Pro-posed control system assures: rfour quadrant operation energy saving, rgood stabilization of the dc-voltage allows to reduce a dc-link capacitor, rconstant switching frequency, ralmo
Trang 1II-11 Direct Power and Torque Control Scheme 273 Moreover, additional power feedforward control loop was implemented and tested Pro-posed control system assures:
rfour quadrant operation (energy saving),
rgood stabilization of the dc-voltage (allows to reduce a dc-link capacitor),
rconstant switching frequency,
ralmost sinusoidal line current (low THD) for ideal and distorted line voltage,
rnoise resistant power estimation algorithm,
rhigh dynamics of power and torque control,
rlow 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 Converter 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 Kim and S K Sul, “New control scheme for ac–dc–ac converter without dc link electrolytic 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 without power-source voltage sensors,” 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
Trang 2274 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 Liao and S.N Yen, “A Novel Instantaneous Power Control Strategy and Analytic Model for Integrated Rectifier/Inverter 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
Trang 3II-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 presents different methods used for experimental verification of field-circuit finite 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 the three-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.
2006 Springer.
Trang 4276 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 a special 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 the gap (Fig 1) It gives time of displacement of one element equal to about 2.5× 10−5s 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 observed
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.
Trang 5II-12 Field-Circuit Finite Elements Models 277
-2 -1 0 1 2 3 4 5 6
torque [Nm]
time [s]
Figure 2 Torque vs time during soft-starting starting.
-5
-4
-3
-2
-1
0
1
2
3
4
5
current [A]
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
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 machines despite the transient calculation of the 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
Trang 6278 Kom˛eza et al.
-4
-2
0
2
4
6
8
measured
calculated torque [Nm]
time [s]
Figure 5 Torque vs time during frequency starting.
-4
-3
-2
-1
0
1
2
3
4
5
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
measured
calculated speed [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
Trang 7II-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 parts 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 this test 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
current [A]
measured
voltage [V]
Figure 9 The short-circuit current vs voltage.
Trang 8280 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
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
current [A]
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
LM
Figure 12 The classical equivalent circuit of the motor.
Trang 9II-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+ s L m (R r + sL r)
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)
s
R s + sL s+ s L m (R r + sL r)
R r + s(L r + L m)
where U cis 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 − s1)(s − s2)(L s L r + L s L m + L r L m) (4)
where s1and s2—simple poles of the current function are the roots of the equation
s2(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 ) = A1e s1t + A2e s2t + A3e s3t s3= 0 (6) where
A1 = U c (R r + s1(L r + L m))
s1(s1− s2)(L s L r + L s L m + L r L m) (7)
A2 = U c (R r + s2(L r + L m))
s2(s2− s1)(L s L r + L s L m + L r L m) (8)
s2s2(L s L r + L s L m + L r L m) = U c
R s
(9)
When the time constant s1 and s2 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 higher value current curve vs time differs significantly from the curve described
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
Trang 10282 Kom˛eza et al.
-8
-7
-6
-5
-4
-3
-2
-1
0
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
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
time [s]
A 1 e s 1 t
A 2 e s 2 t
current [A]
calculated A 1 e s 1 t + A 2 e s 2 t
measured
0,03
Figure 15 Decomposition of measured current curve vs time into exponential components for DC
voltage 13.4 V