A NEW EQUIVALENT CIRCUIT OF THE THREE-PHASE INDUCTION MOTOR (CASE STUDIES:CURRENT AND POWER FACTOR OF THE MOTOR)

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1 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. A NEW EQUVAENT CRCUT OF THE THREE-PHASE NDUCTON OTOR (CASE STUDES:CURRENT AND POWER FACTOR OF THE OTOR uriman Anthony 1, Erhaneli Erhaneli 1 and Buran Buran 1 Department of Electrical Engineering, Faculty of ndutrial Technology, ntitute of Technology Padang, ndoneia Department of nformatic, Faculty of ndutrial Technology, ntitute of Technology Padang, ndoneia E-ail: antolah@gmail.com ABSTRACT Characteritic of the three-phae induction motor can be analized by uing a conventional uivalent circuit. The parameter of the circuit can be obtained through of everal experiment' reult in the laboratory uch a dc tet, noload tet, and blocked-rotor tet. All data mut be gotten accurately if they are ued for predicting the characteritic of the three-phae induction motor. f one data i not gotten accurately, the characteritic of the motor can not be predicted accurately. Thi tudy i purpoed to give a imple uivalent circuit for analyzing the characteritic of the 3-phae induction motor by uing only the nameplate and the no-load tet data of the motor. So, the blocked-rotor tet and dc tet of the motor are not ruired for the purpoed circuit. Thi tudy i focued to dicu about the line current and power factor of the three-phae induction motor. The object ued in thi tudy wa the 3-phae induction motor of 1.5 HP, 380/0V, Y/,.7/4.7 A, 4 pole, 50 Hz, 1400 RP. The reult of thi tudy how that the uivalent circuit propoed in thi tudy can be ued to predict the characteritic of the three-phae induction motor, epecially the input current and power factor of the motor with an accurate rate above 90%. Keyword: three-phae induction motor, new uivalent circuit, characteritic of the motor. NTRODUCTON Three-phae induction motor are widely ued in many ection, epecially in indutrial ector becaue thee motor are imple and robut contruction. Thee motor are uually produced in high power rating. Thee motor are normaly operated by uing a three-phae power upply. On pecific application condition, thee motor can be operated on ingle-phae power by intalling the capacitor bank to the winding of the motor[1]-[6]. There are many kind other modification of ingle-phae power upply can be ued for operating the three-phae induction motor on ingle phae upply uch a ingle-phae inverter and PW control technique [7], [8]. f the three-phae induction motor operated on power upply ytem, the motor can be analyzed by uing characteritic of the motor that monitored during operation. n other condition, the motor can alo be analyzed by uing an uivalent circuit to predict the characteritic of the motor[9]. The uivalent circuit can be ued to predict the characteritic of the motor on variou load condition, even in blocked rotor condition. Several formula had been developed in conventional method for calculating the current, and power factor of the 3-phae induction motor. The parameter ued in conventional circuit mut be obtained from three experimental reult uch a dc tet, no-load tet and blocked-rotor tet[1], [3], [6], [10]-[15]. Alo, ome application like automatic recue device (ARD [16] and the reference frame theory to the dynamic analyi of a three-phae induction motor fed from a ingle-phae upply have been developed []. But thi method need ome parameter that are received from three experimental reult uch a dc tet, no-load tet and blocked-rotor tet. f any of the given data i not accurate, the parameter are ued for predicting the characteritic of the motor can not be done accurately. So, thi tudy i porpoed to give a new uivalent circuit for predicting the characterti of the three-phae induction motor by uing only the data of the no-load tet and full-load tet of the motor (nameplate data. EQUVAENT CRCUT AND PREVOUS WORKS Three-phae nduction motor i the three-phae alternating current motor that widely ued in many aplication. The motor ha a trong contruction and eay to operate. The naming i derived from the fact that thi motor operate by induction the tator magnetic field to the rotor, o that the motor i called the induction motor. The current generated by the rotor (moving part i not obtained from a particular ource, but i an induced current a a reult of the relative difference between the rotation of the rotor and the rotating magnetic field generated by the tator current. When the tator winding of the three-phae induction motor i connected to a three-phae power upply, the induced voltage will produce rotor current and torque to the rotor. Then, the rotor will tart rotating and reach a teady-tate peed N that i le than ynchronou peed N, at which the tator rotating field rotate in the air gap of the motor. The difference between the rotor peed and the tator rotating magnetic field rotate in the air gap by referencing to rotating the magnetic field rotate in the air gap i called the lip that can be dicribed a follow. N N N (1 6967

2 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. N N = lip = tator peed rotating field rotate in the air gap (RP = rotor peed rotating (RP Conventional method The three-phae induction motor are uualy upplied by a balance three-phae voltage ource. Therefore, the three-phae induction motor can be analyzed by uing a one phae upply uivalent circuit. Figure-1 how a conventional uivalent circuit for analyzing the three-phae induction characteritic when operated on three-phae ytem [9]. All data impedance of the motor mut be obtained by doing ome teting on the motor uch a dc-ource tet, no-load tet, and blocked-rotor tet. f one data i not true, the characteritic of the motor can not be predicted well [3], [6], [9]. V 1 R1 1 jx1 jx m jxm R R' 1 Figure-1. Conventional uivalent circuit of the threephae induction motor per phae[9]. By referring to Figure-1 can be explained that V 1 = phae voltage ource R 1 = reitance of the tator winding per phae X 1 = inductive reactance of the tator winding per phae R = reitance of the rotor winding per phae referred to the tator X = inductive reactance of the rotor winding per phae referred to the tator X m = magnetic reactance of the motor per phae 1 = current through the tator winding = current through the rotor winding referred to the tator = lip nduction motor ue electrical energy a their energy upply. Some energy are lot in the form of power loe becaue the reitance component of the tator and rotor winding inide the motor. Power loe in thi motor are copper loe, core loe, wind loe and friction loe. The power decription can be calculated mathematically by referring to the uivalent circuit of the motor a hown in Figure-1. From Figure-1 can be calculated the magnitude of the power that croe the ai gap (P ag from the tator through to the rotor a follow [9]. P ag R' (1 ( ' ( ' ( R' R' ( Then, the power loe in the rotor circuit (rotor copper lo i P (3 ( ' R' The mechanical power developed (P mech by the induction motor can be calculated a follow. P mech (1 ( ' ( R' (4 When the three power are compared to the lip (, it can be made a follow. P ag : P : P 1: :(1 (5 mech The current ( 1 and power factor (pf of the induction motor can be calculated from Figure-1 a follow. V 1 1 (6 R pf (7 circuit R X R jx = the al inpedance of the motor = the al reitance of the motor circuit = the al raeactance of the motor circuit All data of the impedance of the induction motor mut be obtained accurately from three experimental reult uch a dc tet, no-load tet and blocked-rotor tet. Automatic Recue Device (ARD Automatic Recue Device (ARD i a method of enorle low range peed and parameter identification etimation devoted to lift automatic recue device[16]. The uivalent circuit of thi method i hown in Figure

3 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. R Q Q (.. r (14 _ R rref The referred rotor reitance (R rref can be determine a follow: U1 R rref T ' (15 r Figure-. nduction motor inuoidal teady tate uivalent electrical circuit[16]. From the uivalent circuit hown in Figure-, the uivalent impedance can be determined a follow. R X R jx (8 = uialent motor reitance = uialent motor reactance = uialent motor impedance From uation (8 can be explained that the uivalent reitance (R and the uivalent reactance (X are R X R T r ɷ... T R 1 (. ' r. Tr (9 '.. ' 1 (.. T (10 = tator reitance = tator tranient inductance = referred magnetizing inductance = rotor time contant = tator angular fruency The active (P and reactive induction motor are P (. R r (Q power of (11 By ubtituting uation (15 in (9 and (10 then are obtained a follow: R X.. 1 (.. / R P rref R (16 / Rrref Q.. ' (17 1 (.. / Rrref By comparing uation (13 and (14 repectively with uation (16 and (17, then both the active and reactive power delivered to the rotor from the tator are... 1 (.. / R rref r (18 / Rrref P Q r.. (19 1 (.. / R By dividing uation (18 by (19 then will be obtained a follow: P.. Q R r rref rref r (0 Then, the uation (0 can be ubtituted in the econd term of the denominator in uation (19 giving the value of the referred magnetizing inductance a follow: Q (. X (1 = tator pae phaor current P r 1 Q r Pr Qr Ar Q r (1... Q.. Q r r Then, the active power delivered to the rotor (P r and the reactive power delivered to the rotor (Q r are repectively a follow: P P (. R r (13 A r = apparent power delivered to the rotor By ubtituting uation (1 in (0, the expreion of the motor lip ( i obtained a follow: 6969

4 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. R rref P Pr. r Rrref.. Qr Ar The peed can be calculated a follow: r ( 1 p ( (3 Ω r = rotor angular peed Previou work and propoed menthod The 3-phae induction motor have multiple winding placed in the lot. The uivalent circuit model for one coil of the motor can be drawed a hown in Figure-3[17]. U1 C R(f Re (f U By referring to Figure-4 can be explained that R OC = no load tet reitance of the motor winding per phae X OC = no load tet reactance of the motor winding per phae X A = additional reactance of the motor (uually capacitive reactance 1 = phae current through to the motor at full load OC = no load tet current through the winding of the motor R = the additional current through the reitance of the motor A = the additional current through the additional reactance = phae voltage of the motor V 1 Figure-4 i a imple uivalent circuit model that can be ued for analyzing the characteritic of the 3-phae induction motor when operated on the 3-phae power ytem. By uing Figure-4 we only need the data of noload tet and full-load tet (nameplate data of the motor. So, we need not DC tet and blocked-rotor tet for analyzing the characteritic of the motor. By referring to Figure-4, the magnitude of the no load tet impedance ( OC of the motor can be written a follow: Cg/ Cg/ OC R jx (4 OC OC Figure-3. The uivalent circuit model for one coil of the motor[17]. By referring to Figure-3 can be explained that R(f = reitance cover one coil of the winding (f = elf-inductance cover one coil of the winding Re = iron loe Cg = capacitance to the ground U1, U = voltage between one coil With reference to Figure-1 and Figure-3, a new uivalent circuit for the 3-phae induction motor can be created a hown in Figure-4. Thi Figure i a another parallel uivalent circuit from Figure-1 with combine to Figure-3. There are two way to determine the impedance of no-load tet ( OC of the motor depending on the motor winding connection ytem. When the motor winding are connected in 'Delta' connection tandard, the magnitude of the OC for delta tandard ( OC( become: 3. V ( OC( (5 ( OC Then, when the motor winding are connected in 'Wye' connection tandard, the magnitude of the OC for wye tandard ( OC(Y become: V( Y (6 OC( Y 3. ( OC V 1 1 OC R OC j X OC R R R 1 A j X A V (OC OC(Y OC( = line to line voltage ource on no load tet = line current on no load tet = OC for wye tandard motor = OC for delta tandard motor Figure-4. A new uivalent circuit for analyzing the characteritic of the three-phae induction motor (propoed method. The full-load current of the motor (nominal current of the motor can be obtained from full-load tet data or from the data written on the nameplate of the motor. f the motor i operated on Delta ( connection tandard, then 1 from Figure-4 i ual to the full load current divided by Then, if the motor i operated 6970

5 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. on Wye (Y connection tandard, 1 from Figure-4 i ual to the full load current (nominal current. So, the line current magnitude of the 3-phae induction motor for and Y connection tandard can be writen a follow: ( 3. 1 (7 ( Y 1 (8 The current, R and A from the Figure-4 then can be written a follow: 1 (9 OC R. co( (30 A. in( (31 = the angle of the full load current = the angle of the no-load current = the angle of the current The magnitude of R 1, R and X A from the Figure-4 then can be calculated a follow: V 1 X A A (3 R' V 1 R1 R (33 By auming R 1 = R, then will be obtained a follow: V R R ' 1 1 (34 (1 1/. R For certain condition, the data of power factor of the motor i not given on the motor nameplate, o that the motor hould be operated directly under full load condition to find the power factor of the motor. By referring to Anthony reearch about the capacitance of the run capacitor 'Cr y ' that ued to operate the 3-phae induction motor on ingle phae upply, the full load power factor of the motor can be calculated accurately a hown in formula of uation (35 to uation (38 [5]. The 'Cr y ' i ued for operating the three-phae induction motor on ingle phae upply that can be calculated a follow[5]. Cry k (35 1,5664( f.( V V N Cr y k ( N = line current of the 3-phae induction motor = line to neutral of the ingle phae upply = capacitance of the run capacitor for wye connection tandard = contant factor When the 'k' i 1 (for the motor i operated with a cloe to 3-phae rating, the run capacitor in uation (35 hould have reactive power (Q C a follow. Q. Cr.( V. V. (36 C V C f y C N = volltage on capacitor =.π.f = fruency f the full-load reactive power of the motor 'Q ' i compared againt to the 'Q C ' from the uation (36, the magnitude of 'Q = Q C ' (referring to the rotor peed tandard of the motor or 'Q = Q C ' (referring to the nominal current of the motor. Therefore, the magnitude of 'Q ' would be defined a follow: Q (37 Q C Then, the power factor of the motor can be calculated a follow. co 1 co tan (38 Q S tan (39 and, S 3. V. (40 co = power factor of the motor = apparent power of the motor S ETHODOOGY The motor ued in thi tudy wa the 3-phae induction motor of 1.5 HP, 380/0V, Y/,.7/4.7 A, 4 pole, 50 Hz, 1400 RP. The tudy i focued about for calculating the line current and power factor of the motor by uing the uivalent circuit a hown in Figure-4. The 6971

6 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. uivalent circuit and the formula created in thi tudy will be compared with the experiment reult in the laboratory. The motor i operated by uing Wye connection tandard winding. The circuit uipment and acceorie ued for operating the 3-phae induction motor i hown in Figure-5. 3-phae ource AC FUKE Power Quality Analyzer 3-phae nduction motor 1-phae alterntor Figure-5. Circuit uipment and acceorie ued in the laboratory. oad of alternator RESUT AND DSCUSSONS The reult of thi tudy are given in Table-1 and Table- a below. Table-1. The input current during operation againt the calculation reult by uing the formula created. No. (exp (c Error (% Nr (RP , (exp (c Error (% Nr(RP = the current from motor operation data condition = the current from the calculation reult by uing the formula created = percentage error calculation reult when compared againt to the reult of the experiment = rotor peed (Rotation per minute Table-. The power factor during operation againt the calculation reult by uing the formula created. No. PF (exp PF (c error (% Nr (RP PF (exp PF (c = power factor from motor operation data condition = power factor from the calculation reult by uing the formula created Characteritic of the line current and power factor of the motor are hown in Table-1 and Table-. By refering to Table-1 can be een that the error of the calculation reult when compared to the experimental reult are below 5%. So, it can be aid that the uivalent circuit and the formula given have hight accuracy for predicting the line current of the motor (accuracy level i about 95%. Then, by referring to Table-, the formula created have good reult for calculating the power factor of the motor at the rotor peed below 145 RP (the error i below 10%. Therefore, the formula created on the circuit are uitable for analyzing the power factor of the motor for hight load condition (accuracy level i about 90%. f both table are converted into graph, the reult can be een in Figure-6 and Figure-7. Figure-6. Comparion characteritic between current (exp againt to current (c. 697

7 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. [] Y. A. Al-turki and H. Al-umari Application of the reference frame theory to the dynamic analyi of a three-phae induction motor fed from a ingle-phae upply. Elevier. 53: [3]. Anthony Equivalent Circuit for the 31D- A otor ethod (Cae Studie : Current and Power Factor of the motor. JETT. 5(1: [4]. Anthony, A Simple ethod for Operating the Delta Connection Standard of the 3-phae nduction otor on Single Phae Supply. JETT. 15(9: Figure-7. Comparion characteritic between power factor PF (exp againt to power factor PF (c. From both Figure-6 and Figure-7 can be een that the characteritic of the motor between calculation reult and operation reult are imilar. So, the uivalent circuit with the formula created i uitable for predicting the characteritic of the line current and the power factor of the motor. CONCUSONS The reult of thi tudy how that the uivalent circuit and formula created have high accuracy. The error of the calculation reult when compared to the experimental reult are below 5%. So, the formula created have hight accuracy for predicting the line current of the motor (accuracy level i about 95%. Then, the formula created alo have a good reult for calculating the power factor of the motor epecially at the rotor peed below 145 RP (high load condition, where the error are below 10%. Therefore, the formula created on the circuit are alo uitable for analyzing the power factor of the motor for hight load condition (accuracy level i about 90%. The current and power factor characteritic of the calculation reult are imilar with the operating characteritic of the motor. ACTKNOWEDGEENTS We would like to thank the team at the laboratory of electrical engineering of the ntitute of Technology Padang (ntitut Teknologi Padang whoe have helped thi tudy run moothly. We would alo like to thank for the Directorate General of Human Reource for Science, Technology and Higher Education of ndoneia that ha funded thi reearch by agreement No. 175/7.O10.4./PN/016. REFERENCES [1] N. A. Ahmed Three-phae induction motor operating from ingle-phae upply with an electronically controlled capacitor. Electr. Power Syt. Re. 73(: [5]. Anthony. 03. A Simple ethod for Operating the Three-Phae nduction otor on Single Phae Supply (For Wye Connection Standard. JETT. 5(1: [6]. Anthony Analyzing Characteritic of the Sheda ethod for Operating the 3-phae induction otor on Single Phae Supply (Cae tudie : output power and efficiency of the motor. JETT. 33(4: [7] N. A. Ahmed, K. Amei, and. Sakui AC chopper voltage controller-fed ingle-phae induction motor employing ymmetrical PW control technique. Electr. Power Syt. Re. 55(1: [8] A. Al, S. Bandri, A. Y. Dewi, and A. Syofian Effective Power Output Single Phae nverter Deign in Home Scale Application with Arduino icrocontroller a Control Pule. JETT. 6(: [9] P. C. Sen, Principle of Electrical achine and Power Electronic, nd ed. New York: John Wiley & Son, [10] V. Ghial,. Saini and J. Saini Parameter Etimation of Permanent Split Capacitor Run Single Phae nduction otor Uing Computed Complex Voltage Ratio. EEE Tran. nd. Electron., no. c, pp [11] T. iu,. in, and H. Wu A ingle phae induction motor drive with improved performance. 47: [1]. akhlouf, F. eai and H. Benalla. 01. odeling and control of a ingle-phae grid connected photovoltaic ytem. J. Theor. Appl. nf. Technol. 37(:

8 VO. 1, NO. 3, DECEBER 017 SSN ARPN Journal of Engineering and Applied Science Aian Reearch Publihing Network (ARPN. All right reerved. [13] K. akowki. 00. Determination of performance characteritic of a ingle-phae haded pole induction motor by circuit-field method. Electr. Eng. 84(5: [14] G. A. Shanhurov A athematical odel of a Single-Phae nduction otor with an Aymmetric Stator Winding. 78(9: [15] A. Yahyaouy, J. Sabor, H. Gualou and. amrini. 01. odeling and implementation of a multi-agent architecture for intelligent energy management in an electric vehicle. J. Theor. Appl. nf. Technol. 37(: [16] A. O. Di Tommao and R.. Ferrigno Senorle low range peed etimation and parameter identification of induction motor drive devoted to lift automatic recue device. 19 th nt. Conf. Electr. ach. CE 010. pp [17] B. Heidler, K. Brune, and. Doppelbauer High-fruency model and parameter identification of electrical machine uing numerical imulation. EEE. pp