Comparative Performance Study between DTC_C and DTNC Multi-level Inverter Fed DSIM
Abstract — A comparative performance study between the classical direct torque control (DTC_C) and that of a direct torque control improved by applying the technique of artificial intelligence based on the neural network (DTNC) is proposed in this paper. The command is applied to a double-stator induction machine (DSIM) fed by a multi-level inverter.
Simulation results of the speed control of the machine and the improvement of the torque and the flux by reducing the fluctuations are studied by illustrating the DTNC merits compared to the classical DTC_C.
Keywords- A double-Stator Induction Machine, Direct Torque Control, Neural Network, Multi-level Inverter.
I. INTRODUCTION
Given the high dynamic torque DTC structure obtained by different proposed algorithms. It is envisaged in this paper the application of these algorithms to control a double-stator machine which meets the need for high power applications.
Thus, a simplified model will be developed on which the control strategy will be assessed.
The technique of DTC introduced in 1985 by TAKAHASHI [1, 2] uses an attractive approach due to its effectiveness and implementation simplicity. Several studies have allowed a rigorous modeling of this approach [2, 3, 4].
Our work is focused on the use of a simple model of the DSIM. This double stator machine has several advantages such as robustness and reliability and meets the best performance criteria than the simple induction machine because it reduces the electromagnetic torque ripples and enhances the power factor [5].
This DTC technique allows calculating the control values which are the stator flux and the electromagnetic torque from measurements of stator currents without using mechanical sensors. The technique has outstanding dynamic performance as well as robustness against motor parameter variations. It seems particularly well suited to the artificial neural network application in terms of the ability of learning, the parallelism of operation, the speed of calculation and the generalization ability.
II. MODELISATION OF THE DSIM
The DSIM is not a simple system, consisting of nine differential equations whose coefficients are periodic functions of time. The PARK model simplifies solving these equations;
it consists in the development of a knowledge model reflecting the dynamic behavior of electrical and electromagnetic modes.
This model describes a system of nonlinear differential equations, admits several classes of state representation, which depend directly on the objectives of the control (torque, speed, position), the nature of the power source (voltage, current), the operating referential and finally the choice of state components (flux, stator current).
A. Model of DSIM in the Sub-space (α- β).
After the application of the transformation matrix to the stator variables and the Park transformation to the rotor variables, the final model of the machine is obtained in the reference related to the stator and is given by the following equations:
) i i
( 2P 1
i L i L
i L i L
j p i r 0
p i r V
s s s s em
r r m s r
m r s s
s
r r r r
r s s s s
(1)
r r
r
s s
s
r r r
s s s
s s s
j j ji i
i
ji i
i
jv v
v
(2) O.Benaouda1,2, A.Boutaghane1,A.Bendiabdellah 2,S.Chaouch2,3
2 Groupe Diagnostic, Laboratoire LDEE, Université des Sciences et de la Technologie d’Oran, ALGERIA
1Centre de recherche en technologies industrielles CRTI, Division DSTC, Alger, ALGERIA
3 Université de Batna , Département d’électrotechnique ,ALGERIA
[email protected] [email protected] [email protected] [email protected]
The Angle between the stator flux and the rotor flux
The state representation is to express the model of the machine as follows:
The control voltage is chosen as the current and the stator flux as the state variables.
Fig. 1. Model of DSIM in the α-β coordinate system
Where matrices A and B are given as:
With:
Note that the study of this motor is not easy because the harmonic effects are very important .The harmonics can be classified into several groups, depending on their orders and the angle γ between the two stators. For a standard machine with the harmonic group of the order k =12n±1, (n= 1, 2, 3 ...) and the group of harmonics of order k =6n±1, (n= 1, 3, 5 ...) have different equivalent circuits, only the first group which participates in the conversion of the electromechanical energy.
The arrangement of coils minimizes the harmonics enormously by increasing the coupling between the two stators and the sixth harmonic torque is removed [6][7].
III. DTC–DSIMSTRATEGY CONTROL
In its basic principle, the direct torque control is a method that is based on the switching tables of torque and stator flux hysteresis, on the minimization of the commutations of the inverter switches, on the torque/stator flux decoupling, on the control of UPS without the PWM generator, on the estimation of quantities in open loop in the referential connected to the stator and on the control without mechanical sensor.
A. Vector Model of a Six-phase Two-level Inverter
The block diagram of the six-phase inverter supplying the DSIM is shown by Fig.2. The switches of the higher half bridge are rated Sa1, Sb1, Sc1 for the stator1 and Sa2, Sb2, Sc2 for stator2. Let n1 and n2 be the neutral of the stator1 and stator2 respectively, and ‘o’ the neutral point of the source.
The phase voltages can be written as:
Fig.2. Schematic diagram of a six-phase inverter supplying the DSIM.
1 1
1 0 0 0
0 0
0 1 1 1
3 ) sin(5 3 ) sin(
) sin(
3) sin(2 3) sin(4 ) 0 sin(
3 ) cos(5 3 )
cos(
) cos(
3) cos(2 3) cos(4 ) 0 cos(
3) sin( 4 3) sin( 2 ) sin(
3) sin(4 3) sin(2 ) 0 sin(
3) cos( 4 3) cos( 2 ) cos(
3) cos(4 3) cos(2 ) 0 cos(
3
T6 1 1 (3)
:
DU CX Y
BU AX X
With
X state vector U input vector Y output vector
(4)
Vs1,Vs2,Vs1,Vs2
tU
s1, s2, s1, s2,is1,is2,is1,is2
tX
s
V1 s
V1
s
V2 s
V2
s
1
s
1
s
2
s
2
s
i1 s
i1 s
i2 s
i2
Model of DSIM Supplied by Voltage
Stator Reference
Cr
d c 0
h r h r Lh Lh
b a 0 h
r h r Lh Lh
0 d c Lh Lh h
r h r
0 b
a Lh Lh h r h r
r 0 0 0 0 0 0 0
0 r 0 0 0 0 0 0
0 0 r 0 0 0 0 0
0 0 0 r 0 0 0 0
A
' 1 r 2 r ' 1 2
2 r 1 r 2 1
' 1 2 '
1 r 2 r
2 1 2 r 1 r
2 s 2 s 2 s 1 s
(5)
' 1 2
2 1
' 1 2
2 1
Lh Lh
0 0
Lh Lh
0 0
0 0
Lh Lh
0 0
Lh Lh
1 0
0 0
0 1
0 0
0 0
1 0
0 0
0 1
B
(6)
r 2 m 2 2 s r 2 s r m 1 s r 1 s r
m.(l l ) ll ].[l .(l l ) ll ] l .l
l [
y
r
m l
l
L
y l l ) l l ( h l y ,
l l ) l l (
h lm r s1 r s2 '1 m r s1 r s1
1
)]
l l .(
r ) l l ( r [ h y ,
l
h2lm r 3 r s1 m s1 s1 m )]
l l .(
r ) l l ( r [
h4 r s2 m s2 r m
] h h h l r [ b ], h l r h h [
a 3 1 r m 2 r m 2 2 4 ] h l r h h [ d ], h h h l r [
c r m 1' 2 3 4 1' r m 2
1 on o 1 c 1 n 1 c 1 cs
1 on o 1 b 1 n 1 b 1 bs
1 on o 1 a 1 n 1 a 1 as
v v v v
v v v v
v v v v
3 on o 3 c 3 n 1 c 3 cs
2 on o 2 b 2 n 2 b 2 bs
2 on o 2 a 2 n 2 a 2 as
v v v v
v v v v
v v v v
(7)
Vdc
a1 a2 b1 b2 c1 c2
1
ias ias2 ibs1 ibs2 ics1 ics2
1
vas vas2 vbs1 vbs2 vcs1 vcs2
1 1 1bc
Na
2 2 2bc
Na
Assuming that both stator windings of the stator1 and stator2 are balanced, the phase voltages cannot contain zero sequence components as neutral are not connected. So we have:
It is deduced therefrom the inverter-MSDS connection matrix that gives the terminal voltages of the machine in terms of the output voltages of the inverter.
Vdc is the DC voltage to the input of the inverter.
B. Flux control strategy
The control structure which is employed in this paper consists of a DSIM powered separately by two two-level voltage inverters and an individual control of flux φs1 and φs2.The control is performed by applying the voltage vectors generated by each inverter. In the normal operation of the machine, the α-β components of φs2 are ahead as compared with those of φs1 by an angle of 30°, see Fig. 3.
The two stators are fed separately by two inverters which are controlled by the DTC technique by estimating the stator flux and the torque developed in the machine [8]. The modules
of the individual fluxes φs1 and φs2 are considered equal to half the modulus of the resulting flux φsres.
Fig. 4. General structure of the direct control of flux and torque of a DSIM
C. Selection of the Voltage Vector Vs
The choice of vector Vs depends on the position of ɵs in the reference frame (S), of the variation for the desired module of ɵs, of the desired change of the torque and of the direction of rotation. The evolution in space (S) is divided into twelve zones i, with i = [1...12], as shown in, Fig.5.
Fig. 5. Voltage vectors in a two-level inverter
The electromagnetic torque is calculated from the estimated flux and the currents measurement. The total torque developed by the DSIM can be determined by an algebraic sum as in the equation 16. In this method the stator flux are estimated by the same model previously described. Thus, the modules of these are given by [9]:
0 v v v , 0 v v
vas1 bs1 cs1 as1 bs1 cs1 (8)
1 on o 1 c 1 n 1 c 1 cs
1 on o 1 b 1 n 1 b 1 bs
1 on o 1 a 1 n 1 a 1 as
v v v v
v v v v
v v v v
(9)
cso o 2 b
o 2 a
o 1 c
o 1 b
o 1 a
2 cs
2 bs
2 as
1 cs
1 bs
1 as
v v v v v v
2 1 1 0 0 0
1 2 1 0 0 0
1 1 2 0 0 0
0 0 0 1 2 1
0 0 0 1 2 1
0 0 0 1 1 2
3 1
v v v v v v
(10)
] v ].[
C [ ] v
[ s ond (11)
] S S S S S S .[
v ] S .[
v ] v
[ ond dc dc a1 b1 c1 a2 b2 c2 (12)
axe axe A1 axe A2 axe
axe axe
Fig. 3. Description of the various fluxes.
representaon
2
1 Sres
2
1 s
1
s
2
s2
1
s
s
1
300 2
s
V1 100
V'1 100
V2 110
V'2
V3 110
V'3 010 010
V4 011
V'4 011
V5 001 V'5
001
V6 101
V'6 101
1
S
2
S
2 2 s 2
2 s 2
s 2
1 s 2
1 s 1
s ,
(13)
) i i
( P C
) i i
( P C
2 s 2 s 2 s 2 s 2
em
1 s 1 s 1 s 1 s 1
em
(14)
2 em 1 em
em C C
C (16)
1
s s2
ems1s2
1
ss2 vdc
S11
cflx2 ccpl cflx1
ccpl
DSIM O
N D 1
Look up tabble 1
S21
S41
S51
S61
commutation
I N V 1
I N V 2
Look up tabble 2
ccpl +
-
*em
em
+
- cflxl
1
*s
2
s
+
- cflx2
2
*s
1
s
Estimation of flux, torque and position Vsα1 Vsα2 Vsβ2 Vsβ1 isα1 isα2 isβ1 isβ2
S31
(15)
IV. DTRECT TORQUE CONTROL OF THE DSIM Fig. 6 depicts the general structure of the DTC of the DSIM. In this method the stator flux and the electromagnetic torque are controlled in the subspace (α-β). This technique is an extension of the classical DTC (hexagon of six vectors) using the twelve voltage vectors making the exterior polygon.
In total there are 49 different voltage vectors that are generated by the six-phase voltage inverter (4 zero vectors, 24 modes generating the 12 vectors of the second polygon).
Figure. 6. Synoptic diagram of the direct flux and torque control of a DSIM.
V. DTCBASED ON NEUTRAL NETWORK (DTNC) A. Artificial neural network principle
Neural networks are a set of nonlinear functions to build, by learning, a broad family of models and nonlinear Correctors [10]. The formal neuron model presented here by McCulloch and Pitts, is a very simple mathematical model derived from an analysis of the biological reality. It starts with a simple summation of the signals reaching the neuron (these signals are commonly called the inputs of the neuron) see Fig.7 [11]. From a mathematical point of view, the artificial neural can be represented as follows by Figure 7.
Fig. 7. Neural Network Multilayer Structure.
In this neural network, 12 neurons are used in the hidden layer.
The log- sigmoid function is selected for the activation function.
B. Direct neural control torque (DTNC)
Applying the technique of neural networks in the control of electrical machines is simple and has allowed the resolution of several problems related to the control of these systems.
The neural network used in this paper is a multi-local network connection using the back-propagation algorithm for learning.
After describing the neural network structure to be used, the input and output matrices are loaded as follows: the example of DTNC of a two-level inverter with 12 sectors is considered:
% Input matrices (E_Torque, E_Flux, E_Position).
P=[311;211;111;011;301;301;101;001;312;212;112;012;302;2 02;102;002;313;213;113;013;303;203;103;003;314;214;114;0 14;304;204;104;004;315;215;115;015;305;205;105;005;316;2 16;116;016;306;206;106;006;317;217;117;017;307;207;107;0 07;318;218;118;018;308;208;108;008;319;219;119;019;309;2 09;109;009;3110;2110;1110;0110;3010;2010;1010;0010;311 1;2111;1111;0111;3011;2011;1011;0011;3112;2112;1112;01
12;3012;2012;1012;0012]
% Output matrices (Switching state)
P=[110;110;100;101;010;011;111;001;010;110;100;100;011;0 11;101;010;010;110;100;011;001;000;101;011;010;110;110;0 01;001;100;100;011;011;010;110;001;101;111;100;001;011;0 10;101;001;100;110;001;001;011;010;101;100;000;110;101;0 01;011;011;100;100;110;010;101;101;001;011;100;010;111;0 10;100;101;001;001;110;110;011;011;100;100;101;001;110;0
10;000;011;110;100;101;101;010;010;011; 001] b2=min(a);
b1=max(a);
RNA=newff([b2' b1'],[24 3],{'logsig' 'logsig'});
%bdids.IW{1}=A';
%bdids.LW{2,1}=B';
%bdids.LW{3,2}=C;
RNA.trainParam.epochs =207;
[RNA,tr] = train(RNA,a',d');
%gensim(RNA) Where RNA: Artificiel Neural Network
VI. COMPARATIVE STUDY BETWEEN DTC_C&
DTNC AND SIMULATION RESULTS
A comparative performance study between the classical direct torque control (DTC_C) and that of a direct torque control improved by applying the technique of artificial intelligence based on the neural network (DTNC) is proposed in this paper.
*s
*em
C
s
1 1 1bscs
vas
Cem
is
vs
2 2 2bscs
vas
1 1 1bscs
ias
2 2 2bscs
ias 2
2 2bc
sa 1 1 1bc
sa
vdc
s
s
vdc
T6
Xn
Output Summation
Threshold X1
X2
∑
W1j
W2j
Wnj
Input
y Synapt
weights ic
3 3 +
Flux estimation Torque
estimation
Reconstruction of voltage DTC
DSIM
+ +
- -
-
[T
6]
A. Results of flux and torque using the DTC-C control strategy
Fig. 8, Fig. 9 and Fig. 10 illustrate simulation of the DTC structure known here as the classical DTC (DTC_C). The obtained results show high dynamic performance. In fact, the electromagnetic torque appears to have fewer ripples. The trajectory of the stator flux illustrated by Fig.9 shows that it is almost perfectly constant. The stator current responds well to the changes imposed by the torque and that its value remains close to a sinewave as shown in Fig.10.
Fig. 8 Reference change and evolution of torque versus time, case:
(DTC_C).
Fig. 9 Evolution of flux versus time for a reference: φs0 = 1.207wb, case:
(DTC_C)
Fig.10. Stator current of α phase and the voltage Vsa, if (DTN_C).
B. Results of flux and torque using the DTNC control strategy
Fig. 11, Fig. 12 and Fig. 13 illustrate the DTNC when applied to the DSIM powered by a two-level voltage inverter for the case of switching tables of three-level for the torque correction and two-level for the stator flux.
Fig. 11 Reference change and evolution of torque versus time, case: (DTNC).
Fig. 12. Evolution de flux en fonction du temps pour une consigne : φs0=1.207wb, cas : (DTNC).
Fig.13. Stator current of the α phase and the voltage Vsa, if (DTNC)
The simulation for the DTNC technique case shows better performance than those obtained by the classical direct torque control DTC_C. It is interesting to note in Fig.11, a dynamic torque response with a very fast transient. The stator flux shows a very good response as in Fig.12, where it is noticed that there is less overshhoots in comparison with those obtained by the DTC_C, see the flux effect in Fig. 9. Fig. 12 shows a fast transient of the stator flux module which has a perfectly circular shape without any ripple in steady state. It is noticed that the torque and flux follow their references with static errors that are virtually zero, as well as a significant reduction of current ripple that results in a sinusoidal waveform as in Fig.13.
VII. CONCLUSION
The present paper is investigating the merits of the DTNC (DTC based on the neural network) control performance in comparison with the classical DTC_C. The paper is studying the impact of the two control techniques on the DSIM performance when fed by a multi-level inverter. The various
0 0.002 0.004 0.006 0.0080.010.012 0.014 0.016 0.0180.02 -5
0 5 10 15 20 25
Time (s)
electromagnetic torque(N.m)
0 0.5 1 1.5 2 2.5 3
-5 0 5 10 15 20 25
Time (s)
electromagnetic torque(N.m)
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.0180.02 -5
0 5 10 15 20 25
Time (s)
electromagnetic torque(N.m)
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5 -1 -0.5 0 0.5 1 1.5
phis-alpha
phis-bitta
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5 -1 -0.5 0 0.5 1 1.5
phis-alpha
phis-bitta
0 0.5 1 1.5 2 2.5 3
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Temps(s)
Flux statorique(Web)
0 0.5 1 1.5 2 2.5 3 3.5
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Temps(s)
Flux statorique(Web)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-35 -30 -25 -20 -15 -10 -5 0 5 10
Time (s)
Is-alpha(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500 -400 -300 -200 -100 0 100 200 300 400 500
Time (s)
Voltage Vsa(V)
0 0.5 1 1.5 2 2.5 3 3.5
-500 -400 -300 -200 -100 0 100 200 300 400 500
Temps(s)
tension Vsa(V)
0 0.5 1 1.5 2 2.5 3
-5 0 5 10 15 20 25
Time(S)
electromagnetique torque(N.m)
0 0.002 0.004 0.006 0.0080.01 0.012 0.014 0.016 0.0180.02 -5
0 5 10 15 20 25
Time(S)
electromagnetique torque(N.m)
0 0.5 1 1.5 2 2.5 3
-5 0 5 10 15 20 25
Time(S)
electromagnetique torque(N.m)
0 0.002 0.004 0.006 0.0080.01 0.012 0.014 0.016 0.0180.02 -5
0 5 10 15 20 25
Time(S)
electromagnetique torque(N.m)
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5 -1 -0.5 0 0.5 1 1.5
phis-alpha
phis-bitta
0 0.5 1 1.5 2 2.5 3
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Temps(s)
Flux statorique(Web)
-1.5 -1 -0.5 0 0.5 1 1.5
-1.5 -1 -0.5 0 0.5 1 1.5
phis-alpha
phis-bitta
0 0.5 1 1.5 2 2.5 3
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Temps(s)
Flux statorique(Web)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-35 -30 -25 -20 -15 -10 -5 0 5 10
Time(s)
Is-alpha(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500 -400 -300 -200 -100 0 100 200 300 400 500
Time(s)
Voltage Vsa(V)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-35 -30 -25 -20 -15 -10 -5 0 5 10
Time(s)
Is-alpha(A)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-500 -400 -300 -200 -100 0 100 200 300 400 500
Time(s)
Voltage Vsa(V)
results are obtained and presented so as to illustrate the enhancement of both the torque and flux quality due to the DTNC-DSIM control strategy. The DTC_C control has depicted some advantages, such as the flux and the torque are well controlled; the stator current is almost sinusoidal. It unfortunately presents a major drawback related to some overshoot torque bands. By cons, the use of the DTNC has shown more benefits, the torque is well controlled, the flux and torque follow perfectly their references and the stator
current is quite sinusoidal. The only main problem of the DTNC is the difficulty choice of the learning.
BIBLIOGRAPHIE
Logic Logic and Neuron Network on the Performance of a Multi-Level Inverter fed Induction Machine ” , IMPACT: International Journal of
Current is quite sinusoidal.The only main problem of the DTNC is the difficulty choice of the learning.
BIBLIOGRAPHIE
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[3] T.G. Habetler and D.M. Divan, “Control strategies for direct torque control using discrete pulse modulation”, IEEE Trans. Ind.
Applicat., IA-27(5): 893-901,1991.
[4] Benaouda, O; Bendiabdellah, A. ; “La contribution du contrôle direct du couple d'une MAS alimentée par des onduleurs multiniveaux:Application de l'intelligence artificielle (Logique Floue).” , seconde international Conférence on Power Electronics and Electrical Drives, ICPEED'12.
[5] Monti, A.; Morando, A.P.; Resta, I; Riva, M. ; “Comparing two level GTOinverter feeding a double star asynchronous motor with a three level GTO-inverter feeding a single star asynchronous motor”, proceedings of EPE’1995, 19-21 September 1995, Sevilla Spain, pp 2.419-2.425.
[6] Gierse, G; Schuermann, W. ; “ Microprocessor control for two magnetically coupled three-phase PWM inverters”, IEEE Trans.
Power Electron., vol. PE-1, No. 3, pp. 141-147, July 1986.
[7] Hadiouche, D; Razik, H; Rezzoug, A.; “Modeling of a double star-induction motor with an arbitrary shift angle between its three windings”. Proc. EPEPEMC’2000, Kosice, Solvak Republic, 5-7 September 2000.
[8] Zaimeddine, R. ; Berkouk, E.M.; “Switching Strategies in Direct Torque Control of Double-Star Induction Motors”, JOURNAL WSEAS TRANSACTION ON CIRCUITS AND SYSTEMS, Issue 2, Volume 5, February 2006, ISSN 1109-2734.
[9] Brassfield, W.R.; Spee, R.; Habetler, T.G.; “Direct torque control for brushless doubly-fed machines”, Industry Applications, IEEE Transactions on Volume32, Issue 5, Sept.-Oct. 1996 Page(s):1098 – 1104.
[10] Benaouda,O ; Bendiabdellah, A. ; “A comparative Study of Two Types of DTC With Application of Artificial Intelligence: Fuzzy Logic and Neuron Network on the performance of a multi-level inverter fed induction machine’’ ,IMPACT:International Journal of Research in Engineering 8843;ISSN (E):2321- 8843;ISSN(P):2347-4599 Vol. 2,Issue 9,Sep 2014,1-12.
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