Recent Developments of Electrical Drives - Part 29 pdf

II-11. Direct Power and Torque Control Scheme 273 Moreover, additional power feedforward control loop was implemented and tested. Pro- posed control system assures: r four quadrant operation (energy saving), r good stabilization of the dc-voltage (allows to reduce a dc-link capacitor), r constant switching frequency, r almost sinusoidal line current (low THD) for ideal and distorted line voltage, r noise resistant power estimation algorithm, r high dynamics of power and torque control, r low motor current and torque ripple Power feedforward loop from the motor side to the PWM rectifier improved control dy- namics of the dc-link voltage. It allows fulfilling power matching conditions under transient for PWM rectifier and inverter/motor system. References [1] H. Hur, J. Jung, K. Nam, “A Fast Dynamics DC-link Power-Balancing Scheme for a PWM Converter-Inverter System”. IEEE Trans. on Ind. Elect., vol. 48, No. 4, August 2001, pp. 794– 803. [2] L. Malesani, L. Rossetto, P.Tenti and P. Tomasin, “AC/DC/AC Power Conver ter with Reduced Energy Storage in the DC Link,” IEEE Trans. on Ind. Appl., vol. 31, No. 2, March/April 1995, pp. 287–292. [3] J. Jung, S. Lim, and K. Nam, “A Feedback Linearizing Control Scheme for a PWM Converter- Inverter Having a Very Small DClink Capacitor,” IEEE Tran. on Ind. App., vol. 35, No. 5, September/October 1999, pp. 1124–1131. [4] J.S.KimandS.K.Sul, “Newcontrol scheme forac–dc–acconverter withoutdclinkelectrolytic capacitor,” in Proc. of the IEEE PESC’93, 1993, pp. 300–306. [5] R. Uhrin, F. Profumo “Performance Comparison of Output Power Estimators Used in AC/DC/AC Converters,” IEEE, 1994, pp. 344–348. [6] A. Tripathi, A.M. Khambadkone, S.K. Panda, “Space-vector based, constant frequency, direct torque control and dead beat stator flux control of AC machines,” Proc. of the IECON ’01, Vol.: 2, pp. 1219–1224 vol. 2. [7] T. Noguchi, H. Tomiki, S. Kondo, I. Takahashi, “Direct Power Control of PWM converter withoutpower-sourcevoltagesensors,”IEEE Trans.on Ind.Appl.Vol.34,No. 3,1998,pp.473– 479. [8] T. Ohnishi, “Three-phase PWM converter/inverter by means of instantaneous active and reac- tive power control,” In Proc. of the IEEE-IECON Conf., 1991, pp. 819–824. [9] J. Holtz “Pulsewidth Modulation for Electronics Power Conversion,” In Proc. of The IEEE, vol. 82, no. 8, August 1994, pp.1194–1214. [10] M. P. Kazmierkowski, R. Krishnan and F. Blaabjerg, Control in Power Electronics, Academic Press, 2002, p. 579. [11] M. Malinowski, M. Jasinski, M.P. Kazmierkowski, “Simple Direct Power Control of Three- Phase PWM Rectifier Using Space Vector Modulation,” in IEEE Trans. on Ind. Elect., vol. 51, No. 2, April 2004, pp. 447–454. [12] I. Takahashi, and T. Noguchi, “A New Quick-Response and High Efficiency Control Strategy of an Induction Machine,” IEEE Trans. on Ind. Appl., vol. IA-22, No. 5, September/October 1986, pp. 820–827. 274 Jasinski et al. [13] D. Swierczynski, M.P. Kazmierkowski, “Direct Torque Control of Permanent Magnet Syn- chronous Motor (PMSM) Using Space Vector Modulation (DTC-SVM),”—Simulation and Experimental Results”, IECON 2002, Sevilla, Spain, on-CD. [14] S.G. Perler, “Deriving Life Multipliers for Electrolytic Capacitors,” IEEE PES Newsletter, First Quarter 2004, pp. 11–12. [15] H. Tajima, and Y. Hori, “Speed Sensorless Field-Oriented Control of the Induction Machine”. IEEE Trans. on Ind. Appl., vol. 29, No. 1, 1993, pp. 175–180. [16] T.G. Habatler, “A space vector-based rectifier regulator for AC/DC/AC converters”. IEEE Trans. on Power Electr., vol. 8, February 1993, pp. 30–36. [17] J.Ch.LiaoandS.N.Yen, “A NovelInstantaneous PowerControlStrategyandAnalyticModel for Integrated Rectifier/Inver ter Systems”. IEEE Trans. on Power Electr., vol. 15, No. 6,November 2000, pp. 996–1006. [18] P. Vas, “Sensorless Vector and Direct Torque Control,” Oxford University Press, 1998, p. 729. II-12. EXPERIMENTAL VERIFICATION OF FIELD-CIRCUIT FINITE ELEMENTS MODELS OF INDUCTION MOTORS FEED FROM INVERTER K. Kom ˛ eza, M. Dems and P. Jastrzabek Institute of Mechatronics and Information Systems, Technical University of Lodz, Stefanowskiego 18/22, 90-924 Lodz, Poland kom ˛ eza@p.lodz.pl, mdems@p.lodz.pl, piastrza@posejdon.wpk.p.lodz.pl Abstract. The main aim of the paper is the presentation of the different methods that can be used during experimental verification of the validity of the field-circuit model of an induction machine for inverter feeding simulation. The second aim is to discuss, based on the DC feeding method, whether field-circuit methods or circuit methods with changeable parameters should be used to simulate transient characteristics of induction machines. Introduction The paper presentsdifferent methodsusedfor experimentalverification of field-circuitfinite elements models of induction motors. The field-circuit models can be used in the modeling of transient states of induction motors by taking advantage of the real shape of voltage generated by the inverter [1–4]. The current and speed curves vs. time of the induction motors during transient state can be simply compared with the calculated curves to indicate the validity of the simulation. The torque curve vs. time, especially for inverter feeding, is very distorted. It is widely known that only part of torque harmonics can be obtained from measurements. The measurement of the torque during transient state is very difficult because the measured signals are the results of the mechanical systems response. According to this problem, it is very important to work out different methods to verify the validity of used field-circuit models of induction motors. Examined motor The object of investigation was thethree-phase induction squirrel-cage motor of 380 V (star connected) rated output power 0.37 kW. Table 1 shows the specification of the motor. Field-circuit model Electromechanical transients of the examined induction motor have been computed using the program Opera 2D based on the field-circuit model. S. Wiak, M. Dems, K. Kom ˛ eza (eds.), Recent Developments of Electrical Drives, 275–289. C  2006 Springer. 276 Kom ˛ eza et al. Table 1. Specification of analyzed motor Diameter of rotor and stator 60.5 mm, 106 mm Air gap length, core length 0.25 mm, 56 mm Number of phase and poles 3 phases, 4 poles Primary winding pitch Single layer, 5/6 short pitch Number of series turns in stator winding 612 Rotor winding Aluminum cage Number of stator and rotor slots 24, 18 Depth of secondary slot 10.56 mm The field-and-circuit model [1,5] is made by the assumption of a 2D electromagnetic field. In this model, coil outhangs and shorting rings of the rotor were taken into account by joining properly lumped parameters to several circuits. The application of the described method to model the magnetic field distribution in an induction motor, taking into account the movement of the rotor, required the introduction of aspecial element to the model which properly joined the unmoving and moving parts. In the applied module RM [6] of the software package Opera 2D this element took the form of a gap-element. The gap region is divided uniformly on 3,168 elements along the circumference of thegap(Fig.1). It gives time ofdisplacement of oneelementequal to about 2.5 × 10 −5 s at synchronous speed, comparable with the average time step of computation. The gap region division is fundamental for avoiding erroneous oscillation generations of computed electromagnetic torque. The comparison of the calculated and measured values of rotational speed, current, and torque for starting state feeding by soft-starting (Figs. 2–4) and frequency starting devices (Figs. 5–7) can be obser ved. Verification Methods Traditional methods The traditional methods, which are used to measure induction machine parameters, are: no-load test and short-circuit test. No-load test is useful for comparing the value of the magnetizing current measured and that calculated. Specifically in low-powered machines we focused on the problem of the air gap width estimation due to the effects of the cutting process and its influence on the sheet borders. Because dynamic field-circuit models of induction motors usually do not incorporate eddy currents, hysteresis, and mechanical losses in the stator core, it is necessary to obtain experimentally only the magnetization Figure 1. The gap region division. II-12. Field-Circuit Finite Elements Models 277 -2 -1 0 1 2 3 4 5 6 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 measured calculated torque [Nm] time [s] Figure 2. Torque vs. time during soft-starting starting. -5 -4 -3 -2 -1 0 1 2 3 4 5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 current [A] measured c alculated time [s] Figure 3. Comparison of calculated and measured current curves vs. time during soft starting. 0 200 400 600 800 1000 1200 1400 1600 1800 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 measured calculated speed [rpm] time [s] Figure 4. Comparison of calculated and measured speed curves vs. time during soft starting. part of the no-load current. The quasi-static solvers calculate element permeability using amplitude of the magnetic flux density. This can introduce some errors in highly saturated small machinesdespite the transient calculation ofthe magnetization current needed[7-10]. In the presented motor, a comparison of measured and calculated values of the magnetizing current is made. The second test concerns the shape of calculated and measured currents at no-load. Comparing the shape of the two currents informs whether the flux distribution in the different part of the examined motor is near to the real one. The maximum value is mainly dependent on the air gap representation and saturation of the main parts of the 278 Kom ˛ eza et al. -4 -2 0 2 4 6 8 0 0,05 0,1 0,15 0,2 0,25 measured calculated torque [Nm] time [s] Figure 5. Torque vs. time during frequency starting. -4 -3 -2 -1 0 1 2 3 4 5 0 0,05 0,1 0,15 0,2 0,25 measured calculated current [A] time [s] Figure 6. Comparison of calculated and measured current curves vs. time during frequency starting. 0 200 400 600 800 1000 1200 1400 1600 1800 2000 0 0,05 0,1 0,15 0,2 0,25 measured calculated s peed [rpm] time [s] Figure 7. Comparison of calculated and measured speed curves vs. time during frequency starting. magnetic core. Fig. 8 shows the comparison of the current vs. time calculated with transient and quasi-static solvers. The results of comparison between two methods (AC and TR) and measurement are summarized in Table 2. The best results are obtained by TR method. It is very difficult in practice to obtain accu- racy better then 5% especially for small power motors due to inaccuracies in the production process and the results of the die-casting of the rotor cage and mechanical processing. II-12. Field-Circuit Finite Elements Models 279 Table 2. The relative error between calculation and measurement Relative error Phase A Phase B Phase C Average AC 9,544 9,512 7,912 8,989 RT 3,535 8,524 8,376 6,812 Short-circuit test examines the accuracy of the leakage reactance estimation (end par ts reactance are included as lumped parameters) and the skin effect in the rotor bars. The main problem of the short-circuit test is the level of test current because of the local saturation effects of the leakage fluxes. Therefore, if possible, only a test with a nominal voltage will be really satisfactory. The measurement of the torque during thistest is very helpful (Fig. 9). -1,5 -1 -0,5 0 0,5 1 1,5 0,1 0,11 0,12 0,13 0,14 0,15 0,16 0,17 0,18 time [s] current [A] measured transient steady-state AC Figure 8. Current vs. time curves for steady-state, transient calculation, and measurement. calculated 0 1 2 3 4 5 6 0 50 100 150 200 current [A] measured voltage [V] Figure 9. The short-circuit cur rent vs. voltage. 280 Kom ˛ eza et al. Using the impulse DC supply test Using this method we use the DC supply of one or two windings of the motor. With DC impulse method it is possible to test many aspects of the motor’s behavior: the nonlinearity of the main flux path, influence of saturation due to leakage flux of the windings and skin effect of the currents induced in the rotor bar as well. Figs. 10 and 11 show the comparison between the measured and calculated values of input current at different DC voltage value. It is also possible to have a look on the classical equivalent circuit of the motor (Fig. 12). 0 0,5 1 1,5 2 2,5 3 3,5 0 0,02 0,04 0,06 0,08 0,1 0,12 0,14 calculated measured current [ A ] time [ s ] Figure 10. Current vs. time curves for DC supply at DC voltage value 63.05 V. 0 1 2 3 4 5 6 7 0 0,05 0,1 current [A] 0,15 0,2 calculated times [s] measured Figure 11. Current vs. time curves for DC supply at DC voltage value 138 V. R s U s L s L M R R L R Figure 12. The classical equivalent circuit of the motor. II-12. Field-Circuit Finite Elements Models 281 Using the simplified, without current induced in stator and rotor cores, model of the induction motor, the transfer function under linear condition is Z(s) = R s + sL s + sL m (R r + sL r ) R r + s(L r + L m ) (1) When the DC impulse signal (step) is applied to the one phase terminals of the motor the transient current response will be I s (s) = U s (s) Z(s) = U c s  R s + sL s + sL m (R r + sL r ) R r + s(L r + L m )  (2) where U c is the value of applied DC voltage I s (s) = U c (R r + s(L r + L m )) s((R s + sL s )(R r + s(L r + L m )) + sL m (R r + sL r )) (3) I s (s) = U c (R r + s(L r + L m )) s(s − s 1 )(s − s 2 )(L s L r + L s L m + L r L m ) (4) where s 1 and s 2 —simple poles of the current function are the roots of the equation s 2 (L s L r + L s L m + L r L m ) + s(R s L r + R s L m + R r L s + R r L m ) + R s R r = 0 (5) The current vs. time function can be obtain using Heaviside’s formula I s (t) = A 1 e s 1 t + A 2 e s 2 t + A 3 e s 3 t s 3 = 0 (6) where A 1 = U c (R r + s 1 (L r + L m )) s 1 (s 1 − s 2 )(L s L r + L s L m + L r L m ) (7) A 2 = U c (R r + s 2 (L r + L m )) s 2 (s 2 − s 1 )(L s L r + L s L m + L r L m ) (8) A 3 = U c R r s 2 s 2 (L s L r + L s L m + L r L m ) = U c R s (9) When the time constant s 1 and s 2 differs significantly it is possible to separate them from the measured current curve. On the accuracy of the motor representation is shown by the values of the voltages induced in open windings vs. time (Figs. 13 and 14). Upon examining the obtained results it was obvious that separation of the current curve exponential components would only be possible for small values of the instantaneous DC current,for highervaluecurrent curve vs.time differs significantly from the curvedescribed by equation (3) (Figs. 15–18). The parameters calculated from measured curves are shown in Table 3. Even when approximation was possible, the obtained values changed with voltage value. Explanation of this result can be found easily by observing the field and current density distributions calculated using field-circuit method. In Figs. 19 and 20 the distribution of the relative permeability for DC voltage equals 138 V for two different time instances are shown. 282 Kom ˛ eza et al. -8 -7 -6 -5 -4 -3 -2 -1 0 0 0,05 0,1 0,15 0,2 measured calculated times [s]voltage [V] Figure 13. The voltage induced in open winding vs. time at DC voltage value 63.05 V. -19 -17 -15 -13 -11 -9 -7 -5 -3 -1 1 0 0,05 0,1 0,15 0,2 calculated measured voltage [V] times [s] Figure 14. The voltage induced in open winding vs. time at DC voltage value 138 V. 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0 0,06 0,09 0,12 0,15 0,18 time [s] A1e s1t A2e s2t current [A] calculated A 1e s1t + A2e s2t measured 0,03 Figure 15. Decomposition of measured current curve vs. time into exponential components for DC voltage 13.4 V. . al. -8 -7 -6 -5 -4 -3 -2 -1 0 0 0,05 0,1 0,15 0,2 measured calculated times [s]voltage [V] Figure 13. The voltage induced in open winding vs. time at DC voltage value 63.05 V. -1 9 -1 7 -1 5 -1 3 -1 1 -9 -7 -5 -3 -1 1 0. of the main parts of the 278 Kom ˛ eza et al. -4 -2 0 2 4 6 8 0 0,05 0,1 0,15 0,2 0,25 measured calculated torque [Nm] time [s] Figure 5. Torque vs. time during frequency starting. -4 -3 -2 -1 0 1 2 3 4 5 0. starting. -5 -4 -3 -2 -1 0 1 2 3 4 5 0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 current [A] measured c alculated time [s] Figure 3. Comparison of calculated and measured current curves vs. time during soft starting. 0 200 400 600 800 1000 1200 1400 1600 1800 0