Journal of Power Electronics, Vol. ??, No. ?, pp. ?-?,MonthYear1
http://dx.doi.org/10.6113/JPE.2014.14.1.???
ISSN(Print): 1598-2092 / ISSN(Online): 2093-4718
JPE ??-?-?
Performance Evaluation of Field-Oriented Control of
Star-Connected 3-Phase Induction Motor Drives
under Stator Winding Open-Circuit Fault
Mohammad Jannati*, Nik Rumzi Nik Idris†, and Mohd Junaidi Abdul Aziz*
*†
UTM-PROTON Future Drive Laboratory, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, Johor
Bahru, Malaysia
Abstract
A method for fault-tolerant vector control of star-connected 3-phase Induction Motor (IM) drive system based on Field-Oriented
Control (FOC) is proposed in this paper. This method enables the control of a 3-phase IM upon an open-phase failure in one of its
phases without the need of control structure changes to the conventional FOC algorithm. The proposed drive system significantly
reduces the speed and torque pulsations, which are caused by an open-phase fault in the stator windings. The performance of the
proposed method was verified using MATLAB (M-File) simulation as well experimental tests on a 1.5kW 3-phase IM drive system.
This paper experimentally compares the operation of proposed fault-tolerant vector controller and conventional vector controller
during open-phase fault.
Keywords: Fault-tolerant control, Field-Oriented Control, Speed and torque pulsations, Star-connected, Stator winding
open-circuit fault, 3-phase induction motor drive
I.
INTRODUCTION
Field-Oriented Control (FOC) technique for 3-phase
Induction Motors (IMs) is widely adopted by industries to
obtain high performance of 3-phase IM drive systems.
Conventional FOC algorithm, which is used for healthy
3-phase IM drives, cannot be used for a faulty 3-phase IM
drive due to the fact that the conventional FOC is designed
based on a healthy machine model [1]. Using conventional
FOC for faulty 3-phase IM drives will degrade the dynamic
performance of the drive system. In this regard, it is necessary
to design a drive system that provides robustness against the
fault conditions [1]-[5].
Generally, 3-phase IM drives are exposed to various failures;
failures in the in the inverter [6], [7], failures in the mechanical
or electrical sensors [5], [8] and failures related to electrical
motor including faults in the stator [1], [9] and/or faults in the
Manuscript received Month. Date, Year; acceptedMonth. Date, Year
Recommended for publication by Associate Editor Gil-Dong Hong.
CorrespondingAuthor:author@hangook.ac.kr
Tel: +82-2-554-0185,Fax: +82-2-554-0186, Hangook University
*
Department of Electrical and Computer Engineering, Illinois Institute of
Technology, U.S.A.
**
School of Electrical Engineering, Hangook University, Seoul, Korea
†
Fig. 1. Classification of faults in squirrel-cage 3-phase IM drive.
rotor [10], [11]. Fig. 1 shows the classification of faults in
squirrel-cage 3-phase IM drives. In some critical applications,
the operation of the drive system cannot be interrupted by
faulty conditions mainly for safety reasons. Thus, for these
applications, fault-tolerant control is essential. Based on this
classification of faults, various fault-tolerant control methods
have been suggested in the literature, including passive and
active methods. A passive method can be ensured by
conventional robust control methods such as H∞ [12], [13].
Despite the robustness of this method against disturbances, its
© 2014 KIPE
2Journal of Power Electronics, Vol. ??, No. ?, Month Year
performance under healthy conditions is not optimized. In an
active method after fault detection and fault diagnostic, a new
set of control parameters or a new control structure is applied
[1]-[5] and [14]-[20]. This method has good performances
under both healthy and faulty conditions. However, it requires
a different control algorithm under faulty conditions.
A large number of studies have been conducted on the
implementation of vector control techniques for electrical
machines under stator open-circuit fault [1]-[4] and [14]-[20].
Most of the pervious works have focused on developing vector
control methods of faulty Permanent Magnet Synchronous
Motors (PMSMs) and multi-phase IMs (five and six phases)
[14]-[17]. In [18], [19] the analysis of the star-connected
3-phase IM in the open-phase fault indicates that, to
compensate torque pulsations, odd harmonic voltages of the
magnitude and phase angle can be injected at the machine
terminal. In [3], [20], vector and scalar control methods to
control delta-connected 3-phase IM drive under stator winding
open-phase fault based on current controller has been proposed
and implemented. Modeling and FOC of a star-connected
3-phase IM under open-phase fault using current controller
have also been presented in [4]. In this work, using suitable
transformation matrix for stator current variables, a new model
of IM is adopted during faulty conditions. This method is only
verified by some simulation tests. Moreover, the use of current
controller introduces problems under light load conditions,
which can be an important issue for vector control of
single-phase IMs. The proposed strategy in this paper not only
can be used for 3-phase IMs under open-phase fault it can be
also implemented for single-phase IM with main and auxiliary
windings.
The major contribution of this research is the development
of FOC algorithm for star-connected 3-phase IM drives, which
can be used for healthy and faulty (open-circuit fault) 3-phase
IMs. The proposed active fault-tolerant control method in this
paper does not need new FOC algorithm when a fault occurs. It
is based on conventional FOC algorithm, which is modified for
faulty conditions. It is shown that by switching the motor
parameters and using two different unbalanced transformation
matrices for stator current and voltage variables, the vector
control of faulty 3-phase IM is possible. Simulation and
experimental results are presented to show the main
characteristics of the proposed method and to confirm the
methodology and the modeling technique used in this research.
II.
Stator voltage equations:
0  idss  Md p 0  idrs 
vdss  rs  Lds p
 s 
 
  (1)
rs  Lqs p iqss   0 Mq p iqrs 
vqs   0
Rotor voltages equations:
vdrs   M d p
 s 
vqr   r M d
r M q  idss  rr  Lr p r Lr  idrs 
 
 
M q p  iqss    r Lr rr  Lr p  iqrs 
(2)
Stator flux equations:
sds  Lds 0  idss  Md 0  idrs 
 s 
 s 
 s 
qs   0 Lqs  iqs   0 Mq  iqr 
Rotor flux equations:
sdr   M d
 s 
qr   0
0  idss   Lr
  
M q  iqss   0
0  idrs 
 
Lr  iqrs 
(4)
Torque equations:

pole
M q iqss idrs  M d idss iqrs
2
2
Jpr  Br 
Te  Tl 
pole
Te 

(5)
where:
3
3
Lms , M q 
Lms
2
2
d
1
3
Lds  Lls  Lms , Lqs  Lls  Lms , p 
dt
2
2
Md 
(6)
In these equations, vsds, vsqs are the stator d-q axes voltages,
are the stator d-q axes currents, isdr, isqr are the rotor d-q
axes currents, λsds, λsqs are the stator d-q axes fluxes and λsdr and
λsqr are the rotor d-q axes fluxes in the stationary reference
frame (superscript “s”). rs and rr indicate the stator and rotor
resistances. Lds, Lqs, Lr, Lms, Md and Mq denote the stator and
rotor d-q axes self and mutual inductances. r is the motor
speed. Te and Tl are electromagnetic torque and load torque, J
and B are the moment of inertia and viscous friction coefficient
respectively. As can be seen from (1)-(5), the structure of
healthy and faulty 3-phase IM are the same. Actually, by
replacing Md=Mq=M=3/2Lms and Lds=Lqs=Ls=Lls+3/2Lms in the
faulty 3-phase IM equations, the equations of the healthy IM
are obtained [1], [4]. In summary, the difference between
model of healthy and faulty 3-phase IM is summarized in
Table 1.
isds, isqs
MATHEMATICAL MODEL OF FAULTY 3-PHASE
IM
The d-q model of 3-phase IMs under open-phase fault can be
expressed by the following equations (it can be noted that these
equations are not depended on which phase of stator windings
is opened; the modeling of 3-phase IM under open-phase fault
is fully discussed in [1], [4]):
(3)
TABLE I
THE DIFFERENCE BETWEEN MODEL OF HEALTHY AND FAULTY
3-PHASE IM
Faulty 3-Phase IM
Mq=√3/2Lms
Lqs=Lls+1/2Lms
Healthy 3-Phase IM
Mq=M=3/2Lms
Lqs=Ls=Lls+3/2Lms
Preperation of Papers for Journal of Power Electronics3
TABLE II
THE COMPARISON BETWEEN EQUATIONS OF FLUX, SPEED AND TORQUE FOR HEALTHY AND FAULTY 3-PHASE IM IN THE ROTATING
REFERENCE FRAME
Healthy IM
ai  cosmr , bi  sinmr
a i , bi , c i , d i
Transformation
matrix for stator
current
variables
Flux equation
Torque
equation
Speed
equation
ci  sinmr , di  cosmr

T   cos
sin 
mr
is
mr

r 
Te 
mr
sin  mr 
cos mr 
ai 
Faulty IM [4]
Md
cos mr , bi  sin mr
Mq
ai  M d / M q cos mr , bi  M q / M d sin mr
M
ci   d sin mr , d i  cos mr
Mq
T 
mr
is
Midsmr
1  Tr p
pole M
 r iqsmr
2 Lr
 mr   r 
Faulty IM [1]
Mi qsmr
Tr  r
 Md
 M cos mr
 q
 M d sin 
mr
 M
q

r 
Te 
T 
mr
s
mr
is
d

q
d
r 
1  Tr p
Te 
M q iqsmr
mr
M d M q idsmr
pole
2
mr   r 
Tr r
M q / M d sin mr 

M q / M d cos mr 
mr
q
M q idsmr
 mr   r 
1  Tr p
MdMq
Lr
 r iqsmr
M d M q iqsmr
Tr r
(8)
Among the various kinds of the vector control methods,
FOC method is the most highly adopted method for high
performance control of IM. In conventional Rotor FOC
(RFOC) the equations of machine is transformed to the rotating
reference frame. The transformation matrix that is used for this
purpose is:
sin  mr 
cos  mr 


T    MM / /MM cos
sin
pole M q
 r iqsmr
2 Lr
III. ROTOR FOC OF 3-PHASE IM UNDER
OPEN-PHASE FAULT
 cos  mr

 sin  mr

sin  mr 

cos mr 


ci   M d / M q sin mr , d i  M q / M d cos mr
(7)
In (7), θmr is the angle between the stationary reference
frame and the rotating reference frame (in this paper
superscript “mr” indicates that the variables are in the rotating
reference frame). For the unbalanced conditions used in this
paper, the conventional transformation matrix can be applied to
the rotor variables. However, to overcome the effect of
asymmetrical stator winding structure and thus to obtain a
non-pulsating torque, it is required to define an unbalanced
transformation matrix for stator variables. The reason of using
this transformation matrix is to obtain a model of faulty IM
with balanced structure.
A: Transformation matrix for stator current variables
A transformation matrix for stator current variables can be
considered as:
It can be shown that, structure of the torque equation for the
faulty IM can be obtained similar to a balanced 3-phase IM
torque using two different transformation matrices as presented
in [1] and [4]. In [1], the transformation matrix is given by:
ai 
Md
M
cos mr , bi  sin  mr , ci   d sin  mr , d i  cos mr
Mq
Mq
(9)
whereas in [4], it is given by:
ai  M d / M q cos mr , bi  M q / M d sin  mr
ci   M d / M q sin  mr , di  M q / M d cos mr
(10)
Based on (9) and (10), the transformation matrix, for stator
current variables are obtained as (11) and (12) respectively:
idsmr 
mr
 mr   Tis
i
 qs 
 
 Md
cos  mr
idss   M q


s
M
iqs    d sin  mr
 Mq

idsmr 
idss 
mr
 mr   Tis  s 
iqs 
iqs 
 M d / M q cos mr

 M d / M q sin  mr

sin  mr  s
i 
  dss 
cos  mr  iqs 


(11)
 
M q / M d sin  mr  idss 
 
M q / M d cos mr  iqss 
(12)
Using (11) and (12) and after simplification, the
4Journal of Power Electronics, Vol. ??, No. ?, Month Year
electromagnetic torque can be obtained as (13) and (14)
respectively [1], [4]:
TABLE III
THE COMPARISON BETWEEN EQUATIONS OF STATOR VOLTAGES FOR HEALTHY AND FAULTY 3-PHASE IM IN THE ROTATING REFERENCE
FRAME
Healthy IM
Stator
d-axis
voltage
equation
Stator
q-axis
voltage
equation
Te 
vdsmr  rs idsmr  ( Ls 
  mr ( Ls 
M
) pidsmr
Lr
mr
M 2 mr
M Mi  r
)iqs  ( )( ds
)
Lr
Lr
Tr
vqsmr  rs iqsmr  ( Ls 
  mr ( Ls 
Faulty IM
2
M2
) piqsmr
Lr

M 2 mr
)ids   mr M r
Lr
Lr
vdsmr  (
(
Mq
Lr
vqsmr  (
rs M  rs M
2
q
2 M d2
)(
(13)
pole
M d M q (iqsmr idrmr  idsmr iqrmr )
2
(14)
M q idsmr  r
Tr
rs M q2  rs M d2
2 M d2
  mr M q
pole
M q (iqsmr idrmr  idsmr iqrmr )
2
2
d
r
Lr
(
)idsmr  ( Lqs 
)(
M q2
Lr
) pidsmr   mr ( Lqs 
rs M q2  rs M d2
2 M d2
)iqsmr  ( Lqs 
rs M q2  rs M d2
2 M d2
M q2
Lr
M q2
Lr
)iqsmr
)(cos 2 mr idsmr  sin 2 mr iqsmr )
) piqsmr   mr ( Lqs 
M q2
Lr
)idsmr
)(  sin 2 mr idsmr  cos 2 mr iqsmr )
and,
Te 
As can be seen, by using (11) and (12), the torque equation
of a faulty 3-phase IM becomes similar to the torque equation
of a healthy 3-phase IM. The only difference between (13) and
healthy 3-phase IM torque equation is that, in (13) we have:
Mq=√3/2Lms but in the healthy conditions we have: M=3/2Lms.
Moreover, the difference between (14) and healthy 3-phase IM
torque equation is that, in (14) we have: √MdMq≈1.14Lms but in
the healthy conditions we have: M=3/2Lms. In conclusion, the
comparison between equations of flux, speed and torque for
healthy and faulty 3-phase IMs in the rotating reference frame
based on the presented transformation matrices for stator
current variables (equation (11) and (12)) is summarized in
Table 2 (to obtain these equations the assumptions λdrmr=|λr| and
λqrmr=0 have been considered). In Table 2, Tr is the rotor time
constant (Tr=Lr/rr). From the results of Table 2, it is possible to
adopt the indirect field-oriented control scheme, as shown in
Fig. 2, where |λr*| and Te* represent the reference flux and
torque respectively. In Fig. 2, the blue blocks represent the
portions of conventional FOC that require modifications under
faulty conditions.
Fig. 2. Current controller block diagram of Indirect RFOC for
star-connected 3-phase IM under normal and open-phase fault
conditions.
B: Transformation matrix for stator voltage variables
Like equation (8), a transformation matrix for stator voltage
variables can be written as:
(15)
Using equation (15), the faulty 3-phase IM stator voltage
equations can be written as:
T  vv
mr
vs

s
ds
s
qs
0  mr

rs  Lds p
mr
T
  Tvs 
rs  Lqs p  is
 0

  T  ii
 
1
mr
is


  (16)
s
ds
s
qs
0  mr 1 mr idrs 
M d p
T
Ts  s 
 Tvsmr 
M q p  s
 0
iqr 
In equation (16), for simplicity, (11) (rather than (12)) is
used for [Tismr]. As a result, equation (16) can be written as:
 
  
Preperation of Papers for Journal of Power Electronics5
 Mq
 mr
M
bv   q rds cos  mr
rds sin  mr  ids 
M
Md
 i mr 
d v   d
rqs cos  mr   qs 
 rqs sin  mr
 Mq

M
mr
bv   q Lds cos  mr
Lds sin  mr   pids 
M
M

d
  piqsmr 
d v   d


sin
cos
L
L


qs
mr
qs
mr


vdsmr  av
 mr   
vqs   cv
a
 v
 cv
a
 mr  v
 cv
a
 mr  v
 cv
a
 v
 cv
 Mq
 mr
 Mq
bv  
Lds sin  mr
Lds cos  mr  ids 
M
Md
 i mr 
d v   d
 Lqs sin  mr   qs 
 Lqs cos  mr
bv   M d sin  mr  M d cos  mr  idrmr 
 

d v   M q cos  mr  M q sin  mr  iqrmr 
bv  M d cos mr

d v   M q sin  mr
 M d sin  mr   pidrmr 


M q cos mr   piqrmr 
the faulty 3-phase IM stator voltage equations are obtained
similar to the balanced 3-phase IM stator voltage equations. As
a result, av, bv, cv and dv can be considered as:
av   cos mr , bv  (
cv  sin  mr , d v  (
 Lds Lr M q  M d2 M q
Lqs Lr M d  M d M q2
 Lds Lr M q  M d2 M q
Lqs Lr M d  M d M q2
) sin  mr
(19)
) cos mr
Based on (19) and by considering (Md/Mq)2=Lds/Lqs the
proposed transformation matrix for stator voltage variables is
obtained as (20) (in 3-phase IM under open-phase fault:
Mq=√3/2Lms, Md=3/2Lms, Lqs=Lls+1/2Lms, Lds=Lls+3/2Lms,
Lms˃˃Lls therefore the assumption Lqs/Lds=(Mq/Md)2 is valid).
(17)
TABLE IV
THE COMPARISON BETWEEN CONVENTIONAL AND PROPOSED VECTOR CONTROL METHODS
3 to 2 or 2 to 2 transformation for the
stator currents based on [1], [4]
Rotational transformation matrix for
the stator currents based on (11), [1]
Conventional controller
Proposed controller
1
1

1 
 ias 
idss 
2
2
2 i 


 s 
3
3  bs 
3
iqs 
0
 ics 
2
2 

idss 
2 1  1 ias 
 s 
2 1 1  ibs 
iqs 
idsmr   cos mr
 mr   
iqs   sin  mr
Inverse of transformation matrix for
the stator voltages
based on (20)
vdss  cos mr
 s 
vqs   sin mr
Stator self and mutual inductance
based on Table 2, Table 3
Ls  Lls 
Stator resistance based on Table 3
sin  mr  idss 
 
cos mr  iqss 
 sin mr  vdsmr 
 
cos mr  vqsmr 
3
3
Lms , M  Lms
2
2
rs
 Md
cos  mr
idsmr   M q


 mr 
iqs   M d sin 
mr
 Mq

 cos mr
vdss  
 s    M q sin 
mr
vqs   M
d


sin  mr  s
i 
  dss 
cos mr  iqs 


sin  mr  mr
 vds 
Mq

cos mr  vqsmr 
Md
  
1
3
Lms , M q 
Lms
2
2
rs M q2  rs M d2 2
 rs
2 M d2
3
Lqs  Lls 
Extra terms in the stator voltage
equations based on Table 3
--------------------
assuming that,
av  bv .Z 5 . cot  mr , cv  d v .Z 5 . tan  mr

M q2

Lqs 
Lr

Z5  
Lds M q M d M q



Md
Lr








(20)
(18)
It is expected using (20), the stator voltage equations of
faulty motor in the rotating reference frame becomes similar to
6Journal of Power Electronics, Vol. ??, No. ?, Month Year
the healthy 3-phase IMs stator voltage equations. The
comparison between equations of stator voltages for healthy
and faulty 3-phase IM is given in Table 3. As can be seen from
Table 3, the structures of stator voltage equations for healthy
and faulty 3-phase IMs are similar; the difference is in the
parameters (rs→rsMq2+rsMd2/2Md2, M→Mq and Ls→Lqs). It is
also noted that the stator voltage equations of faulty machine
contain the extra terms:
vdset  (
v qset  (
rs M q2  rs M d2
2 M d2
rs M q2  rs M d2
2 M d2
)(cos 2 mr idsmr  sin 2 mr iqsmr )
(21)
)(  sin 2 mr idsmr  cos 2 mr iqsmr )
(22)
In summary the comparison between equations of RFOC of
faulty 3-phase IM using the proposed method and the equations
of RFOC for healthy 3-phase IM is summarized in Table 4.
Finally, based on Table 2, Table 3 and Table 4, the proposed
vector control of 3-phase IM under normal and open-phase
fault conditions can be constructed as shown in Fig. 3. In this
figure, the blue blocks show the required modifications needed
to the conventional vector control so that it can be applied to
link voltage. The reason of using M-File instead of using the
IM model from SimPowerSystem provided with MATLAB is
that the neutral point of the IM in SimPowerSystem is not
accessible and hence cannot be used to model the faulty IM
applied in this work. The parameters of simulated IM are listed
in Appendix. The fourth order Runge-Kutta algorithm has been
used to solve the healthy and faulty IM equations.
Fig. 4 shows the results obtained from the simulation of a
3-phase IM which is directly connected to a balanced 3-phase
power supply. From t=0s to t=10s, the IM runs in healthy mode
and the motor is modeled using a healthy 3-phase IM equations.
At t= 10s, an open-phase fault is introduced in phase “c” and
hence for t൒ 10s the motor is simulated using the faulty
machine equations as given by (1)-(6).
As can be seen from Fig. 4, a significant amount of
oscillation in the torque, and hence speed, appears right after
the open-phase fault is introduced. The oscillation in the torque
is due to the unbalanced structure of the IM, mainly in its d and
q inductances. Due to the connection between the neutral point
of the stator and the neutral point of the supply, independent
currents flow in the remaining phases as can be seen from
Fig. 3. Block diagram of the proposed IRFOC for star-connected 3-phase IM under normal and open-phase fault conditions.
the faulty 3-phase IM.
IV. SIMULATION RESULTS
To show the dynamic behavior of 3-phase IM under
open-phase fault, simulations are conducted by using
MATLAB (M-File) software. The model of the faulty IM
(equations (1)-(6)) assumes a connection between the neutral of
the star connected IM machine and the mid-point of the DC
Figure 4(d).
Preperation of Papers for Journal of Power Electronics7
(a)
(d)
(b)
(e)
(c)
(f)
Fig. 4. Simulation results of dynamic behavior of 3-phase IM
under normal and open-phase fault operating conditions; (a): Stator
a-axis current, (b): Stator b-axis current, (c): Zoom of stator b-axis
current, (d): Zoom of stator currents, (e): Speed, (f): Torque.
8Journal of Power Electronics, Vol. ??, No. ?, Month Year
V.
EXPERIMENTAL RESULTS
To study on the performance of the conventional and
proposed methods for vector control of healthy and faulty
3-phase IM, a prototype implementation of a star-connected
3-phase IM drive was carried out. Experimental tests were
carried out based on Fig. 3. The scheme used for the
experimental setup is shown in Fig. 5.
Fig. 5. Scheme used for experimental setup.
This paper investigates the use of the scheme in Fig. 5 for
feeding a 3-phase IM under open-phase fault. Two large
capacitors are connected in series between the positive and
negative rail of the DC link voltage in order to create a
mid-point DC link voltage. When an open-phase fault occur in
one of the phases, the remaining two phases can only be
controlled independently if the neutral point of the IM is
connected to mid-point of the DC link (as indicated in Fig. 5).
During healthy mode operation, the 3-phase machine is fed
with PWM voltage generated by the FOC controller. In healthy
Fig. 6. Photograph of the experimental system.
mode, the stator current that flows in the neutral wire is very
small, which is only due to the PWM operation of the inverter
[21]. This paper considers the use of the simple topology
shown in Fig.5; it should be emphasized that the focused is not
on the topology but on the analysis, design and implementation
of the vector control strategy based FOC for a star-connected
3-phase IM drive under open-phase fault.
A photograph of the developed experimental rig is shown in
Fig. 6 where the 3-phase IM is supplied by a 3-phase IGBT
Voltage Source Inverter (VSI). To emulate the fault condition,
an electronic switch is connected in series with phase “c” and it
is opened under faulty condition. The torque transient is
expected to cause due to the high di/dt in phase “c” where it
is cut-off. The high di/dt causes large induced voltage across
the inductances and subsequently high voltage across the
switches. To prevent large induced voltages due to the high
di/dt at the instant of the fault, the phase can be opened at a
zero crossing as used in [21]. However, in practice an open
phase fault can occur at any time (and at any current level)
and as a result an electrical arc will temporarily present at the
instant of an open phase fault. It is not the scope of this paper
to suppress this high voltage transient. In the experimental, a
simple RC snubber circuits are employed for high voltage
protection.A DC voltage of 240V is used for the DC link and
two Hall effect sensors and an incremental encoder are used to
measure the stator phase currents and rotor speed respectively.
An open-phase fault is introduced in phase “c” of the stator
windings therefore, the two sensors are placed in phase “a” and
“b” (in practice three sensors should be used since the faulty
phase is not known).The code is automatically generated using
MATLAB/SIMULINK and downloaded to dSPACE DS1104
real-time R&D Controller Board. To generate the PWM
signals, a sinusoidal PWM method with a switching frequency
of 10kHz with a dead time of 2μs is used. The sampling time of
the control algorithm is 200μs.
The conventional and proposed control strategies for both
healthy and faulty 3-phase IMs, are individually tested under
the same conditions and experimental setup to obtain proper
comparison results (the conventional IRFOC method based
voltage controller is fully discussed in [22]). The parameters
for the star-connected 3-phase IM are given in Appendix. In
order to verify the proposed fault-tolerant control strategy,
several experiments are conducted as follows.
A: No-load condition
To confirm the effectiveness of the proposed control strategy
under no-load condition, two tests were performed. In the first
test (Fig. 7), the 3-phase IM is started under normal condition
and then a phase cut-off is applied at 20.3s. In the second test
(Fig. 8), the 3-phase IM started under normal condition and
then a phase cut-off is applied at 21.4s. In the first test,
conventional FOC is applied throughout the duration, however
Preperation of Papers for Journal of Power Electronics9
for the second test, the proposed FOC (as outline in Table 4) is
applied immediately after the fault (instantaneous fault
detection is assumed; the fault detection in this paper is based
on comparison between real speed and reference speed). In Fig.
7 and Fig. 8 the reference speed during open-phase fault is
changed from 55rad/s to 60rad/s. Moreover, the reference
rotor flux is kept constant at the nominal value of 1Wb.
Throughout the experiment, the torque during the healthy and
faulty conditions is estimated based on equations given in
Table 2.
As shown in Fig. 7 and Fig. 8, during fault condition, the
proposed algorithm exhibits a good tracking error
performances and faster response when compared to the
conventional FOC. As can be seen from Fig. 8, the proposed
FOC method produces smaller torque and speed ripples
compared to the conventional FOC method (Fig. 7). From the
zoomed torque response of Fig. 7 and Fig. 8 it can be seen
that the ripple of the conventional technique is almost 4N.m,
whereas for the proposed FOC, the ripple is around 2N.m (in
this test the ripple of the FOC technique for healthy machine
is almost 0.6N.m). Also, it is noted that using the proposed
controller, the time to reach steady-state is shorter than
conventional controller. As shown, the time to reach
steady-state using conventional controller is about 2.5s
whereas the time to reach steady-state using proposed
controller is about 2s. It can be seen that in comparison with
proposed controller, the conventional controller is not able to
provide such a desired performance due to the unbalance
structure of the faulty IM.
Notice that although both conventional and proposed
schemes are able to almost control star-connected 3-phase IM,
in general, the proposed vector control drive system provides
10Journal of Power Electronics, Vol. ??, No. ?, Month Year
Fig. 7. Experimental results of the conventional IRFO controller from top to bottom: Stator a-axis current, Zoom of stator a-axis
current, Stator c-axis current, Speed, Zoom of speed, Torque, Zoom of torque.
Preperation of Papers for Journal of Power Electronics11
Fig. 8. Experimental results of the proposed IRFO controller from top to bottom: Stator a-axis current, Zoom of stator a-axis
current, Stator c-axis current, Speed, Zoom of speed, Torque, Zoom of torque.
faster response and better steady-state performance especially
in decreasing the speed and torque oscillations.
12Journal of Power Electronics, Vol. ??, No. ?, Month Year
B: Load condition
Fig. 9 shows the experimental results of the proposed FOC
applied to the open-phase fault IM under loaded condition. The
motor is operated at a steady speed of 55rad/s and a step load
torque of 1.5N.m applied at 29s (the limitation of the maximum
permissible torque for star-connected 3-phase IM during
open-phase fault is about 38% of the rated torque [23]). Fig.
9(a) shows the reference and the actual (measured) rotor speed
signals and Fig. 9(b) shows the applied load step and torque
response. As can be seen from Fig. 9, the torque of faulty
machine increases accordingly to applied load disturbance.
Moreover, after a slight disturbance, the speed recovered to the
reference speed of 55rad/s. With the proposed FOC controller,
the torque oscillation of faulty machine of about 2N.m is
recorded before and after the load disturbance is introduced. It
can be seen that the rotor speed signal closely follows the
reference speed before and after the load disturbance.
significantly affect the accuracy of the proposed RFOC method
and hence, the dynamics of the drive system. In this work, the
gains of the PI controllers during healthy and faulty conditions
are obtained based on trial-and-error process. A further
investigation on the optimum selection of the gains for the PI
controllers has to be carried out to improve the performance of
the open-phase fault IM.
VI. CONCLUSION
This paper has presented a fault-tolerant control strategy
based on FOC for a high performance vector control of
star-connected 3-phase IM drive. It is shown that with some
modifications, it is possible to apply conventional FOC
algorithm to 3-phase IMs under open-phase fault. The
proposed fault-tolerant control method is based on
transformation matrices which are used to obtain a model of
faulty IM with balanced structure. The proposed FOC of faulty
3-phase IM drive under open-phase fault can also be applied to
a single-phase IM with two windings (main and auxiliary
windings). In comparison with conventional FOC, the modified
FOC algorithm has managed to reduce the torque and speed
oscillation and at the same has improved the dynamic response.
Experiments are used to validate the effectiveness of the
proposed controller.
APPENDIX
(a)
Ratings and parameters of 3-phase IM:
Power: 1.5kW, V=400V, f=50Hz, poles=4, rs=5.5Ω, rr=4.51Ω,
M=0.292H, Ls=Lr=0.3065H, J=0.0086kg.m2
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Fig. 9. Experimental results of the proposed IRFO controller
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Mohammad Jannati received the B.Sc.
degree in electrical engineering from the
University of Mazandaran, Iran, in 2008, the
M.Sc. degree in electrical engineering from
the University of Guilan, Iran, in 2010, and is
currently pursuing the Ph.D. degree in
electrical engineering at the Universiti
Teknologi Malaysia, Malaysia. His research
interests include the control of AC drives.
Nik Rumzi Nik Idris received the B.Eng.
degree in Electrical Engineering from the
University of Wollongong, Australia, the
M.Sc. degree in power electronics from
Bradford University, West Yorkshire, U.K.,
and the Ph.D. degree from Universiti
Teknologi Malaysia (UTM) in 1989, 1993,
and 2000, respectively. He is an Associate
Professor at the Universiti Teknologi Malaysia, and currently the
Chair for the Power Electronics Chapter of IEEE Malaysia
Section. His research interests include control of ac drive
systems and DSP applications in power electronic systems.
Mohd Junaidi Abdul Aziz was born in
Kuala Terengganu, Malaysia, in 1979. He
received his B.S. and M.S. in Electrical
Engineering from the Universiti Teknologi
Malaysia (UTM), Malaysia, in 2000 and
2002, respectively, and his Ph.D. in Electrical
Engineering from The University of
Nottingham, U.K, in 2008. Since 2008, he has
been with the Faculty of Electrical Engineering, Universiti
Teknologi Malaysia (UTM), Malaysia, where he is currently a
Senior Lecturer. His research interests include power electronics
and electric vehicles with a special focus on battery management
systems.