Download 127 A direct torque control of induction motor based on three

A direct torque control of induction motor
based on three-level NPC inverter and fuzzy
PI speed controller
Aissa Oualid
Samir Moulahoum
Nadir Kabache
Research Laboratory of Electrical Engineering & Automatic LREA, University of Médéa, Algeria
E-Mails: [email protected], [email protected], [email protected]
Keywords
Induction motor, DTC, Three-level NPC, Fuzzy logic, Fuzzy PI controller.
Abstract
The direct torque control of induction motor has good dynamic performance of torque and flux.
However, the switching frequency is variable and difficult to control due to the use of hysteresis
controllers. This lack of control over frequency is the origin of torque ripples and flux. Similarly,
the use of a voltage inverter with two levels limits the power of the drive system. To overcome
these problems, this paper propose to study a modified DTC approach by using a three-level
inverter (NPC structure) instead of the two-level inverter and the control of the speed loop is
ensured by fuzzy controller instead the classic PI controller. This allows not only minimizing the
undulations of flux and torque but also to increasing the power range of the drive system.
I.
Introduction
Among many control methods of induction machines, one of the most important today is the Direct
Torque Control (DTC) method. It can provide a very fast, accurate, reliable flux control and torque
responses [1-2]. However, the power limitation of the two-level inverter and the torque and flux
ripples, due to the presence of hysteresis controllers, are the two main drawbacks of this control. In the
two-level inverter traditionally used in electrical drives, the maximum voltage that can be supported
by the semiconductor switching devices is the value of DC bus voltage. In addition, the output
voltages and currents of the inverter have a high harmonic distortion. New multilevel converter
topologies however can considerably reduce many of these limitations [3]. The application of DTC for
high power machines became possible due to the progress on the power components and the choice of
a multi-levels inverter voltage structure, which give a high number of voltage levels. We can verify
that an extension of the concept DTC can easily improve system performance. Thus, we establish a
switching table with more rules and the voltage vector will be optimal [1-2].
II.
General Structure
The three-level NPC inverter is shown in Fig.1. The input DC bus consists of two capacitors in series
(C1, C2) forming a rated midpoint (O) that allows the inverter to reach a voltage level relative to
supplementary conventional inverter two levels. The total voltage E of the DC bus, under nominal
operating conditions, is uniformly distributed over the two capacitors so that an E/2 voltage is obtained
for each capacitance.
Each of the three branches of the inverter consists of four controlled switches (Sa1, Sa2, Sa3 and Sa4)
and two clamp diodes (DCa1 and DCa2) connected to the midpoint of the DC bus. Controlled switches
are unidirectional and bidirectional voltage supply, composed by an associations of a IGBT transistor
and a diode in antiparallel. Thus, three possible levels of output voltages ((-E)/2, 0 and E/2) are
obtained depending on the choice of switches turned [4], [5].
Fig. 1: Schematic diagram of a three-level NPC
By combination of the four switches, we can obtain three different voltage levels shown in Table I [5],
[6], [7]:
Table I: Switches of the three-level inverter structure NPC
Sa1
Sa2
Sa3
Sa4
Vao
1
0
1
1
0
1
0
0
E/2
0
0
1
1
-E/2
The three Boolean variables control Si (i  a, b, c) are given as:
Si  1  (Si1, Si 2 , Si 3 , Si 4 )  (0,0,1,1)
Si  0  ( Si1, Si 2 , Si3 , Si 4 )  (0,1,1,0)
Si  1  (Si1, Si 2 , Si 3 , Si 4 )  (1,1,0,0)
(1)
In this case, the inverter can be modeled as the following equation:
E

 Van  6  2Sa  Sb  Sc 

E

Vbn   2Sb  Sa  Sc 
6

E

 Vcn  6  2Sc  Sa  Sb 

(2)
The expression of the inverter vector voltage Vs can be given in the form below:
j
2E
Vs 
( S a  Sb e
3 2
2
3
 Sc e
j
4
3 )
(3)
The combination of the three variables Sa, Sb, Sc shows that compared to the two levels inverter which
can provide only eight voltage vectors including two zero vectors, the three-level inverter can produce
twenty seven voltage vectors with three zeros vectors as shown Fig.2. [2], [3], [4].
Fig. 2 : Voltage vectors of a three-level NPC inverter
III.
Presentation of the proposed DTC strategy
Basically, DTC schemes require the estimation of the stator flux and electromagnetic torque. The flux
evaluation can be carried out by different techniques depending on whether the rotor angular speed or
(position) which are measured or observed. For sensorless application, the "voltage model" is usually
employed. The stator flux can be evaluated by integrating from the stator voltage equation [2], [4]:
t
s (t)   (Vs  R sIs )dt
0
(4)
Further to the calculation of the components of the flux, the estimated torque is determined from the
following equation [2], [4] :
Tem  P(s Is  s Is )
(5)
As shown in figure 4, DTC strategy only needs the output voltages and currents of the inverter which
feeds the induction machine, the instantaneous values of flux and torque in the machine are calculated
and then compared to the reference values (Tref and Φsref). In this approach two hysteresis comparators
were performed to control the electromagnetic torque and the flux with respectively five and two
levels as shown in Fig.3.
Fig. 3: Hysteresis blocks
((-2/-1/0/+1/+2): high decreases/decreases/equal/increases/high increases)
For the switching vector selection, it is necessary to known the angular sector in which the actual flux
is located. The actual position of the stator flux can be determined by equation 6, from the orthogonal
flux components: [2], [5] :
  tan 1 (
 s
s
)
(6)
The flux position in the (α, β) plane is quantified in twelve (12) sectors of 30° degrees starting with the
first sector situated between 0° and 30°.
Using the hysteresis comparator outputs flux CΦ and torque CΓ and the stator flux sector S, the flux
and the torque are controlled directly and independently with an appropriate selection of voltage
vector imposed by the inverter. The inverter provides twenty seven voltage vectors. These vectors are
chosen from a switching table based on errors of flux and torque and the stator flux vector position
(Table II). The switching configuration is made step by step. The selection of a voltage vector at each
cycle period Te is carried in order to maintain the flux and torque within the limits of two hysteresis
bands.
Several switching tables for three-level inverter are presented in literature. Also, a new table for the
inverter selector has been developed, to achieve an accurate control. In order to simplify, the
mechanical rotor speed will be considered when assigning the voltage vectors needed at each one of
those sectors. The speed of the stator flux linkage vector is given by the modulus of the applied
voltage vector [2].
Table II: Switching table
C
-2
-1
0
1
2
CT
0
1
0
1
0
1
0
1
0
1
1
V20
V25
V13
V5
V0
V0
V2
V3
V22
V17
2
V26
V20
V8
V6
V7
V7
V3
V4
V17
V23
3
V15
V26
V1
V13
V14
V14
V10
V11
V23
V18
4
V21
V15
V2
V8
V0
V0
V11
V12
V18
V24
5
V16
V21
V9
V1
V7
V7
V4
V5
V24
V19
6
V22
V16
V10
V2
V14
V14
V5
V6
V19
V25
7
V17
V22
V3
V9
V0
V0
V12
V13
V25
V20
8
V23
V17
V4
V10
V7
V7
V13
V8
V20
V26
9
V18
V23
V11
V3
V14
V14
V6
V1
V26
V15
10
V24
V18
V12
V4
V0
V0
V1
V2
V15
V21
11
V19
V24
V5
V11
V7
V7
V8
V9
V21
V16
12
V25
V19
V6
V12
V14
V14
V9
V10
V16
V22
Fig.4: Structure of direct torque control with a three-level inverter and fuzzy logic PI controller
III.1 Fuzzy logic PI controller
The electromagnetic torque reference in this approach is generated from a fuzzy logic PI controller.
This controller has two inputs, the error (which is the difference between the reference speed ωrref and
the measured speed of the process ωr) and the derivative of this error, the controller output is the
Fig. 5: Structure of the fuzzy controller
reference torque that must be apply to the input of the process. The developed controller uses the
simple structure that is shown in Fig.5. [10], [11].
The speed controller has two inputs and one output. To apply the fuzzy algorithm, we must define a
set of control strategy based on error between a reference speed and the actual speed of the process
and the derivative of the error, this to adjust the control variable. At each sampling period, the inputs
of the fuzzy controller are:
The error e, expressed by: [9], [10]
e(K)  r _ ref (K)  r (K)
(7)
The derivative of error, expressed by:
de(K) 
e(K)  e(K  1)
Te
(8)
With: Te is the sampling period.
The output of fuzzy controller is the increment of the torque reference is obtained as follows:
Tref  Tref (K)  du(K)
(9)
The output u represents the command that must be applied to the system. At each sampling period Te,
the fuzzy controller delivers the control u corresponding to a pair of input (error (e) and its derivative
(Δe)). The fuzzy controller is composed of three blocks: fuzzification, rule bases, and defuzzification.
The increase in the number of fuzzy sets to five (NL, NS, Z, PS, PL) requires the processing of 25
rules. The distribution of these sets on the universe of discourse of each variable must be made from a
judicious choice. [8], [9], [11]
The linguistic values: NL: Negative Large, NS: Negative Small, Z: Zero, PS: Positive Small and
PL: Positive Large.
Fig.6: The fuzzy membership functions of input variables error, change in error and output variable
Table III: Fuzzy rules
Error e(t)
Derived e(t)
NL
NS
Z
PS
PL
NL
NS
NL
NL
NL
NS
Z
Z
NL
NS
NS
Z
PS
IV.
PS
NL
NS
Z
PS
PL
PL
NS
Z
PS
PS
PL
Z
PS
PL
PL
PL
Simulation results
The behavior of the DTC control structure with three-level inverter, applied to a 4kW induction
machine and shown in Fig.3, is simulated by using the environment MATLAB/SIMULINK. The
simulation is performed under the following conditions:
• The hysteresis band of the torque comparator is set at ± 0.45 Nm.
• The hysteresis band of the flux comparator is taken to ± 0.01Wb.
• The electromagnetic torque reference is recovered at the output of a fuzzy logic PI controller.
• The reference flux is kept constant and equal to its nominal value 1Wb.
The parameters of the induction machine used in this paper are summarized in the following table:
Table IV: The parameters of the induction machine
Rated machine power
Rated speed
Rated voltage
Rated frequency
Stator resistance Rs
Rotor resistance Rr
Stator inductance Ls
Rotor inductance Lr
Mutual inductance Lm
Pole pairs p
Inertia J
Friction coefficient f
4 KW
1420 rpm
230 V
50 Hz
1.2 Ω
1.8 Ω
0.1554 H
0.1568 H
0.15 H
2
0.07 kg.m2
0.0001
Fig.7 and Fig.9 show the simulation results of the conventional direct torque control (with two levels
inverter and PI speed controller) applied to an induction machine for a reference speed variation and
nominal load application. The real speed is obtained from the mechanical sensor. The obtained
simulation results show that in the conventional DTC, the flux and the torque are decoupled and
follow theirs references. The real speed tracks its reference in good agreement. In addition, even with
the presence of load torque, the DTC operates correctly.
To prove the effectiveness of the proposed approach, Fig.8 and Fig.10 show the simulation results of
the proposed direct torque control (with three levels inverter and fuzzy speed controller) applied to an
induction machine for the same operating conditions.
It is very clear that the torque and flux ripples are significantly reduced with a good agreement
between the machine flux and torque and the controller flux and torque. Moreover, the stator current
ripples are reduced and the static error of the speed is minimized from 0.15 rpm to 0.02 rpm thanks to
fuzzy speed controller. We can conclude from these simulation results that the proposed DTC is
preferred. These results demonstrate that the proposed DTC control algorithm is able to keep the
torque, the flux and the speed at their reference values with the minimum of ripples.
Current Isa [A] Torque [Nm] Speed [Rad/sec]
Flux [Wb]
100
50
0
60
40
20
0
-20
-40
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
Time [Sec]
2.5
3
3.5
50
0
-50
1
0.5
0
Flux [Wb]
Current Isa [A]
Torque [Nm] Speed [Rad/sec]
Fig.7: Simulation results of conventional DTC
100
50
0
60
40
20
0
-20
-40
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
2.5
3
3.5
0
0.5
1
1.5
2
Time [Sec]
2.5
3
3.5
50
0
-50
1
0.5
0
Fig.8: Simulation results of proposed DTC
0
-100
-200
1.42
1.44
Time [Sec]
99.9
99.85
1.02
1
0.98
1.4
1.42
1.44
Time [Sec]
1.46
20
18
16
99.8
1.4
1.46
Flux alpha and betta [Wb]
-300
1.4
22
99.95
Torque [Nm]
100
1.42
1.44
Time [Sec]
14
1.4
1.46
1.5
1.42
1.44
Time [Sec]
1.46
1.42
1.44
Time [Sec]
1.46
1.42
1.44
Time [Sec]
1.46
1.42
1.44
Time [Sec]
1.46
10
1
Stator current [A]
200
Flux [Wb]
24
100
Speed [Rad/sec]
Stator voltage Vsa [V]
300
0.5
0
-0.5
-1
-1.5
1.4
5
0
-5
-10
1.42
1.44
Time [Sec]
1.46
1.4
Fig.9: the static responses of conventional DTC
100.01
0
-100
-200
-300
1.4
1.42
1.44
Time [Sec]
1.46
Flux [Wb]
1.02
1
0.98
1.4
1.42
1.44
Time [Sec]
1.46
22
100
Torque [Nm]
100
24
99.99
99.98
99.97
1.4
1.42
1.44
Time [Sec]
18
14
1.4
1.46
1.5
1
0.5
0
-0.5
-1
-1.5
1.4
20
16
Stator current Isa [A]
Speed [Rad/sec]
200
Flux alpha and betta [Wb]
Stator voltage Vsa [V]
300
1.42
1.44
Time [Sec]
1.46
10
5
0
-5
-10
1.4
Fig.10: the static responses of proposed DTC
V.
Conclusion
In this paper, we proposed a direct torque control of induction motor with three levels inverter
NPC structure and a fuzzy PI speed controller. The first purpose of this study is to minimize
the flux and torque ripples and increasing power range of the drive system. The second
objective is to develop a fuzzy supervisor that controls the effect of disturbances and adjust
the gains of PI controller under the effect of a change. It is clear that this combination of
improvements in: The robustness of the control chain vis-a-vis the change in load and reverse
the direction of rotation of the machine.
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