Download A novel direct torque control (DTC) method

‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
Classical Direct Torque Control (DTC)
for Symmetrical Six Phase Induction Motors
R. Kianinezhad1 , S. Gh. Seifossadat2
Abstract
This paper introduces classical direct torque control (DTC) for six-phase induction machines (SPIM). The
machine has two, three-phase windings spatially shifted by 60 electrical degrees with one or two neutrals.
SPIM drive has 64 inverter switching states which provide higher possibility in selecting space voltage
vectors than three-phase induction machines. We will show that classical DTC for SPIM with two
isolated neutrals gives satisfactory results, by selecting space voltage vectors whose amplitude is high
enough on  plane where their components on z1-z2 and z3-z4 planes give minimum amplitudes. We
will show this method suppresses harmonic currents for DTC of SPIM. In the contrary, in the case of
SPIM with one common neutral, we will show that it is not possible to use conventional DTC, because of
producing high harmonic currents. We will validate our analysis by simulation results.
Keyword.: six-phase induction machines; direct torque control.
‫کنترل مستقيم کوپل به روش کالسيک ماشينهای‬
‫القایی شش فازه‬
2
‫ سيد قدرت اله سيف السادات‬،1‫رضا کيانی نژاد‬
‫چکيده‬
‫( به روش کالسیک برای ماشینهای‬DTC) ‫در این مقاله کنترل مستقیم کوپل‬
‫ این ماشین دارای دو دسته سیم پیچ سه فازه‬.‫القایی شش فازه ارائه می شود‬
‫ درجه‬06 ‫با نوتر الهای مستقل و یا متصل به هم می باشد که به فاصله‬
06 ‫ درایوهای شش فازه دارای‬.‫الکتریکی از یکدیگر در استاتور قرار می گیرند‬
‫حالت کلید زنی می باشند که نسبت به درایوهای سه فازه که دارای هشت حالت‬
‫ قابلیت انتخاب بردارهای ولتاژ بیشتری در اختیار ما قرار می‬،‫می باشند‬
‫ با انتخاب بردارهای‬:‫ کالسیک‬DTC ‫ در این مقاله نشان می دهیم که روش‬.‫دهد‬
Z1-Z2 ،Z3-Z4 ‫ (که دارای مولفه های کوچکی در صفحات‬ - ‫ولتاژ بزرگ در صفحه‬
‫ نتایج خوبی‬،‫می باشند) برای ماشینهای القایی شش فازه با نوتر الهای مجزا‬
‫ در این مقاله نشان داده خواهد شد که روش کنترلی به کار‬.‫ارائه می دهد‬
‫هارمونیک های نا مطلوب جریان را در ماشینهای القایی شش فازه با‬
،‫رفته‬
‫ بر خالف نتایجی که این روش برای ماشینهای‬.‫نوتر الهای مجزا حذف می کند‬
‫ در ماشینهای القایی با‬،‫القایی شش فازه با نوتر الهای مجزا ارائه می کند‬
‫ هارمونیک های نا مطلوب بسیاری را تولید می کند به نحوی‬،‫نوتر الهای مشترک‬
‫ ارزیابی نتایج‬.‫که کاربرد آن را برای اینگونه ماشینها غیر ممکن می سازد‬
‫ارائه شده در این مقاله با استفاده از شبیه سازی کامپیوتری صورت گرفته‬
.‫است‬
1-Assistant Professor, Electrical Engineering Department.,
.‫ استادیار گروه برق دانشکده مهندسی دانشگاه شهید چمران اهواز‬-1
Shahid Chamran University of Ahvaz.
2-Assistant Professor, Electrical Engineering Department.,
Shahid Chamran University of Ahvaz.
‫ استادیار گروه برق دانشکده مهندسی دانشگاه شهید چمران اهواز‬-2
[email protected]
[email protected]
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
1-INTRODUCTION
In the industrial applications that high
reliability is demanded, multi-phase
induction machine (IM) instead of
traditional three-phase induction machine is
used. In the multi-phase drive systems, the
electric machine has more than three phases
in the stator and the same numbers of
inverter legs are in the inverter side. The
advantages of multi-phase drive systems
over conventional three-phase drives are:
total rating of system is multiplied, the
torque pulsations will be smoothed, the rotor
harmonic losses as well as the harmonics
content of the DC link current will be
reduced and the loss of one machine phase,
does not prevent the machine working, so
improving the system reliability. The most
common multi-phase machine drive
structure is the six-phase induction machine
(SPIM), which has two sets of three-phase
winding, spatially phase shifted by 30 or 60
electrical degrees with two isolated or one
common neutral. For simplicity we show the
configurations with 60 electrical degrees and
two isolated neutrals by SPIM-60-2n, and
the configuration with 60 electrical degrees
and one common neutral by SPIM-60-1n
It is clear that one way to deal with SPIM
drives is to extend control techniques used
for three-phase induction machines in order
to improve reliability and fault-tolerance.
During the some last years, the literature
related to control of SPIM drives has
covered:
-Machine modelling in the normal and open
phase fault conditions; [1][2].
-Steady state analyse using VSI and CSI [3].
-Vector control in mode normal and fault
tolerant [4]-[6]
- PWM techniques [7]-[9].
The rotor field oriented control uses current
control loops and coordinate transformation
to impose the flux and torque. DTC provides
a fast torque response and also is robust
against machine parameter variations,
without coordinate transformation [10].
DTC controls stator flux and electric torque
by means of hysteresis comparators of
electric torque and stator flux. The only
factor that must be adjusted is the amplitude
of the hysteresis band. In the three-phase IM
drive one of the six non-zero space voltage
vectors and two zero space voltage vectors
are applied to the motor. The number of
available space voltage vectors, determines
the presence of ripple in the stator current
and torque. In comparison with three phase
IM drives, SPIM drives Fig.1, have 2 6  64
space voltage vectors [11], so SPIM drives
have more voltage vectors than three-phase
IM that can improve ripple content of stator
current and torque.
Some papers concern DTC for SPIM with
30 electrical degrees between two threephase windings [11]-[12], this paper
concerns DTC for SPIM with 60 electrical
degrees between two three-phase windings,
with one common or two isolated neutrals .
This paper is organized in seven sections.
The model of SPIM is described in the next
section. The third section presents the space
voltage vectors of SPIM. In section four
application of DTC to SPIM will be
introduced.
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
γ
γ
Fig 1-a: SPIM with two isolated neutrals
Fig 1-b: SPIM with one common neutral
The simulation results will be shown in the
fifth section. Finally some conclusions and
perspectives will be discussed in the sixth
section.
2-MODEL OF SPIM
The basic equations of SPIM have been
expressed briefly in [1]. The voltage
equations of the SPIM are as follow:
for stator circuit we can write:
α-β subspace:
The stator and rotor voltage equation of this
59 ▓ 2
subsystem is:
Vs   Rs . is   p(Lss . is   Lsr . ir )
The stator and rotor flux linkages of this
subspace are:
Vr   Rr ir   p(Lrr . ir   Lrs . is )
(2)
The SPIM can be decomposed into three
two-dimensional orthogonal subspaces, α-β,
z1-z2, and z3-z4, by the following
transformation:
1
2
3
2
1

2
3

2
cos(2/3   )
0
1
0
1
1
0
1
0
1
cos( )
0
sin(  )
1
cos( -  )
0
sin(  -  )
1
0

sin(2 /3   )
cos(/3 -  )
sin( /3 -  )
(4)
(1)
and for rotor circuit we have:







1 
T   
3






di s
di r

v s  R s .i s  Ls dt  M dt

di s
di r

v  R s .i s  Ls
M

 s
dt
dt

di
di
r
0  R .i  L
  r .Lr .i r  M s   r .M .i s
r r
r

dt
dt

di
di s
r
0  R .i  L
  r Lr i r   r .M .i s  M
r r
r

dt
dt

1
2
3

2
1

2
3
2


cos(4/3   )


sin(4 /3   ) 

cos(5/3   ) 


sin(5 /3   ) 


0



1

(3)
In this matrix, γ is the electrical angle
between the two, three-phase windings,
which is 30 or 60 electrical degrees. By
applying the transformation (3) to the
voltage equations (1) and (2), we can obtain
decoupled models for SPIM in the following
different subspaces are described:
s  Ls is  Mir

r  Mis  Lr ir
(5)
with: M = 3 Lms , Ls = Lls + M , Lr = Llr +
M
z1-z2 subspace:
disz1
dt
disz 2
 Rs .isz 2  Lls
dt
v sz1  Rs .isz1  Lls
(6)
v sz 2
(7)
z3-z4 subspace:
disz3
(8)
dt
di
v sz 4  Rs .isz 4  Lls sz 4
(9)
dt
As it can be seen from these three
subsystems, the electromechanical energy
conversion takes place in the α-β subsystem,
and the other subsystems do not contribute
in the energy conversion. The z1-z2 and z3vsz3  Rs .isz3  Lls
58 ▓ 3
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
z4 subsystems are only producing losses, so
they should be controlled to be as small as
possible. It can be concluded that analysing
the SPIM is performed by help of the α-β
subspace. The mechanical equation is the
following:
d
J m   Tm  T L
(10)
dt
in which Jm is the inertia coefficient, and:
(11)
Tm  p  s * i s 
is the torque generated by the motor.
TL is the load torque;
p is the number of pair of poles.
3-SPACE VOLTAGE VECTORS IN SPIM
Based on the state of the upper or lower
switches of the inverter, each phase
switching functions, which are called Sa1,
Sb1, Sc1, Sa2, Sb2, and Sc2 can take either 1 or
0 value. If the upper switch is “on” then the
switching function assumes a value of “1”,
else “0”. Therefore, the phase voltages with
respect to the mid point of the inverter
source are:
Va1o  ( 2* Sa1 -1 )*E/ 2

Vb1o  ( 2* Sb1 -1 )*E/ 2
Vc1o  ( 2* Sc1 -1 )*E/ 2

Va2o  ( 2* Sa 2 -1 )*E/ 2
(12)
Vb2o  ( 2* Sb2 -1 )*E/ 2
Vc2o  ( 2* Sc2 -1 )*E/ 2
In the SPIM-60-2n configuration, the phase
voltages with respect to their neutrals will
be written as follows:
Va1n  1/ 3*[ 2*Va1o-Vb1o-Vc1o]
Vb1n  1 / 3*[ 2*Vb1o-Va1o-Vc1o]

Vc1n  1/ 3*[ 2*Vc1o-Vb1o-Va1o]

Va 2n  1/ 3*[ 2*Va 2o-Vb2o-Vc 2o]
Vb2n  1/ 3*[ 2*Vb2o-Va 2o-Vc 2o]

Vc2n  1/ 3*[ 2*Vc2o-Vb2o-Va 2o]
(13)
The phase voltages in the SPIM-60-1n
configuration are:
Va1n  1/ 6*[ 5*Va1o-Vb1o-Vc1o-Va 2o-Vb2o-Vc 2o]
Vb1n  1/ 6*[- Va1o  5*Vb1o-Vc1o-Va 2o-Vb2o-Vc 2o]


Vc1n  1/ 6*[- Va1o-Vb1o  5*Vc1o-Va 2o-Vb2o-Vc 2o]

Va2n  1/ 6*[- Va1o-Vb1o-Vc1o  5*Va2o-Vb2o-Vc 2o]
Vb2n  1/ 6*[- Va1o-Vb1o-Vc1o-Va 2o  5*Vb2o-Vc 2o]


Vc2n  1/ 6*[- Va1o-Vb1o-Vc1o-Va 2o-Vb2o  5*Vc2o]
(14)
Applying transformation matrix (3) yields
six-phase voltages of three orthogonal
subsystems. Using α-β subspace and taking
into account stator flux linkage equation (5),
we can write:
d

v s  rs is  s


dt

d

v  r i  s
s
s s

dt

(15)
The stator flux linkage in every sampling
period can be obtained by the following
equation:
t

s   (v s  rs is )dt

0

t
  (v  r i )dt
s

0 s s s


(16)
We can write discrete time model of this
equation as follows:
s (k )  s (k  1)  vs T  rs is T
(17)

57 ▓ 4

(
k
)


(
k

1
)

v
T

r
i
T
s

s

s

s
s


These equations describe that stator flux
linkage is depended to v s and v s , and so to
the voltage vectors of the inverter.
The stator flux angle can be calculated by
the following equation:

(18)
 S  tan 1 ( s )
s
Thus by selecting the proper space voltage
vector, the stator flux can be controlled.
From (11), electric torque equation can be
expressed verses α-β parameters as follow:
Tm  p s is  s is 
(19)
By combinational analysis of all states of
12 inverter keys, a total of 64 switching
modes can be obtained. By applying
transformation (3), 64 voltage vectors are
projected on the α-β, z1-z2 and z3-z4
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
subspaces. We have used SPIM-60-1n and
SPIM-60-2n as illustrated in Fig 1. In the
case of SPIM-60-2n, the projection of the
voltage vectors on the z3-z4 subspace is zero
[11] [12], and the space voltage vector
selection is performed only on the α-β and
z1-z2 subspaces. Fig 2 and Fig 3 show space
voltage vectors on the α-β and z1-z2
subspaces for SPIM-60-1n and SPIM-60-2n,
and Fig. 4 shows space voltage vectors on
the z3-z4 subspaces for SPIM-60-1n. The
decimal numbers in the figures, show
switching states of the inverter switches. By
converting each decimal number to a six
digit binary number, the 1’s indicate, on
state of the upper switch in the
corresponding arm of the inverter. The most
significant bit (MSB) of the number
represents the switching state of phase a1,
the second MSB for phase a2, the third for
phase b1, and so on.
4-APPLICATION OF DIRECT
CONTROL TO SIX PHASE DRIVES
4-1- Space voltage vector selection
24,6
0
28
a : 4, 10, 13, 22, 31,46
b : 8, 20, 26, 29, 44, 62
c : 16, 25, 40, 52, 58, 61
d : 17, 32, 41, 50, 53, 59
e : 1, 19, 34, 37, 43, 55
f : 2, 5, 11, 23, 38, 47
o : 0, 9, 18, 21, 27, 36
42, 45, 54, 63
TORQUE
12,30
c
b
48,5
7
o
a
14
56
d
f
6,15
7
e
49
33,51
35
3,39
Fig. 2: Projection on the α-β plane, for SPIM-60-1n, and SPIM-60-2n
22,50
18
a : 3, 10, 17, 24, 31,59
b : 2, 16, 23, 30, 51, 58
c : 6, 20, 34, 48, 55, 62
d :4, 32, 39, 46, 53, 60
e : 5, 12, 33, 40, 47, 61
f : 1, 8, 15, 29, 43, 57
o : 0, 7, 14, 21, 28, 35
42, 49, 56, 63
19,2
6
c
b
f
11,25
9
38,5
2
o
a
27
54
d
e
41,1
Fig. 3: Projection on the z1-z2 plane, for SPIM-60-1n, and SPIM-60-2n
36
37,4
45
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
a : 5, 17, 20, 23, 29,53
b : 1, 4, 7, 13, 16, 19, 22, 25
28, 31, 37, 49, 52, 55, 61
c : 2, 8, 11, 14, 26, 32, 35, 38
41, 44, 47, 50, 56, 59, 62
d : 10, 34, 40, 43, 46, 58
o : 0, 3, 6, 9, 12, 15, 18, 24, 27
30, 33, 36, 39, 45, 48, 51, 54
57, 60, 63
21
a
b
o
c
d
42
Fig. 4: Projection on the z3-z4 plane, for SPIM-60-1n..
The aim of DTC is to select proper stator
components on z1-z2 and z3-z4 planes give
space voltage vector to maintain both the 56 ▓ 5 minimum amplitude vectors. According to
stator flux and electric torque within the
Figs. 2-4, we choose the voltage vector set
limits
of
their
hysteresis
bands.
illustrated in (20). As can be seen, there are
Electromechanical energy conversion take
6 voltage vectors which symmetrically
place in the α-β subspace, thus for obtaining
spatially distributed on  plane. But the 6
maximum electromagnetic torque, the main
vectors on  plane correspond to zero
idea is to choose the switching modes that
voltage projection on z1-z2 and z3-z4 plane
permit to have the maximum amplitude of
for SPIM with two isolated neutrals, while
 voltage vectors (maximum projection
their z3-z4 components are not null for
on the α-β subspace), and to minimize z1-z2
SPIM with one common neutral. This
and z3-z4 voltage vectors.To do this, one
reduces significantly the harmonic currents
may choose the following switching modes
on z1-z2 plane while z3-z4 currents for
that permit to have the maximum amplitude
SPIM-1n are not null because of none zero
 voltage vectors (Fig. 2):
voltage components on this plane.
49, 56, 28, 14, 7 and 35
(20)
4-3- Switching tables
It must be noted that the switching modes
This section introduces control tables for
(20) generate zero voltage vectors on z1-z2
DTC of SPIM. Table 1 shows how different
plane for both configurations (Fig. 3), The
stator space voltage vectors change the
projection of these voltages on the z3-z4
stator flux and electric torque in
subspace for SPIM-60-2n are zeros, but for
symmetrical SPIM. In this table it is
SPIM-60-1n we see none zero voltage
assumed that the stator flux is in the first
vectors (Fig. 4). These none zero voltages
sector of the space voltage vector plane. For
generate harmonic currents on z3-z4 plane.
showing influence of each space voltage
These currents may be too much large if the
vector on stator flux and electric torque, we
machine leakage inductance or the inverter
have used the arrows. For example, two
switching frequency is little.
arrows upward (↑↑) or downward (↓↓)
represent that the quantity (stator flux or
electric torque) is maximum or minimum,
4-2- CLASSICAL DTC METHOD FOR SPIM
The proposed space voltage vector
while one arrow shows less influence. The
selection for SPIM is based on the fact that,
arrow (↑↓), shows that the quantity doesn’t
there is always vectors whose amplitude is
change.
high enough on  plane where their
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
According to table 1, changing stator flux
amplitude and electric torque by space
voltage vectors can be explained as follow:
if the stator flux is less than its reference, the
space voltage vectors 35, 49, and 56 can be
applied to increase the stator flux amplitude.
For decreasing stator flux, space voltage
vector 7, 14, and 28 can be selected. The
space voltage vectors 14 and 49 have the
greatest effect on the stator flux amplitude.
The zero voltage vectors 0 and 63 haven’t
any effect on the stator flux amplitude,
except that flux weakening due to the stator
resistance voltage drop.
Like stator flux, for torque control also,
effect of each space voltage vector can be
explained. Space voltage vectors 28 and 56
increase electric torque while 0, 7, 14, 35,
49, and 63 decrease electric torque. Space
voltage vectors 7, 28, 35, and 56 have the
greatest effect on the electric torque.
For controlling both stator flux and
electric torque, we can conclude following
laws based on the table 1. For decreasing
both stator flux and electric torque we can
apply space voltage vectors 7 or 14. For
increasing both stator flux and electric
torque we must apply space voltage vector
56. For increasing stator flux and decreasing
electric torque, space voltage vectors 35 or
49 can be applied. For decreasing stator flux
and increasing electric torque, the space
voltage vector 28 must be used. For
maintaining the stator flux amplitude and
decreasing the electric torque, space voltage
vectors 0, or 63 can be applied. This
algorithm might be performed in every
sampling period so that the stator flux and
electric torque follow their references.
According to these criteria, we introduce
table 2, for DTC of symmetrical SPIM. This
table have been used to perform space
voltage vector selection process in every
period. The same procedure has been used
to apply DTC of SPIM-60-1n with selected
voltage vector shown in (20).
5- SIMULATION RESULTS
In order to predict the SPIM behaviour
under classical DTC method, a simulation
program using MATLAB/Simulink software
has been developed. The torque and flux
references are Tm*=0.2 N.m, and
λs*0.06wb. The sampling period is fixed at
50 µs. The parameters of the simulated
motor are given in table 3.
Figs. 5 and 6 show simulation results for
SPIM-60-1n and SPIM-60-2n respectively.
The figures depict, the quadrature
component of stator flux versus horizontal
component of stator flux in the stationary
reference frame, timing response of
developed electromagnetic torque, the stator
phase currents, α-β, z1-z2, and z3-z4 stator
current components. As the Figs.5-a and 6-a
show, after some transient, the stator flux
locus becomes a circle and amplitude of
stator flux remains almost constant in the
command value. Figs.5-b and 6-b show the
torque response of machine when a 0.3 N.m
torque reference is applied in t=0 s. The
figures show developed electromagnetic
torque deviation from reference value is
very low. Figs.5-c shows the phase currents
are in their nominal amplitude for SPIM-602n (less than 5 A). Fig. 6-c shows some
deviation from nominal values due to z3-z4
harmonic components for SPIM-60-1n
(more than 5 A). As can be seen from Fig.
6-f, harmonic currents due to z3-z4 voltage
components are more than 4 A.
Table 1: Stator flux and electric torque
variations
14 28 56 49 35 7 0, 63
↓↓ ↓ ↑ ↑↑ ↑ ↓
↓↑
↓ ↑↑ ↑↑ ↓ ↓↓ ↓↓
↓
λ
Te
Table 2: Stator flux and electric torque control
in different sectors
sector
Uλs UTe
1
1
1
0
0
0
1
0
-1
1
0
-1
1
2
3
4
5
6
56
0
35
28
63
7
28 14 7 35 49
0 0 0 0 0
49 56 28 14 7
14 7 35 49 56
0 0 0 0 0
35 49 56 28 14
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
Table 3: Induction machine parameters
Rated power
Rated torque
VSI DC bus voltage
Number of poles
Mutual inductance
Stator resistance
Stator leakage
inductance
Rotor resistance
Rotor leakage
inductance
Friction coefficient
Inertia
90 W
0.3 Nm
42 V
2
30.9 mH
1.04 
0.30 mH
0.64 
0.65 mH
410-4 kg.m2/s
9.510-5 kg.m2
From the illustrated test results, it can be
noted that the stator flux is well controlled
in its reference value. The harmonic
components of the stator phase currents Iz1Iz4 are almost near zeros for SPIM with two
isolated neutrals, this is due to zero voltage
vectors on z1-z2 and z3-z4 planes as we
have shown it in Fig. 3 section 4. In the case
of SPIM with one common neutral we see
none zero current components on the z3-z4
plan, this is due to non-zero projections of
the selected voltages on the z3-z4 plane.
These results show the validity of classical
DTC for SPIM with two isolated neutrals,
while for SPIM with one common neutral
classical DTC is not applicable.
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
0.1
1
0.5
T [Nm]
  [web]
0.05
m
0
0
-0.05
-0.1
-0.1
-0.05
0
  [web]
0.05
0.1
-0.5
0.8
1.2
1.4
t [s]
Fig. 5b- Electromagnetic torque
10
10
5
5
Is Is [A]
Iphase [A]
Fig. 5a- Stator flux
0
-5
-10
0.8
1
1.2
0
-5
-10
1.4
0.8
10
10
5
5
Isz3 Isz4 [A]
Isz1 Isz2 [A]
t [s]
Fig.5c- Stator phases current
0
-5
-10
0.8
1
1.2
t [s]
Fig. 5e- Stator z1-z2 currents
1
1.2
1.4
t [s]
Fig.5d- Stator α-β currents
0
-5
-10
1.4
1
0.8
1
1.2
1.4
t [s]
Fig. 5f- Stator z3-z4 currents
Fig. 5- Simulation results for DTC of SPIM-60-2n.
6- CONCLUSION
In this paper, we have proposed classical
direct
torque
control
method
for
symmetrical six-phase induction machines.
This method consists in choosing the
switching modes in such a way that
corresponding to high amplitude voltage
vectors on  plane, and minimum
projected voltages on the z1-z2 and z3-z4
planes. Based on this criterion, we have
proposed six voltage vectors among 64
space voltage vectors for application to
SPIM. By the simulation results we have
shown that the stator flux as well as the
electromagnetic torque is well controlled in
53 ▓ 6
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
0.1
1
T [Nm]
  [web]
0.05
m
0
0.5
-0.05
-0.1
-0.1
-0.05
0
  [web]
0.05
0
-0.5
0.1
10
10
5
5
Is Is [A]
Iphase [A]
Fig. 6a- Stator flux
0
-5
-10
0.8
1
1.2
1
1.2
1.4
t [s]
Fig. 6b- Electromagnetic torque
0.8
1
0
-5
-10
1.4
0.8
10
10
5
5
Isz3 Isz4 [A]
Isz1 Isz2 [A]
t [s]
Fig.6c- Stator phases current
0
-5
-10
0.8
1
1.2
0
-5
-10
1.4
t [s]
Fig. 6e- Stator z1-z2 currents
1.2
1.4
t [s]
Fig.6d- Stator α-β currents
0.8
1
1.2
1.4
t [s]
Fig. 6f- Stator z3-z4 currents
Fig. 6-Simulation results for DTC of SPIM-60-1n.
its reference value. The stator phase
harmonic currents Iz1-Iz4 are almost zeros for
SPIM with two isolated neutrals that is due
to zero voltage vectors on z1-z2 and z3-z4
planes. But in the case of SPIM with one
common neutral we see none zero current
components on the z3-z4 plan, this is due to
non-zero projections of the selected voltage
vectors on the z3-z4 plane.
The results show the efficiency of the
proposed method for DTC of SPIM with
two isolated neutrals, while for SPIM with
one common neutral the high amplitude
current harmonics shows the method is not
applicable.
52 ▓ 9
‫ سيد قدرت اله سيف السادات‬،‫ رضا کيانی نژاد‬/‫ علوم و مهندسي نصير‬-2 ‫شماره‬-3 ‫ جلد‬-68 ‫زمستان‬
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