Healthy Operation of Permanent Magnet
Synchronous Machine (PMSM) with Field Oriented
Control (FOC)
Mohamad Irfan bin Mazlan
Wan Noraishah Wan Abdul Munim
Faculty of Electrical Engineering
Universiti Teknologi MARA
Shah Alam, Malaysia
irfanmazlan18@gmail.com
Faculty of Electrical Engineering
Universiti Teknologi MARA
Shah Alam, Malaysia
aishahmuni@salam.uitm.com.my
Abstract—This paper provides a healthy operation of a fivephase permanent magnet synchronous machine connected by
field oriental control or knowns as FOC. The results are based on
actual and reference voltage which both of these theoretically
need to be in the same shape or same amplitude to have the
correct results. This project uses T5 transformation based on the
Clark Transformation where the number of n is based on the
number of phases. In this project, the number of n is 5. FOC also
connected to PMSM that uses the value of gain to produce a
waveform based on torque and flux. MatLab-Simulink is the
medium that was used in this project to simulate the results from
the machine to get the sinusoidal waveform where it has fivephases.
Keywords—PSMM, FOC, Healthy condition waveform, T5
Clark Transformation Matrix
I. INTRODUCTION
Since the beginning of this century, the area of multiphase
motor drives in general and in particular multiphase induction
motor drives has experienced substantial growth[1]. This is
due to their usefulness in an area of applications where the
power per stage, especially the high device machine, the
capability to use a machine that has more phases under
defective conditions[2], improving noise characteristics and
reducing the copper loses in the machine[3]. Electric vehicles
and many more applications or wind power generation
systems are examples of the latest technology that has taken
advantage of the ability in multiphase to continue operating
under faulty conditions[4]. Since the beginning of the 20th
century, the multi-phase machines completely transformed in
this scenario[5]. A whole new field was evolved during this
re-emergence period and the knowledge three-phase drive
technology has been expanded to cover multi-phase modeling,
design, modulation, and control issues.
The revolution in machine technology and the ability to
control the speed in machines making people can control
machines that base on speed, which can be said as the most
common and been used in many applications today. Research
shown multiphase induction machines that has more phases is
a practical solution for a larger and more efficient motor. As
an example, the three-phases machine has emerged to fivephases machine or six-phase machine. Some researchers had
been done to more than six-phase such as nine-phase because
multiphase has many advantages to the industry[6].
The symmetric five-phase machines are probably one of
the most frequently considered multi-phase machines in recent
studies of the available multi-phase machines. Many multiphase devices are also being used in recent years, due to the
growth of more robust microprocessors. In traditional
implementations of electrical machines, a three-phase stator
winding is chosen because the three-phase supply is easy to
access. Besides, if an AC system is supplied from an inverter,
the need for a predefined number of stator phases such as three
phases and other phase numbers may be selected.
The multi-phase drive systems give the following features
compared with the three-phase drive systems [2][3]:
1. High-power
variable-speed
drive
can
be
accomplished by using low-power switching equipment in
multiphase drive implementations. When a three-phase
engine scheme is transformed into a multi-phase one, the
rated voltage per stage can be efficiently decreased. This is
particularly appropriate for electric vessel propulsion and
locomotive attraction implementation, where the power
distribution voltage is restricted.
2. The amplitude of torque ripples may be increased
while the amplitude of torque oscillation may be
decreased. The torque ripples are caused by spatial
harmonics from the Magneto-Motive Force (MMF). The
MMF is excited mainly by the basic current in the stator
phases. With the increased phase number, the harmonic
orders of MMF are also increased while the corresponding
amplitudes are decreased Therefore, the torque ripples
could be removed and the efficiency of the machine
improved.
3. Multiphase machines have a greater ability to tolerate
faults than 3-phase machines. The redundancy of the phase
number allows multi-phase machines to operate with the
remaining healthy phases when one or more stator phases
are open-circuited, although at a de-rated power level.
4. A drive system's number of control degrees is equal
to the machine's number of independent stator phases.
Multiphase machines, therefore, have more degrees of
freedom (DOFs) than the counterparts in three phases.
These DOFs supply additional ways of improving drive
efficiency. For instance, injecting low-order current
harmonics can optimize the air-gap flux of multi-phase
machines with concentrated windings, which can increase
iron utilization and power density.
The multiphase has been recognized and getting famous in
research because of its advantages especially in capability in
fault tolerance of multiphase. Multiphase has been growing
from the early 20th century and the induction machine from
three phases has been growing to more than three-phases such
as five-phase or six-phases[7]. Fault tolerance in multiphase is
better than three-phase and that can be said as the main reason
why multiphase is more important than three-phase[8]. All
machines such as the permanent-magnet need to be able to
work in faulty conditions such as short-circuit and one open
fault circuit. A healthy condition in machines can be said as
no-fault happen during that particular time and can produce a
nice waveform[7].
II. HISTORY OF MULTIPHASE
A five-phase motor induction was introduced back in
1969, the writers looked at the first report of a multiphase
machine or drives. Multiphase drives have produced constant
but rather minimal visibility over the next 20 years. The speed
started to rush in 1990, but it wasn't until the beginning of this
century that multi-phase motor became a topic for the major
global interest in the research community of drives. This has
resulted in significant improvements in some specific areas of
implementation, which are the propulsion of electric ships,
traction, and the' further electric' principle of aviation. While
the possible reasons for looking for multi-phase motor use in
these implementation areas vary widely (and the specific type
of ac motor and electronic power converter topology often
vary), the basic feature is that multi-phase motor use is viewed
by providing significant benefits by using their equivalents in
three phases.
In 1960, E. E Ward as well as H. Harer performed
theoretical analysis and evaluation for a five-phase induction
machine (IM) and found that the rise in phase numbers
resulted in decreased ripple frequency amplitude and increased
torque. The multi-phase drive was introduced in 1980 to
increase the sensitivity and performance of AC drive units.
Nevertheless, the multi-phase drive scheme is very difficult to
implement due to the technical limitations of that time.
As a result, a small study was conducted on the multiphase drive. The advancement of technology, such as
microcontrollers, power electronics, and variable speed drive,
has opened the way for multi-phase drive implementation
since around the 1990s. High-power, low-voltage and highreliability implementations such as electrical ship
construction, multi-phase machine research, and drive
methods have evolved tremendously over the past 30 years
with increasing demand for motor drive technologies. A wide
range of new multi-phase system models, multi-phase
converter topology, and multi-phase motor control methods
are being developed by researchers around the world.
Acquired from the Field-Oriented Control (FOC) system
for three-phase induction machine researchers from the T. A.
Lipo’s group at the University of Wisconsin-Madison. A. Lipo
group suggested a six-phase (dual three-phase) induction
machine field-oriented command. However, under opencircuited failures and fault-tolerant FOC, the theoretical
development for the six-phase induction machine was
analyzed. A Toliyat indicated that by introducing optimized
stator windings, the torque density of the multi-phase system
could be increased and proposed robust current control
techniques for the five-phase induction machine's faulttolerant function.
The research group led by E.Levi at Liverpool John
Moores University spent a great deal of time on multi-phase
Pulse Width Modulation (PWM) techniques and proposed new
advanced PWM methods such as maximizing the use of DC
buses, reducing Standard Mode Voltage (CMV), and so on, L.
Parsa and her Rensselaer Polytechnic Institute co-investigators
focused on a multi-phase permanent synchronous magnet
(PMSM) fault-tolerant control in both open-circuit and shortcircuit faults and put forward a remarkably simple worldwide
fault-tolerant solution. E. Semail and his team members chose
open-end winding five-phase PMSM that can be managed
easily by reconfiguring the legs of the converter when shortcircuit failure occurs. F. Barrero and M. J. Duran proposed
Model Predictive Control (MPC) solutions for multi-phase
variable-speed drive devices built for open-circuit or IGBT
fault-tolerant operations any further.
III. FIVE-PHASE INDUCTION MOTOR OPERATION
In this section, the generation of five-phase will be
described and field-oriented control will be explained as a
controller. Healthy operation of a five-phase permanent magnet
synchronous machine will be described in this section.
A. The Generalization of Five-Phase Drive
This five-phases machine consists of Iα, Iβ, Ix, Iy, and I0+
and the multi-phase induction machine is controlled using the
vector space decomposition (VSD) model approach and the
generalized Clarke transformation matrix[2] as shown in
Equation (1).
[T5]=
α
β
x
y
0+
1
0
1
0
0.707
cosθ
sinθ
cos2θ
sin2θ
0.707
cos2θ
sin2θ
cos4θ
sin4θ
0.707
cos3θ
sin3θ
cos6θ
sin6θ
0.707
cos(n-1)θ
sin(n-1)θ
cos2(n-1)θ
sin2(n-1)θ
0.707
(1)
where θ=72 and n=5
The n is the number of phases so in this case, we are using
a five-phase motor so the n is equal to 5. The angle can be get
by dividing 360 to 5 so the angle for every phase is 72° and by
substituting every value to equation (1) we will get the value
as the show in Equation(2).
[T5]=
α
β
x
y
0+
1
0
1
0
0.707
0.309
0.951
-0.809
0.588
0.707
-0.809
0.588
0.309
-0.951
0.707
-0.809
-0.588
0.309
0.951
0.707
0.309
-0.951
-0.809
-0.588
0.707
(2)
B. Field-Oriented Control(FOC)
The FOC for traditional three-phase motors usually
employs an orthogonal transformation matrix to map the
control variables in the a-b-c coordinates to those in the d-q-0
coordinates but in a five-phase machine model, we need to add
two more variables to make the controller five-phase so it
becomes a-b-c-d-e. Therefore, the flux and the torque can be
decoupled by regulating current components on the d- or qaxis, respectively as shown in figure 1. The gain for Kp can be
calculated by using the formula in equation(3) and Ki can be
calculated using the formula in equation(4). Currents on the
d1-q1 plane contribute most of the electromechanical energy
conversion in multiphase machines, especially for those with
sinusoidally distributed windings. Consequently, the d1-q1
plane is called the fundamental plane, and id1 and iq1 are
regulated as the flux and torque components. Other d-q planes
are called harmonic planes, and currents on these planes are
regulated to specific values.
C. Permanent-Magnet Synchronous Machine
PMSM is widely used in industrial products, digital control
centers, industrial machine drive fields as it has many
strengths like high power/weight ratio, simple structure, and
small volume[9]. The PMSM is composed of traditional threephase windings in the stator and permanent rotor magnets. The
field windings in the modern synchronous system are
performed in PMSM with permanent magnets. The traditional
synchronous machine needs a supply of AC and DC, while the
PMSM needs an only supply of AC for its operation. One of
PMSM's biggest benefits over its counterpart is the absence of
dc supply for field excitation. Compared to the conventional
three-phase in PSMM, two more phases were added in the
machine to make it become five-phase PSMM. In PSMM the
angle between every phase is 72° because we divide 360° with
five so the value will become 72° and we can see it in figure 2.
Figure 2: Abcde coordinate system[10]
D. Operation of Healthy Mode
Steady-state phase currents form a balanced five equal
peak values for a healthy operation in each stage. In this
healthy mode operation, the currents of Ix, Iy, and I0+ are zero
and to produce a rotating MMF that drives the system
smoothly with a steady torque, the stage of iα and iβ
determines a circle by following the equation below.
Iα=Iβ
(5)
Based on some journals there is a result of a healthy
condition on five-phase PSMM where all amplitudes are the
same and the shapes are sinusoidal as we can see in figure 3
but in that waveform minimum losses was added as one opencircuit fault happen during that time but in this project, the
condition will be used as the result only based on the healthy
condition from the simulation in MatLab-Simulink.
Figure 1: Block diagram for FOC
(3)
(4)
where:
J= Jmotor+Jload reflected motor
ωn= motor drive bandwidth
Figure 4: Stator phase current waveforms for healthy and
minimum losses modes for one open-circuit fault [2]
IV. METHODOLOGY
Figure 5 shows the flow process in a five-phase induction
motor and an oriental field control or FOC in the MatLabSimulink. First, we need to make sure all the transformation in
T5 and also inverse transformation is correct based on the
Clark transformation matrix. After that, the value in Kp and Ki
needs to be set first and the output waveform from that gain
needs to be correct by testing some values until the waveform
follows each other. Next, the settings in the step size all need
to be set for the result to come out based on the settings and
after all the settings were correct we can run the simulation
and get the results from the machine.
Figure 6: FOC circuit in MatLab-Simulink
In figure 6, the FOC connection was shown in the
MatLab-Simulink that acts as a controller to a permanent
magnet synchronous machine. In this stage, the value in Kp
and Ki needs to be fine-tuned to make the outcome results are
correct. If the value is not correct, the two values that will be
compared will produce the wrong results such as the actual
and reference value did not follow each other.
Figure 7: PSMM circuit in MatLab-Simulink
In figure 6, the PSMM connection was shown in the
MatLab-Simulink, and in the drive, it consists of five phases
which are a,b,c,d, and e. Both references value are being
compared to get the results. The load also set to zero to get
better results in healthy condition mode. The scope was set to
current, torque, speed, and rotor angle.
Figure 5: Flowchart of the project
V. RESULTS AND DISCUSSION
Figure 7: Speed results on FOC
Based on figure 7 there were two waveforms which are
actual speed and references speed in the field-oriented control
that acts as a controller to the machine. Supposedly the
waveform follows each other because theoretically the actual
speed needs to follow the reference value but in this case, the
settings in FOC are not correct that resulting in the wrong
waveform as can be shown above.
Figure 8: Ids results on FOC
Figure 9: Iqs results on FOC
Figure 8 shows the current from d axis and in the FOC
and this waveform two values also compared to get the results.
The actual and reference value was compared and the
waveforms almost have the same shape so it can be considered
as correct results. In figure 9 the concept is the same as figure
8 but it is compared from the d axis. In this case, the results
are not correct because the waveforms are not the same at all
and this error may have happened because the settings are not
correct.
Figure 10: Healthy condition from the five-phase machine
The circuit in MatLab-Simulink was simulated to get a
healthy condition operation as shown in figure 10 and this
condition, the load was set to zero to get a correct healthy
condition waveform and to make sure the load does not
become too much distorted. The waveforms take time to
produce because we need to set the time for the machine in
what time the waveforms can take the sinusoidal shape. Iβ, Iα,
Ix, Iy, and I0+ will form a five-phase sinusoidal waveform and
in this condition, only Iα and Iβ only play the role while other
value will become zero. In this condition, there were no fault
happens so every phase will be available in the waveforms.
VI. CONCLUSION
The conclusion is we were able to determine the
mathematical modeling for a five-phase induction machine
using a five-phase permanent magnet synchronous machine
that consists of Iα. Iβ, Ix, Iy, and I0+. In this system, fieldoriented control(FOC) was connected to the machine that acts
as a controller in the system where it has q and d axis that
plays a vital role in balancing the machine.
In FOC, the inverse transformation was being used to
generate a five-phase system that using the value of angle with
72° and n equal to five. This transformation was called Clark
transformation and the machine model was controlled by
vector space decomposition(VSD). In this system, the only
condition that was being measured in healthy conditions for
the machine as we compare the value from actual and
references value and it was supposed to be the same value in
the waveform. The output needs to be in the same value or
same amplitude and if the value is not the same it means the
setting has some error.
In healthy conditions, only the Iα and Iβ will play the main
role and others values will become zero to produce a healthy
sinusoidal waveform. In this condition, there will be no fault
and all amplitude will become same and all setting needs to be
correct in the MatLab to get a correct result. The Kp and Ki
need to be fine-tuned to get the actual signals tracking the
reference signals for both in the current and speed controller.
ACKNOWLEDGMENT
The author would like to acknowledge the supervisor,
colleagues, and family for financial support, facilities, and
numerous contributions.
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