A method for the faulttolerant vector control of starconnected 3phase Induction Motor (IM) drive systems based on FieldOriented Control (FOC) is proposed in this paper. This method enables the control of a 3phase IM in the presence of an openphase failure in one of its phases without the need for control structure changes to the conventional FOC algorithm. The proposed drive system significantly reduces the speed and torque pulsations caused by an openphase fault in the stator windings. The performance of the proposed method was verified using MATLAB (MFile) simulation as well experimental tests on a 1.5kW 3phase IM drive system. This paper experimentally compares the operation of the proposed faulttolerant vector controller and a conventional vector controller during openphase fault.
I. INTRODUCTION
The FieldOriented Control (FOC) technique for 3phase Induction Motors (IMs) is widely adopted by industries to obtain high performance from 3phase IM drive systems. The conventional FOC algorithm, which is used for healthy 3phase IM drives, cannot be used for a faulty 3phase IM drive due to the fact that the conventional FOC was designed based on a healthy machine model
[1]
. Using the conventional FOC for faulty 3phase IM drives will degrade the dynamic performance of drive systems. In this regard, it is necessary to design a drive system that provides robustness against fault conditions
[1]

[5]
.
Generally, 3phase IM drives are exposed to various failures including failures in the in the inverter
[6]
,
[7]
, failures in the mechanical or electrical sensors
[5]
,
[8]
and failures related to the electrical motor including faults in the stator
[1]
,
[9]
and/or faults in the rotor
[10]
,
[11]
.
Fig. 1
shows the classification of faults in squirrelcage 3phase IM drives. In some critical applications, the operation of the drive system cannot be interrupted by faulty conditions for mainly safety reasons. Thus, for these applications, faulttolerant control is essential. Based on this classification of faults, various faulttolerant control methods have been suggested in the literature including both passive and active methods. A passive method can be ensured by conventional robust control methods such as the H
_{∞}
[12]
,
[13]
. Despite the robustness of this method against disturbances, its performance under healthy conditions is not optimized. In active methods after fault detection and fault diagnosis, a new set of control parameters or a new control structure is applied
[1]

[5]
and
[14]

[20]
. These methods have good performances under both healthy and faulty conditions. However, they requires a different control algorithm under faulty conditions.
Classification of faults in squirrelcage 3phase IM drive.
A large number of studies have been conducted on the implementation of vector control techniques for electrical machines under stator opencircuit faults
[1]

[4]
and
[14]

[20]
. Most of these works focused on developing vector control methods of faulty Permanent Magnet Synchronous Motors (PMSMs) and multiphase IMs (five and six phase)
[14]

[17]
. In
[18]
,
[19]
the analysis of starconnected 3phase IMs in an openphase fault indicates that the odd harmonic voltages of the magnitude and phase angle can be injected at the machine terminal to compensate torque pulsations. In
[3]
,
[20]
, vector and scalar control methods to control deltaconnected 3phase IM drives under a stator winding openphase fault based on a current controller has been proposed and implemented. The modeling and FOC of a starconnected 3phase IM under openphase fault using a current controller has also been presented in
[4]
. In this study, by using a suitable transformation matrix for the stator current variables, a new model of an IM is adopted during faulty conditions. This method is only verified by simulation results. Moreover, the use of a current controller introduces problems under light load conditions, which can be an important issue for the vector control of singlephase IMs. The proposed strategy in this paper can be used for 3phase IMs under an openphase fault and for singlephase IMs with main and auxiliary windings.
The major contribution of this study is the development of a FOC algorithm for starconnected 3phase IM drives, which can be used for healthy and faulty (opencircuit fault) 3phase IMs. The proposed active faulttolerant control method in this paper does not need a new FOC algorithm when a fault occurs. It is based on the 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 the stator current and voltage variables, the vector control of a faulty 3phase IM is possible. Simulation and experimental results are presented to show the main characteristics of the proposed method and to confirm the methodology and modeling technique used in this paper.
II. MATHEMATICAL MODEL OF A FAULTY 3PHASE IM
The dq model of 3phase IMs under an openphase fault can be expressed by the following equations (it should be noted that these equations do not depend on which phase of the stator windings is opened; and the modeling of 3phase IMs under an openphase fault is fully discussed in
[1]
,
[4]
):
Stator voltage equations:
Rotor voltages equations:
Stator flux equations:
Rotor flux equations:
Torque equations:
where:
In these equations,
v^{s}_{ds}
and
v^{s}_{qs}
are the stator dq axes voltages,
i^{s}_{ds}
and
i^{s}_{qs}
are the stator dq axes currents,
i^{s}_{dr}
and
i^{s}_{qr}
are the rotor dq axes currents,
λ^{s}_{ds}
and
λ^{s}_{qs}
are the stator dq axes fluxes, and
λ^{s}_{dr}
and
λ^{s}_{qr}
are the rotor dq axes fluxes in the stationary reference frame (superscript “
s
”).
r_{s}
and
r_{r}
indicate the stator and rotor resistances.
L_{ds}
,
L_{qs}, L_{r}, L_{ms}, M_{d}
and
M_{q}
denote the stator and rotor dq axes self and mutual inductances.
ω_{r}
is the motor speed.
T_{e}
and
T_{l}
are the electromagnetic torque and load torque,
J
and
B
are the moment of inertia and the viscous friction coefficient, respectively. As can be seen from (1)(5), the structure of healthy and faulty 3phase IMs are the same. Actually, by replacing
M_{d}
=
M_{q}
=
M
=3/2
L_{ms}
and
L_{ds}
=
L_{qs}
=
L_{s}
=
L_{ls}
+3/2
L_{ms}
in the faulty 3phase IM equations, the equations of healthy IMs are obtained
[1]
,
[4]
. The differences between the models of healthy and faulty 3phase IMs are summarized in
Table I
.
THE DIFFERENCE BETWEEN MODEL OF HEALTHY AND FAULTY 3PHASE IM
THE DIFFERENCE BETWEEN MODEL OF HEALTHY AND FAULTY 3PHASE IM
III. ROTOR FOC OF 3PHASE IMS UNDER AN OPENPHASE FAULT
Among the various kinds of vector control methods, the FOC method is the most highly adopted method for the high performance control of IMs. In the conventional Rotor FOC (RFOC) the equations of a machine are transformed to the rotating reference frame. The transformation matrix that is used for this purpose is:
In (7),
θ_{mr}
is the angle between the stationary reference frame and the rotating reference frame (in this paper the 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 the asymmetrical stator winding structure to obtain a nonpulsating torque, it is necessary to define an unbalanced transformation matrix for stator variables. The reason for using this transformation matrix is to obtain a model of a faulty IM with a 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 the structure of the torque equation for a faulty IM can be obtained similar to that of a balanced 3phase IM torque using two different transformation matrices as presented in
[1]
and
[4]
. In
[1]
, the transformation matrix is given by:
Meanwhile, in
[4]
, it is given by:
Based on (9) and (10), the transformation matrixes for the stator current variables are obtained as (11) and (12) respectively:
Using (11) and (12) and after simplification, the electromagnetic torque can be obtained as (13) and (14), respectively
[1]
,
[4]
:
and:
As can be seen, by using (11) and (12), the torque equation of a faulty 3phase IM becomes similar to that of a healthy 3phase IM. The only difference between (13) and a healthy 3phase IM torque equation is that, in (13):
M_{q}
=√3/2
L_{ms}
, but in the healthy condition:
M
=3/2
L_{ms}
. Moreover, the difference between (14) and a healthy 3phase IM torque equation is that, in (14): √
M_{d}
M_{q}
≈1.14
L_{ms}
, but in the healthy condition:
M
=3/2
L_{ms}
. A comparison between the equations of the flux, speed and torque for healthy and faulty 3phase IMs in the rotating reference frame based on the presented transformation matrices for stator current variables (equation (11) and (12)) is summarized in
Table II
(to obtain these equations the assumptions
λ_{dr}^{mr}
=
λ_{r}
 and
λ_{qr}^{mr}
=0 have been considered). In
Table II
,
T_{r}
is the rotor time constant (
T_{r}
=
L_{r}
/
r_{r}
). From the results of
Table II
, it is possible to adopt the indirect fieldoriented control scheme, as shown in
Fig. 2
, where 
λ_{r}
^{*}
 and
T_{e}
^{*}
represent the reference flux and torque, respectively. In
Fig. 2
, the blue blocks represent the portions of the conventional FOC that require modifications under faulty conditions.
Current controller block diagram of Indirect RFOC for starconnected 3phase IM under normal and openphase fault conditions.
THE COMPARISON BETWEEN EQUATIONS OF FLUX, SPEED AND TORQUE FOR HEALTHY AND FAULTY 3PHASE IM IN THE ROTATING REFERENCE FRAME
THE COMPARISON BETWEEN EQUATIONS OF FLUX, SPEED AND TORQUE FOR HEALTHY AND FAULTY 3PHASE IM IN THE ROTATING REFERENCE FRAME
 B. Transformation Matrix for Stator Voltage Variables
Like equation (8), a transformation matrix for the stator voltage variables can be written as:
Using equation (15), the faulty 3phase IM stator voltage equation can be written as:
In equation (16), for the sake of simplicity, (11) (rather than (12)) is used for [
T_{is}^{mr}
]. As a result, equation (16) can be written as:
assuming that:
The faulty 3phase IM stator voltage equations are obtained similar to the balanced 3phase IM stator voltage equations. As a result,
a_{v}, b_{v}, c_{v}
and
d_{v}
can be considered as:
Based on (19) and by considering (
M_{d}
/
M_{q}
)
^{2}
=
L_{ds}
/
L_{qs}
, the proposed transformation matrix for the stator voltage variables is obtained as (20) (in a 3phase IM under openphase fault:
M_{q}
=√3/2
L_{ms}
,
M_{d}
=3/2
L_{ms}
,
L_{qs}
=
L_{ls}
+1/2
L_{ms}
,
L_{ds}
=
L_{ls}
+3/2
L_{ms}
, and
L_{ms}
˃˃
L_{ls}
. Therefore, the assumption
L_{qs}
/
L_{ds}
=(
M_{q}
/
M_{d}
)
^{2}
is valid).
Using (20), it is expected that the stator voltage equations of a faulty motor in the rotating reference frame will become similar to the healthy 3phase IMs stator voltage equations. A comparison between the equations of the stator voltages for healthy and faulty 3phase IMs is given in
Table III
. As can be seen from
Table III
, the structures of the stator voltage equations for healthy and faulty 3phase IMs are similar. The difference is in the parameters (
r_{s}
→
r_{s}
M_{q}
^{2}
+
r_{s}M_{d}
^{2}
/2
M_{d}
^{2}
,
M
→
M_{q}
and
L_{s}
→
L_{qs}
). It is also noted that the stator voltage equations of a faulty machine contain the extra terms:
THE COMPARISON BETWEEN EQUATIONS OF STATOR VOLTAGES FOR HEALTHY AND FAULTY 3PHASE IM IN THE ROTATING REFERENCE FRAME
THE COMPARISON BETWEEN EQUATIONS OF STATOR VOLTAGES FOR HEALTHY AND FAULTY 3PHASE IM IN THE ROTATING REFERENCE FRAME
A comparison between the equations of the RFOC of a faulty 3phase IM using the proposed method and the equations of the RFOC for a healthy 3phase IM is summarized in
Table IV
.
THE COMPARISON BETWEEN CONVENTIONAL AND PROPOSED VECTOR CONTROL METHODS
THE COMPARISON BETWEEN CONVENTIONAL AND PROPOSED VECTOR CONTROL METHODS
Finally, based on
Table II
,
Table III
and
Table IV
, the proposed vector control of a 3phase IM under normal and openphase fault conditions can be constructed as shown in
Fig. 3
. In this figure, the blue blocks show the modifications needed for the conventional vector control so that it can be applied to a faulty 3phase IM.
Block diagram of the proposed IRFOC for starconnected 3phase IM under normal and openphase fault conditions.
IV. SIMULATION RESULTS
To show the dynamic behavior of a 3phase IM under an openphase fault, simulations are conducted using MATLAB (MFile) software. The model of a faulty IM (equations (1)(6)) assumes a connection between the neutral of the star connected IM machine and the midpoint of the DC link voltage. The reason for using MFile instead the IM model from SimPowerSystem provided with MATLAB is that the neutral point of the IM in SimPowerSystem is not accessible. As a result, it cannot be used to model the faulty IM applied in this paper. The parameters of the simulated IM are listed in the Appendix. The fourth order RungeKutta algorithm has been used to solve the healthy and faulty IM equations.
Fig. 4
shows the results obtained from the simulation of a 3phase IM which is directly connected to a balanced 3phase power supply. From t=0s to t=10s, the IM runs in the healthy mode and the motor is modeled using healthy 3phase IM equations. At t= 10s, an openphase fault is introduced in phase “c”. As a result, at t≥10s, the motor is simulated using the faulty machine equations given by (1)(6).
Simulation results of dynamic behavior of 3phase IM under normal and openphase fault operating conditions. (a) Stator aaxis current. (b) Stator baxis current. (c) Zoom of stator baxis current. (d) Zoom of stator currents. (e) Speed. (f) Torque.
As can be seen from
Fig. 4
, a significant amount of oscillations appear in the torque, and hence speed, right after the openphase fault is introduced. The oscillations in the torque are 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 in Figure 4(d).
V. EXPERIMENTAL RESULTS
To study the performances of the conventional and proposed methods for the vector control of healthy and faulty 3phase IMs, a prototype of a starconnected 3phase IM drive was built in the laboratory. Experimental tests were carried out based on
Fig. 3
. The scheme used for the experimental setup is shown in
Fig. 5
.
Scheme used for experimental setup.
This paper investigates the use of the scheme shown in
Fig. 5
for feeding a 3phase IM under an openphase fault. Two large capacitors are connected in series between the positive and negative rails of the DC link voltage in order to create a midpoint DC link voltage. When an openphase fault occurs in one of the phases, the remaining two phases can only be controlled independently if the neutral point of the IM is connected to the midpoint of the DC link (as indicated in
Fig. 5
). During healthy mode operation, the 3phase machine is fed with PWM voltage generated by the FOC controller. In the healthy mode, the stator current that flows in the neutral wire is very small 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 focuse is not on the topology but on the analysis, design and implementation of the vector control strategy based FOC for a starconnected 3phase IM drive under an openphase fault.
A photograph of the developed experimental rig is shown in
Fig. 6
, where the 3phase IM is supplied by a 3phase IGBT Voltage Source Inverter (VSI). To emulate the fault condition, an electronic switch is connected in series with phase “c” and it is opened to achieve the faulty condition. A torque transient is expected due to the high di/dt in phase “c” where it is cutoff. The high di/dt also causes a large induced voltage across the inductances and a subsequently high voltage across the switches. To prevent the large induced voltages due to a high di/dt at the instant of a fault, the phase can be opened at the zero crossing as in
[21]
. However, in practice, an open phase fault can occur at any time (and at any current level). As a result, an electrical arc temporarily presents at the instant of an open phase fault. However, it is not within the scope of this paper to suppress this high voltage transient. In the experimental, 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 openphase fault is introduced in phase “c” of the stator windings. Therefore, the two sensors are placed in phases “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. Then it is downloaded to a dSPACE DS1104 realtime 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.
Photograph of the experimental system.
The conventional and proposed control strategies for both healthy and faulty 3phase IMs, are individually tested under the same conditions to obtain proper comparison results (the conventional IRFOC method based voltage controller is fully discussed in
[22]
). The parameters of the starconnected 3phase IM are given in the Appendix. In order to verify the proposed faulttolerant control strategy, several experiments are conducted as follows.
 A. NoLoad Condition
To confirm the effectiveness of the proposed control strategy under the noload condition, two tests were performed. In the first test (
Fig. 7
), the 3phase IM is started under normal conditions and then a phase cutoff is applied at 20.3s. In the second test (
Fig. 8
), the 3phase IM is started under normal conditions and then a phase cutoff is applied at 21.4s. In the first test, the conventional FOC is applied throughout the duration of the text. However, for the second test, the proposed FOC (as outline in
Table IV
) is applied immediately after the fault (instantaneous fault detection is assumed; the fault detection in this paper is based on a comparison between the real speed and the reference speed). In
Fig. 7
and
Fig. 8
the reference speed during an openphase 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 the equations given in
Table II
.
Experimental results of the conventional IRFO controller from top to bottom: Stator aaxis current, Zoom of stator aaxis current, Stator caxis current, Speed, Zoom of speed, Torque, Zoom of torque.
Experimental results of the proposed IRFO controller from top to bottom: Stator aaxis current, Zoom of stator aaxis current, Stator caxis current, Speed, Zoom of speed, Torque, Zoom of torque.
As shown in
Fig. 7
and
Fig. 8
, during the fault condition, the proposed algorithm exhibits good tracking error performances and a faster response when compared to the conventional FOC. As can be seen from
Fig. 8
, the proposed FOC method produces a smaller torque and fewer speed ripples compared to the conventional FOC method (
Fig. 7
). From the zoomed in torque response of
Fig. 7
and
Fig. 8
it can be seen that the ripple of the conventional technique is almost 4N.m. Meanwhile, for the proposed FOC, the ripple is around 2N.m (in this test the ripple of the FOC technique for a healthy machine is almost 0.6N.m). In addition, it is noted that when using the proposed controller, the time to reach the steadystate is shorter than with the conventional controller. As can be seen, the time to reach the steadystate using the conventional controller is about 2.5s, whereas the time to reach steadystate using the proposed controller is about 2s. It can be seen that when compared with proposed controller, the conventional controller is not able to provide such a desired performance due to the unbalance structure of the faulty IM.
Although the conventional and proposed schemes are both able to almost control the starconnected 3phase IM, in general, the proposed vector control drive system provides a faster response and a better steadystate performance especially in decreasing speed and torque oscillations.
 B: Load Condition
Fig. 9
shows experimental results of the proposed FOC applied to an openphase fault IM under the loaded condition. The motor is operated at a steady speed of 55rad/s and a step load torque of 1.5N.m is applied at 29s (the limitation of the maximum permissible torque for a starconnected 3phase IM during an openphase fault is about 38% of the rated torque
[23]
).
Fig. 9
(a) shows the reference and 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 the faulty machine increases according to the 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 the 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.
Experimental results of the proposed IRFO controller during load condition. (a) Speed. (b) Torque.
In this paper, the vector control of a starconnected 3phase IM under an openphase fault is implemented with some minor changes to the conventional FOC strategy. These are changes to the transformation matrices, motor parameters and PI controller coefficients. It should be noted that the PI controller coefficients significantly affect the accuracy of the proposed RFOC method and subsequently the dynamics of the drive system. In this paper, the gains of the PI controllers during healthy and faulty conditions are obtained based on the trialanderror 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 openphase fault IM.
VI. CONCLUSION
This paper presented a faulttolerant control strategy based on FOC for the high performance vector control of a starconnected 3phase IM drive. It is shown that with some modifications, it is possible to apply the conventional FOC algorithm to 3phase IMs under an openphase fault. The proposed faulttolerant control method is based on transformation matrices that are used to obtain a model of a faulty IM with a balanced structure. The proposed FOC of a faulty 3phase IM drive under an openphase fault can also be applied to a singlephase IM with two windings (main and auxiliary windings). Compared with the conventional FOC, the modified FOC algorithm has managed to reduce the torque and speed oscillations. In addition, it has also managed to improve the dynamic response. Simulation and experimental results are used to validate the effectiveness of the proposed controller.
Acknowledgements
The authors would like to thank the Universiti Teknologi Malaysia (UTM) (Q.J130000.2523.12H30) and the Ministry of Education of the Malaysian government for providing the funding for this research.
BIO
Mohammad Jannati received his B.S. degree in Electrical Engineering from the University of Mazandaran, Babolsar, Iran, in 2008; and his M.S. degree in Electrical Engineering from the University of Guilan, Rasht, Iran, in 2010. He is presently working towards his Ph.D. degree in Electrical Engineering at the Universiti Teknologi Malaysia (UTM), Kuala Lumpur, Malaysia. His current research interests include the control of AC drives.
Nik Rumzi Nik Idris received his B.S. degree in Electrical Engineering from the University of Wollongong, Wollongong, NSW, Australia, in 1989; his M.S. degree in Power Electronics from Bradford University, West Yorkshire, England, UK, in 1993; and his Ph.D. degree from the Universiti Teknologi Malaysia (UTM), Kuala Lumpur, Malaysia, in 2000. He is currently working as an Associate Professor at the UTM. He is presently serving as a Chair for the Power Electronics Chapter of the IEEE Malaysia Section. His current research interests include the 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. degrees in Electrical Engineering from the Universiti Teknologi Malaysia (UTM), Kuala Lumpur, Malaysia, in 2000 and 2002, respectively; and his Ph.D. in Electrical Engineering from The University of Nottingham, Nottingham, England, UK, in 2008. Since 2008, he has been with the Faculty of Electrical Engineering, UTM, where he is presently a Senior Lecturer. His current research interests include power electronics and electric vehicles with a special focus on battery management systems.
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