Fg 1 a) Three-phae tator oltage Fg 11.b) Current and Fg 1.b) Two-ax coponent of the tator oltage Fg.1 Sulaton oltage waefor of Inducton otor Fg 11.c) Stator Current Fg.11 Sulaton current waefor of Inducton otor Fg 11.a) Current d and Fg 1. Rotor peed (rad/ec) 11 ISSN (PRINT) : , olue -1, Iue -5, 13

ITSI Tranacton on Electrcal and Electronc Engneerng (ITSI-TEEE) Fg.13 Torque waefor. CONCUSION Thu ulaton of three phae a well a two ax coponent of tator oltage and current are obtaned.

5 ITSI Tranacton on Electrcal and Electronc Engneerng (ITSI-TEEE) Fg.13 Torque waefor. CONCUSION Thu ulaton of three phae a well a two ax coponent of tator oltage and current are obtaned. The nducton otor odel deeloped ay be ued alone, a n the ect-on-lne tartng. It can be ncorporated n an adanced otor e yte, e.g. feld orented control. It alo helpful n degnng of nducton otor accordng to the requreent. I. REFERENCES 1] K..SHI, T.F.CHAN, Y. K. WONG and S..HO, Modelng and ulaton of the three-phae nducton otor ung ulnk, Int. J. Elect. Engng. Educ., ol. 36, pp , Mancheter U.P., 1999 [] Trzynadlowk, Anzej, Control of Inducton Motor Unted State of Aerca (1994) [3] Kraue, P. C., Waynczuk, O. and Sudhoff, S. D., Analy of Electrc Machnery, IEEE (1995) [4] Adel Aktab & Daw Ghan, Dynac Sulaton of a Three-Phae Inducton Motor Ung Matlab Sulnk, IEEE [5] B. Ozpnec,. M. Tolbert, Sulnk pleentaton of nducton achne odel A Modular approach, IEEE, 3, pp [6] Muhaad Rahd, Power electronc handbook. [7] Electrcal Machne by SK Bhattacharya, Tata Mc Graw Hll, New Delh [8] Electrcal Machne by Nagrath and Kothar, Tata Mc Graw Hll, New Delh [9] B.K.Boe, Modern power electronc and AC e. New Delh, PHI earnng Prate ted, 11.pp ISSN (PRINT) : , olue -1, Iue -5, 13

Dynamic d-q Model of Induction Motor Using Simulink

Dynamic d-q Model of Induction Motor Using Simulink Anand Bellure #1, Dr. M.S Aspalli #2, #1,2 Electrical and Electronics Engineering Department, Poojya Doddappa Appa College of Engineering, Gulbarga,