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Slip energy recovery of a rotor-side field oriented controlled wound rotor induction motor fed by matrix converter
ARTICLE IN PRESS
Journal of the Franklin Institute 345 (2008) 419–435 www.elsevier.com/locate/jfranklin
Slip energy recovery of a rotor-side field oriented controlled wound rotor induction motor fed by matrix converter Sedat Su¨nter Department of Electrical-Electronic Engineering, Faculty of Engineering, Firat University, 23119 Elazig, Turkey Received 18 November 2005; received in revised form 3 December 2007; accepted 3 December 2007
Abstract This paper investigates rotor-side field oriented control of a wound-rotor induction motor using the slip energy recovery principle. The proposed drive system uses a matrix converter to transfer the slip energy from the rotor into the mains instead of using ac–dc–ac converter whilst the stator side is fixed to the grid. Operation at both subsynchronous and supersynchronous regions is possible with the proposed drive system. Simulation studies of the proposed doubly fed induction motor drive system verify the good control performance of the system in transient and steady-state conditions. r 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Matrix converter; Wound-rotor induction motor; Vector control; Slip recovery
1. Introduction The operation of an induction motor in slip energy recovery drive system at subsynchronous and supersynchronous speeds is well known. The topology known as Scherbius drive, employs a doubly fed wound-rotor induction motor (WRIM) using an ac–dc–ac converter in the rotor circuit [1]. Such a scheme requires a low rating converter for handling rotor slip power. However, the converter requires two-stage power conversion, namely rectification and inversion, which demands a complicated control strategy and large dc link capacitors, making the system bulky and expensive. In addition, the system allows the motor operating only at subsynchronous speed region if uncontrolled E-mail address: ssunter@firat.edu.tr 0016-0032/$32.00 r 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2007.12.001
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rectifier is used. This restriction can be eliminated by using a pair of phase-controlled thyristor bridges. One of the bridges operates at slip frequency as a rectifier or inverter, and the other operates at mains frequency as an inverter or rectifier [2]. But, a difficulty is experienced near synchronous speed when the slip-frequency back emfs are insufficient for natural commutation. In this case, devices with a self-turn-off capability are necessary for the passage through synchronism. An attractive solution is to use back-to-back PWM converters connected between rotor side and mains [3]. In such a configuration, sinusoidal currents can be obtained at both the stator and rotor windings. However, complex control strategy of the converter and large dc link capacitors make the system bulky and costly. Another approach to achieve bi-directional power flow in the circuit is to use a linecommutated cycloconverter in which the ac power conversion is performed in single stage. The cycloconverter must be controlled so that the frequency of the injected slip-ring voltages follows the rotor slip frequency. By using the cycloconverter in slip energy recovery drive system it is possible to operate at both subsynchronous and supersynchronous speed regions [1]. However, cycloconverters cause harmonic pollution both at the supply side and the motor side since their output contains several harmonic frequencies, and the input power factor is very low due to natural commutation [4]. In addition, in line-commutated cycloconverters the maximum rotor frequency is approximately one-third of supply frequency with near-sinusoidal low-frequency voltage and current. This corresponds to operation at 67% of synchronous speed. In this paper, a matrix converter is used to control the speed and the rotor-side currents of wound-rotor induction motor. Such a configuration can offer the advantages given by its back-to-back counterpart while converting ac power in a single stage and eliminating the large dc link capacitor. In addition, the control scheme required by a direct ac–ac conversion scheme is simpler than that of a two-stage power conversion [5]. The maximum rotor frequency limitation in the cycloconverter is also eliminated by the use of the matrix converter. In this work, modelling and simulation of rotor-side field oriented control of a wound-rotor induction motor using the slip energy recovery principal with the matrix converter are realised. Low speed operation of a wound-rotor induction motor can be simply obtained by introducing an external rotor resistance to dissipate the slip power. Variation of the external resistance can be achieved either in discrete steps by using a variable resistor or continuously by using a high-frequency chopper across a constant resistor. However, it is not essential that the slip power is dissipated in the external rotor resistance. It can be removed from the rotor circuit and utilised externally to improve the overall efficiency of the drive system. Such a drive system is shown in Fig. 1 where the slip power is taken from the rotor circuit and returned to the grid via a matrix converter. The proposed drive system combines a matrix converter and rotor-side field oriented controlled wound-rotor induction motor in a slip energy recovery drive system as shown in Fig. 1. This drive system may find place in wind-power generation applications. 2. Matrix converter Matrix converter shown in Fig. 2 is a direct ac–ac converter [6,7] which converts input line voltages into variable voltage with unrestricted frequency without using any intermediate dc link circuit. Matrix converter is an array of controlled semiconductor switches that directly connects the three-phase source to three-phase load. A three-phase matrix converter consists of nine bi-directional voltage-blocking switches, arranged in
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C B A f=50 Hz, and Three-Phase AC Source UC UB UA Supply Voltage Measurement Is-abc
WRIM
Rotor Current Measurement +
e-jθsl
A-B-C
* Ird
PI Speed Control
ω*r
Ira
Ua
Irb
Ub
Irc
Uc
Imc-abc
Target Voltage signals for the Matrix Converter d-q
Nine PWM Signals
d-axis voltage correction terms
ejθsl
+
MATRIX CONVERTER
Ird +
-
* Irq
+
-
Irq
PI Current Control
+
PI Current Control
+
-
* Urd
d-q
A-B-C -
* Urq
q-axis voltage correction terms Fig. 1. Vector controlled slip energy recovery drive system with a matrix converter.
three groups of three each group being associated with an output line. This arrangement of bi-directional switches connects any of the input line A, B or C to any of the output lines a, b or c as schematically represented in Fig. 2. In order to achieve the safe operation of the converter when operating with bi-directional switches two basic rules must be observed. Normally the matrix converter is fed by a voltage source and therefore the input terminals should not be short circuited. The load has typically an inductive nature and for this reason output phase must never be opened. An input filter is necessary to remove the high frequency ripple from the input current because the matrix converter is capable of directly connecting the load to the grid. For protection purposes a clamp circuit is needed to achieve the safe shut down of the converter during over current at the output side or voltage disturbances at the input side.
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VA
VB
VC
IA
SAa
SAb
SAc
SBa
SBb
SBc
SCa
SCb
SCc
IB
IC
Ia
Va
Ib
Vb
Ic
Vc
Fig. 2. Three-phase to three-phase matrix converter power circuit.
A simplified version of the Venturini algorithm is used in this work [8]. This algorithm is defined in terms of the three-phase input and output voltages at each sampling instant, and is convenient for closed loop operations. A detailed analysis of the switching control strategy can be found in Ref. [9]. Ideal switches have been assumed in the simulation of the matrix converter power circuit. Modelling and simulation of the system are performed using Matlab/Simulink package program [10]. Fig. 3 illustrates Simulink block diagram of the three-phase matrix converter. Fig. 4 shows the Simulink model for one output phase of the matrix converter in detail. The other two phases are not shown for clarity, since they are the same except for a phase shift of 1201 and 2401. In Fig. 4, the input variables of the matrix converter are the clock and target output voltages obtained from the vector controller. The Simulink blocks in Fig. 4 represent the equations of the switching control algorithm which are given in Appendix A. 3. d–q model of wound-rotor induction motor Equations used in the simulation of a wound-rotor induction motor in synchronously rotating d–q reference frame are given as [11]: 32 3 2 3 2 32 3 2 p csq os 0 0 U sq I sq Rs 0 0 0 76 7 6 U sd 7 6 0 Rs 0 6 7 6 os p 0 0 0 7 76 csd 7 6 7 6 76 I sd 7 6 6 7 6 7 6 7¼6 76 7þ 6 7 0 p ðos or Þ 7 0 Rr 0 54 I rq 5 6 4 U rq 5 4 0 4 0 54 crq 5 crd 0 0 ðos or Þ p U rd I rd 0 0 0 Rr (1)
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Fig. 3. Simulink scheme of a three-phase matrix converter.
2
3
2 Ls 7 6 6 6 csd 7 6 0 7 6 6 crq 7 ¼ 6 5 4 Lm 4 crd 0 csq
Te ¼ 3
0
Lm
Ls 0
0 Lr
Lm
0
P L2m ðI sq I rd I sd I rq Þ 2 Ls
0
32
I sq
3
6 7 Lm 7 76 I sd 7 76 7 0 54 I rq 5 I rd Lr
(2)
(3)
dom ¼ T e T L Bom (4) dt where quantities with subscript q or d denote q-axis or d-axis quantities and quantities with subscript s or r denote stator or rotor quantities. c denotes flux linkage, R is resistance, U is voltage and Lm is the magnetising inductance. Ls and Lr denote the self-inductances of the stator and rotor, respectively. Te and TL are the motor torque and load torque, respectively. P is the number of poles and B is the friction constant coefficient. J is inertia J
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Fig. 4. Detail Simulink representation of one output phase of the matrix converter.
and om is the mechanical angular speed of the rotor. Simulink model of the wound-rotor induction motor is shown in Fig. 5. The motor parameters are given in Appendix B. 4. Rotor-side field oriented controller The fundamental power delivered to the rotor of wound-rotor induction motor across the airgap, Pag is delivered between the mechanical power output, Pm and the rotor copper loss, PRcl. PRcl ¼ sPag
(5)
Pm ¼ ð1 sÞPag
(6)
Pag ¼ T e os
(7)
where Te is the electromagnetic torque and os is the synchronous angular velocity. It is obvious from Eqs. (5)–(7) that the rotor cupper loss is proportional to the slip under constant load operating condition. Therefore, speed control of the wound-rotor induction motor is inefficient by introducing external resistors to the rotor circuit, especially at low speeds. The rotor resistance method of speed control is not preferable except for a narrow speed range near the synchronous region. However, the slip power can be recovered and
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Fig. 5. Simulink model of the wound-rotor induction motor.
transferred into the ac supply through the matrix converter resulting in an increase in overall efficiency of the drive system. The field oriented control strategy has been implemented in the matrix converter woundrotor induction motor drive. Fig. 1 shows a schematic block diagram for the rotor-side field oriented control of the wound-rotor induction motor fed by the matrix converter where three rotor currents and rotor position have to be measured. The induction machine is controlled in synchronously rotating d–q axis frame with the d-axis oriented along the stator flux vector position. In this way a decoupled control between the electrical torque and the stator excitation current is obtained. Eqs. (8)–(15) are the fundamental equations for field oriented control [12] and allow the induction motor to act like a separately excited dc machine with decoupled control of torque and flux, making it possible to operate the induction motor as a high-performance four-quadrant servo drive. By setting the stator flux vector aligned with d-axis: csd ¼ cs and csq ¼ 0
(8)
Ts dI msd U sd þ I rd ¼ I msd þ T s Lm dt
(9)
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o¼
U sq T s =Lm þ I rq T s I msd
(10)
I rd þ sT r
dI rd U rd dI msd ¼ þ sT r osl I rq ð1 sÞT r dt Rr dt
(11)
I rq þ sT r
dI rq U rq ¼ sT r osl I rd ð1 sÞT r osl I msd dt Rr
(12)
Fig. 6. Simulink model of the whole drive system.
Fig. 7. Stator, rotor, mechanical and net power results of WRIM at 10 N m constant load torque operating in subsynchronous region.
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P L2m I msd I rq 2 Ls dom P L2m ¼ 3 J I msd I rq T L Bom 2 Ls dt
427
Te ¼ 3
s¼1
L2m ; Ls Lr
Ts ¼
Ls ; Rs
Tr ¼
Lr ; Rr
ð13Þ
osl ¼ o or
(14)
where s is the leakage coefficient, Ts and Tr are time constants of the stator and rotor, respectively, Imsd is the fictitious magnetising current representing the stator flux linkage, o is the stator flux angular frequency, osl is the slip frequency and or ¼ Pom/2 is the rotor electrical frequency. The current and speed controllers in Fig. 1 are implemented according to Eq. (11) and Eq. (12) which are the d-axis and q-axis current-controller equations including correction terms. Eq. (13) represents the speed controller equation.
Fig. 8. Matrix converter input current and motor speed variations.
Fig. 9. Controlled rotor voltage and motor speed variations in subsynchronous region.
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The correction terms are given as: dI msd dt ð1 sÞLr osl I msd
U rdcor ¼ sLr osl I rq ð1 sÞLr U rqcor ¼ sLr osl I rd
ð15Þ
5. Simulation results Complete Simulink model of the drive system is given in Fig. 6. Simulation results have been obtained for subsynchronous and supersynchronous operating conditions. The switching frequency of the matrix converter was chosen 5 kHz. First, for subsynchronous
Fig. 10. d–q currents of the rotor in subsynchronous region.
Fig. 11. Rotor phase current and voltage waveforms in steady-state: (a) n ¼ 500 rpm (b) n ¼ 1000 rpm.
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operation mode the motor was accelerated from standstill to 500 rpm where the steadystate operation is achieved and then 1000 rpm of reference speed command was given at the instant of 1 s. The machine was loaded with 10 N m. The corresponding simulation results of stator power (Ps), rotor power (Pr), mechanical power (Pm) and net power (Pn ¼ Ps+Pr) are shown in Fig. 7. The slip energy is transferred from the rotor to the utility through the matrix converter. Therefore, under this operating condition the total power received from the supply was reduced and resulted with the net power, Pn as shown in Fig. 7. For the same operating conditions, the simulation results for input current of the matrix converter, controlled rotor voltage and motor speed are given in Fig. 8 and Fig. 9, respectively. Decrease in the slip frequency causes a reduction in the slip energy returned to the utility. This is illustrated in Fig. 8 as the input current amplitude of the matrix
Fig. 12. Matrix converter input current and voltage waveforms in steady-state: (a) n ¼ 500 rpm (b) n ¼ 1000 rpm.
Fig. 13. Stator, rotor, mechanical and net power results of WRIM at 5 N m constant load torque operating in both subsynchronous and supersynchronous regions.
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converter decreases with the increase of the motor speed. Corresponding results for d–q currents of the rotor are given in Fig. 10. Fig. 11 illustrates the rotor current and applied rotor voltage. As can be seen they are in opposite phase and this is the requirement for slip energy recovery drives. Fig. 11(a) and (b) show the simulation results for 500 and 1000 rpm, respectively, in steady-state. Fig. 12(a) and (b) show the input current and voltage waveforms of the matrix converter. Here, it is obvious that the converter and control strategy perform two functions; transferring the slip energy from the rotor into the mains and applying the required rotor voltage corresponding to the reference speed. Similar results have been obtained at 5 N m load torque to demonstrate the machine’s behaviour in supersynchronous operation mode. Results given in Fig. 13 through Fig. 17 demonstrate the steady-state operation following acceleration of the machine from standstill to 1750 rpm. Notice that transition between the subsynchronous and supersynchronous
Fig. 14. Rotor phase current and motor speed variations in both operating regions.
Fig. 15. Matrix converter input current and motor speed variations in both operating regions.
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regions occurs at 1500 rpm. In Fig. 13, the instantaneous motor power variations are given for both subsynchronous and supersynchronous regions. As can be seen from the figure, the rotor power, Pr is negative in subsynchronous region which approximately corresponds to the interval between 0 and 0.85 s. Then, the rotor power reverses at instant t ¼ 0.85 s which corresponds to the transition from subsynchronous to supersynchronous region. This means that rotor is now receiving power from the supply through the matrix converter. The corresponding rotor current, input current of the matrix converter and motor speed variations are shown in Figs. 14 and 15. Note that the input current of the matrix converter in Fig. 15 is zero at the transition instant between the regions. Zoomed view of this region is also given in the figure. The controlled rotor voltage, torque and motor speed variations are shown in Figs. 16 and 17. Rotor voltage and current, and input current and phase voltage of the matrix converter are given in Fig. 18 and Fig. 19. As seen from the figures the currents are in
Fig. 16. Controlled rotor voltage and motor speed variations in both operating regions.
Fig. 17. Motor torque and speed variations in both operating regions.
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Fig. 18. Controlled rotor voltage and rotor current results in transition interval.
Fig. 19. Simulation results for the matrix converter input current and phase voltage in transition interval.
opposite phase with the voltages in the subsynchronous region where the rotor power is negative, and they are in phase at supersynchronous region. It has been shown that the motor requires energy both from the stator and rotor at supersynchronous region. In subsynchronous region, the stator withdraws power from the grid whilst the rotor feeds the supply via the converter. This is proven by input waveforms of the matrix converter given in Fig. 19. 6. Conclusions The rotor-side field oriented control of wound-rotor induction motor using the slip energy recovery principle has been modelled and simulated in Matlab/Simulink. In the drive system, a matrix converter has been used to transfer the slip energy from the rotor into the mains in subsynchronous region, and to supply the rotor in supersynchronous region. It has been shown that the use of the matrix converter in the drive system has the
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advantages of single stage power conversion, operation in both subsynchronous and supersynchronous speed regions, sinusoidal voltage and current waveforms and simpler control scheme than other converters used instead. The simulation results indicate that the matrix converter drive system operates efficiently at subsynchronous speeds where the slip power is transferred from rotor windings to the mains through the matrix converter with sinusoidal currents and voltages. Simulation results have also shown that the system allows the machine to operate at supersynchronous speeds, as well. Appendix A. Matrix converter algorithm A simplified version of the Venturini algorithm is defined in terms of the three-phase input and output voltages at each sampling instant and is convenient for closed loop operations. For the real time implementation of the proposed modulation algorithm, it is required to measure any two of three input line-to-line voltages. Then, Vim and oit are calculated as: 4 V 2im ¼ ðv2AB þ v2BC þ vAB vBC Þ 9 vBC oi t ¼ arctan pffiffiffi 3ðð2=3ÞvAB þ ð1=3ÞvBC Þ
(A.1) ! (A.2)
where vAB and vBC are the instantaneous input line voltages. The target output peak voltage and the output position are calculated as: 2 V 2om ¼ ðv2a þ v2b þ v2c Þ 3 vb vc oo t ¼ arctan pffiffiffi 3v a
(A.3) (A.4)
where va, vb and vc are the target phase output voltages. Alternatively, in a closed loop system (for example, a field oriented controlled drive), the voltage magnitude and angle may be direct outputs of the control loop. Then, the voltage ratio is calculated as: sffiffiffiffiffiffiffiffiffi V 2om q¼ (A.5) V 2im where q is the desired voltage ratio, Vim is the peak input voltage. Triple harmonic terms are found as follows: 2 q sinðoi tÞ sinð3oi tÞ 9 qm 2 q 2p ¼ sin oi t sinð3oi tÞ 9 qm 3 qffiffiffiffiffiffiffiffiffi 1 1 1 ¼ V 2om cosð3oo tÞ cosð3oi tÞ 6 4 qm
K 31 ¼
(A.6)
K 32
(A.7)
K 33
(A.8)
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where qm is the maximum voltage ratio (0.866). Then, the three modulation functions for output phase, a are given as: 1 2 2 1 v v ðv þ k Þ þ M Aa ¼ þ k31 þ (A.9) a 33 AB BC 3 3 3 3V 2im M Ba
1 2 1 1 ¼ þ k32 þ ðva þ k33 Þ vBC vAB 3 3 3 3V 2im
M Ca ¼ 1 ðM Aa þ M Ba Þ
(A.10) (A.11)
The modulation functions for the other two output phases, b and c are obtained by replacing va with vb and vc, respectively, in Eqs. (A.9) and (A.10). Note that the modulation functions have third harmonic components added to them at the input and output frequencies to produce output voltage, vo. This is a requirement to get the maximum possible voltage ratio [7]. It should be noted that in Eq. (A.3) there is no requirement for the target outputs to be sinusoidal. In general, three-phase output voltages and input currents can be defined in terms of the modulation functions in matrix form as: voph ¼ Mviph 32 3 va M Aa M Ba M Ca vA 6v 7 6M 76 v 7 M M Bb Cb 54 B 5 4 b 5 ¼ 4 Ab M Ac M Bc M Cc vc vC
(A.12)
iiph ¼ M T ioph 32 3 iA M Aa M Ab M Ac ia 6i 7 6M 7 6 7 4 B 5 ¼ 4 Ba M Bb M Bc 54 ib 5 iC M Ca M Cb M Cc ic
(A.13)
2
2
3
3
2
2
where the superscript T denotes a transpose and M is the instantaneous input-phase to output-phase transfer matrix of the three-phase matrix converter. viph and voph are the input and output phase voltage vectors, and iiph and ioph represent the input and output phase current vectors. Alternatively, from Eqs. (A.12) and (A.13) the output-line voltages and input-line currents can be expressed as: voLine ¼ mviLine 32 3 vab mAb mBb mCb vAB 6v 7 6m 76 7 4 bc 5 ¼ 4 Ac mBc mCc 54 vBC 5 vca mAa mBa mCa vCA 2
3
2
(A.14)
and i ¼ mT ioLine 2iLine 32 3 iAB mAb mAc mAa iab 6i 7 6m 7 6 7 4 BC 5 ¼ 4 Bb mBc mBa 54 ibc 5 2
3
iCA
mCb
mCc
mCa
ica
(A.15)
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where mAb ¼ 13 ðM Aa M Ab Þ 13 ðM Ba M Bb Þ mBb ¼ 13 ðM Ba M Bb Þ 13 ðM Ca M Cb Þ mCb ¼ 13 ðM Ca M Cb Þ 13 ðM Aa M Ab Þ mAc ¼ 13 ðM Ab M Ac Þ 13 ðM Bb M Bc Þ mBc ¼ 13 ðM Bb M Bc Þ 13 ðM Cb M Cc Þ
(A.16)
mCc ¼ 13 ðM Cb M Cc Þ 13 ðM Ab M Ac Þ mAa ¼ 13 ðM Ac M Aa Þ 13 ðM Bc M Ba Þ mBa ¼ 13 ðM Bc M Ba Þ 13 ðM Cc M Ca Þ mCa ¼ 13 ðM Cc M Ca Þ 13 ðM Ac M Aa Þ Appendix B The wound-rotor induction motor rated values and parameters: 380 V, 1500 rpm, with 10 N m maximum torque. Rotor inertia: 0.05 kg m2, pole numbers: 4. Stator and rotor resistances: 2.33 and 2.55 O, respectively. Stator and rotor self-inductances: 0.213 and 0.22 H, respectively. Mutual inductance: 0.2 H. References [1] J.M.D. Murphy, F.G. Turnbull, Power Electronic Control of AC Motors, Pergamon Press, 1988. [2] I. C - adırcı, M. Ermis-, Double-output induction generator operating at subsynchronous and supersynchronous speeds: steady-state performance optimisation and wind-energy recovery, IEE Proc. B, Electr. Power Appl. 139 (5) (1992) 429–442. [3] R. Pena, J.C. Clare, G.M. Asher, A doubly fed induction generator using back-to-back PWM converter supplying an isolated load from variable speed wind turbine, IEE Proc., Electr. Power Appl. 143 (5) (1996) 380–387. [4] H. Keyuan, H. Yikang, Investigation of a matrix converter-excited brushless doubly-fed machine windpower generation system, Power Electronic and Drive System, PEDS’03, vol. 1, 17–20 November, 5th International Conference on PEDS, 2003, pp. 743–748. [5] H. Altun, Application of a matrix converter in a slip energy recovery drive system, Int. J. Eng. Modell. 18 (3–4) (2005) 69–80. [6] M. Venturini, A new sine wave in sine wave out conversion technique which eliminates reactive elements, in: Proceedings of the Powercon 7, San Diego, CA, 1980, pp. E3-1–E3-15. [7] A. Alesina, M. Venturini, Solid-state power conversion: a Fourier analysis approach to generalized transformer synthesis, Proc. IEEE Trans. Circuit Syst. CAS-28 (4) (1981) 319–330. [8] S. Su¨nter, J.C. Clare, A true four quadrant matrix converter induction motor drive with servo performance, IEEE-PESC’96, May 1996, pp. 146–151. [9] H. Altun, S. Su¨nter, Matrix converter induction motor drive: modeling, simulation and control, Electr. Eng. 86 (1) (2003) 25–33. [10] MATLABs for Microsoft Windows, The Math Works Inc., 1999. [11] P.C. Krause, Analysis of Electrical Machinery, McGraw-Hill, New York, 1986. [12] R. Datta, V.T. Ranganathan, A simple position-sensorless algorithm for rotor-side field-oriented control of wound-rotor induction machine, IEEE Trans. Ind. Electron. 48 (4) (2001) 786–793.
Journal of the Franklin Institute 345 (2008) 419–435 www.elsevier.com/locate/jfranklin
Slip energy recovery of a rotor-side field oriented controlled wound rotor induction motor fed by matrix converter Sedat Su¨nter Department of Electrical-Electronic Engineering, Faculty of Engineering, Firat University, 23119 Elazig, Turkey Received 18 November 2005; received in revised form 3 December 2007; accepted 3 December 2007
Abstract This paper investigates rotor-side field oriented control of a wound-rotor induction motor using the slip energy recovery principle. The proposed drive system uses a matrix converter to transfer the slip energy from the rotor into the mains instead of using ac–dc–ac converter whilst the stator side is fixed to the grid. Operation at both subsynchronous and supersynchronous regions is possible with the proposed drive system. Simulation studies of the proposed doubly fed induction motor drive system verify the good control performance of the system in transient and steady-state conditions. r 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. Keywords: Matrix converter; Wound-rotor induction motor; Vector control; Slip recovery
1. Introduction The operation of an induction motor in slip energy recovery drive system at subsynchronous and supersynchronous speeds is well known. The topology known as Scherbius drive, employs a doubly fed wound-rotor induction motor (WRIM) using an ac–dc–ac converter in the rotor circuit [1]. Such a scheme requires a low rating converter for handling rotor slip power. However, the converter requires two-stage power conversion, namely rectification and inversion, which demands a complicated control strategy and large dc link capacitors, making the system bulky and expensive. In addition, the system allows the motor operating only at subsynchronous speed region if uncontrolled E-mail address: ssunter@firat.edu.tr 0016-0032/$32.00 r 2008 The Franklin Institute. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.jfranklin.2007.12.001
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rectifier is used. This restriction can be eliminated by using a pair of phase-controlled thyristor bridges. One of the bridges operates at slip frequency as a rectifier or inverter, and the other operates at mains frequency as an inverter or rectifier [2]. But, a difficulty is experienced near synchronous speed when the slip-frequency back emfs are insufficient for natural commutation. In this case, devices with a self-turn-off capability are necessary for the passage through synchronism. An attractive solution is to use back-to-back PWM converters connected between rotor side and mains [3]. In such a configuration, sinusoidal currents can be obtained at both the stator and rotor windings. However, complex control strategy of the converter and large dc link capacitors make the system bulky and costly. Another approach to achieve bi-directional power flow in the circuit is to use a linecommutated cycloconverter in which the ac power conversion is performed in single stage. The cycloconverter must be controlled so that the frequency of the injected slip-ring voltages follows the rotor slip frequency. By using the cycloconverter in slip energy recovery drive system it is possible to operate at both subsynchronous and supersynchronous speed regions [1]. However, cycloconverters cause harmonic pollution both at the supply side and the motor side since their output contains several harmonic frequencies, and the input power factor is very low due to natural commutation [4]. In addition, in line-commutated cycloconverters the maximum rotor frequency is approximately one-third of supply frequency with near-sinusoidal low-frequency voltage and current. This corresponds to operation at 67% of synchronous speed. In this paper, a matrix converter is used to control the speed and the rotor-side currents of wound-rotor induction motor. Such a configuration can offer the advantages given by its back-to-back counterpart while converting ac power in a single stage and eliminating the large dc link capacitor. In addition, the control scheme required by a direct ac–ac conversion scheme is simpler than that of a two-stage power conversion [5]. The maximum rotor frequency limitation in the cycloconverter is also eliminated by the use of the matrix converter. In this work, modelling and simulation of rotor-side field oriented control of a wound-rotor induction motor using the slip energy recovery principal with the matrix converter are realised. Low speed operation of a wound-rotor induction motor can be simply obtained by introducing an external rotor resistance to dissipate the slip power. Variation of the external resistance can be achieved either in discrete steps by using a variable resistor or continuously by using a high-frequency chopper across a constant resistor. However, it is not essential that the slip power is dissipated in the external rotor resistance. It can be removed from the rotor circuit and utilised externally to improve the overall efficiency of the drive system. Such a drive system is shown in Fig. 1 where the slip power is taken from the rotor circuit and returned to the grid via a matrix converter. The proposed drive system combines a matrix converter and rotor-side field oriented controlled wound-rotor induction motor in a slip energy recovery drive system as shown in Fig. 1. This drive system may find place in wind-power generation applications. 2. Matrix converter Matrix converter shown in Fig. 2 is a direct ac–ac converter [6,7] which converts input line voltages into variable voltage with unrestricted frequency without using any intermediate dc link circuit. Matrix converter is an array of controlled semiconductor switches that directly connects the three-phase source to three-phase load. A three-phase matrix converter consists of nine bi-directional voltage-blocking switches, arranged in
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C B A f=50 Hz, and Three-Phase AC Source UC UB UA Supply Voltage Measurement Is-abc
WRIM
Rotor Current Measurement +
e-jθsl
A-B-C
* Ird
PI Speed Control
ω*r
Ira
Ua
Irb
Ub
Irc
Uc
Imc-abc
Target Voltage signals for the Matrix Converter d-q
Nine PWM Signals
d-axis voltage correction terms
ejθsl
+
MATRIX CONVERTER
Ird +
-
* Irq
+
-
Irq
PI Current Control
+
PI Current Control
+
-
* Urd
d-q
A-B-C -
* Urq
q-axis voltage correction terms Fig. 1. Vector controlled slip energy recovery drive system with a matrix converter.
three groups of three each group being associated with an output line. This arrangement of bi-directional switches connects any of the input line A, B or C to any of the output lines a, b or c as schematically represented in Fig. 2. In order to achieve the safe operation of the converter when operating with bi-directional switches two basic rules must be observed. Normally the matrix converter is fed by a voltage source and therefore the input terminals should not be short circuited. The load has typically an inductive nature and for this reason output phase must never be opened. An input filter is necessary to remove the high frequency ripple from the input current because the matrix converter is capable of directly connecting the load to the grid. For protection purposes a clamp circuit is needed to achieve the safe shut down of the converter during over current at the output side or voltage disturbances at the input side.
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VA
VB
VC
IA
SAa
SAb
SAc
SBa
SBb
SBc
SCa
SCb
SCc
IB
IC
Ia
Va
Ib
Vb
Ic
Vc
Fig. 2. Three-phase to three-phase matrix converter power circuit.
A simplified version of the Venturini algorithm is used in this work [8]. This algorithm is defined in terms of the three-phase input and output voltages at each sampling instant, and is convenient for closed loop operations. A detailed analysis of the switching control strategy can be found in Ref. [9]. Ideal switches have been assumed in the simulation of the matrix converter power circuit. Modelling and simulation of the system are performed using Matlab/Simulink package program [10]. Fig. 3 illustrates Simulink block diagram of the three-phase matrix converter. Fig. 4 shows the Simulink model for one output phase of the matrix converter in detail. The other two phases are not shown for clarity, since they are the same except for a phase shift of 1201 and 2401. In Fig. 4, the input variables of the matrix converter are the clock and target output voltages obtained from the vector controller. The Simulink blocks in Fig. 4 represent the equations of the switching control algorithm which are given in Appendix A. 3. d–q model of wound-rotor induction motor Equations used in the simulation of a wound-rotor induction motor in synchronously rotating d–q reference frame are given as [11]: 32 3 2 3 2 32 3 2 p csq os 0 0 U sq I sq Rs 0 0 0 76 7 6 U sd 7 6 0 Rs 0 6 7 6 os p 0 0 0 7 76 csd 7 6 7 6 76 I sd 7 6 6 7 6 7 6 7¼6 76 7þ 6 7 0 p ðos or Þ 7 0 Rr 0 54 I rq 5 6 4 U rq 5 4 0 4 0 54 crq 5 crd 0 0 ðos or Þ p U rd I rd 0 0 0 Rr (1)
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Fig. 3. Simulink scheme of a three-phase matrix converter.
2
3
2 Ls 7 6 6 6 csd 7 6 0 7 6 6 crq 7 ¼ 6 5 4 Lm 4 crd 0 csq
Te ¼ 3
0
Lm
Ls 0
0 Lr
Lm
0
P L2m ðI sq I rd I sd I rq Þ 2 Ls
0
32
I sq
3
6 7 Lm 7 76 I sd 7 76 7 0 54 I rq 5 I rd Lr
(2)
(3)
dom ¼ T e T L Bom (4) dt where quantities with subscript q or d denote q-axis or d-axis quantities and quantities with subscript s or r denote stator or rotor quantities. c denotes flux linkage, R is resistance, U is voltage and Lm is the magnetising inductance. Ls and Lr denote the self-inductances of the stator and rotor, respectively. Te and TL are the motor torque and load torque, respectively. P is the number of poles and B is the friction constant coefficient. J is inertia J
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Fig. 4. Detail Simulink representation of one output phase of the matrix converter.
and om is the mechanical angular speed of the rotor. Simulink model of the wound-rotor induction motor is shown in Fig. 5. The motor parameters are given in Appendix B. 4. Rotor-side field oriented controller The fundamental power delivered to the rotor of wound-rotor induction motor across the airgap, Pag is delivered between the mechanical power output, Pm and the rotor copper loss, PRcl. PRcl ¼ sPag
(5)
Pm ¼ ð1 sÞPag
(6)
Pag ¼ T e os
(7)
where Te is the electromagnetic torque and os is the synchronous angular velocity. It is obvious from Eqs. (5)–(7) that the rotor cupper loss is proportional to the slip under constant load operating condition. Therefore, speed control of the wound-rotor induction motor is inefficient by introducing external resistors to the rotor circuit, especially at low speeds. The rotor resistance method of speed control is not preferable except for a narrow speed range near the synchronous region. However, the slip power can be recovered and
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Fig. 5. Simulink model of the wound-rotor induction motor.
transferred into the ac supply through the matrix converter resulting in an increase in overall efficiency of the drive system. The field oriented control strategy has been implemented in the matrix converter woundrotor induction motor drive. Fig. 1 shows a schematic block diagram for the rotor-side field oriented control of the wound-rotor induction motor fed by the matrix converter where three rotor currents and rotor position have to be measured. The induction machine is controlled in synchronously rotating d–q axis frame with the d-axis oriented along the stator flux vector position. In this way a decoupled control between the electrical torque and the stator excitation current is obtained. Eqs. (8)–(15) are the fundamental equations for field oriented control [12] and allow the induction motor to act like a separately excited dc machine with decoupled control of torque and flux, making it possible to operate the induction motor as a high-performance four-quadrant servo drive. By setting the stator flux vector aligned with d-axis: csd ¼ cs and csq ¼ 0
(8)
Ts dI msd U sd þ I rd ¼ I msd þ T s Lm dt
(9)
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o¼
U sq T s =Lm þ I rq T s I msd
(10)
I rd þ sT r
dI rd U rd dI msd ¼ þ sT r osl I rq ð1 sÞT r dt Rr dt
(11)
I rq þ sT r
dI rq U rq ¼ sT r osl I rd ð1 sÞT r osl I msd dt Rr
(12)
Fig. 6. Simulink model of the whole drive system.
Fig. 7. Stator, rotor, mechanical and net power results of WRIM at 10 N m constant load torque operating in subsynchronous region.
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P L2m I msd I rq 2 Ls dom P L2m ¼ 3 J I msd I rq T L Bom 2 Ls dt
427
Te ¼ 3
s¼1
L2m ; Ls Lr
Ts ¼
Ls ; Rs
Tr ¼
Lr ; Rr
ð13Þ
osl ¼ o or
(14)
where s is the leakage coefficient, Ts and Tr are time constants of the stator and rotor, respectively, Imsd is the fictitious magnetising current representing the stator flux linkage, o is the stator flux angular frequency, osl is the slip frequency and or ¼ Pom/2 is the rotor electrical frequency. The current and speed controllers in Fig. 1 are implemented according to Eq. (11) and Eq. (12) which are the d-axis and q-axis current-controller equations including correction terms. Eq. (13) represents the speed controller equation.
Fig. 8. Matrix converter input current and motor speed variations.
Fig. 9. Controlled rotor voltage and motor speed variations in subsynchronous region.
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The correction terms are given as: dI msd dt ð1 sÞLr osl I msd
U rdcor ¼ sLr osl I rq ð1 sÞLr U rqcor ¼ sLr osl I rd
ð15Þ
5. Simulation results Complete Simulink model of the drive system is given in Fig. 6. Simulation results have been obtained for subsynchronous and supersynchronous operating conditions. The switching frequency of the matrix converter was chosen 5 kHz. First, for subsynchronous
Fig. 10. d–q currents of the rotor in subsynchronous region.
Fig. 11. Rotor phase current and voltage waveforms in steady-state: (a) n ¼ 500 rpm (b) n ¼ 1000 rpm.
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operation mode the motor was accelerated from standstill to 500 rpm where the steadystate operation is achieved and then 1000 rpm of reference speed command was given at the instant of 1 s. The machine was loaded with 10 N m. The corresponding simulation results of stator power (Ps), rotor power (Pr), mechanical power (Pm) and net power (Pn ¼ Ps+Pr) are shown in Fig. 7. The slip energy is transferred from the rotor to the utility through the matrix converter. Therefore, under this operating condition the total power received from the supply was reduced and resulted with the net power, Pn as shown in Fig. 7. For the same operating conditions, the simulation results for input current of the matrix converter, controlled rotor voltage and motor speed are given in Fig. 8 and Fig. 9, respectively. Decrease in the slip frequency causes a reduction in the slip energy returned to the utility. This is illustrated in Fig. 8 as the input current amplitude of the matrix
Fig. 12. Matrix converter input current and voltage waveforms in steady-state: (a) n ¼ 500 rpm (b) n ¼ 1000 rpm.
Fig. 13. Stator, rotor, mechanical and net power results of WRIM at 5 N m constant load torque operating in both subsynchronous and supersynchronous regions.
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converter decreases with the increase of the motor speed. Corresponding results for d–q currents of the rotor are given in Fig. 10. Fig. 11 illustrates the rotor current and applied rotor voltage. As can be seen they are in opposite phase and this is the requirement for slip energy recovery drives. Fig. 11(a) and (b) show the simulation results for 500 and 1000 rpm, respectively, in steady-state. Fig. 12(a) and (b) show the input current and voltage waveforms of the matrix converter. Here, it is obvious that the converter and control strategy perform two functions; transferring the slip energy from the rotor into the mains and applying the required rotor voltage corresponding to the reference speed. Similar results have been obtained at 5 N m load torque to demonstrate the machine’s behaviour in supersynchronous operation mode. Results given in Fig. 13 through Fig. 17 demonstrate the steady-state operation following acceleration of the machine from standstill to 1750 rpm. Notice that transition between the subsynchronous and supersynchronous
Fig. 14. Rotor phase current and motor speed variations in both operating regions.
Fig. 15. Matrix converter input current and motor speed variations in both operating regions.
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regions occurs at 1500 rpm. In Fig. 13, the instantaneous motor power variations are given for both subsynchronous and supersynchronous regions. As can be seen from the figure, the rotor power, Pr is negative in subsynchronous region which approximately corresponds to the interval between 0 and 0.85 s. Then, the rotor power reverses at instant t ¼ 0.85 s which corresponds to the transition from subsynchronous to supersynchronous region. This means that rotor is now receiving power from the supply through the matrix converter. The corresponding rotor current, input current of the matrix converter and motor speed variations are shown in Figs. 14 and 15. Note that the input current of the matrix converter in Fig. 15 is zero at the transition instant between the regions. Zoomed view of this region is also given in the figure. The controlled rotor voltage, torque and motor speed variations are shown in Figs. 16 and 17. Rotor voltage and current, and input current and phase voltage of the matrix converter are given in Fig. 18 and Fig. 19. As seen from the figures the currents are in
Fig. 16. Controlled rotor voltage and motor speed variations in both operating regions.
Fig. 17. Motor torque and speed variations in both operating regions.
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Fig. 18. Controlled rotor voltage and rotor current results in transition interval.
Fig. 19. Simulation results for the matrix converter input current and phase voltage in transition interval.
opposite phase with the voltages in the subsynchronous region where the rotor power is negative, and they are in phase at supersynchronous region. It has been shown that the motor requires energy both from the stator and rotor at supersynchronous region. In subsynchronous region, the stator withdraws power from the grid whilst the rotor feeds the supply via the converter. This is proven by input waveforms of the matrix converter given in Fig. 19. 6. Conclusions The rotor-side field oriented control of wound-rotor induction motor using the slip energy recovery principle has been modelled and simulated in Matlab/Simulink. In the drive system, a matrix converter has been used to transfer the slip energy from the rotor into the mains in subsynchronous region, and to supply the rotor in supersynchronous region. It has been shown that the use of the matrix converter in the drive system has the
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advantages of single stage power conversion, operation in both subsynchronous and supersynchronous speed regions, sinusoidal voltage and current waveforms and simpler control scheme than other converters used instead. The simulation results indicate that the matrix converter drive system operates efficiently at subsynchronous speeds where the slip power is transferred from rotor windings to the mains through the matrix converter with sinusoidal currents and voltages. Simulation results have also shown that the system allows the machine to operate at supersynchronous speeds, as well. Appendix A. Matrix converter algorithm A simplified version of the Venturini algorithm is defined in terms of the three-phase input and output voltages at each sampling instant and is convenient for closed loop operations. For the real time implementation of the proposed modulation algorithm, it is required to measure any two of three input line-to-line voltages. Then, Vim and oit are calculated as: 4 V 2im ¼ ðv2AB þ v2BC þ vAB vBC Þ 9 vBC oi t ¼ arctan pffiffiffi 3ðð2=3ÞvAB þ ð1=3ÞvBC Þ
(A.1) ! (A.2)
where vAB and vBC are the instantaneous input line voltages. The target output peak voltage and the output position are calculated as: 2 V 2om ¼ ðv2a þ v2b þ v2c Þ 3 vb vc oo t ¼ arctan pffiffiffi 3v a
(A.3) (A.4)
where va, vb and vc are the target phase output voltages. Alternatively, in a closed loop system (for example, a field oriented controlled drive), the voltage magnitude and angle may be direct outputs of the control loop. Then, the voltage ratio is calculated as: sffiffiffiffiffiffiffiffiffi V 2om q¼ (A.5) V 2im where q is the desired voltage ratio, Vim is the peak input voltage. Triple harmonic terms are found as follows: 2 q sinðoi tÞ sinð3oi tÞ 9 qm 2 q 2p ¼ sin oi t sinð3oi tÞ 9 qm 3 qffiffiffiffiffiffiffiffiffi 1 1 1 ¼ V 2om cosð3oo tÞ cosð3oi tÞ 6 4 qm
K 31 ¼
(A.6)
K 32
(A.7)
K 33
(A.8)
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where qm is the maximum voltage ratio (0.866). Then, the three modulation functions for output phase, a are given as: 1 2 2 1 v v ðv þ k Þ þ M Aa ¼ þ k31 þ (A.9) a 33 AB BC 3 3 3 3V 2im M Ba
1 2 1 1 ¼ þ k32 þ ðva þ k33 Þ vBC vAB 3 3 3 3V 2im
M Ca ¼ 1 ðM Aa þ M Ba Þ
(A.10) (A.11)
The modulation functions for the other two output phases, b and c are obtained by replacing va with vb and vc, respectively, in Eqs. (A.9) and (A.10). Note that the modulation functions have third harmonic components added to them at the input and output frequencies to produce output voltage, vo. This is a requirement to get the maximum possible voltage ratio [7]. It should be noted that in Eq. (A.3) there is no requirement for the target outputs to be sinusoidal. In general, three-phase output voltages and input currents can be defined in terms of the modulation functions in matrix form as: voph ¼ Mviph 32 3 va M Aa M Ba M Ca vA 6v 7 6M 76 v 7 M M Bb Cb 54 B 5 4 b 5 ¼ 4 Ab M Ac M Bc M Cc vc vC
(A.12)
iiph ¼ M T ioph 32 3 iA M Aa M Ab M Ac ia 6i 7 6M 7 6 7 4 B 5 ¼ 4 Ba M Bb M Bc 54 ib 5 iC M Ca M Cb M Cc ic
(A.13)
2
2
3
3
2
2
where the superscript T denotes a transpose and M is the instantaneous input-phase to output-phase transfer matrix of the three-phase matrix converter. viph and voph are the input and output phase voltage vectors, and iiph and ioph represent the input and output phase current vectors. Alternatively, from Eqs. (A.12) and (A.13) the output-line voltages and input-line currents can be expressed as: voLine ¼ mviLine 32 3 vab mAb mBb mCb vAB 6v 7 6m 76 7 4 bc 5 ¼ 4 Ac mBc mCc 54 vBC 5 vca mAa mBa mCa vCA 2
3
2
(A.14)
and i ¼ mT ioLine 2iLine 32 3 iAB mAb mAc mAa iab 6i 7 6m 7 6 7 4 BC 5 ¼ 4 Bb mBc mBa 54 ibc 5 2
3
iCA
mCb
mCc
mCa
ica
(A.15)
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where mAb ¼ 13 ðM Aa M Ab Þ 13 ðM Ba M Bb Þ mBb ¼ 13 ðM Ba M Bb Þ 13 ðM Ca M Cb Þ mCb ¼ 13 ðM Ca M Cb Þ 13 ðM Aa M Ab Þ mAc ¼ 13 ðM Ab M Ac Þ 13 ðM Bb M Bc Þ mBc ¼ 13 ðM Bb M Bc Þ 13 ðM Cb M Cc Þ
(A.16)
mCc ¼ 13 ðM Cb M Cc Þ 13 ðM Ab M Ac Þ mAa ¼ 13 ðM Ac M Aa Þ 13 ðM Bc M Ba Þ mBa ¼ 13 ðM Bc M Ba Þ 13 ðM Cc M Ca Þ mCa ¼ 13 ðM Cc M Ca Þ 13 ðM Ac M Aa Þ Appendix B The wound-rotor induction motor rated values and parameters: 380 V, 1500 rpm, with 10 N m maximum torque. Rotor inertia: 0.05 kg m2, pole numbers: 4. Stator and rotor resistances: 2.33 and 2.55 O, respectively. Stator and rotor self-inductances: 0.213 and 0.22 H, respectively. Mutual inductance: 0.2 H. References [1] J.M.D. Murphy, F.G. Turnbull, Power Electronic Control of AC Motors, Pergamon Press, 1988. [2] I. C - adırcı, M. Ermis-, Double-output induction generator operating at subsynchronous and supersynchronous speeds: steady-state performance optimisation and wind-energy recovery, IEE Proc. B, Electr. Power Appl. 139 (5) (1992) 429–442. [3] R. Pena, J.C. Clare, G.M. Asher, A doubly fed induction generator using back-to-back PWM converter supplying an isolated load from variable speed wind turbine, IEE Proc., Electr. Power Appl. 143 (5) (1996) 380–387. [4] H. Keyuan, H. Yikang, Investigation of a matrix converter-excited brushless doubly-fed machine windpower generation system, Power Electronic and Drive System, PEDS’03, vol. 1, 17–20 November, 5th International Conference on PEDS, 2003, pp. 743–748. [5] H. Altun, Application of a matrix converter in a slip energy recovery drive system, Int. J. Eng. Modell. 18 (3–4) (2005) 69–80. [6] M. Venturini, A new sine wave in sine wave out conversion technique which eliminates reactive elements, in: Proceedings of the Powercon 7, San Diego, CA, 1980, pp. E3-1–E3-15. [7] A. Alesina, M. Venturini, Solid-state power conversion: a Fourier analysis approach to generalized transformer synthesis, Proc. IEEE Trans. Circuit Syst. CAS-28 (4) (1981) 319–330. [8] S. Su¨nter, J.C. Clare, A true four quadrant matrix converter induction motor drive with servo performance, IEEE-PESC’96, May 1996, pp. 146–151. [9] H. Altun, S. Su¨nter, Matrix converter induction motor drive: modeling, simulation and control, Electr. Eng. 86 (1) (2003) 25–33. [10] MATLABs for Microsoft Windows, The Math Works Inc., 1999. [11] P.C. Krause, Analysis of Electrical Machinery, McGraw-Hill, New York, 1986. [12] R. Datta, V.T. Ranganathan, A simple position-sensorless algorithm for rotor-side field-oriented control of wound-rotor induction machine, IEEE Trans. Ind. Electron. 48 (4) (2001) 786–793.