International Journal on Electrical Engineering and Informatics - Volume 7, Number 3, September 2015
Direct Torque Control of Doubly Fed Induction Machine
Fraid Boumaraf, M.L. Bendaas, Rachid Abdessemed, and Sebti Belkacem
LEB- Research Laboratory, Department of Electrical Engineering, University of Batna – Algeria [email protected]
Abstract: The present paper proposes a novel Doubly Fed Induction Machine (DFIM) control strategy using Direct Torque Control (DTC) linked with two Switching Tables in order to control electromagnetic torque of DFIM via stator and rotor flux vector. The proposed scheme is described clearly and simulation results are reported to demonstrate its effectiveness. The entire control scheme is implemented with Matlab/Simulink.
Keywords: Dual direct torque control, doubly fed induction machine, switching tables.
1. Introduction Due to its excellent speed controllability, reduced converter size, high performance and relatively low cost compared to other machines [2]. Doubly-fed induction machines have been proposed in the literature, among other industrial applications as motor in high power applications such as traction, marine propulsion or as generator in wind energy conversion systems like wind turbine, or pumped storage systems. Several methods of control are used to control the doubly fed induction machine among which the vector control or field orientation control that allows a decoupling between the torque and the flux, in order to obtain an independent control of torque and the flux like DC motors [3]. Therefore, decoupling the control scheme is required by compensation of the coupling effect between q- axis and d-axis current dynamics. It is well known that vector control needs quite complicated to on line coordinate transforms to decouple the interaction between flux control and torque control in order to provide a fast torque control. In recent years an innovative control method, called direct torque control has gained the attraction of researchers. Direct torque control (DTC) strategy was introduced by Takahashi to give a fast and good dynamic performance and can be considered as an alternative to the field oriented control (FOC) strategy [4]. Therefore, in recent years the industrial application areas of the high performance AC drives based on DTC technique have gradually increased due to the following advantages over the field oriented control technique, such as Excellent dynamic performance, precise and quick control of stator flux and electromagnetic torque, absence of co-ordinate transformation, which reduce the complexity of algorithms involved in FOC, robust against machine parameters variations and no current control loop. In this study a new Dual-Direct Torque Control scheme is developed with flux model of DFIM. Two Switching Tables (ST) linked to VSI are defined for stator and rotor flux vector control. We propose separate control of stator and rotor flux. In fact, in order to applied DTC strategy to this configuration, we define a first switching table to control the stator flux vector, and a second switching table to control the rotor flux vector. The next part of the control strategy makes possible to control interaction between both flux vectors. Consequently, we are able to control the electromagnetic torque and to regulate the mechanical speed [3]. The performance of such a scheme depends on the error band set between the desired and measured stator and rotor flux values. In this control scheme, the stator inverter switching frequency is changed according to the hysteresis bandwidth of stator flux and stator flux angular position, and the rotor inverter switching frequency is changed according to the hysteresis bandwidth of rotor flux and rotor flux angular position.
th st Received: November 10 , 2013. Accepted: September 21 , 2015 DOI: 10.15676/ijeei.2015.7.3.15
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2. Mathematical model of DFIM The model of three-phase doubly fed induction machine in the laboratory frame (α,β) is given by the following equations (1): d V R I φ sα s sα dt sα d V R I φ (1) sβ s sβ dt sβ d Vrα R rIrα φrα ωrφrβ dt d V R I φ ω φ rβ r rβ dt rβ r rα φ L I μI ,φ L I μI sα s sα rα sβ s sβ rβ (2) φ L I μI ,φ L I μI rα r rα sα rβ r rβ sβ
Sβ Rβ
I I Sβ rβ Irα ω R α
θ Sα I Sα Figure 1. Two phase reference frame
And the electromagnetic torque of doubly fed induction machine can be expressed as: 3 Np.μ T .φ φ (3) e 2 σ.L .L s r s r
Where Te is the electromagnetic torque, Np is the number of Pole pairs, Ls ,Lr are the stator and rotor self inductances, μ is the mutual inductance and φs ,φr are the stator and μ2 rotor flux space vectors and σ 1 is the leakage coefficient. We can use: LsLr Te K φs . φr sinγ (4)
is the angle between stator and rotor flux as shown in Fig1. This angle is referred 3N μ K p 2σσ L as torque angle. The constant K is defined as below: s r
Y
φ r φ s γ X C e
Z Figure 2. Flux Vector Diagram of DFIM
542 Direct Torque Control of Doubly Fed Induction Machine
Figure 1 shows this reference frame where Isα, Isβ are the stator currents, and Irα, Irβ the rotor current. We can express the two-phase equations describing the electrical behavior as below [3]:
φs L μ(θ) α,β s (5) T φ μ(θ) L rα,β r Where: 4.π 2.π cos(θ) cos(θ+ ) cos(θ+ ) 33 2.π 4.π (6) μ θ =μ . cos(θ+ ) cos(θ) cos(θ+ ) 0 33 4.π 2.π cos(θ+ ) cos(θ+ ) cos(θ) 33
We express the Laplace operator as s and obtain some disturbance terms noted
Psα ,Psβ ,Prα ,Prβ defined as follows: μ P (φ sinθ φ cosθ) sα rβ rα σ.Ts .Lr μ P (φ sinθ φ cosθ) (7) sβ rα rβ σ.Ts .Lr μ P (φ sinθ φ cosθ) rα sβ sα σ.Tr .Ls μ P (φ sinθ φ cosθ) rβ sα sβ σ.Tr .Ls
Where: Ls Lr Ts ,Tr Rs R r The stator and rotor transmittances terms are defined as:
s σ.Ts Tφ (s) 1 σ.Ts.s (8)
r σ.Ts Tφ (s) 1 σ.Tr.s It can be seen from (5), (7) and (8) that the DFIM in flux mod can be represented as shown in figure 3.
Psα
Ts (s) Vsα φ φs Psβ
Vsβ φsβ Prα
Vrα r φ Tφ (s) r
Prβ
V rβ φr β Figure 3. Bloc diagram of DFIM flux model.
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The stator and rotor flux vectors φ s, , are obtained by integrating the motor emf space vector, measured stator and rotor currents, stator and rotor resistances. t φ (s) (V R .I )dt φ s s s s s0 0 (9) t φ (s) (V R .I )dt φ r r r r r0 0 V >>R .I During the switching interval, 0,Te we have: s s Et s V r >>R r .I r. We can express:
φs (t) φs0 Vs.Te (10) φr (t) φr0 Vr .Te We adopt a “standard” assumption for the considered frequencies. It consists in neglecting the resistive effect in the windings compared with the inductive effect. We can observe that this assumption is especially valid for high power machines. Consequently, we can express [3]:
σTs.S 1,for :s (11) σTr.S 1,for :s
s σ.Ts 1 Tφ (s) , when :s 1 σ.Ts.s s So: (12) r σ.Ts 1 Tφ (s) , when :s 1 σ.Tr .s s
A second assumption is used. It consists in neglecting the coupling terms Psα ,Psβ ,Prα ,Prβ This can be done because the coupling terms are a low value in relation to the nominal values of the voltages level Vsα ,Vsβ ,Vrα ,Vrβ If we use the sign n for the nominal value of the considered term, this assumption can be expressed as below [3]:
Psα Vsα ,Psβ Vsβ (13) Prα Vrα ,Prβ Vrβ According to the equation (12), that the flux expression as the voltage integrals, and by using the two lusts assumption, we can formulate the DFIM global model as shown in Figure 4.
Us1 Us2 Vs 1 φs Stator s Us3 VSI Te Te φs φr
Ur1 φ Ur2 Vr 1 r Rotor s Ur3 VSI Figure 4. Block scheme of VSI and DFIM.
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3. Dual direct torque control strategy The basic idea of DTC depends on the error band set between the desired and measured torque and flux values, the inverter switching frequency is changed according to the hysteresis bandwidth of flux and torque controllers and the variation of speed and motor parameters. In this paper; we propose separate control of stator and rotor flux. In fact, in order to applied dual DTC strategy to this configuration, we define a first switching table to control the stator flux vector with his angular position, and a second switching table to control the rotor flux vector with his angular position. The next part of the control strategy makes possible to control interaction between both flux vectors. Consequently, we are able to control the electromagnetic torque and to regulate the mechanical speed [3].
4. Dual DTC applied to the DFIM From equation (4) it is clear that the DFIM torque can be varied by changing the rotor or stator flux vectors. The dual DTC uses the hysteresis band to directly control the stator flux and his angular position ρs and rotor flux with his angular position ρr of the DFIM. When the stator or rotor flux falls out-side the hysteresis band, the inverter switching stator or rotor is changed so that the flux takes an optimal path toward. So VSI outputs (stator and rotor) can be deduced from two estimated and two required values of stator and rotor flux.
A. Vectors flux control
The equation (10) can be easy transformed to: Δφ φ φ (0) V .T s s s s e (14) Δφr φr φr (0) Vr .Te So: φ φ T .V s(tn1) s(tn ) e s(tn ) (15) φ φ T .V r(t n1) r(t n ) e r(t n )
The voltage vector application time Te equal to sampling time).Consequently, Vs ,Vr remain constant during the interval Tn ,Tn1 . Where: Tn1 Tn Te φn1 φn T .Vn s s e s (16) n1 n n φr φr Te.Vr
Sβ Rβ Component n1 φs for torque n φr n n Tes .V Ter .V Compone nt for flux n1 n φr R φs
S Figure 5. Stator and rotor flux vector deviation.
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By neglecting the stator and rotor resistances, (10) implies that the ends of the stator and rotor flux vectors will moves in the direction of the applied voltage vectors as shown in this figure. The appropriate voltage vector on VSI outputs can be deduced from two estimated and two required values of stator and rotor flux. To select the voltage vectors for controlling the amplitudes of the stator and rotor flux linkage, the voltage vectors plane is divided into six regions, as shown in Figure.5.
T .V e (s,r)3 Te.V(s,r)2
T .V Te.V(s,r)4 e (s,r)1 φ(s,r) Te.V(s,r)5 Te.V(s,r)6
(s,r)
Figure 6. Applicable voltage vectors for stator and rotor flux vectors control.
In each region, two adjacent voltage vectors, which give the minimum switching frequency, are selected to increase or decrease the flux amplitudes. If Vs1,r1 is applied, the magnitude of
φs,r increase. Where as the angular position ρs,r of decrease. When a specific voltage vector is applied, the evolution of and the magnitude of can differ according to the initial value. Consequently, if is in the same sector, use of identical voltage vector leads to a similar phase and magnitude evolution of the flux vector. We manage the rotor flux vector in the same way. Thus, the voltage vector to apply depends on: - The sector number (according to ), - The required flux angular position, - The required flux magnitude evolution.
β
3 2 φ s,r α 4 ρs,r 1
V ,V 5 6 07
Figure 7. Sector definition in (α,β) reference frame.
546 Direct Torque Control of Doubly Fed Induction Machine
For instance, vectors are selected to increase and decrease the amplitude of flux vectors and ours angular position as:
if V(s,r)i 1 is selected then φs,r increase and ρs,r increase; if V(s,r)i 1 is selected then increase and decrease; if V(s,r)i 2 is selected then decrease and increase;
if V(s,r)i 2 is selected then φs,r decrease and decrease.
B. Stator and rotor flux estimation The magnitude of stator and rotor flux, which can be estimated as following t φ (V R .I )dt s s s s (17) 0 t φ (V R .I )dt r r r r 0
The stator and rotor flux linkage phasors are given by: 2 2 2 2 φs φsα φsβ , φr φrα φrβ (18)
The stator and rotor flux linkage phasors positions are:
1 φsα 1 φrα ρs tan ,ρr tan (19) φsβ φrβ
C. Flux corrector In this dual DTC we are needed to use four hysteresis comparators: two stator hysteresis comparators in order to control the stator flux magnitude φs and his angular position .The outputs of these comparators are connected to stator switching table; and two rotor hysteresis comparators in order to control the rotor flux magnitude φr and his angular position ρr . The outputs of these comparators are connected to rotor switching table. The input of these for comparators is the difference between reference values and estimated values of flux magnitudes and angular position; flux magnitude reference values φsreff and φrreff are constant and equal to their nominal values. For the stator flux reference ρsreff , the flux position value depends only on measured mechanical speed. For the rotor flux reference ρrreff the flux position value depends on torque angle γ , rotor position θ and stator flux position reference as shown in (10). The outputs of the comparators with the number of sector at which the stator and rotor flux space vector is located ( ) are fed to a switching tables to select an appropriate inverter voltage vector. The selected voltage vector will be applied to the DFIM at the end of the sample time, as are shown in (8)
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V4 V3
3 2
V2 V5 4 5 6
V1 V6
Figure 8. Forming of the (stator and rotor) flux trajectory by appropriate voltage vectors selection.
Δφs,r
φ(s,r)reff
1
φ φ 0 (s,r)reff (s,r) Δφ Δφ s,r s,r Figure 9. The hysteresis controllers.
D. Elaboration of the switching table
Figure 10. Bloc diagram of the dual DTC of the DFIM
For the stator and rotor flux vector laying in sector 1 (Figure 7) in order to increase its magnitude the voltage vectors V2 ,V6 can be selected. Conversely, a decrease can be obtained
548 Direct Torque Control of Doubly Fed Induction Machine
by selecting V3,V5 . For the stator and rotor flux angular position ρs,r is used therefore, to increase it’s the voltage vectors V2 ,V3 can be selected and to decrease V6 ,V5 . The above considerations allow construction of the selection table as:
Sector number Torque Flux evolution 1 2 3 4 5 6
Te φs,r ρ Voltage vector V2 V3 V4 V5 V6 V1 V6 V1 V2 V3 V4 V5 V3 V4 V5 V6 V1 V2 V5 V6 V1 V2 V3 V4 Switching table
The overall structure of the proposed control is shown in figure10.
5. Simulation results To verify the effectiveness of the proposed dual DTC of the doubly fed induction machine; the simulation are performed by using the MATLAB/Simulink. In the performed simulation the speed, torque, stator and rotor flux and current response has been analyzed in transitoir and stady stat.
A. Speed reversal 150
100
50
0
-50 Speed(Rd/s) -100
-150 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(s) 100
50
0
Torque(N.m) -50
-100 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S)
549 Fraid Boumaraf, et al.
2
1.5
s (web)
r 1
, ,
s
r 0.5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 1.5
1
0.5
(Web) s r
0
r
,
-0.5
s -1
-1.5 -1.5 -1 -0.5 0 0.5 1 1.5 , (Web) s r 50 40
10
(A)
30 s 0 , I ,
-10
s I
(A) 20
s 1.4 1.6 1.8 2 Time(S)
, I , 10
s I 0 -10 -20 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 50
40 10
(A)
r 0
30 ,I
r -10 I
(A) 20
1.4 1.6 1.8 2
r Time
,I 10
r I 0 -10 -20 0 0.5 1 1.5 2 2.5 3 3.5 4 Time Figure 11. Simulation results for speed reversal
The DFIM reference speed is changed from 100 rad/s to -100 rad/s at 1s and then again, speed is changed from -100rd/s to 20 rd/s at 2 s and then , speed is set to -20 rad/s at 3 s . without any change in parameters during the operating time. The performance of the proposed controller for such kind of speed reference is shown in Figure11. Plots the reference speed and, actual DFIM speed with respect to time. It is observed that the actual DFIM speed follow the reference with good accuracy.
550 Direct Torque Control of Doubly Fed Induction Machine
B. Variation of the load torques 80
60
40
Torque(N.m) 20
0
0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 120
100
80 load torque load torque 60 applied removed
40 Speed(Rd/s) 20
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 2
1.5 s
(Web) 1
r
s r 0.5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 40
10
(A) s 0
30 I
s I -10
20 1 1.2 1.4 1.6 1.8 2
Time(S)
(A)
s 10
I
s I 0
-10
-20 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) Figure 12. Simulation results under load torque change
Figure 12 depicts the simulation results after the introduction of load torque of 8 Nm between 1s and 2s after a leadless starting. We can see the insensibility of the control algorithm to load torque variation and the stator and rotor flux responses are less affected by this perturbation.
551 Fraid Boumaraf, et al.
C. Variation in the stator resistance
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4 Reference of stator resistance stator of Reference Time(S) 120
100
80
60
40 Speed(Rd/s) 20
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 2
1.5 s
(Web) 1 r
, , r s
0.5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) Figure 13. Simulation results under stator resistance change
These tests investigate the influence of the electrical parameters change on the drive performance. Figure13 depicts the drive performance for brusque changes in the stator resistance. it can be seen that the impact of the electrical parameters change on the drive performance is more important. However, those results shown also that the drive robustness and rejection of the perturbations is significantly enhanced.
D. Variation in the rotor resistanc
2.5
2
1.5
1
0.5
0 Reference of rotor resistance rotor of Reference 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S)
552 Direct Torque Control of Doubly Fed Induction Machine
120
100
80
60
40 Speed(Rd/s) 20
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 2
1.5
s
1
(Web)
r
s r 0.5
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) Figure 14. Simulation results under rotor resistance change
Figure 14 depicts the simulation results after the introduction of the rotor resistance change between 1s and 3s.
E. Variation in the inertia coefficient Figure15 shows the drive dynamic under different values of inertia with constant speed reference. It is clear that the speed tracking is little affected by those changes. 120
100 J=0.5*Jn 80 J=Jn 60 J=2*Jn
40 Speed(Rd/s) 20
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) 1.4
1.2 s 1
0.8 (Web) r
0.6 r
, s 0.4
0.2
0 0 0.5 1 1.5 2 2.5 3 3.5 4 Time(S) Figure 15. Simulation results under different inertia values
6. Conclusion A novel doubly Fed Induction Machine (DFIM) control strategy using Dual direct torque control has been presented in this paper. Two Voltage Source Inverters (VSI) feed the stator
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and rotor windings, and Two Switching Tables (ST) linked to VSI are defined for stator and rotor flux vector control in order to control electromagnetic torque of DFIM via stator and rotor flux vector. The complete dynamic model of the dual DTC system is developed and simulated by using MATLAB-SIMULINK. The correct flux vector control behavior, torque and speed tracking performances shown in the simulation results confirm the fast and good response of the proposed drive system and their robust to the variations of motor mechanical and electrical parameters variations. The major disadvantage of dual DTC control is the steady state ripples in torque and flux. To overcome this problem we are going to introduce the intelligent techniques.
7. References [1]. W. Cheng, L. Xu “Torque and Reactive Power Control of a Doubly-Fed Induction Machine by Position Sensorless Scheme”, 0-7803-1993-1194 $4.00 0 1994 IEEE. [2]. A. Farrokh Payam “An Adaptive Backstepping Controller for Doubly-Fed Induction Machine Drives”,0-7803-9772-X/06/$20.00 ©2006 IEEE. [3]. F. Bonnet, P Vidal and M pietrzk-david, “Dual Direct Torque control Of Doubly fed Induction Machine”, IEEE Trans Industrial Electronices, vol, 54, No, 5, October 2007. [4]. B. Robyns, B. François, P. Degobert et J. P. Hautier, “Commande Vectorielle de la Machine Asynchrone: Désensibilisation et Optimisation par la Logique floue”, Editions Technip, Paris, 2007. [5]. J. Soltani, A. Farrokh payam, M.A. Abbasian, “Speed Sensorless Sliding-Mode controller For Doubly-Fed Induction Machine Drives Adaptive Backstepping Observers", 1-4244- 0726-5/06/20.00;2006, IEEE . [6]. F. Zidani, D. Diallo, M. E. H. Benbouzid and R. Na¨ıt-Sa¨ıd, “Direct Torque Control of Induction Motor with Fuzzy Stator Resistance Adaptation”, IEEE Transactions on Energy Conversion, VOL. 21, NO. 2, JUNE 2006 [7]. N.R.N. Idris, C.L. Toh and M.E. Elbuluk, “A New Torque and Flux Controller for Direct Torque Control of Induction Machines”, IEEE Transactions on Industrial Applications, Vol. 42, No. 6, pp. 1358 – 1366, November- December 2006. [8]. S. Benaicha, R. Nait Said, F. Zidani and M.S. Nait. Said “Direct Torque with Fuzzy Logic Torque Ripple Reduction based Stator Flux Vector Control”, Mediamira Science PuPlisher, ACTA Electrotechnica, Vol. 50, N° 1, pp. 31 - 37, 2009. [9]. R.Toufouti, S Meziane, H Benalla “direct torque control of induction motor using fuzzy lgic, ”ACSE journal,Vol.6, issue 2, june 2006. [10]. S.R.Kaper, V.P. Dhote “fuzzy logic based direct torque control of induction motor”, IJESAT, VOL 2, Issue 942, 2012. [11]. J. Breckling, Ed. “The Analysis of Directional Time Series: Applications to Wind Speed and Direction, ser. Lecture Notes in Statistics”. Berlin, Germany: Springer, 1989, vol. 61. [12]. F. Bonnet, P. Vidal, and M. Pietrzak-David, “Adaptive variable structure control of a doubly fed induction machine”, Proc. ofInt. Conf. Pelincec, Warsaw, on CD (2005). [13]. Y. Kawabata, E. Ejiogu, and T. Kawabata, “Vector controlled double inverter fed wound rotor induction motor suitable for high power drives”, IEEE Trans. Industry Appl. 35 (5), 1058–1066 (1999). [14]. G.S. Buja and M.P. Ka´zmierkowski, “Direct torque control of pwm inverter-fed ac motor – a survey,” IEEE Trans. on Industrial Electronics 51 (4), (2004). [15]. P.E. Vidal and M. Pietrzak-David, “Stator flux oriented control of a doubly fed induction machine”, Proc. EPE, Toulouse, on CD (2003). [16]. Hong-Hee Lee, H.M.N., Tae-Won Chun and Won-Ho Choi. “Implementation of Direct Torque Control Method Using Matrix Converter Fed Induction Motor.” In IEEE, 2007 [17]. Der-Fa Chen, C.-W.L., Kai-Chao Yao. “Direct Torque Control for a Matrix Converter Based on Induction Motor Drive Systems” in IEEE 2007
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Fraid Boumaraf received the Magisterium Degree in Electrical Engineering from Batna University in 2009. and the Ph.D degree in 2014 He is member in the Electrical Engineering Laboratory (LEB). His research interests, Fuzzy logic control, Wind energy systems and direct torque control.
Rachid Abdessemed was born in Batna, Algeria in 1951. He received the M.Sc. and Ph.D. degrees in Electrical Engineering from Kiev Polytechnic Institute, Kiev, Ukraine, in 1978 and 1982, respectively. He has been working for more than 28 years with the Department of Electrical Engineering, University of Batna, as a Professor. Currently, he is the director of the Electrical Engineering Laboratory (LEB). His current area of research includes design and control of doubly feed induction machines, reliability, magnetic bearing, adaptive control and renewable energy.
Sebti Belkacem was born in Batna, Algeria in 1976; He received the Master Degree in Electrical Engineering from Batna University in 2005, and Ph.D. degrees in Electrical Engineering in 2011. He is member in the Electrical Engineering Laboratory (LEB). His research interests, adaptive control, nonlinear control and direct torque control.
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