Iqbal et al., Cogent Engineering (2016), 3: 1134040
http://dx.doi.org/10.1080/23311916.2015.1134040
ELECTRICAL & ELECTRONIC ENGINEERING | RESEARCH ARTICLE
Vector control of asymmetrical six-phase
synchronous motor
Arif Iqbal1*, G.K. Singh1 and Vinay Pant1
Received: 22 October 2015
Accepted: 09 December 2015
First Published: 19 January 2016
*Corresponding author: Arif Iqbal,
Department of Electrical Engineering,
Indian Institute of Technology Roorkee,
Roorkee 247667, Uttarakhand, India
E-mails: arif.iqbal.in@gmail.com,
arif0548@gmail.com
Reviewing editor:
Wei Meng, Wuhan University of
Technology, China
Additional information is available at
the end of the article
Abstract: Vector control scheme has been well adopted for higher performance
applications of AC motor. Therefore, this paper presents an extensive development
and investigation of vector control scheme for asymmetrical six-phase synchronous
motor in a new two-axis (M–T) coordinate system. Phasor diagram has also been
developed in a simplified way, followed by its implementation technique. Analytical
results have been presented for four-quadrant operation of synchronous motor,
employing the developed vector control scheme. In analytical control model, common mutual leakage reactance between the two winding sets occupying same stator slot has been considered.
Subjects: Automation Control; Mechatronics; Systems & Controls
Keywords: six-phase synchronous motor; vector control; motor drive
1. Introduction
The multiphase (more than three phase) AC motor drives are used as a substitute of conventional
three-phase motor in different applications particularly, in propulsion system of ship and vehicle,
textile and steel industries, rolling mills, power plants, etc. This is because it offers certain potential
advantages when compared with its three-phase counterpart, like reduction in space and time harmonics, reduced torque pulsation, increased power handling capability, higher reliability, etc. (Levi,
2008; Singh, 2002).
Field-oriented control (i.e. vector control) technique has been widely used in high performance of
AC motor drives. In this regard, an abundant number of literatures are available for three-phase
motor (Bose, 2002; Das & Chattopadhyay, 1997; Jain & Ranganathan, 2011; Krause, Wasynczuk, &
Sudhoff, 2004), but a few for six-phase induction motor (Bojoi, Lazzari, Profumo, & Tenconi, 2003;
Singh, Nam, & Lim, 2005), wherein d–q model of machine has been used in synchronously rotating
Arif Iqbal
ABOUT THE AUTHOR
PUBLIC INTEREST STATEMENT
Arif Iqbal received his BTech and MTech degrees
both in electrical engineering in 2005 and 2007,
respectively, from Aligarh Muslim University,
Aligarh, India. After having experience in industry
and teaching in the field AC drives and power
system for a few years, he is currently pursuing
his PhD from Indian Institute of Technology
Roorkee, India. His area of interest is multiphase
AC machine and drives, power electronics, and
renewable energy system.
It is always advantageous to use the electrical
machine with its performance at higher level
using a suitable technique. Among different
techniques, vector control is widely used as it
provides the decoupled control of torque and flux
component of machine current. Therefore, the
paper explores a detailed asymmetrical six-phase
synchronous motor operation employing this
technique. Analysis and simulation of complete
drive system has been carried out in Matlab/
Simulink environment, where dynamic behavior
of motor was found to be substantially improved.
It is believed that the paper will serve as a
source toward higher performance of six-phase
synchronous motor.
© 2016 The Author(s). This open access article is distributed under a Creative Commons Attribution
(CC-BY) 4.0 license.
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reference frame. But the utilization of this scheme has not been reported for field excited six-phase
synchronous motor. Therefore, the paper is dedicated to explore and develop the control technique
for asymmetrical six-phase synchronous motor. In the control scheme, a new two axis (M–T coordinate) has been introduced along which the decoupled control of flux and torque is achieved.
Following the inclusion of control technique, a detailed analytical results have been presented for
motor operation in four quadrants.
2. Mathematical modeling
For the purpose of realizing the six-phase motor, it is a common practice to split the existing threephase stator winding into two, namely a b c and a′b′c′. Both splitted stator winding sets (a b c and
a′b′c′) are physically displaced 30° apart to realize asymmetrical six-phase winding configuration.
Asymmetrical six-phase winding configuration yields the reduced torque pulsation (Singh, 2002,
2011) due to the elimination of lower order harmonics. On the rotor side, it is equipped with field
winding fr together with the damper windings Kd and Kq along d and q-axis, respectively.
The equation of the motor can be written using machine variables. But this will yield a set of nonlinear differential equations. Nonlinearity is due to the existence of inductance term which is time
varying in nature. Such equations are computationally complex and time-consuming. Therefore, to
simplify the motor equations with constant inductance term, it will be conveniently written in rotor
reference frame using Park’s variables (Iqbal, Singh, & Pant, 2014, in press; Schiferl & Ong, 1983;
Singh, 2011).
v dqk = r sk i dqk +
𝜔r
p
𝝍 +
𝝍
𝜔b dqk 𝜔b dqk
v dqr = r dqr i dqk +
p
𝝍
𝜔b dqr
[
vdqk =
vdk
vqk
rdqk =
rdk
{
for k =
[
vdqr =
(3)
]T
𝜓dk
[
1,
2,
vKd
vfr = exfd
rfr
xmd
(4)
−𝜓qk
rqk
]T
(5)
for winding set a b c
for winding set a� b� c�
vKq
vfr
]T
]T
rdqk =
𝜓Kd
[
rKd
𝜓Kq
rKq
𝜓fr
rfr
(6)
(7)
[3, 12]
[
𝜓dqr =
(2)
]T
[
𝜓dqk =
(1)
]T
(8)
(9)
Equations of motor flux linkage per second may be conveniently written as the function of currents,
𝜓 = xi
(10)
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where i =
[
idqk
idqk
]T
,𝜓 =
]T
[
𝜓dqk
𝜓dqk
x is defined in Appendix 1.
The developed motor torque is expressed as
𝜏e = 𝜏e1 + 𝜏e2
(11)
where τe1 and τe2 are the developed motor torque associated with winding sets a b c and a′b′c′,
respectively, and expressed as
𝜏e1 = c(iq1 𝜓d1 − id1 𝜓q1 )
(12)
𝜏e2 = c(iq2 𝜓d2 − id2 𝜓q2 )
(13)
with c =
3P 1
2 2 𝜔b
The rotor dynamics having P number of poles is expressed as
]
[
)
𝜔r
1 1 P 1(
=
𝜏e − 𝜏 l
𝜔b
p 𝜔b 2 J
(14)
wherein, τl is the load torque, p represents the derivative function w.r.t. time and all symbols stand
to their usual meaning (Iqbal et al., in press). Evaluation of motor parameters is determined from the
standard test procedure (Aghamohammadi & Pourgholi, 2008; Alger, 1970; Jones, 1967).
3. Vector control scheme
The operating performance of vector-controlled motor is greatly improved and similar to that of a
separately excited DC motor (Bose, 2002). This is because of decoupled control of both flux component and torque component of stator current. The inclusion of vector control scheme is not similar
to that of induction motor drive. The main difference lies on the fact that the air gap flux is attributed
by both stator flux as well as field flux. Therefore, the resultant air gap flux will align along the axis
which is different from conventional d-axis. Hence, a new (M–T) coordinate axis has been introduced
wherein, the resultant flux vector and torque current component will align along M and T axis, respectively. Machine variables in newly defined coordinate axis (M–T axis) may be readily transformed
to its equivalent d–q or vice versa by relation
[
Mk
Tk
]
[
=
cos𝛿k
sin𝛿k
−sin𝛿k
cos𝛿k
][
dk
qk
]
(15)
In above relation, the torque angle δ1 and δ2 are associated with winding sets a b c and a′b′c′,
respectively, and defined as
𝛿1 = 𝛿 0
(16)
𝛿1 = 𝛿0 + � + 𝜉
(17)
δ0 is the initial value of load angle, whereas ∅ is the phase difference between voltage fed to phase
a and a′. Hence, torque attributed by each stator winding sets a b c and a′b′c′ is given by Equations
(12) and (13) may be readily written in M–T axes,
𝜏e1 = c(𝜓M1 IT1 − 𝜓T1 IM1 )
(18)
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Figure 1. Phasor diagram of
vector-controlled six-phase
synchronous motor.
T2
T1
,
Va = Va e
qs
j
M1
Va
s1
IM1 Is1
I T1
I T2
Is2
ØI
M2
I m1
I T1
1 I m2
I T2
2
,
r 1 2
I fr
a
M2
s2
a
,
fr
ds
𝜏e2 = c(𝜓M2 IT2 − 𝜓T2 IM2 )
(19)
where, the flux linkage ψMk and ψTk, and stator current IMk and ITk are aligned along Mk–Tk axes respectively, for winding sets a b c (for k = 1) and a′b′c′ (for k = 2). Since, the resultant armature air gap flux
is only aligned along flux axis (i.e. Mk axis). Therefore,
ψT1 = 0 and ψM1 = ψs1, where
√
2
2
+ 𝜓T1
𝜓s1 =
𝜓M1
(20)
ψT2 = 0 and ψM2 = ψs2, where
√
2
2
+ 𝜓T2
𝜓s2 =
𝜓M2
(21)
Hence, motor torque equation may be simplified as
𝜏e = 𝜏e1 + 𝜏e2 = c(𝜓s1 IT1 + 𝜓s2 IT2 )
(22)
The developed motor torque is dependent on flux linkage ψs1 (and ψs2) and current IT1 (and IT2) which
are orthogonal. This is the introduction of vector-controlled six-phase synchronous motor. The motor operation during steady state has been shown in the developed phasor diagram in Figure 1.
4. Implementation of vector control scheme
The implementation of developed vector-controlled synchronous motor drive system has been
shown in Figure 2. In this paper, motor operation has been investigated in constant torque region up
to base speed, but same may be extended in field weakening region above base speed. In the figure,
∗
the outer speed loop is used to generate the reference value torque component of stator current ITk
∗
through a speed controller (PI controller), whereas the reference value magnetizing current Imk is
generated by the flux controller (PI controller) associated with each winding sets a b c (for k = 1) and
a′b′c′ (for k = 2). The reference magnetizing current is used to establish the required flux ψsk in air
gap, which related to field current by the relation,
�
Im1 = Ifr cos 𝛿1
�
Im2 = Ifr cos 𝛿2
}
(23)
In phasor diagram, current component IT1 (and IT2) is in the direction of T1 (and T2) axis along which
the voltage vector is also aligned. Further, the magnetizing component of current Im1 (and Im2) is
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Figure 2. Schematic diagram
of vector-controlled six-phase
synchronous motor drive.
aligned along M1 (and M2) axis which is used to establish the flux vector ψs1 (and ψs2). At steady state,
both the stator flux and armature flux vectors are orthogonal to each other, i.e. ψs1 (and ψs2) is perpendicular to ψa1 (and ψa2) as shown in phasor diagram. Therefore, at steady state, both the vectors
ITk and Isk are equal i.e. IT1 = Is1 for winding set a b c (and IT2 = Is2 for winding set a′b′c′) and becomes
in phase with voltage vector, signifying the motor operation at unity power factor. In control scheme,
it may be noted that the magnetizing current component Im1 (and Im2) is related to field current Ifrk
∗�
∗�
associated with winding sets a b c and a′b′c′. Field current commands Ifr1 and Ifr2 are synthesized
using Equation (23) in feedback loop. In field control loop, the field current error is fed to the field
controller (PI controller) to establish the required field excitation. It may be noted here that the
magnitude of field current magnitude associated with each winding set a b c and a′b′c′ is assumed
�
to be same Ifr (= 0.5Ifr ). Now, the flux component of stator current is generated by
�
∗
∗
IM1
= Im1
− Ifr cos 𝛿1
�
∗
∗
IM2 = Im2
− Ifr cos 𝛿2
}
(24)
Above relation will yield a finite value of IM1and IM2. But at steady state, it becomes zero (i.e.
∗
∗
∗
and IMk
= IM2
= 0) and Equation (23) will be satisfied. As soon as stator current component ITk
are synthesized for winding sets a b c (k = 1) and a′b′c′ (k = 2), the reference value of current in stationary reference frame is generated. For this purpose, following two-step transformation is carried
out.
∗
∗
∗
IM1
(1) Current component ITk and IMk are transformed to d–q component in stationary reference
frame, using angle αk in transformation in relation (15).
∗
∗
(2) Above obtained stationary d–q component of current is transformed into its equivalent threephase current (Krause et al., 2004).
The reference current generated in above steps in stationary reference frame are then compared
with actual phase current of stator windings which results in current error. This current error is fed to
the hysteresis current controller to regulate switching of inverter circuit feeding the motor.
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5. Simulation results
The developed system of vector-controlled six-phase synchronous motor drive was implemented in
Matlab/Simulink environment. For this purpose, a 3.7-kW motor (parameters are given in Appendix
1) was operated in four quadrant. Initially, speed command was given at time t = 0.1 s. in ramp way,
following to which motor starts to run at synchronous speed after time t = 0.65 s, showing its operation in first quadrant. A load of 50% of base torque was applied at time t = 1.5 s which results a small
dip in speed by 0.03 rad/s, but regains its original speed (i.e. synchronous speed) after time t = 0.5 s,
as shown in Figure 3. In order to examine the motor operation in second quadrant, the direction of
load torque was reversed at time t = 3 s, resulting in a small increase in rotor speed by 0.05 rad/s. A
small change in rotor speed due to sudden change in load torque signifies the disturbance rejection
property of the drive system. A zoomed view of speed variation has been shown in Figure 3(a).
Following to the change in load torque, not only the variation in q-component of stator current but
also resulted a small variation in d-component of current, as shown in Figure 5. Change in stator
current is also reflected in T-axis component of motor current flowing in winding sets a b c and a′b′c′,
in Figures 4 and 6. In order to shift the motor operation to third quadrant, a speed reversal command
was initiated at time t = 4 s in ramp way. The motor is then finally operates in reverse motoring mode
after time t = 5 s at synchronous speed. Further, at time t = 6 s the load torque is reversed to operate
the drive in fourth quadrant. It is important to note here that the switching of motor operation to
different quadrant results in a large variation in d-component stator current whose effect is compensated by rotor field current, as shown in Figure 7(b). But the field circuit has a larger time constant, making the response slow (Das & Chattopadhyay, 1997; Jain & Ranganathan, 2011; Krause et
al., 2004). This sluggish response of field circuit is substantially improved due to the magnetizing
current injection along flux direction, as depicted by reference value of current in Figure 4(b and c)
as well as in actual current in Figure 6(c and d). Input phase voltage fed to winding sets a b c and
a′b′c′, is shown in Figure 8(a) and (b), respectively.
6. Conclusion
The scheme of vector control applicable for asymmetrical six-phase synchronous motor has been
developed and extensively investigated in four quadrant operation. In this control technique, stator
current is maintained for motor operation at unity power factor, which minimizes the stator current
Figure 3. Motor response (a)
rotor speed ωr and (b) torque Te.
(a)
(b)
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Figure 4. Reference current in
∗
∗
M–T coordinate (a) IT1
, (b) IM1
∗
and (c) IM2.
(a)
(b)
(c)
Figure 5. Stator current in d–q
coordinate (a) iq1 (b) id1 (c) iq2
(d) id2.
(a)
(b)
(c)
(d)
Figure 6. Actual current in M–T
coordinate (a) IT1, (b) IT2 (c) IM1
and (d) IM2.
(a)
(b)
(c)
(d)
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Figure 7. Voltage–current in
field circuit (a) reference Ifr∗ , (b)
actual Ifr (c) voltage Efr.
(a)
(b)
(c)
Figure 8. Inverter output
voltage (a) phase a (b) phase a'.
(a)
(b)
and hence less losses. The dynamic behavior of six-phase synchronous motor in different quadrant
operation was found to be substantially improved because of the decoupled/independent control of
flux as well as torque component of current along M–T axis, respectively. Furthermore, sluggish response of the rotor field circuit was also noted to be improved because of the magnetizing current
injection from armature side.
The present work may be further extended and investigated under different practical application
with their experimental validation.
Funding
The authors received no direct funding for this research.
Author details
Arif Iqbal1
E-mail: arif.iqbal.in@gmail.com, arif0548@gmail.com
ORCID ID: http://orcid.org/0000-0002-7113-6007
G.K. Singh1
E-mail: gksngfee@gmail.com
Vinay Pant1
E-mail: vpantfee@gmail.com
1
Department of Electrical Engineering, Indian Institute of
Technology Roorkee, Roorkee 247667, Uttarakhand, India.
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Citation information
Cite this article as: Vector control of asymmetrical six-phase
synchronous motor, Arif Iqbal, G.K. Singh & Vinay Pant, Cogent
Engineering (2016), 3: 1134040.
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Appendix 1
Motor parameter of 3.7 kW, 6 poles, 36 slots are
r1 = 0.210 Ω
xmq = 3.9112 Ω
rfr = 0.056 Ω
r2 = 0.210 Ω
xmd = 6.1732 Ω
xldq = 0
rKq = 2.535 Ω
xlKq = 0.66097 Ω
xlm = 0.001652 Ω
rKd = 140.0 Ω
xlKd = 1.550 Ω
xlfr = 0.2402 Ω
xl1 = xl2 = 0.1758 Ω
�
⎡
⎢
⎢
⎢
⎢
⎢
⎢
x=⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎣
xl1 + xlm + xmd
0
�
�
xlm + xmd
xldq
�
0
�
�
xl1 + xlm + xmd
�
�
xlm + xmd
−xldq
�
�
xl2 + xlm + xmd
xldq
�
�
xlm + xmq
0
�
xmd
0
0
xmq
xmd
0
0
xmq
�
−xldq
�
�
xlm + xmq
0
xmd
0
xmd
0
xmd 0
xmq
0xmq
0
0
xmd
0
xmd 0
xl2 + xlm + xmq
�
xlKd + xmd
�
0
xmd
�
�
xlKq + xmq
�
�
xlfr + xmd
xmd ⎤
0 ⎥⎥
xmd ⎥
⎥
0 ⎥
⎥
⎥
⎥
⎥
⎥
0 ⎥⎥
⎥
⎦
Page 9 of 10
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