异步电机参数.pdf异步电机数学模型及参数转换www.ietdl.org here the ript

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详细说明：异步电机数学模型及参数转换www.ietdl.org here the ript I is omitted for compactness in the notation. In Appendix 3, the relationship between the Ku L kW transformation and the Park transformation is given in detail The dynamic equations expressed with Park variables are also included. The relationship between the coefficients in the dynamic equations (3)and the steady- state star equivalent circuit parameters in Fig. 1b is M=x/01,=(x+x)/0 +‰)/a7 +X)/ The double-cage model of Fig. 1c using the Ku 218.61.41.2 080.6040.20 transformation [10] in the synchronously rotating reference framc has the following transformed cquations Figure 2 Torque-speed and current-speed curves for a US=(R,+L: (p+ja))is+M(p+ja)i1+M(p+jo)i2 0=M(p+x)i+(R1+L1(P+xo)i1+M12(+io)i could be concluded from the experimental 0=M(p+jso)i+M(p+json+(R2+L2(p+jso)) measurements that the single-cage model does not agree T=2,M,Im(i(i1+边)5=(-90n)/o ith the experimental data. Fig. 2 shows the torque-speec and current-speed curves of a 1-kW motor for slip valu (5) in the range s=(0, 2). The torque and current values are normalised with the nominal torque, TN, and current, IN where the superscript II is omitted for compactness in the rcspcctivcly. The cxpcrimcntal mcasurcments in Fig. 2 arc notation represented with small circles. The continuous line represents the torque-speed and current-speed curves Thc rclationship bctwccn thc cocfficicnts in the dynamic calculated with the double-cage model of Fig. 1b and the equations (5) and the steady -state star equivalent circuit parameters of Table 1 parameters in Fi ig. lc is These parameters are determined from the measured M=Ym/ M12=(x12+rm)/w L,=d(x+rm)) torquc and current for diffcrcnt speeds. The non-lincar equations used for finding out the double-cage parameters L1=(412+Xm)/(L2=(+X12+Xm)/o f the equivalent circuit of fig. 1b are f(x)=(M()-C(k)=0 The induction motor is usually delta or isolated Wye connected calculated considering that the motor is Wye connected it are The parameters in the steady-state equivalent cird f+n(x)=(I(k)-l()=0k 3 Experimental measurements x=(Rl, R2, Xm, Xsd Xid) is the vector of the parameters Expcrimcntal mcasurcmcnts of diffcrcnt squirrcl-cagc n is thc numbcr of mcasurcments induction motors of low-and medium-rated power are studied. The steady-state measurements in Fig. 2 are made in TM(sk and IMS) are the measured torque and ci the laboratory of the Department of Electrical Engineering, values for k-1 to n EUETTT-UPC. The steady-state measurements in Fig 3 are realised in the abb laboratory, where there are five test Tc(s) and Ic(se) are the calculated torque and current beds for testing motors of 1-90 kw values for k= 1 to n, using the vector of parameters x The test bed used for testing the induction motors consisted The stator resistance R s is measured and the equality of the following main parts: a) loading machine and speed restriction X2d= xsd[4, 7]is used.The non-linear controller (DC machine and DC adjustable speed drive); b) equations are solved with the Solve function of MATLAB torque transducer mounted on the motor axis and speed and [11, which uses a non-linear least-square algorithm. current sensors; c)variable three-phase source 2 shows that the agreement of the calculated torque Thc torquc-spccd curvcs arc mcasured at rcduccd voltage, spccd and current-spccd curves with the expcrimcntal data is m=U/V3, where U is the nominal voltag very good. Fig 4 shows the total torque- speed cllrve an e lET Electr. Power Appl., 2009, Vol 3, Iss. 2, pp. 111-122 113 doi:10.1049/ let-epa20080043 C The Institution of Engineering and technology 2009 www.ietdl.org torque-speed curves of the inner-cage (Ri, Xi)and the nominal point and the maximum torque. The single-cage outer-cage(R2, X2) Parameter determination is detailed in [7] Fig 3 shows the torque-speed and current-speed curves From Fig. 3, it can be noted that five squirrel-cage induction motors. The experimental measurements of torque and current at different speeds are There is a good agreement between the experimental data represented with small circles. The continuous line and the values of torque and current predicted by the double represents thc tord nd current calculated with thc caac m ouble-cage model of Fig. 1b, and the motor parameters of Table 2 are calculated with (7). The broken line A double-cage model is essential to predict available represents the torque-speed and current-speed curves starting torques alculated using the single-cage model of Fig. la and the single-cage parameters of Table 2. The single-cage The single-cage model is clearly an inadequate model parameters are obtained by using the information of the when the motor speed varies in a wide rar 8 90kW 90 kw 75kW 75 kW 48kw 4 48 k W i7kW 37 kW 18.5kW 6 ≈ 18.5k 0 0.6 0.4 0. 0.4 Figure 3 Torque-speed and current-speed curves and measured torque and current data of five squirrel-cage induction 114 /ET Electr. Power Appl. 2009, Vol. 3, Iss. 2, pp. 111-122 C The Institution of Engineering and Technology 2009 doi:10.1049/ et-epa:20080043 www.ietdl.org Table 1 Double-cage parameters for a 1 kW induction in PSCAD-EMTDC [12]. Only conversion of motor (U= 230 V) parameters of an eight-Parameter model into a six-parameters model is studied in [4. An algorithm to calculate the motor R、1.05809 2.5286 10866 parameters from manufacturer data by using the equivalent X115929x=x2d1.57119xd7.26329 circuit of Fig. 16 is developed in [7]. Therefore, it is necessa to know how to calculate the motor paramete 1g. of the equivalent circuit in Fig. 1b are ViCe versa To simplify this conversion of parameters, if the conditions rll Ouier-caye---so R=R=和=X (10 Inncr-cagc 一 are imposed, then the circuits of Fig. 5 must be equivalent l81614l210.8063.40.20 These conditions can be imposed because, as discussed in [4] Slip the doublc-cagc modcl has only six independent paramctcrs When a seven-parameter model is used, like the equivalent Figure 4 Torque-speed curves for a 1 kw motor of Figs. 1b and lG, one parameter can be arbitrarily because there is a degree of freedom. The election The real values of the motor parameters can be calculated Xd= xsd, automatically implies the conditions Rs=Rand from table 2 as m. These conditions can be easily confirmed imposing that the slip is null,s=0, in the equivalent circuits RI=ZB R2=T2Zg X=xr of figs. 1b and 1 14=A1d∠B The input impedance of the circuit in Fig. 5u is where the impedance base is ZB=0/P z(a,0)=1/(0+R()+1(i+2)(1) U being the rated line voltage and p the rated mechanical nd can be rewritten as ower 32a2+ro2+a (12) 4 Equivalent circuit parameter z2(m,9)-n2oDl+5 determination In [4], there is a detailed study of the equivalence between diftcrcnt doublc-cage motor modcls with six, seven and cight paramctcrs. In this study, only the equivalence bctwccn the 2+12R equivalent circuit of Figs. 1b and lc is studied. The reason for RI Ri+R this election is that these are the equivalent circuits most 3 widely used in practice. For example, the equivalent circuit of c- RiRi d- Lia+ li Fig. 1c is the model for the double-cage induction motor used R1+R! r1+R Table 2 Parameters of double-cage model of Fig. 1b and single-cage model in p u. U=400 V) P(kW) Double-cage model Single-cage model 2d rd 90 0.00340.01300.11712.65950.06820.12060.00340.01162.63980.08250.013 75 0.00270.01000.1008309250.069201105000270.009130772008010010 0.0045001660.09601.92230.05790.14630.00450.0139189060.08060.016 37 0.00500.01230.11291.98600.05720.14790.00500010819518008700.013 18.5 0.00660.01710.15111.567100718 0.11860.00660.0151155370.08320018 lET Electr. Power Appl., 2009, Vol 3, Iss. 2, pp. 111-122 115 doi:10.1049/ let-epa20080043 C The Institution of Engineering and technology 2009 www.ietdl.org 4.2 Parameter determination of circuit rom circuit∥ Rs/ In this section the method of determining the parameters circuit I from the parameters of circuit Ii is discussed the parameters nd d are known, and usins Figure 5 equivalence between different models the auxiliary parameters yi and y2, defined as The input impedance of the circuit of fig. 5b is y一2c2mV(12_4C (19) z(o,0)=1012+1(/s+1(m+R(14 2C cNv(bll2-4ACll and can be rewritten as hc paramctcrs of thc cquivalent circuit in Fig. 1b can bc calculated as z(o,) 5202a+isaB+C js2aDll+s (15) R1 y1y y1 where ld= riyi l 2i= riv2 L1(R1+R)+ R +R r+RIl These relations are deduced in Appendix 2 6 4.3 Numerical examples Tablc 3 shows the numcrical valucs of the paramctcrs of thc Both circuits will be equivalent when double-cage circuit in Fig. 1c, which are equivalent to the parameters of the double-cage circuit in Fig. 1b in Table 2 B=bl CI D1(17) These parameters are the result of applying (10),(13 )and (18) 4. 1 Parameter determination of circuit l from circuit 5 Per unit system In this section the method of determining the parameters of The parameters of the equivalent circuit of the squirrel-cage circuit ll from that of circuit I is discussed. If the parameters induction motor are usually expressed in per unit(p. . )on A, B, C and dare known, the parameters of the equivalent the notor base. This can lead to confusion because circuit in Fig. 1c can be calculated as although the use of p.u. quantities is common in the literature, it is not always clear which base quantities are (18) In this study, base power is defined as Sb= P, where P is R r1+R the rated mechanical power and the base voltage, UB, is the R line-to-line voltage. Other studies, such as 13 l, use the t the inal slip, Sr= sn, as b These relations are deduced in Appendix 1 power. The relation between the rated mechanical power, Table 3 Parameters of double-cage model in Fig. 1c P(kW) 12 90 0.0034 0.0682 2.6595 0.0436 0.0495 0.0153 0.0940 75 0.0027 0.0692 3.0925 0.0426 00396 0.0118 0.0834 0.0045 0.0579 1.9223 0.0415 0.0506 0.0196 0.1274 37 0.0050 0.0572 1.9860 0.0412 0.0597 0.0136 0.1201 18.5 0.0066 0.0718 1.5671 0.0447 0.0611 0.0205 0.0924 116 /ET Electr. Power Appl. 2009, Vol. 3, Iss. 2, pp. 111-122 C The Institution of Engineering and Technology 2009 doi:10.1049/ et-epa:20080043 www.ietdl.org P, and the apparent power at the nominal slip, SN, is Table 4 Estimated double-cage induction motor parameters P=SNnPF (21) 0362Pk0392 1=0.0713P0135 where m is the efficiency and PFis the power factor at nominal 2=01090604xm=12609Py slip. A motor is always labelled according to its mcchanical power. Therefore in the authors'opinion, it is more natural x:=00519P8032x12=0.0379p0323 to use rated mechanical power as base power instead of the x2=0160603 apparent power that must be given as additional data Nominal power Pk in kW Another source of confusion is the fact that the motor data are divided by its rated values, like TM/TN, TST/TN, IST/IN, double-cage model in Fig. lc. The p u. system used in the in addition, thc basc torquc and basc current arc not cqual to equations of Table 4 is defined as Sb=p, where P is the the motor nominal torque and current rated mechanical power (or nominal mechanical power) and the base voltage, UB, is the line-to-line voltage. In this On the base used in this study the relations between base ay,the real values of the motor parameters can be easily torque and nominal torque, and base current and nominal calculatcd using(8)and(9) current are The parameters of three notors using the equivalent (22) circuit in Fig. lc are shown in Table 5. They are calculated N nPF using the equations of Table 4, with the values P:= 630, 90 and 11 kW. Tables 5 and 6 show motor data suitable and on the base used in [13] the relations are for the Explicit' and the EMTP Type 40, options rcspcctivcly. Thc manufacturer data in Table arc alculate of table 5 TBMPF The 'EMrp Type 40 option, which uses manufacturer data, does not inform the user about the parameters of the equivalent circuit obtained by the program (in the EMTP 6 Induction motor in PSCAD/ RV program, these parameters are shown to the user). To EMTDC identify the characteristics of the motor that the program is using, the torque-speed curve in steady-state can be The double-cage model of the induction motor in the calculated with PSCAD/EMTDC PSCAD/EMTDC program [12] has three data entries named T ypical Data, 'EMTP Type 40 andExplicit'. The The torque-speed curve of an induction motor can be input datum in the Typical Data'option is motor power obtained by using an Electromagnetic Transient Program and only three different options are given: P<. 10Hy pcrforming a simulation whcrc spccd changes vcry slowly 10 Hp 500 Hp. The input data This can be achieved by setting a high inertia value. The in the EMTP Type 40' option are manufacturer data. The conditions of the transient in PSCAD/EMTDC are input data in the Explicit' option are the parameters of the cquivalent circuit in Fig. 1c 30 s at zero spccd to allow clcctric transients to vanish The Typical Data option is simple, as it has only three 60 s at zero torque, with a high inertia value chosen in different cases. When the user knows the motor power such a way that the motor can reach the nominal speed at ly, more realistic equivalent motor parameters can be he end of the simulation alculated with the equations of [14], which are applicable to the double-cage model in Fig. 16. Table 4 shows an Fig. 6 shows the torque-speed curves calculated for the cquivalent sct of cquations to dctcrminc the motor thrcc induction motors in Tablc 6. Each plot has thrcc parameters as a function of the motor power for the curves, namely the torque-speed curve, calculated with the Table 5 Parameters of double-cage model in Fig. 1c P(kW) 12 630 0.0029 0.0732 2.8718 0.0467 0.0305 0.0064 0.0936 90 0.0062 0.0660 2,2399 00438 0.0395 0.0151 0.1102 0.0141 0.0590 1.7126 0.0410 00520 0.0380 0.1314 lET Electr. Power Appl., 2009, Vol 3, Iss. 2, pp. 111-122 117 doi:10.1049/ let-epa20080043 C The Institution of Engineering and technology 2009 www.ietdl.org Table 6 Manufacturer data(U=400V, f=50 Hz) P(kW P M/N IST/IN 630 0.8817 2.5639 1.5151 66697 0.0059 0.9904 90 0.8561 2.7351 1.9960 66380 0.0123 0.9792 11 0.8256 2.9740 2,4671 6.2774 0.0256 0.9533 obtaining correct parameters from manufacturer data can be solved by using the algorithm of [7] and the conversion 630kW EMTP Type 40 equations(18) Figs. 6a and 6b show a slight difference in maximum torquc betwcen the curve calculated with the stcady-statc Equivalent circuit equivalent circuit and the curve calculated with the Explicit licit option. This effect can be a the motor inertia. Fig. 7a shows the infuence of the inertia value on the shape of the torque-speed curve. The figure g0 kw d by a solid line, a broken li and a dotted line for values of the inertia constant H=40 S, 10 s and 5 s, rcspcct n Fig. 7b, the torque-speed curve in the zone near the maximum torque is magnified (the range of the slip is from s=0.2 0.025). It can be observed that for low values of the inertia constant, H, a greater error occurs in the value of the maximum torque I1 kW 7 Induction motor in EMtP-Rv The doublc-cagc modcl of thc induction motor in thc EMTP-RV program [15 has two data cntrics namcd 'Basic and Enable nameplate input calculator. The input data in the "Basic option are the parameters of the Slip, s equivalent circuit in Fig. 16. The input data in the Figure 6 Torque-speed curves calculated using the equivalent circuit, the ' EMTP Type 40'and the ' Explicit 630kW 2,0 options 10 steady-state equivalent circuit (shown by a solid line), the 00 torque-speed curve, calculated with the option Explicit and the parameters of Table 5(shown by a broken line) 0.6 0.0 and the torque-speed curve, calculated with the option EMTP Type 40and the parameters of Table 6(shown by a dotted line). The values of the inertia constant, H, used with the motors of 630. 90 and 11 kw are 40. 7.5 and 7.5 s respectively ig. 6 shows that the Explicit option works correctly(the Fi resulting torque-speed and current-speed curves obtained 05 fit the manufacturer data: starting current and torque maximum torque etc.), whereas the EMTP Type 40 20l750.150.1250.100750.050.0250-0,025 option in PSCAD/EMTDC does not. The starting torque D and current valucs arc similar to thc correct valucs but thc maximum torque is very different. The problem of Figure 7 Influence of inertia on the torque-speed curve 118 /ET Electr. Power Appl. 2009, Vol. 3, Iss. 2, pp. 111-122 C The Institution of Engineering and Technology 2009 doi:10.1049/ et-epa:20080043 www.ietdl.org Table 7 Parameters of double-cage model in Fig. 1b P(kW) 2 630 0.00117 0.06171 29742 0.05714 0.06171 0.00704 0.06418 90 0.00294 0.05972 2.5458 0.06890 0.05972 0.01666 0.08556 11 0.00837 0.06214 2.1835 0.08082 0.05214 0.04482 0.12564 Enable nameplate input calculator'are the manufacturer Fig. 8 plots the torque-speed curve of three motors of 630, ata. In this option, thc paramctcrs of the cquivalent 90 and 11 kW. Thc correct torquc-spccd curve calculatcd circuit in Fig. 1b are calculated using the algorithm in using the equations of the steady-state circuit with the [16]. The manufacturer input data that the user must parameters of Table 5 is represented by a solid line. The introduce in the progran does not include Maximum incorrect torque-speed curve calculated with the equations torque Therefore the algorithm does not use the of the steady-state circuit using arameters of Table 7 maximum torque, and the torque-speed curve calculated given by the EMTP-RV program is represented by a with the parameters supplied by the 'Enable manufacturer broken line. Fig. 8 shows clearly that maximum torque of input calculator will be incorrect the torquc-spccd curve calculatcd by EMTP-RV is too high. This is bccausc the algorithm in [16 docs not usc Table 7 shows the double-cage parameters given by the the maximum torque as the input data EMTP-RV program by using the entries in Table 6. The parameters in Table 7 are in per unit. The base power is the apparent power at the nominal slip, SB 8 Conclusions Experimental data confirm that the double-cage model must be used to obtain realistic models of the squirrel-cage induction motor because the single-cage motor produces 30 kW very large errors. Moreover, manufacturer data always show Nameplate input calculator a starting torque that cannot be fitted to the single-cage model. The equivalence between the two most common linear double-cage models is analysed and the relation between their parameters is obtained. The induction motor Equivalent circuit" in PSCAD/EMTDC is studicd; and the EMTP Typc 40 option to calculate motor parameters using manufacturer data is shown as not working correctly. A similar problem is found in the EMTP-RV program 4_90kW 9 Acknowledgments The authors acknowledge the financial support of the Comision interministerial de Ciencia Technolo gT (CICYT) under the project DP12004-00544. The authors also thank Amalia Barrera and Francesc Quintana from Asea Brown Boveri, S. A. Fabrica de motores for IkW providing the experimental data of the motors in Fig. 4 3 10 References [1] LEVY. General method of magnetizing flux saturation modelling in d-q axis models of double-cage induction nachines,IEE Proc. Electr. Power Appl., 1997, 144,(2) pp.101-109 Figure 8 Torque-speed curves calculated using the [2 PEDRA J, SAINZ L : Parameter estimation of squirrel-cage equivalent circuit with the parameters of table 5 and the induction motors without torque measurements, /EE Proc. parameters calculated by Emtp-Rv Electric Power Appl., 2006, 153,(2), pp. 263-270 lET Electr. Power Appl., 2009, Vol 3, Iss. 2, pp. 111-122 119 doi:10.1049/ let-epa20080043 C The Institution of Engineering and technology 2009 www.ietdl.org [3] VAS P. 'Electric machines and drives. A space-vector (14), can also be written as theory approach(Clarendon Press, Oxford, 1992) pp.279-280 7(a,S orl isaa+6 24 [4] CORCOLES F, PEDRA J, SALICHS M, SAINZ L. Analysis of the nduction machine parameter identification, IEEE Trans Energy Conver.,2002,17,(2),pp.183-190 [5] SUDHOFF S.D.,ALIPRANTIS D.C,KUHN BT,CHAPMAN PL 3o2L14+o(12+a)+b Experimental characterization procedure for use with an Z(o, s) advanced induction machine model, IEEE Trans. Energy Conver,2003,18,(1),pp.48-56 where the comparison with(15)rcsults in [6] SMITH A C, HEALEY R C, WILLIAMSON S. ' A transient induction motor model including saturation and deep bar effect,IEEE Trans. Energy Conver 1996, 11,(1), pp.8-15 R1+(26) [7 PEDRA J, CORCOLES F 'Double-cage induction motor parameters estimation from manufacturers data IEEE If the circuits of Figs. 5a and 5b are equivalent, the Trans. Energy Conver, 2004, 19,(2),pp. 310-317 impedances(12)of Fig. 5a and (25)of Fig 5b must be equal. The comparison between both equations results in [8http://www.energy.wsu.edu/software:Motormaster+ Ver 4.0, Washington State University Energy Program L12+a (27) [9]http://energyefficiencyjrcceceu.int/eurodeem:Euro DEEM 2000, European Data base of Efficient Electric Motors The first and the fourth relation allow Ll to be obtained [10」 LESENNE」, NOTELET F, SEGUIER G:‘ Introduction a I'Electrotechnique Approfondie. Paris: Technique Documentation 1981 D)L1+ (28) [11 The Math Works, Inc. MATLAB 5.3 and Simulink 3.0, Natick, MA, 1999 The division of the first relation by the third of(26)and using the second and fourth equations of (27) [12]Manitoba HVDC Research Center: 'PSCAD/EMTDC Jser's Manual Guide, Version 4, 2004 bILI (29) [13]JOHNSON B.K., WILLIS J.R. Tailoring induction motor analytical models to fit known motor performance characteristics and satisfy particular study needs, IEEE ds./EEE From the second relation of(26)and the third of(27),we Trans. Power Systems, 1991, 6, 3), pp. 959-965 havc [14] PEDRA J. ' Estimation of typical squirrel-cage induction motor parameters for dynamic performance simulation /EE Proc. Gener Transm. Distrib., 2006, 153, (2), pp 137-146 ri-b ri- cI (3 [15] EMTP Development Coordination Group: EMTP-RV, Finally, from the third relation of(26)and the fourth of(27) 2003 we obtain [16 ROGERS G. SHIRMOHAMMADI D. Induction machine modeling for electromagnetic transient programIEEE L=d(R1+R2)=D(R1+R)(31) Trans. Energy Conver, 1987, 2,(4),pp 622-628 11 Appendix 1 12 Appendix 2 In this appendix, the parameters of the equivalent circuit in In this appendix, the parameters of the equivalent Fig. lc arc deduced from thc quantities, A, B, C and D. circuit in Fig. 1b arc deduced from the quantities The input impedance of the equivalent circuit in Fig. 5b, C and D) 120 /ET Electr. Power Appl. 2009, Vol. 3, Iss. 2, pp. 111-122 C The Institution of Engineering and Technology 2009 doi:10.1049/ et-epa:20080043

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