PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1456
Direct Electromagnetic Torque Control of Induction Motors
Powered by High Power PWM Inverters for Two Levels or Three
Levels
M. R. Douiri1 , M. Cherkaoui1 , T. Nasser2 , and A. Essadki3
1
2
Mohammadia School of Engineers (EMI), Morocco
National School of Computer Science and System Analysis (ENSIAS), Morocco
3
Superior School of Technical Education (ENSET), Morocco
Abstract— This study aims to develop a control strategy for high power induction motor
capable of providing, in solicitations binding load torque, electromagnetic torque responses in
wide dynamic. Direct torque control will achieve those goals. Indeed, by selecting from a table of
switching vectors of the inverter output voltage, it imposes directly the states of power switches
based on the electromagnetic state of the motor. Two applications are processed as part of this
work. The first concerns the control of an induction motor fed by an inverter 2-voltage levels.
The second develops new switching tables for direct torque control of induction motor fed by
an inverter 3-voltage levels and structure of NPC. The characteristics of these tables justify the
use of such a control strategy for systems implementing high power components such as GTOs.
Particular attention is paid to maintaining the balance of the midpoint of the final structure of
inverter.
1. INTRODUCTION
With the advancement of power electronics and digital technologies command, several control
structures for the AC machines were proposed, in order get performance identical to those of
the DC machine [1]. Among these structures, the direct torque control has been in recent years
towards the most important research and best suited to industrial requirements [2, 3]. In addition,
the development of variable speed control of induction machines has encouraged the use of threelevel inverters. The increase in levels of the latter proves to be the best solution in high power
drives. This structure of multilevel inverter was introduced by A. Naba and H. Akagi in 1981 [4–8],
the aim was to reduce the amplitude of harmonics injected by the inverter. This term describes the
connection point “O” through the diodes S40 , S 1 and S10 . The paper is organized as follows. The
principle of classical DTC is presented in the second section. Section three and four describes the
two level inverters and three level inverters fed DTC drive respectively. Section five presents the
simulation results of the proposed DTC drive, compares them to those obtained with a classical
DTC.
2. PRINCIPLE OF DIRECT TORQUE CONTROL
The principle of the command DTC is different. The objective is the direct regulation of the
couple of the machine, by the application of the various vectors of tension of the inverter, which
determines her state. The two controlled variables are: the flow statorique and the electromagnetic
couple which who are usually commanded by regulators in hysteresis [1, 2]. It’s about maintaining
the greatnesses of statorique flux and the electromagnetic couple inside these bands of hystrsis.
The output of this regulator determines the voltage vector of the optimal inverter to be applied to
each switching instant. The use of this type of regulators supposes the existence of a frequency of
switching in the variable converter requiring a step of very low calculation [2, 3].
Estimation of Stator Flux and Torque: The estimation of the flux and torque can be
realized from the measures of the greatnesses stator current and motor voltage, we obtain the
components α and β of the vector Ψ̄s and Γe :

Rt
 Ψsα = 0 (Vsα − Rs Isα )dt
Rt
(1)
Ψ
=
sβ
0 (Vsβ − Rs Isβ )dt

Γe = pp (Ψsα Isβ − Ψsβ Isα )
Vector Control of Torque: The general expression of electromagnetic torque:
Γe = pp
Lm
\
Ψs Ψr sin(Ψ̄
s Ψ̄s )
σLs Lr
(2)
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1457
The torque depends on the amplitude of both vectors Ψ̄r and Ψ̄s and their relative position. If
we succeed in controlling perfectly the flux Ψ̄s (from V̄s ) in module and in position, we can thus
control the amplitude and the relative position of Ψ̄r and thus the torque.
Vector Control of Flux: The statorique flux of the asynchronous machine is obtained from
following equation:
Z t
Ψ̄s =
(V̄s − Rs I¯s )dt
(3)
0
3. DIRECT TORQUE CONTROL WITH TOW-LEVEL INVERTER
The switches of the inverter of voltage (see Figure 1) must be commanded so as to maintain the
flux and the torque of the motor [5]. The vector of the voltage stator can be written under the
shape:
r
´
2π
4π
2 ³
(4)
Vs =
E0 Sa + Sb ej 3 + Sc ej 3
3
where (Sa , Sb , Sc ) represent the logical state of three switches: Si = 1 mean that the high switch is
closed and the low switch is opened (Vi = +E0 ) and Si = 0 mean that the high switch is opened and
the low switch is closed (Vi = −E0 ). We seek to control the flux and the torque via the choice of
the vector of tension which will be made by a configuration of switches. As we have three switches,
there are thus 23 = 8 possibilities for the vector Vs . Two vectors (V1 and V8 ) correspond to the
zero vector: (Sa , Sb , Sc ) = (0, 0, 0) and (Sa , Sb , Sc ) = (1, 1, 1).
Switching Table: The control table is built according to the state of variables dΨ and dΓe
and to the Si zone and Ψ̄s position, and so, it is shaped as presented in the Table 1.
Figure 1: Partition of the (α; β) plane into six sectors and Schematic diagram of a two-level GTO inverter.
Table 1: Switching table for direct torque control (two levels inverter).
dΨ
1
0
Sectors
dΓ S1
1
V2
0
V7
−1 V6
1
V3
0
V0
−1 V5
(Si :
S2
V3
V0
V1
V4
V7
V6
i = 1 to 6)
S3 S4 S5
V4 V5 V6
V7 V0 V7
V2 V3 V4
V5 V6 V1
V0 V7 V0
V1 V2 V3
S6
V1
V0
V5
V2
V7
V4
4. DIRECT TORQUE CONTROL WITH TREE-LEVEL INVERTER
Figure 2 presents the general scheme of the inverter voltage three levels of structure called the
neutral point “clamped” (NPC Neutral-Point-Clamped), it is one of the structures of inverter at
three levels of tension [7, 8]. It has many advantages, such as the number of generated voltage is
higher, less harmonic distortion
and low frequency
switching. Each arm of the inverter is comprised
0
0
0
of four switches: Si , Si , Sj , Sj Switches Si and Si have a complementary function. The combination
0
0
of four switches of the same arm (Si , Si , Sj , Sj ), we can impose on the phase three levels of different
tension: (0, 0, 1, 1) → − E2 ,(0, 1, 1, 0) → 0, (1, 1, 0, 0) → E2 the combinations (1, 1, 1, 0) and (0, 1, 1, 1)
realize a short circuit of the one both demies sources of continuous tension for it he are prohibited [8].
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
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Figure 2: Structure of a three-level voltage inverter.
Figure 3: Hexagon of the voltages of a three-level inverter.
Vectors of output voltage of the inverter at three levels: The set of vectors voltages supplied by an
inverter at three levels as well as sequences corresponding phase levels are shown in Figure 3.
The group of vectors “Zero voltage”: they are obtained by three different combinations from
states of three arms: (1, 1, 1), (−1, −1, −1) and (0, 0, 0), and that we named respectively V7 , V14
and V0 . They have no influence on the voltage of the middle point of the inverter.
The group of vectors “voltage half”: we can decompose this group into two other subgroups:
The first one is constituted by vectors named V1 , V2 , V3 , V4 , V5 and V6 . Other one is constituted by
vectors V8 , V9 , V10 , V11 , V12 and V13 . These vectors constitute the internal hexagon “voltage half”.
The application of a vector of the one or the other subgroup has an opposite effect on the evolution
of the voltage of the middle point E, indeed, the application of a vector of the first subgroup
(respectively of the second) will cause a discharge of input capacitor C1 (respectively of capacitor
C2 ) [5, 7, 8].
The group of vectors “voltage full”: this group contains vectors voltage named V15 , V16 , V17 , V18 ,
V19 and V20 . These vectors constitute the outside hexagon “voltage full”. The voltage of the
middle point middle E, is not affected by the application of these vectors, because the current
which circulates in C1 and in C2 is the same.
The group of vectors “intermediate voltage”: vectors voltage of this group are called V21 , V22 , V23 ,
V24 , V25 and V26 . During the application of these vectors, we cannot know if he is going to be to
increase him or to decrease the tension of the middle point E, where the we are going to seek both
capacitors, but currents which will cross them will not be equal. There will be an imbalance of E
which depends on currents circulating in the phases during this functioning [4, 8].
The construction of switching tables (Tableau 2) is based on choice of the stator voltage vector
applied to allow you to increase or decrease the modulus of the stator flux and electromagnetic
torque value. A particular attention was dedicated to the synthesis of the table and to the comparators in hystrsis. In our case we use a hystrsis comparator in five level for the torque and at
two levels for the regulation of flux in more we shall suppose that Uc1 = Uc2 = E2 .
5. SIMULATION RESULTS
Induction motor parameters: Pn = 3 Kw, Vn = 220 v, Rs = 5.27 Ω, Rr = 5.07 Ω, Ls = 0.416 H,
Lr = 0.423 H, Lm = 0.458 H, J = 0.2 kg · m2 , p = 2.
Figures below represent the answer of the electromagnetic torque, flux statorique, and stator
current for DTC 2-levels and DTC 3-levels. The reference torque Γ∗e is a level of [7–20–8] and a
reference flux of Ψ∗s = 1 Wb. Figures 4(a) and 5(b), show that in the case of the inverter 3-levels, the
good dynamics of the torque with fewer oscillations and overtaking of instruction, the torque follows
Progress In Electromagnetics Research Symposium Proceedings, Marrakesh, Morocco, Mar. 20–23, 2011 1459
Table 2: Switching table for direct torque control (three levels inverter).
dΓ
−2
−1
0
1
2
dΨ
1
0
1
0
1
0
1
0
1
0
S1
V20
V25
V13
V5
V0
V0
V2
V3
V22
V17
S2
V26
V20
V8
V6
V7
V7
V3
V4
V17
V23
S3
V15
V26
V1
V13
V14
V14
V10
V11
V23
V18
Sectors (Si :
S4
S5
V21 V16
V15 V21
V2
V9
V8
V1
V0
V7
V0
V7
V11 V4
V12 V5
V18 V24
V24 V19
i=1
S6
V22
V16
V10
V2
V14
V14
V5
V6
V19
V25
to 12)
S7
V17
V22
V3
V9
V0
V0
V12
V13
V25
V20
S8
V23
V17
V4
V10
V7
V7
V13
V8
V20
V26
S9
V18
V23
V11
V3
V14
V14
V6
V1
V26
V15
S10
V24
V18
V12
V4
V0
V0
V1
V2
V15
V21
S11
V19
V24
V5
V11
V7
V7
V8
V9
V21
V16
S12
V25
V19
V6
V12
V14
V14
V9
V10
V16
V22
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 4: Comparison of the evolution electromagnetic torque,module of stator ux, stator current and stator
Flux circle for DTC 2-level and DTC 3-level.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Figure 5: loupe: Comparison of the evolution electromagnetic torque,module of stator ux, stator current
and stator flux circle for DTC 2-level and DTC 3-level.
perfectly its reference in regime establishes. According to Figures 4(c) and 5(d), we note that the
establishment of the stator flux is a bit slower than the classical DTC Figures 4(c) and 5(d), but
the plan continuous flux module presents a good response which is shown in Figure 4(c) and 5(d),
where the evolution of the vector flux stator in the plan (α, β) is circular (4(g) and 5(h)). The
Figures 4(e) and 5(f), show that the use of the inverter 3-levels entails a decrease of the undulations
of the stator current, and the scheme of the current becomes purely sinusoidal.
6. CONCLUSION
A direct torque control of induction motor based on three levels and two levels inverter has been
described. The system was analyzed, designed and performances were studied extensively by simu-
PIERS Proceedings, Marrakesh, MOROCCO, March 20–23, 2011
1460
lation to validate the theoretical concept. The main improvements by using a three levels inverter
are:
•
•
•
•
imitation of the current amplitude and low distortions for current and torque;
No flux droppings caused by sector changes circular trajectory;
Reduction in Flux, current and torque ripples,
Stability of system.
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