Advanced deep flux weakening operation control strategies for IPMSM

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 11, No. 5, October 2021, pp. 3798~3808
ISSN: 2088-8708, DOI: 10.11591/ijece.v11i5.pp3798-3808  3798
Journal homepage: http://ijece.iaescore.com
Advanced deep flux weakening operation control strategies for
IPMSM
Pham Quoc Khanh1
, Ho Pham Huy Anh2
1
Faculty of Electricity Technology (FEE), Industrial University of Ho Chi Minh City (IUH), Vietnam
2
Faculty of Electrical and Electronics Engineering (FEEE), Ho Chi Minh City University of Technology (HCMUT),
VNU-HCM, Ho Chi Minh City, Vietnam
Article Info ABSTRACT
Article history:
Received Aug 28, 2020
Revised Mar 21, 2021
Accepted Apr 1, 2021
This paper proposes an advanced flux-weakening control method to enlarge
the speed range of interior permanent magnet synchronous motor (IPMSM).
In the deep flux weakening (FW) region, the flux linkage decreases as the
motor speed increases, increasing instability. Classic control methods will be
unstable when operating in this area when changing load torque or reference
speed is required. The paper proposes a hybrid control method to eliminate
instability caused by voltage limit violation and improve the reference
velocity-tracking efficiency when combining two classic control methods.
Besides, the effective zone of IPMSM in the FW is analyzed and applied to
enhance stability and efficiency following reference velocity. Simulation
results demonstrate the strength and effectiveness of the proposed method.
Keywords:
Advanced flux-weakening
control method
Current limit circle
Deep flux-weakening region
Interior permanent magnet
synchronous motors
Maximum torque per ampere
Maximum torque per volt
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ho Pham Huy Anh
Faculty of Electrical and Electronics Engineering (FEEE)
Ho Chi Minh City University of Technology (HCMUT), VNU-HCM
268 Ly Thuong Kiet, 10th District, Ho Chi Minh City, Vietnam
Email: hphanh@hcmut.edu.vn
1. INTRODUCTION
Nowadays, electric vehicles (EV) are widely used to improve efficiency and reduce greenhouse gas
emissions by internal combustion engines [1]. There are many EV manufacturers involved in the production
of electric vehicles, such as Benz, Tesla, Honda, and Toyota [2]. Electric vehicle systems are more efficient
and have a more comprehensive range of speeds than vehicles using internal combustion engines. With
permanent magnet synchronous motor (PMSM) actuators, operating at sub-rated speeds is the central area of
activity, and many studies proposed some approaches to improve operating efficiency [3]-[8]. However,
under certain operating conditions in some electric vehicles, it is also required to accelerate the engine to
above-rated speeds. Therefore, running in the magnetic field is one criterion for evaluating current electric
cars [2]. There are two main types of PMSM mentioned in velocity control: IPMSM and SPMSM. SPMSM
is constructed of magnets that are mounted on or inserted on the rotor. The IPMSM has a structure of
magnets arranged inside the hollow cavities of the rotor. In applications with high rotor speeds, the
centrifugal force will be so great that IPMSM often appears to be more efficient mechanically than SPMSM
[9]. In this paper, IPMSM is used to study the PMSM velocity control problem in the DFW region.
There are three main parts of the operating speed range of PMSM: Constant torque, constant power,
and decreasing power region. The torque always ensured that it does not exceed the manufacturer's value in
the area below the base speed. When the rotor speed exceeds the motor rated speed, the machine will change

Int J Elec & Comp Eng ISSN: 2088-8708 
Advanced deep flux weakening operation control strategies for IPMSM (Pham Quoc Khanh)
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from constant torque to constant power. PMSM power was kept so as not to exceed its rated capacity in the
region above base speed. However, the speeding capability of PMSM is not infinite. When the motor speed
exceeds a certain threshold, its power is decreasing. Figure 1 shows the operating speed range of PMSM.
Based
speed
Constant
Torque
Region
Constant
Power
Region
Power
decreasing
Speed
Figure 1. The operating speed range of PMSM
In the constant-torque region, different algorithms aim to maximize the torque on the stator current
(MTPA). In this functional area, the motor speed changed by changing the q-axis current accordingly. The
d-axis current changed to the operating point is on the MTPA curve, as shown in Figure 2. They lead to the
linkage flux value between the rotor and the stator almost constant. Back electromotive force (BEMF)
increases proportionally to the motor speed. The constant torque region ends when the PMSM velocity
reaches the rated speed, at which time the BEMF also reaches the limit value that can be supplied by the
inverter.
id
iq
ω3
ω2
ω1
MTPA
A
O
B
C
Te1 Te2
MTPV
I
II
III
Figure 2. PMSM operating velocity range in the id-iq plane
When the motor operates at a constant power area with a rotor speed higher than the rated rotor
speed, the Flux linkage must be reduced so that the BEMF does not exceed the limit value at the inverter
output. The rotor flux is made of permanent magnets not to be changed over a wide range, so the stator's
magnetic field is used to weaken the permanent magnet flux associated with the stator coil. Increasing the
d-axis current component in the negative direction leads to reduce flux linkage. The d-axis current will
change until the BEMF on the stator drops below the limit voltage. The q-axis current needs to change
following the d-axis current. The control method for increasing PMSM motor speed above the rated speed by
reducing the flux linkage is called the flux-weakening control.

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Int J Elec & Comp Eng, Vol. 11, No. 5, October 2021 : 3798 - 3808
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In technological development, the demand for motors capable of operating at a wide range of speeds
has also increased. Jahns proposed operation in the FW region for IPMSM in the study [10], and this is the
beginning of research on constant power region in PMSM speed control. There are two ways to increase the
speed range of a PMSM; one is to change the rotor structure so that the motor can increase the operating
range by increasing the motor rated speed. The second way is to apply the PMSM control algorithm in FW to
put the motor at speed greater than the rated speed. The method of structural change to improve the
performance of PMSM has been proposed in the studies [11], [12]. The second direction of research is the
impact on control software, proposed FW algorithms to improve the speed's range. Based on the
classification of the study [13], there are four main methods in PMSM velocity regulation in FW area:
TFLUT test [14]-[16], direct current calculation (DCC) [17]-[19], vector current control (VCC) [20]-[22] và
flux vector control (FVC) [23]-[25]. Bolognani et al. [26] gave some comparisons between these control
algorithms. The comparison is shown in Table 1.
Table 1. Comparison of efficiency between FW methods
Approach VCC DCC FVC LUT
Implementation Simple implementation simple
implementation
simple
implementation
complex
implementation
Stability in the FW region Performance is reduced
between different work
areas under the influence of
controller parameters
Stable operation Stable operation Stable operation
when strong
magnetic saturation
effects
Acceleration state Automatic management of
transitions between MTPA
and flux-weakening control
transitions between
MTPA and flux-
weakening control is
not convenient when
the working point is
always outside the
current limit circle
transitions between
MTPA and flux-
weakening control is
not convenient when
the working point is
always outside the
current limit circle
The roaming is
quite convenient
based on the lookup
table.
The reduced electromagnetic force in the DFW region makes the electromechanical link unstable.
Steady speed control in this area is often more difficult [27]. The inverter's voltage amplitude in the FW
region is also pushed up to the rated value, making the current control more restrictive than the constant
torque region. A slight change in the working conditions of the IPMSM can also cause work point instability.
With changing the speed of electric trams, large fluctuations in speed change are the main disadvantages of
PMSM control in the FW region.
The paper proposed a hybrid speed control algorithm combining two-speed control PMSM in FW,
namely VCC and FVC. The switching between these 2 techniques is done using rotor speed and reference
current value. The proposed hybrid control method is novel. It uses the FVC method's advantages in the
internal area of the FW to eliminate the inverter limit voltage violation and uses the benefits of the VCC
method to shorten the time to accelerate. Simulation results are recorded through simulation modeling using
MATLAB/Simulink software and are presented in detail afterwards.
The remainder is structured with the part 2 presents the math model and workspaces of an IPMSM.
Part 3 presents a hybrid control method for PMSM in the proposed FW region. Part 4 shows the results
obtained after the simulation modeling for the proposed algorithm and the DCC and VCC algorithm used in
the comparison. Part 5 is the conclusion.
2. THE MATH MODEL AND THE CONTROL CURVES OF IPMSM
2.1. IPMSM model and voltage-current limits
According to [28], Basic electrical equations of IPMSM in the dq coordinate system are presented in
the (1), (2), (3):
. . /
d s d d d e q q
v R i L di dt L i

   (1)
. /
q s q q q e d d e pm
v R i L di dt L i
  
    (2)
 
 
1.5 .
e pm q d q q d
T P i L L i i

   (3)

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where
d
L and q
L is the d-axis and q-axis inductance, respectively.
d
v and q
v is the d-axis and q-axis voltage, respectively.
d
i and q
i is the d-axis and q-axis current, respectively.
pm
 is the amplitude of flux linkage due to the permanent magnet and s
R is the stator coil's resistance.
According to [3], (4) determined The acceleration as:
 
1
m
e L m
d
T T F
dt J


   (4)
In which:
J : Inertial value of PMSM-load linked referred to PMSM shaft.
F : Jointed viscous factor of loaded PMSM.
 : Rotating angle location.
e
T : Electromagnetic Torque.
𝑇𝐿 : Load torque.
m
 : Rotating angle speed
PMSM current and voltage are bounded by its nominal magnitudes in which voltage boundary
depends on PMSM isolation capability with maximum voltage magnitude that the inverter could provide.
Manufacturer supplies the current limit. It is related to heat dissipation for the active power losses generated
inside the motor. The (5) and (6) describe the limitations of voltage and current, respectively:
2 2 2 2
,max
d q s s
v v v v
   (5)
2 2 2 2
,max
d q s s
i i i i
   (6)
where vs is the vector amplitude of the inverter voltage, vs,max is the maximum voltage amplitude of the
inverter, s
i is the vector amplitude of the current flows into the stator coil, and ,max
s
i is the rated value of the
current injected into the stator coil.
In case motor velocity is greater than motor nominal value, the BEMF appearing at stator winding
under the influence of the variable flux when the rotor is spinning will be much greater than the voltage drop
the winding caused by the stator resistance. The value of the voltage drop on the stator windings can be
ignored at this time. On the other hand, the dq axis currents in the steady-state are considered constant, which
allows the derivative of the component currents to be eliminated ( / 0; / 0)
d q
di dt di dt
  . At this point, the
stator voltage (1) and (2) rewritten as (7), (8):
d e q q
v L i

  (7)
q e d d e pm
v L i
  
  (8)
The relationship between rotor speed and component currents is built through (9) by substitute (7)
(8) into (5).
   
2
2 2 ,max
2
s
q q d d pm
e
v
L i L i 

   (9)
Based on the (6), the working point of the IPMSM must be inside a solid blue circle centered on O
and the radius OA as shown in Figure 2 While working within this point, current flows in the coil will not
exceed the rated current, thereby ensuring the motor does not overheat. The dashed blue circles form the
relationship between the stator current and the inverter's output voltage. Based on the (9), to ensure that the
stator winding voltage does not exceed the maximum permissible value of the inverter, the working point
must be in this ellipse. Thus, when the IPMSM motor operates at a constant power area, in addition to the
standard current limit, the current is also bound by the limitation of voltage.

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2.2. Optimal working areas of PMSM
MTPA curve: When operating at a low speed below the rated speed, the control goal now is to
minimize the copper loss that causes current to flow in the stator coil. With the same electromagnetic torque
required, the stator component currents are calibrated so that this current amplitude is minimal. According to
[18], the dq-axis current calculated from the stator current amplitude is presented in (10). The OA curve in
Figure 2 shows the working point orbits in the constant moment region.
 
 
2
2 2
,
2 2
, ,
8 .
4
pm pm d q s
d mpta
q d
q mpta s d mpta
L L i
i
L L
i i i
 
  


 
(10)
The maximum current (MC) curve: The BEMF on the stator winding will exceed the inverter's
limiting voltage when the rotor speed exceeds the rated speed value. At this time, the d-axis component
current increases in the negative direction so that the stator voltage drops and avoids overvoltage. The q-axis
component current will also decrease accordingly so that the current amplitude does not exceed the rated
current. Thus, for the obtained electric moment to be maximum during acceleration, the stator current
amplitude must be set to equal the rated current during acceleration. The d-axis current will be increased by
increasing the current vector angle to decrease the stator voltage. The q-axis current will be recalibrated to
the stator current vector, as shown in (11) where β is the current vector angle.
,max
,max
.cos
.sin
d s
q s
i i
i i




(11)
Maximum torque per volt: The contact between the constant moment curve and the voltage limit
ellipse is where the lowest voltage is found in the points on the constant torque curve. This set of contacts
will record the accumulation of the points with the highest torque on the same stator voltage value and is
called the maximum torque per volt (MTPV). The curve BC in Figure 2 represents the MTPV curve. The
working points in the current coordinate dq are determined through (12) based on [29].
2 2 2
,max / ( . )
pm
d
d
s e
q
q
i id
L
V Ld id
i
L



  
 

(12)
 
 
2
2 2 2
,max
. ( . ) 8 /
4
pm q pm q d q s e
d q d
L L L L V
id
L L L
  
   
 

(13)
where id
 is determined based on (13).
3. PROPOSED HYBRID SPEED CONTROL IN FLUX-WEAKENING AREA
3.1. Control principle of VCC and FVC in the FW region
The control principle of VCC and FVC in the FW region in the id-q plane is shown in detail, as
shown in Figure 3. The VCC method changes the PMSM velocity by varying the current vector amplitude.
Assume the motor is operating at the work point ℎ1. When accelerating or decelerating, the working point
shifts to point ℎ3 or ℎ2 shown in Figure 3(a). At this time, the change in rotor speed will take place more
slowly and cause the working point to leap out of the voltage limit ellipse. It leads to instability in PMSM
speed control. Thus, the VCC control method is ineffective in changing motor speed when working in the
FW region. However, when the operating point is at the boundary of the FW region (MTPA, MC, and MTPV
curve), the VCC shows the ability to minimize over-current during control. When it comes to accelerating
with the maximum possible torque (is = imax), VCC is a suitable choice.

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The FVC method changes the PMSM speed by moving along the voltage limit curve. It is easy to
see that the torque at the point h5 is greater than that of h4, as shown in Figure 3(b). The flux angle will be
increasing To increase the torque and lead to an increase the speed. Notice that increasing the flux angle does
not lead to over the back EMF when both operating points stay at the voltage limit ellipse. It shows that if we
want to change the velocity of PMSM while working in the FW region, this method will bring about a more
stable effect. However, increasing the alpha causing the working point to exceed the current limiting circle,
resulting in instability in the rotor speed control. Thus, the FVC control method is highly effective when the
operating point is within the FW region with the reference current amplitude smaller than the maximum
current amplitude. When increasing the torque causes the operating point to go out of the current limiting
curve, the VCC method gives better control results.
id
iq
MTPA
A
O
B
C
MTPV
is
h1
h2
β
h3
id
iq
MTPA
A
O
B
C
MTPV h4
α1 β
h5
α2
(a) (b)
Figure 3. Principle of VCC and FVC methods on the id-q plane
3.2. Combined flux-weakening velocity regulation of VCC and FVC control
In this paper, a hybrid method is proposed to overcome the shortcomings and take advantage of
VCC and FVC. The appropriate PMSM velocity control method was selected when Comparing the desired
current vector amplitude value with the rated current. When accelerating with the rated current amplitude, the
VCC method is used to minimize over-current. When the current vector magnitude is lower than its nominal
value, the FVC method ensures that the limit voltage condition is satisfied. Figure 4 illustrates the principle
of proposed switching regulation technique.
e
 *
 ,
e v
 ,
e based
 max
i
,
e e based
 
 ,
e e v
 

VCC
(MTPA mode)
FVC
VCC
(MC mode)
FVC
VCC
(MTPV mode)
*
max
s
i i

*
max
s
i i

Y
N N
N
N
Y Y
Y
*
s
i
Figure 4. Switching rule in the proposed control method
4. RESULTS AND ANALYSIS
4.1. PMSM speed regulation
IPMSM velocity controller simulation model performed by Matlab/Simulink software was
performed to evaluate the IPMSM velocity control method's obtained efficiency in the FW region. Table 2 is
given The PMSM motor parameters, which follow data from Fadel in [29]. The model consists of two main
blocks, the IPMSM motor block, and the control block, as shown in Figure 5. The model is built with three

 ISSN: 2088-8708
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different control methods: VCC, FVC, and the proposed hybrid control method, to have sufficient data to
estimate the efficiency of the novel hybrid control technique. The results obtained in the simulation are
detailed in the following sections.
Table 2. IPMSM coefficients
Coefficient Rated magnitude Unit
R 0.97 Ω
Ld 4.73 mH
Lq 5.77 mH
λpm 0.0345 Wb
P 5
Imax 8 A
Vdc 200 V
Figure 5. IPMSM speed control diagram
4.2. Results of PMSM combined regulation technique
The reference velocity and loaded moment are proposed to estimate the efficiency of IPMSM
velocity control methods in the FW region in different operating controls, as shown in Figure 6. The
proposed criteria include acceleration time, overshoot speed during variable speed, ability to respond to
variable rotor speed with varying load torque, and the PMSM current and electric torque disturbance to
assess the proposed method's efficacy. The rotor speed shall be capable of withstanding the reference
velocity applied to the controller under different torque conditions, as shown in Figure 6.
Figure 6. Reference PMSM rotor speed and load torque

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Figure 7(a) shows the change of speed of IPMSM according to the reference velocity of different
algorithms. Simulation results show that the rotor speed can follow the reference speed in all three control
methods. However, the ability to follow the reference velocity of each technique is significantly different.
The VCC method and the proposed method have faster response times than the magnetic direct calculation
method. The reason is that fluctuation of the reference working point in the DCC method cannot give the
maximum torque value during acceleration due to violation of the current limit line.
Figure7(b) shows the simulation results of the PMSM speed in response to the change in load torque
when the motor speed reaches the reference speed. At time t=8 s, a decrease in the load torque causes the
overshoot speed. With different algorithms, this change is further. The proposed method has a small
overshoot, while the VCC algorithm has the highest overshoot. Similarly, at t=9 s, the load torque increases,
the imbalance between the load torque and the electromagnetic torque decreases the motor speed. In response
to this reduction, the proposed method has the least reduction in rotor speed. Thus, the proposed method has
a better answer to the change in load torque.
Figure 7(c) shows the response of the algorithms to the change in reference velocity. Through the
results, it can be seen that the VCC method responds faster than the other methods. However, this method
still has high overshoots and takes a long time to stabilize. On the contrary, the proposed method is not as fast
as VCC but has fast stability according to the reference speed and almost prevents the overshoot when
accelerating. Thus, the results in Figure 7(c) show that the ability to stick firmly according to the proposed
hybrid control's PMSM reference speed.
(a) (b)
(c)
Figure 7. IPMSM speed during simulation
Figure 8(a) shows the results of the electromagnetic moment in the PMSM generated during
operation by various control methods. From the picture, we can immediately see that the VCC method has
the most extensive electromagnetic moment disturbance in the FW region. The DCC method has fluctuations
during the start-up process when it passes through the MC region. The cause of the turbulence of this method
is a violation of the current limit circle.

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Figure 8(b) is the enlargement of Figure 8(a). It indicates the change in the electromagnetic torque
with the growth of the load torque. Notice that when the load torque changes, the electromagnetic torque also
changes. During the stabilization process, the electromagnetic torque still fluctuates wildly due to voltage
violations in the VCC method FW region. The other two ways do not oscillate because they do not violate the
voltage in the FW region.
(a) (b)
Figure 8. Electromagnetic torque of IPMSM during simulation
Figure 9(a) shows simulation results of d- and q-axis current. It can be seen from the figure that the
currents via the VCC method still fluctuate when entering the FW region. The reason is that this method is
that the reference voltage is always fluctuating when operating at the voltage limit circle. The other two ways
do not suffer from this phenomenon due to flux as a control variable, so no reference voltage violation
occurs. Also, due to the control axis change measure's use, the current response will be faster, as shown in
Figure 9(b). Based on the obtained simulation results, it is clear to see that the new PMSM combined
regulation technique is highly effective in controlling the PMSM motor in FW when the comparison criteria
give better results than the methods used as reference are VCC and DCC.
(a) (b)
Figure 9. dq-axis current of IPMSM during simulation
5. CONCLUSION
This study introduces a hybrid IPMSM velocity control technique between two typical control
methods, FVC and VCC, operated on FW area. The proposed technique's selection combine these two
methods is made by mapping the reference stator current its rated value. The principle of switching between

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the two modes is simple and requires no additional hardware structure. Compared with the simulation results
of the two classic methods, VCC and DCC, the proposed hybrid velocity control algorithm provide a new
approach with high efficiency in improving control quality and improving speed. Stabilizes and reduces
electromagnetic current and torque. With the hybrid method between the two methods VCC and FVC, newly
proposed PI closed-loop controllers are used, making it challenging to experimentally adjust controllers'
parameters. More research is needed to fix this problem in the coming research.
ACKNOWLEDGEMENTS
We acknowledge the support of time and facilities from Ho Chi Minh City University of
Technology (HCMUT), VNU-HCM for this study.
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BIOGRAPHIES OF AUTHORS
Pham Quoc Khanh received the BS and the M.Sc. degrees in the Department of Electrical and
Electronics Engineering from HCM City University of Technology and Education in 2009 and
2013. He is currently a Lecturer in the Faculty of Electricity Technology (FEE), Industrial
University of Ho Chi Minh City, Vietnam. His current research interests include intelligent
control, renewable energy, modeling and identification of nonlinear dynamic systems, and the
power network's faulty location.
Ho Pham Huy Anh received the B.S. and the M.Sc. degrees in the Department of Electrical and
Electronics Engineering from HCM City University of Technology (HCMUT), VNU-HCM in
1987 and in 1993, respectively. He received the Ph.D. degree from University of Ulsan, Korea in
2008. He is currently an Advanced Lecturer in the Faculty of Electrical and Electronics (FEEE),
HCM City University of Technology, VNU-HCM, HCM City, Viet Nam. Up to now, he
authored and co-authored 4 books and published over 140 papers on national and international
journals and conference proceedings. His current research interests include intelligent control,
robotics, novel energy applications, modeling and identification of nonlinear dynamic system,
soft-computing.

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