异步电机参数2.pdf异步电机数学模型及参数转换2PEDRA et al. STUDY OF AGG

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详细说明：异步电机数学模型及参数转换2PEDRA et al. STUDY OF AGGREGATE MODELS FOR SQUIRREL-CAGE INDUCTION MOTORS 15 4 1.0 93(Ts 0.6 04 I kW 0.2 0 3 200 300 400 500 Power, P(kW Fig. 3. Distribution of the starting torque error of the single-cage model method A)as a function of the motor power. 90KW I1 KW 500kW 0 0.8 0.6 0.4 0.2 Slip, S 90 kw Fig. 2. Torque-speed curves for 11-,90-, and 500-kw motors. Single-cage (mcthod A)and doublc-cagc modcls in broken and continuous lincs, respectively locked-rotor impedance ZsT, the measured stator resistance Rs and the relation Xsd= Xrd 500kW R2+ jXrd R s, Xm=Im(znd-Xsd.(7) 2-Te ∠ST TEN 0 C. Comparison of Models 0.8 6 0.4 0.2 The single-cage model(methods a and b)does not ad Slip, s just well the torque-speed and current-speed curves of the Fig. 4. Torque- speed curves for 11-,90., and 500-kW motors. Single-cage squirrel-cage induction motors Method A has a high error at (method B)and double-cage models in broken and continuous lines the starting point, as can be observed in Fig. 2, and method B respectively fails at the full load and the maximum torque points, as can be observed in Fig. 4. Thus, to obtain an accurate behavior in all where TsTd and ists are the starting torques resulting from the of the speed range, the double-cage model must be used use of the double-cage and the single-cage models, respectively. Fig 2 compares the torque-speed behavior of the double-cage The error has been calculated for the 20 motors of Table I Fig 3 model with the estimated parameters in Table II(continuous shows that the starting torque error due to the use of the single line) and the single-cage model(method A)with the estimated cage model is very high and increases when the motor power parameters in Table II(broken line). The manufacturer data in increases Table I, i.e., the maximum torque TM, the full load torque TFL ig. 4 shows the torque-speed curve for the double-cage(con and the starting torque Tst, are also shown in Fig. 2 with dots. tinuous line)and the single-cage(broken line) models with the Fig 2 shows a good agreement at the full load and the maximum parameters calculated with method b. The single-cage parame torque points between both models, but the starting torque of the ters(method b)have been determined by using(7),where the single-cage model presents a high error no-load impedance ZNL and the locked-rotor impedance ZsT Fig. 3 shows the starting torque error due to the use of the have been calculated by using the double-cage model and the ingle-cage model calculated by method A. The starting torque data of Table ll Fig 4 shows that method B predicts the starting error is defined as torque accurately but has a high error in the maximum torque and the full load slip. Fig. 4 also shows that the shape of the △Tr TSId-Ts (8) from that of the double-cage mode, e model is very different 522 IEEE TRANSACTIONS ON POWER SYSTEMS. VOL, 20. NO. 3. AUGUST 2005 1.0 here R si,Hli,R2iAmi,A sdi, Aldi A 2di are the parameters 0.8 of each motor, and the aggregate motor parameters are 0.6 Zsa= Rsa +oxsda; Zla=Rla+3-x1c 三04 Zoa- r2a +gx2d 三三 02| B. Method 2 0 100 200 300 400 500 The second method uses the parameters at the full load point Power, P(kW) The aggregate double-cage model parameters are obtained as Fig. 5. Distribution of the ImlaximluIn loryue error of the single-cage Imodel (method B)as a function of the motor powe Ma ∑ hows the maximum torque error due to the use of (14) the single-cage model obtained with method B. The error at the ∑ Rli/sFLitjxldi R2i/SLI+j X2d maximum torque point 1s where the mean slip is defined as △YM=Mm-7 Md SFLa aisLe (15) where TM d and TMs are the maximum torques resulting trom and the aggregate motor parameters are the use of the double-cage and the single-cage models, respec tively. Fig. 5 shows that the maximum torque error is very high The starting torque error has also been calculated and it is al 2。a=Bsa+ jSda;Z1a +iX S ways lower than 0.07 +iX2da (16) 上La I. AGGREGATION METHODS The total power of the aggregate motor Pa is C. Method 3 P In this case, the double-cage model parameters are (10) obtained by using the manufacturer data of Table I (P, TM/TFL. TST/TFL, IST/TFL)and the full load reac where mi is the number of motors that have power Pi. The factor tive power of each motor ai indicates the fraction of the total power Pa, which represents the motors of power P QFL= P·sin(FL (17) Four different methods to calculate the parameters of the ag- 7HL·cos(9F) gregate motor are described below. Each aggregation method is compared with the total torque-speed Tt(s) and current-speed The aggregate motor parameters are obtained with the alg It(s) curves obtained as rithm of [13] by using the data T()=∑m();)=∑n(9(1) P=∑mP;CLl=∑ ni cfli niIMi?ist where Ti(s)and I, (s) are the torque-speed and the current 7;1sT (18 speed curves of each motor, and nmi is the number of motors with a power and the mean slip defined as in(15) The draw back of this method is that the maximum torque is elnor produced at a different slip in each motor. Therefore, the max The first nethod uses the motor paraneters at the starting imum of the total torque does not correspond to the addition of point. The aggregate double-cage model parameters Isee the individual maximum torques. Another problem(although it Fig. 1(b)] are calculated as produces a low error) is that the total starting current should have been calculated by addition of the phasor currents D. Method 4 Z2 (12 In this method the maximum torque l Ma and the starting cur- R2i+0-X2d rent IsTa are calculated from the total torque-Speed curve T(s) PEDRA et al. STUDY OF AGGREGATE MODELS FOR SQUIRREL-CAGE INDUCTION MOTORS 1523 Method 6 Method 4208 Method 2 Method 2 086 Method 3 含aa 4 Method 3 208642 Method 4 Method 4 0 0 0.8 0.6 0.2 0.8 0.6 0.2 Slip Fig. 6. Torque-speed and current-speed curves for the aggregate motor of one motor of 500 kw and 45 motors of ll kw and the total current-speed curve I(s), defined in(11). These maximum torque point, because the maximum total torque is values, together with the manufacturer data different from the maximum torque predicted by the aggregate motors calculated with these methods. This type of error usually P ,QFa=>ni QFli, TsTa=>ni ISTi increases when the difference between the power of the differer (19) notors increases The aggregate motor calculated with method 4 has the same and the mean slip defined as(15), are used to calculate the maximum torque as the total torque curve( this method uses the double-cage parameters with the algorithm of [13] correct value). Although that the critical points, starting torque It maximum torque and full load to IV. COMPARISON OF AGGREGATION METHODS have a good agreement( the error is lower than 0.01), the shape of the torque curve does not adjust well at some points. This A. Study of a Simple case is because the shape of the total torque-speed curve(which has A simple case consisting of one motor of 500 kW and m2- been obtained by addition of the torque speed curves) can be 45 motors of 11 k w has been studied. The value of n, has been slightly different from the normal shape of a double-cage model chosen to have a similar power with each type f motor(n2 p= Thus, in some cases, it can be difficult to adjust this total torque 495 kW). Fig. 6 shows the torque-speed and the current-speed speed curve with a double-cage model curves of the four aggregation methods(l to 4)with a contin- The starting torque curve predicted by method 2, based on the uous line. The total torque-speed and current-speed curves de- full load values, has the highest starting torque error. fined as in(11), are shown with a broken line Fig. 6 shows that the current-speed curve of the aggregate Fig 6 shows that the torque error is very low for the four motor and the total current-speed curve have a good agreement methods Methods 1-3 have the highest torque error near the with the four aggregation method 524 IEEE TRANSACTIONS ON POWER SYSTEMS. VOL 20. NO. 3. AUGUST 2005 0.035 0.3 0.030 0.25 Method I 0.025 502 U0.020 015 E0.015 g 0.1 E0.010 0.05 0.005 0 0.3 0.0 0.2 4 0.6 0.8 Method 2 025 Relative power, O1 Fig. 7. Torque error at the maximum torque point with method l Aggregate u 50.2 鲁争 motor of 90 kw and 1l kw with different relative powers a1 0.15 B. Relative power influence on the error 0.05 The shape of the total torque-speed and current-speed curves is clearly influenced by the relative power of each motor in re lation to the total power of the aggregate motor. For example, 0.25 Method 3 when the aggregate motor of one 110 kw motor(n1= 1)and m2 motors of 11 kw is calculated, the error at the maximum 02 torque point varies with the number of motors n2. The relative 2 0.15 power of each motor is E0.1 ◆命 2P2 Pa=B1+m2P2.(20) 0.05 P 0 Fig7 shows the maximum torque error when using method 10.3 as a function of the relative power al. This curve suggests that 0.25 Method 4 the maximum error is always produced near the value C1=0.5. 0.2 In order to make all the motors have a similar influence on the g shape of the total torque-speed curve, all the coefficients ni Pi 5 must have a similar value. If the value ai is small, the influence E on the torque-speed and the current-speed curves of the power Pi. 0.05 motor can be neglected For example, if the aggregate motor of ·1e44F a single 11o-kw motor and a single ll-kw motor is considered 10 1(000 the torque-speed and the current-speed curves of the aggregate Power dispersion, AP motor will be almost identical to those of the 1 10-kw motor 8. Torque error at the maximum torque point for the four methods. Each aggregate motor is composed of two different motors(190 cases) V, ERROR OF AGGREGATION METHODS The maximum torque error, starting torque error, and starting The maximum torque error is represented in Fig 8 versus the current error for each aggregation method are studied. These power dispersion AP between the motors, defined as errors are defined as 2=n △Tn=DM=mMml,△Tsn STt Tai ∑ P.八P=_1 ∑|P-P Mt △Isz Tt STai (21) where the number of different motors m is two in this case STt Fig 8 Shows that the maximum torque error increases when where the subscript t indicates the total torque-speed and cur- the power dispersion between the motors increases, i.e., the error rent-speed curves calculated by(11)and the subscript i the four is lower when the motors have a similar power than when they aggregate methods studied have a different power Table iii shows the mean and the maximum error at the max A. Aggregate Motor of a Group Composed of Two imum torque, the starting torque, and the starting current for the Diferent Motors four methods studied In this section, several aggregate motors are studied. Each The results of Fig 8 and Table Ill indicate the following aggregate motor is composed of two different motors chosen Method 1 has the highest maximum torque error. This from the 20 motors of Table I. This gives 190 cases for each method uses the parameters at the starting point aggregation method. Fig. 8 shows the maximum torque error Method 2 has the highest starting torque error. This for the four methods and the 190 cases method uses the parameters at the full load point PEDRA et al. STUDY OF AGGREGATE MODELS FOR SQUIRREL-CAGE INDUCTION MOTORS 1525 TABLE III TABLE IV ERROR DATA OF AGGREGATE MOTORS COMPOSED erroR DATA OF AGGREGATE MOTORS COMPOSEd oF 8 DIFFERENT MOTORS OF TWO DIFFERENT MOTORS Method ATMn △Ts Method M AlSt Mean Max mean Mean Mux Mean Ma Max Max 10.12410.13810.00490.00740.00610.0097 0.0599026300.00670.05910.00630.0418 0.09990.11420.03450.06050.02020.0268 0.0493026440.03990.16430.01500.0909 0.10730.12030.00020.00070.00190.0029 0.0516025490.00040.00190.00160.0117 0.01830.02010.01220.01340.00170.0026 4 0.0187003680.01350.03370.00160.0117 Grup a Grup a 0,01280,0173000130,0390,00800,0102 0.00790.05180.00340.01300.00460.0201 1234 0.0083005170.02540.09190.00730.0309 234 001320,01720,03870,0489000760,0131 0,01370,01830,00020,00080,00040,0010 0.0081005550.0003000080000400015 0.01130.01240.0088000950.00030.0011 0.0118001670.00890.01180.00030.0016 Grup B p 0.,07120,08990,01510,02030,00820,013 0.04380.15270.01000.05910.00790.0350 20,03870,05180,01030,02480,01170,0286 0.02560.11060.02500.10870.01430.0501 0,04890,06330,00020,00040,00110,0023 0.02950.1162000040.0017000180.0085 0,02650,02830,01940,02150,00110,0024 00263003680.02010.03370.00180.0081 0.06 0.05 Group a 0.01 Method 0 100 200 300 400 500 0.2 0.16 5g9 0.12 08 Method 4 0.04 Group b 0.8 0.6 0.4 2 20 60 70 Power dispersion, AP Fig. 10. Torque-speed curve for the aggregate motor composed by 20 different motors(one case) Fig 9. Maximum torque error for different aggregate motors, separated into two groups(45 cases in each group). Each aggregate motor is composed of two B. Aggregate Motor of a Group Composed of 18 Different Motors The mean error at the maximum torque, starting In this section, the errors produced by aggregate motors are torque, and starting current for each aggregation also studied. Each aggregate motor is composed of 18 different method is low. It must be taken into account that the motors chosen from the 20 motors of Table I. This gives 190 dif- error produced by the use of the single-cage model is ferent cases for each aggregation method. The number of motors gher ni of a power Pi in each group of motors verifies that ni Pi has a To study the influence of the motor power dispersion on similar value. Table Iv shows the maximum error for the max the error, the 20 motors of Table i have been divided into imum torque the starting torque, and the starting current for the two groups. Group a is composed of the ten biggest motors four aggregation methods studied. The mean error and the max (500 kW to 90 kw) and group B is composed of the ten smallest imum error in Table Iv for each aggregation method are clearly motors (75 kw to 8 kW). Fig 9 shows that the maximum torque lower than the mean error and the maximum error of Table Ill error in each different group is lower than when all the motors Therefore, the number of different motors has an influence on are in the same group Table Ill also shows the mean error and the error, too. For a greater number of different motors, the error the maximum error for motor groups a and B The mean error is lower. Table iv also shows a study for the two groups a and and the maximum error are always lower in each separate group b, which have been previously defined. In this case, the aggre A or b than when the motors are not separated in two groups. gate motors are made with eight different motors. Thus, there Therefore, the dispersion between the power of the different are 45 different cases in each group. Moreover, the maximum motors increases the torque and current error produced by the error is also lower than when the motors are not separated in aggregate motor two groups. 526 IEEE TRANSACTIONS ON POWER SYSTEMS. VOL 20. NO. 3. AUGUST 2005 4202 500W|点6 11kW -8 12 MW 6 3.911 1.2 0.8 0.8 0.6 0.6 0.4 0.2 0.2 0 00.10.203040.50.60.70.80.9 00.10.203040.50.60.70.809 Fig. 11. 500-kW and 11-kW motor behavior by using the double-cage model. Three-phase voltage sag, duration At= 0.2 s, depth h=0.1 C. Aggregate Motor of a Group Composed of Twenty Different Motors Finally, the aggregate motor of the 20 different motors of E 0 Table iis studied. In this case, there is only one aggregate motor Again, the number of motors ni of a power Pi in each group of motors verifies that n P, has a similar value. Fig 10 shows the -6 500 and 11 kw torque-speed behavior of the aggregate motors calculated with -8 Imethods l and 4(continuous line). As the slip at the maximum12 torque point varies with the motor power the total torque- speed a 9 curve calculated with(11) has a very flat shape, as can be seen in Fig. 10(broken line) The parameters of the aggregate motor in p u. obtained with 复0 Wwwg method 4(which has the best agreement)are Ts=0.0061,m1=0.0122,2=0.0908 xm=2.0090,xsd=x2a=0.0612,x1d=0.1482(23) 1.2 The shape of the torque-speed curve of the aggregate motor of a Fig. 10 is very different from the aggregate motor recommended 50.8 in the bibliography [14], which is based on the use of the single s0.6 cage model. In [14], it is pointed out that the single-cage motor 3 0.4 parameters are valid only for simulations where motors do not002 sta 0 0.20.30.40.50.60.7 80.9 VI. DYNAMIC STUDY Time,(s) Fig 12. 500-kw and ll-kw motor behavior by using the double-cage model Fig. 11 shows the dynamic behavior of two motors of 500 kw Three-phase voltage sag, duration At=0. 2 s, depth I=0.1 and 1l kW during a three-phase voltage sag of duration At 0. 2 S, depth h=0. 1. The motor parameters are in Table Il, the motor of 500 kw and 45 motors of 1l kw is shown in Fig. 12 inertia constant of each motor is 1=1s, and their load torques The inertia constant of the aggregate motor is 1= l s and are their rated torques. The current and torque oscillations of the load torque the rated torque. The aggregate motor behavior the 500-kw motor decay more slowly than those of the 11-kw is represented with a continuous line and the total torque and motor. The behavior of the aggregate motor that represents one current of the motor group with a broken line. The current and PEDRA et al. STUDY OF AGGREGATE MODELS FOR SQUIRREL-CAGE INDUCTION MOTORS 15 torque oscillations decay is intermediate between those of the [8]T.Kataoka, HUchida,S.Nishikata,T. Kai,and TFunabashi,"A 500-kw motor and the 11-kw motor The agreement between method for aggregation of a group of induction motor loads, "in Proc the aggregate model behavior and the real motors behavior is POWERCON Perth, Australia, 2000, pp. 1683-1688 9] P. Piromthum and A. Kunakorn, "A study of starting current due to a very good during the voltage sag, as the curves coincide when group of induction motors using an aggregation model, Power electron the speed decreases When the speed recovers, the real motors Drive Syst., voL 2, pp. 1054-1057, 2003 have a different behavior because they have a different speed [101 J. Lesenne, F Notelet, and g. seguier, Introduction a Electrotechnique Approfondie. Paris, France: Tcchniquc Documentation, 1981 This results in differences in the torque behavior, as can be ob- [1l] EuroDEEM 2000, European Database of Efficient Electric Motors [On served in fig, 12 line].Availablehttp:energyefficiencyjrc.cec.eu.int/eurodeem From this example, it is clear that the behavior of motors with [12] MotorMaster+ Ver 4.0, Washington State Univ. Energy Program [On line].avAilable:http://www.energy.wsuedu/software different speeds cannot be predicted with the aggregate motor. [13] Pedra and F. Corcoles, " Double-cage induction motor parameters es The hypothesis of the aggregate motor is that all the motors have timation from manufacturers data, IEEE Trans. Energy convers., vol the same speed, 1. e, the speed of the aggregate motor 19,no.2,pp.3l0-317,Jun.2004 [14] IEEE Task Force on Load Representation for Dynamical Performance, Standard load models for power flow and dynamic performance sim ⅤI. CONCLUSION ulation, " IEEE Trans. Power Syst., vol 10, 10. 3, pp. 1302-1313, Aug 1995 The double-cage model must be used to obtain realistic ag gregate models because the single-cage motor produces very high errors. The highest torque error is usually produced near the maximum torque point. The maximum error is produced when Joaquin Pedra(s85-M88)was born in Barcelona the motor group has motors with very different rated power Spain, in 1957. He received the B.s. degree in indus al cnginccring and thc Ph. D. dcgrcc in cnginccring ( the relative power ai between each type of motor is similar from the Universitat Politecnica de catalunya The increase in the number of different motors in the aggregate Barcelona, Spain, in 1979 and 1986. respectively. Since 1985. he has been a Professor with the motor produces a decrease in the torque error. The shape of the Electrical Engineering Department, Universitat torque-speed curve of the aggregate motor is very flat for a great Politecnica de catalunya. His research interest lies number of different motors, and so, the curve is difficult to rep in the areas of power system quality and electrical machines esent by an aggregate motor with the double-cage model. The dynamic study for a voltage sag shows that the predictions of the aggregate motor are accurate if the speeds in the motor group are similar Luis Sainz was born in Barcelona, Spain, in 1965. He received the B.S. degree in industrial engineering and REFERENCES the Ph. D. degree in engineering from the Universitat Politecnica de Catalunya, Barcelona, Spain, in 1990 [1] T. Y.J. Lem and R. T H. Alden, Comparison of experimental and ag and 1995, respectively gregate induction motor responses, IEEE Trans. Power Syst., vol 9, no Since 1991. he has been a Professor with the elec 4,p.1895-1900.Nov.1994 trical Engineering Department, Universitat Politec [2]D. C. Franklin and A. Morclato, " Improving dynamic aggregation of nica de Catalunya. His main field of research is power induction motor models, IEEE Trans. Power Syst., vol. 9, no 4, pp system quality 1934-1941,Nov.1994. [3] P. Pillay. S. M. A Sabur, and M.M. Hay, A Imodel for induction mOtor aggregation for power system studies Elect. Power Syst. Res, vol 42 pp.225-228,1997 [4] M. Taleb, M. Akbaba, and E. A. Abdullah aggregation of induction machines for power system dynamic studies, IEEE Trans. Power Syst vol.9,no.4,pp.2042-2048,Nov.1994. Felipe Corcoles was born in Almansa, Spain, in [5] S. Sriharan, L. H. Tan, and H. M. Ting, Reduced transient model of a 1964. He received the B.s. degree in industrial en group of induction Motors, "IEEE Trans. Energy Convers., vol. 8, 110. 4, gineering and the Ph. D) degree in engineering from pp.769-777,Dec.1993 the Universitat Politecnica de catalunya, Barcelona [6]G. G. Richards, " Reduced order models for an induction motor group Spain, in 1990 and 1998, respectively during bus transfer, IEEE Trans. Power Syst., vol. 4, no. 2, pp. 494498 Since 1gg. he has been a professor with the May 198 Electrical Engineering Department. Universitat [7]G. Rogers, J DiManno, and R. Alden, "An aggregate induction motor Politecnica de Catalunya. His research interest lies in model for industrial plants, IEEE Trans. Power App. Syst., voL. 1013, no he areas of electrical machines and power systems 4,pp.683-690,Apr.1984 quality

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