epreentation of a Group of Three-phae Induction Motor Uing Per Unit Aggregation Model A.Kunakorn and T.Banyatnopparat Abtract--Thi paper preent a per unit gregation model for repreenting a group of three-phae induction motor load connected in the ame bu. All parameter of the model are derived baed on no load tet and block rotor tet with the development for a generalized gregation of induction motor with imilar and different ynchronou peed. Dynamic equation on the d-q axi model with arbitrary reference frame are ued for predicting tranient repone of the three-phae induction motor. The validity of the model i verified by imulating the tarting current due to a group of induction motor uing MATLAB/Simulink compared with meaurement. It i found that the propoed gregation model give acceptably accurate reult and will be ueful for load modeling technique in power ytem tudie. Keyword: Aggregation model, Induction motor, MATLAB I I. ITODUCTIO a power ytem, there are variou type of load. An accurate and reaonable repreentation of the load i very important for tudying and analyzing the tranient repone and dynamic performance of the power ytem uch a fault and tabilitie. Induction motor are employed in many application for indutrie, and in ome particular cae, there are a number of induction motor connected in the ame bu. To tudy the dynamic and tranient performance of uch a ytem, an accurate load model for the group of induction motor i required. The computer model repreenting the group of induction motor have been developed [,,3,4]. Variou tet and imulation have been performed in both tranient and teady tate operation to implement uch model [,,3,4]. Thi type of uch model i normally known a an gregation model of induction motor. The main purpoe for developing of the gregation model i to ubtitute a group of induction motor a a ingle unit load. Although, the previou gregation model have been proved and implemented with many cae tudie, and atifactory reult have been obtained, none of thee model have mentioned on the gregation repreentation for a group of induction motor with different ynchronou peed for being ued in the tranient analyi on the time domain. Thi paper preent a generalized gregation model for repreenting a group of three-phae induction motor uing A.Kunakorn i, and T.Banyatnopparat wa with the Faculty of Engineering, King Mongkut Intitute of Technology Ladkrabang, Bangkok 050, Thailand (e-mail: kkananta@kmitl.ac.th) Paper ubmitted to the International Conference on Power Sytem Tranient (IPST009) in Kyoto, Japan June 3-6, 009 per unit method. Thi approach can overcome the difficulty in modeling the group of the induction motor with different ynchronou peed connected in the ame bu in an indutrial power ytem. The gregation model propoed in thi paper i developed on the bai of parameter and general equation obtained from the previou work [,3,4]. All parameter, then, are converted to per unit form. The per unit model propoed in thi paper i ucceful in repreenting the group of induction motor which have different ynchronou peed. The d-q model of a three-phae induction motor i modified o that the tranient repone for a group of three-phae induction motor can be predicted. The gregation model i contructed and implemented on MATLAB/Simulink and PSCAD/EMTDC. The gregation model i verified with variou cae tudie a well a experimental reult for dynamic performance of the induction motor uch a tarting current. II. PE UIT AGGEGATIO MODEL There have been many gregation model propoed by reearcher. Among thee model, parameter in the model developed by Kataoka et al are determined from a per phae equivalent circuit, and uing d-q analyi to form equation for predicting dynamic performance due to a group of two induction motor connected a a load []. On the bai of the ame procedure for calculating the parameter, an equivalent circuit for the gregation model for the cae of -induction motor ha been illutrated a Fig. All parameter in the equivalent circuit, then, are derived, baed on no load tet and lock rotor tet. When performing the no load tet, the lip of all induction motor in a group i approaching zero. A a reult, the no load per unit impedance of each motor i: Z,i i =,, = + j( ) () n,i l,i + m, i All motor are connected in parallel at the ame bu. A a reult, an equivalent per unit impedance of the group of induction motor during no load i: Z n, = + + +... + () Z Z Z Z n n Z ni Z n, = (3) Z nk k=,k i n3 n
, l l l l, m lr r m lr r m lr r m, IMAG lr, r, Fig. An equivalent circuit of the per unit gregation model Conidering the gregation model hown in Fig, the no load per unit impedance of the model i: Z n, =, + j( l, + m, ) (4) = number of induction motor in a group,i = per unit tator reitance of i th motor l,i = per unit tator leake reactance of i th motor m,i = per unit mnetizing reactance of i th motor, = per unit tator reitance of gregation motor l, = per unit tator leake reactance of gregation motor m, = per unit mnetizing reactance of gregation motor When performing the lock rotor tet, the lip of all induction motor in a group i approaching. A a reult, the lock rotor per unit impedance of each motor i: Z = ( + ) + j( ) (5) b,i,i r,i l,i + lr, i An equivalent per unit impedance of the group of induction motor during the lock rotor tet i: Z b, = + + +... + (6) Z Z Z Z b b Z bi Z b, = (7) Z bk k=,k i Conidering the gregation model hown in Fig, the lock rotor per unit impedance of the model i: Z b3 = ( + ) + j( ) (8) b,, r, l, + b lr, = number of induction motor in a group,i = per unit tator reitance of i th motor r,i = per unit referred rotor reitance of i th motor l,i = per unit tator leake reactance of i th motor lr,i = per unit referred rotor leake reactance of i th motor, r, = per unit tator reitance of gregation motor = per unit referred rotor reitance of gregation motor l, = per unit tator leake reactance of gregation motor lr, = per unit referred rotor leake reactance of gregation motor (, + r, ) = real part of Z b, ( l, + lr, ) = iminary part of Z b, From (4) and (8), the value of determined. To obtain the value of, and r, can be l, and lr,, the ratio of both parameter can be taken from the IEEE tandard -996 which pecify the empirical ditribution of leake inductance in induction motor depending on the motor cla [5]. Thi i correct approximation when all motor in the group are in the ame motor cla. However, if there are variou clae of the motor, it i proper to divide the motor into ubgroup, and each ubgroup conit of the ame cla of the motor. The value of l, and the iminary part of (4), then, are employed for calculating the value of m,. In addition, lip can be determined uing equation propoed by Kataoka et al[4] a follow: = α S + β S + γ 0 (9)
α = β = r, r, r, m, V m,, + ( V,, r, + (, P, ) r, m, ) P γ = ( + ) P β ± β 4αγ S = (0) α There are two root of (0), the lip of the gregation motor i the root with a maller value[]. Chooing bae value a follow: V I bae bae = peak value of the phae volte = peak value of the phae current 3 P bae = VbaeIbae The moment of inertia of the gregation motor can be obtained [,,3,4]: P J = P i J i, i i, () = = () = per unit rated power of gregation motor P P i = rated power of each motor in a group J = moment of inertia of gregation motor J i = moment of inertia of each motor in a group,i = ynchronou peed of each motor in a group, = ynchronou peed of gregation motor ormally, the ynchronou peed of an induction motor i calculated uing the number of pole of the motor. If induction motor in the group which are required to be gregated have different pole number, thi mean that there are variou ynchronou peed among the motor. A a reult, the motor cannot be gregated. In order to overcome uch a problem, a peudo number of pole of the gregation motor ha been invented o that a ynchronou peed of the gregation motor can be determined [6]. The peudo number of pole of the gregation motor i: 0 fp pole = (3) P,i f = upply frequency,i = ynchronou peed of each motor in a group i III. MATLAB/SIMULIK MODELS AD CASE STUDIES Mathematical model of the gregation induction motor are developed on the bai of MATLAB/Simulink o that the tranient analyi on time domain can be performed. The block diram i contructed with dynamic equation of the induction machine on the arbitrary reference frame modified from tandard equation of an induction machine detailed by Chee-Mun Ong[7]. The block diram developed for an gregation model i hown in Fig. To verify the gregation model, tranient tarting current waveform of a group of induction motor were meaured. Direct online tarting tet were performed on variou ize of induction motor. All motor under tet were cla A motor. The detail of the induction motor under the tet are a hown in Table I. TABLE I AME PLATES OF IDUCTIO MOTOS USED I EPEIMETS o. 3 4 Output P hp hp 3 hp 5 hp Power Volte V [V] 380/0 380/0 380/0 380/0 (line-line) Frequency f [Hz] 50 50 50 50 umber of Pole Bae Quantitie: Volte Current Impedance Parameter eitance eactance Moment of Inertia 6 4 4 4 V b [V] 0 0 0 0 I b [A] 7.9 7.9 7.9 7.9 Z b [Ω] 7.85 7.85 7.85 7.85 [pu.] 0.496 0.3770 0.357 0.0738 [pu.] 0.40 0.3638 0.8 0.0705 r l [pu.] 0.3384 0.35 0.385 0.0750 [pu.] 0.3384 0.35 0.385 0.0750 lr [pu.] 5.68 7.7785.9.9839 m J [kg.m ] 0.0049 0.008 0.0056 0.00 Due to the limitation of intrument, all meaurement were recorded with no-load condition only. However, the teady tate current when the motor were loaded wa oberved, and it wa found that the gregation model wa able to calculate correctly the current when comparing with the meaured value. t cae tudy (motor with imilar ynchronou peed in the group) Uing induction motor o., o.3 and o.4 nd cae tudy (motor with different ynchronou peed in the group) Uing induction motor o., o.3 and o.4
Fig. The block diram on MATLAB/Simulink of the per unit gregation model IV. ESULTS Meaurement Fig 3. t cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae A) Meaurement Fig 4. t cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae B)
Meaurement Fig 5. t cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae C) Meaurement Fig 6. nd cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae A) Meaurement Fig 7. nd cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae B)
Meaurement Fig 8. nd cae tudy, Comparion of tarting current waveform of the group of induction motor (Phae C) TABLE II AME PLATES OF IDUCTIO MOTOS USED I FUTHE CASE STUDIES I ODE TO MAKE COMPAISO WITH PSCAD/EMTDC [] o. 3 4 5 Output Power P 3 hp 5 hp 30 hp 50 hp 00 hp Volte (line-line) V [V] 460 460 460 460 460 Frequency f [Hz] 60 60 60 60 60 umber of Pole 4 4 4 4 4 Bae Quantitie : Volte Current Impedance Parameter : V b I b Z b [V] 65.58 65.58 65.58 65.5 8 65.5 8 [A] 85.39 85.39 85.39 85.3 85.3 9 9 [Ω].433.433.433.433.433 eitance [pu.] 3.395.033 0.5096 0.93 0.74 5 [pu.].844 0.64 0.7 0.097 0.055 r 7 8 eactance [pu.].8638 0.56 0.7 0.04 0.069 l 7 8 [pu.].8638 0.56 0.7 0.04 0.069 lr 7 8 [pu.] 59. 7.374 0.44 6.60.77 m 5 9 6 3 Moment of Inertia J [kg.m ] 0.09 0.50.00.66.70 V. CASE STUDIES WITH PSCAD/EMTDC An additional cae tudy wa performed in order to make comparion between imulation reult from the model developed on MATLAB/Simulink and thoe obtained from tandard model on PSCAD/EMTDC. In thi cae tudy, the ytem ued by Pillay et al [] wa employed. The ytem conit of five induction motor connected at the ame bu a hown in Fig 9, while Table II how the detail of all the motor. After tarting the group of the induction motor, the ytem reached the teady tate operation, the circuit breaker, then, wa open for 8 cycle, and cloed. Electromnetic tranient of the ytem were imulated on both MATLAB/Simulink and PSCAD/EMTDC. Fig 9. The ytem ued in verifying the MATLB/Simulink model with a tandard model on PSCAD/EMTDC []
Tranient repone of the Phae A current and the electromnetic torque of the group of the induction motor are obtained a hown from Fig 0 to Fig 3. It can be een that there are mall dicrepancie in time domain repone imulated from the model developed on MATLAB/Simulink and thoe from PSCAD/EMTDC. However, thee imulation give a good reement compared with the reult reported by Pillay et al []. Fig 0. MATLAB/Simulink reult for the tranient current Fig. PSCAD/EMTDC reult for the tranient current VI. COCLUSIOS The per unit gregation model to repreent a group of induction motor ha been preented. Parameter in uch a model have been determined. The peudo number of pole of the gregation model ha been employed with an advante in overcoming the difficulty in modeling the group of the induction motor with different ynchronou peed connected in the ame bu in an indutrial power ytem. Per unit impedance are ued in the model o that the model i more properly ueful in power ytem tudie. The dynamic equation of the gregation model have been contructed a a block diram uing MATLAB/Simulink in order to perform tranient analyi on the time domain. The model ha been implemented in predicting tarting current for two group of induction motor with variou ize and different ynchronou peed. It ha been found that the model give atifactory imulation reult when comparing with meaurement. The error obtained from the model i about le that 0%. In addition, the propoed model ha been verified by making the comparion between the reult imulated on MATLAB/Simulink with thoe from the tandard model available on PSCAD/EMTDC, and the correlation ha been obtained. The limit of the model i that all induction motor in the gregation mut be in the ame motor cla. Fig. MATLAB/Simulink reult for the tranient electromnetic torque VII. EFEECES [] P. Pillay, S.M.A. Sabur and M.M. Haq, A model for induction motor gregation for power ytem tudie, Electric Power Sytem eearch, ovember 997, pp.5-8 [] T. Kataoka, H. Uchida, S. ihikata, T. Kai, T. Funabahi, A Method for Aggregation of a Group of Induction Motor Load, POWECO 000, Perth, Autralia, December 000, pp.683-688 [3] P.Piromthum and A.Kunakorn, A Study of Starting Current due to a Group of Induction Motor Uing an Aggregation Model, IEEE Power Electronic and Drive Sytem (PEDS 003), Singapore, ovember 003, pp.054-057 [4] W.Suwanwej and A.Kunakorn, Etimation of hort circuit current due to a group of induction motor uing an gregation model, IEEE POWECO'004, Singapore, ovember 004, pp.559-563 [5] IEEE tandard -996, Tet procedure for polyphae induction motor and generator [6] M.Akbaba and S.Q.Fakhro, ew model for ingle-unit repreentation of induction motor load, including kin effect, for power ytem tranient tability tudie, IEE Proceeding-B. Vol.39, o.6, ovember 99, pp.5-533 [7] Chee-Mun Ong, Dynamic of Electric Machinery Uing Matlab/Simulink, Prentice Hall, 998 Fig 3. PSCAD/EMTDC reult for the tranient electromnetic torque