Two PWM techniques using space vector pulsewidth modulation (SVPWM) are proposed for a twophase permanent magnet synchronous motor (PMSM) driven by a twophase eightswitch inverter. A twophase motor with two symmetric stator windings is usually driven by a twophase four, six, or eightswitch inverter. Compared with a four and sixswitch inverter, a twophase eightswitch inverter can achieve larger power output. For twophase motor drives, the SVPWM technique achieves more efficient DC bus voltage utilization and less harmonic distortion of the output voltage. For a twophase PMSM fed by a twophase eightswitch inverter under a normal SVPWM scheme, each of the eight PWM trigger signals for the inverter have to be changed twice in a cycle, causing a higher PWM frequency. Based on the normal SVPWM scheme, two effective SVPWM schemes are investigated in order to reduce the PWM frequency by rearranging four comparison values, while achieving the same function as the normal PWM scheme. A detailed explanation of the normal and two proposed SVPWM schemes is illustrated in the paper. The experimental results demonstrate that the proposed schemes achieve a better steady performance with lower switching losses compared with the normal scheme.
1. Introduction
In lowcost and lowpower industrial applications, single and twophase motors are widely applied due to the advantage of their simple and robust structure, as well as simple controls
[1

2]
. In a singlephase motor drive, a singlephase induction motor is popular and easy to work when fed by a singlephase AC power source. A singlephase induction motor can usually be taken as a special twophase motor because it contains a main winding and an auxiliary winding
[3]
. The main types of singlephase induction motor are splitphase, capacitorstart, and capacitorrun motors. However, most singlephase inductions cannot regulate speed over a wide range because the auxiliary winding is designed to start the motor in low speed
[4]
. To improve the starting performance of a singlephase induction motor, the auxiliary winding in series with a capacitor or boost converter can expand the speed range using a twophase sixswitch inverter
[5]
. Although the system performance is improved, there is a new requirement for two switches connected to the auxiliary winding that can pass higher operating current and voltage through compared to that of the rest of the eight switches
[6]
. This increases the cost of the total hardware system compared with a traditional sixswitch inverter for threephase motor drives
[6]
.
Another alternative is a twophase motor drive which utilizes a twophase motor with two symmetrical windings. Currently, it had received more attention because of its low electrical and acoustic noise, as well as its high efficiency
[7]
. Different inverter topologies have been proposed for two phase motor drives, such as twophase four, six, and eightswitch inverters. In the motor drives with a fourswitch inverter, the neural point of two capacitors in series is connected to the common end of the two motor windings, leading to an uncontrollable voltage and eventually a big torque ripple
[8]
. The topology of a sixswitch inverter has a disadvantage in that two switches in series connected to the common end should have a higher power rating to bear up against the force of a bigger current compared with the others. The eightswitch inverter is a preferable solution for twophase motor drives, except for the slightly higher cost of an additional two switches compared to the sixswitch inverter
[9]
.
Moreover, to achieve better performance with a twophase motor drive, high performance control methods and techniques represent the second best alternative. The control methods of vector control and direct torque control (DTC) are the most popular in both highperformance and lowcost applications
[10]
. Meanwhile, the techniques of sinusoidal pulsewidth modulation (PWM), hysteric PWM, and space voltage PWM (SVPWM) are widely applied to optimize the performance of a twophase motor drive
[11]
. In this paper, we investigate two improved SVPWM schemes for a vector control based twophase permanent magnet synchronous motor (PMSM) drive. Compared with a twophase induction motor, a twophase PMSM with two symmetric windings carries some advantages including a more compact size, high torque density, and a high torque to current ratio; also, it has been utilized in many lowpower applications and household products. Therefore, the improved SVPWM schemes reduce the switching frequency and further reduce the noise. The experimental results show that the drive with the new PWM schemes achieves better performance compared with the normal scheme.
2. Space Vector PWM Scheme for Twophase PMSM Drives
It is well known that PWM inverterpowered motor drives offer better efficiency and higher performance compared to fixed frequency motor drives. Three popular PWM techniques, sinusoidal PWM, hysteric PWM, and SVPWM, are mainly applied in the field of threephase AC motor drives
[7]
. Due to its advantages and compatibility for use in field orientation of AC motors, SVPWM is one of the more popular techniques used to generate sinusoidal linetoline voltages and currents with a threephase inverter. Compared with other PWM techniques, the SVPWM technique utilizes DC bus voltage more efficiently and generates less harmonic distortion in a threephase voltagesource inverter. However, the SVPWM technique is also used for twophase voltagesource inverters to improve the performance in a twophase motor drive. The SVPWM technique of a twophase full bridge voltagesource inverter for twophase PMSM drives is addressed below.
A twophase full bridge inverter consists of two singlephase full bridge inverters fed to a twophase PMSM motor with two separate and symmetrical windings distributed as a 90° phase shift to each other. One singlephase full bridge contains four switches (S1, S2, S7, and S8) and four diodes (
D1
,
D2
,
D7
, and
D8
), and the other contains four switches (
Q3
,
Q4
,
Q5
, and
Q6
) and four diodes (
D3
,
D4
,
D5
, and
D6
). Two stator windings (A and B) are connected to two singlephase full bridge inverters, respectively, by four ends represented by
a
,
x
,
b
, and
y
. A block diagram of the twophase motor drive with a twophase eight switch inverter is shown in
Fig. 1
.
Twophase full bridge inverter fed to a twophase 0 0 0 motor
The voltages of a twophase motor can be represented by the space vector model. In the twophase full bridge inverter, the winding ends of
a
,
x
,
b
, and
y
can be applied with positive or negative voltage. Therefore, different switching states can achieve 16 voltage vectors, including 12 active vectors of
V_{0}
(1000),
V_{45}
(1010),
V_{90}
(0010),
V_{135}
(0110),
V_{180}
(0100),
V_{225}
(0101),
V_{270}
(0001), and
V
_{315}
(1001), and four zero vectors of
V_{00}
(0000, 1111, 0011, 1100). The fourdigit numbers represent the switching patterns of the four legs in the inverter. “0” denotes that the winding end is connected to a positive voltage of the DC power source, and “1” denotes that the end is connected to a negative voltage. In order to generate a rotating field, the inverter has to be switched for eight of the 16 vectors. The eight nonzero voltage vectors are 45° apart from one another. Their space distribution in a twodimensional voltage vector space is divided into eight sectors of I, II, III, IV, V, VI, VII, and VIII, as shown in
Fig. 2
. The switching patterns and corresponding voltage outputs of the inverter are shown in
Table 1
.
V_{a}
and
V_{b}
are the projection of the voltage vector, respectively, and the vector’s amplitude,
V_{s}
, is the square root of the two components. The maximum amplitude of the voltage circular trajectory locus is
V_{dc}
.
Space voltage distribution of a twophase full bridge inverter
Switching patterns and corresponding outputs of a Twophase full bridge inverter
Switching patterns and corresponding outputs of a Twophase full bridge inverter
SVPWM achieves less harmonic distortion in the output voltages and currents in the windings of the motor, as well as a more efficient use of the DC supply voltage compared to the sinusoidal PWM technique. SVPWM of twophase motor drives refers to a special way of determining the switching sequence of the upper four power transistors of a twophase full bridge inverter. Its point is to approximate the reference voltage instantaneously by combining the switching patterns corresponding to two basic space voltage vectors. For each position inside of the sector, the time can be calculated, and then applied to the appropriate inverter switching states.
In
Fig. 3
, two basic vectors of
V_{1}
and
V_{2}
and the zero vector,
V_{00}
, are used to synthesize the reference voltage vector, V
_{r}
. The switching states in Sectors I and II are also illustrated in
Fig. 3
. There are four PWM channels with a fixed switching order relative to one another, and every channel with a symmetric PWM pattern switches twice for every PWM period. The zero vectors, V
_{00}
, are inserted at the two ends and at the middle of every period. During one sampling period of
T_{s}
, the timeframes of
T_{1}
and
T_{2}
can be calculated to determine the switching states according to the following equations:
where
θ
_{1}
and
θ
_{2}
denote the vector angles between two basic voltage vectors and the reference voltage vector, respectively, as shown in
Fig. 3
. The basic vectors and the vector angles in the eight sectors are given in
Table 2
.
Spacevector PWM based symmetric switching scheme of a twophase full bridge inverter in Sectors I and II
Basic voltage vectors and the angle of the reference voltage vector synthesis
Basic voltage vectors and the angle of the reference voltage vector synthesis
In
Table 2
,
θ
is the angle of the reference voltage vector,
V_{r}
. To achieve a symmetric PWM pattern in the SVPWM of twophase motor drives, each PWM channel switches twice every sampling period. Therefore, two basic voltage vectors have to be adjusted according to the position of the reference voltage vector in each of the different sectors, as shown in
Table 2
. The PWM patterns of the other sectors (III, IV, V, VI, VII, and VIII) can be derived by
Fig. 3
and
Table 2
.
In the digital signal processor, the PWM waveforms are usually generated by the comparators in the PWM period. One comparator can be treated as a PWM channel, as shown in
Fig. 4
. Four comparative values (
T_{B}
,
T_{A}
,
T_{B}
+
T_{1}
, and
T_{A}
) are input to four different channels, and each PWM channel generates two complementary PWM waveforms with a symmetric pattern in Sector I, such as PWM1 and PWM2, PWM3 and PWM4, PWM5 and PWM6, and PWM7 and PWM8. For any PWM signal, four zero vectors are distributed at the start, middle, and end positions, and two basic vectors (
V_{1}
and
V_{2}
) are wrapped around zero vectors. There are eight PWM signals represented by PWM1, PWM2…, PWM8 for a twophase voltagesource inverter driving a twophase PMSM. The time durations in
Fig. 4
are given as follows:
The switching patterns and duty cycles in Sector I for the normal SVPWM scheme
According to the aforementioned contents in
Fig. 4
and
Table 2
, the normal spacevector PWM based symmetric switching patterns of the twophase inverter for six sectors are derived as in
Fig. 5
.
Spacevector PWM based symmetric switching patterns of a twophase full bridge inverter in eight sectors
In
Fig. 5
, the arrangements of the switching patterns in the eight sectors are summarized as (
V_{00}
,
V_{1}
,
V_{2}
,
V_{00}
,
V_{00}
,
V_{2}
,
V_{1}
,
V_{00}
) with the following properties:

1. Each of the four PWM channels switches twice every PWM period unless the duty cycle is 0% or 100%;

2. In every sector, there is a fixed switching order among all PWM channels;

3. Zero voltage vectors (V00) are inserted at the start, middle, and end positions of the PWM pattern during each PWM period;

4. The number of zero vectors is the same as the number of basic voltage vectors in each PWM period.
To verify the spacevector PWM scheme, the experimental results for all of the switching patterns in each of the eight sectors are illustrated in
Figs. 6
and
Fig. 7
.
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the normal SVPWM scheme after 50ms. (Horizontal axis: 5ms/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/ div).
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the normal SVPWM scheme after 0.2 ms when the reference voltage is located in Sector I. (Horizontal axis: 20us/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/div).
It is known in
Fig. 6
and
Fig. 7
that all of the switches of the inverter are always working in the switching state with a high frequency. Each switch of the inverter has the same switching loss in every period. To produce the reference voltage vector effectively, the switching patterns in each of the eight sectors are different. The experimental results are in agreement with the basic principle of the normal SVPWM scheme.
3. Proposed Spacevector PWM Schemes for Twophase PMSM Drives
To improve the performance of the above SVPWM for twophase motor drives, two effective SVPWM schemes are proposed to reduce switching losses.
 3.1 Proposed PWM scheme I
In order to achieve lower switching losses, a new PWM scheme is investigated to synthesize the same reference voltage vector with a reduced switching frequency. The time duration
T_{A}
is fixed to a constant of
T_{s}
which can keep the output signals of two PWM channels constant in a cycle. The detailed implementation method of the proposed PWM scheme I is illustrated in
Fig. 8
.
The switching patterns and duty cycles in Sector I for the proposed SVPWM scheme I
In
Fig. 8
, four comparative values (
T_{B}
,
T_{A}
,
T_{B}
+
T_{1}
, and
T_{A}
) are used to generate four pairs of complementary PWM waveforms with symmetric patterns in Sector I using four comparators in the digital signal processor. However, in each period, two channels produce a changeless switching state, such as PWM3 and PWM4, and PWM7 and PWM8. Two zero vectors are distributed at the start and end positions of the total PWM waveforms, and two basic vectors (
V_{1}
and
V_{2}
) are concentrated in the middle, symmetrically. The time durations in
Fig. 4
are given by:
Therefore, the switching patterns of the proposed PWM scheme I in eight sectors can be derived as in
Fig. 9
.
Spacevector PWM based symmetric switching pattern I of a twophase full bridge inverter in eight sectors
In the proposed switching pattern I illustrated in
Fig. 9
, the arrangement of the PWM patterns in each period is summarized as (
V_{00}
,
V_{1}
,
V_{2}
,
V_{2}
,
V_{1}
,
V_{00}
) with the following properties:

1. Among all four PWM channels, two channels stay constant while the other two channels switch twice every PWM period unless the duty cycle is 0% or 100%;

2. The dead zones are inserted between the complimentary pairs of PWM channels to avoid shootthrough faults;

3. Zero voltage vectors (V00) are inserted at the start and end positions of the PWM pattern in each PWM period. The number of zero vectors is half of the number of basic voltage vectors in each PWM period.
To verify the proposed SVPWM scheme I, the experimental results for all of the switching patterns in each of the eight sectors are illustrated in
Figs. 10
and
Fig. 11
.
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the proposed SVPWM scheme I after 50 ms (Horizontal axis: 5ms/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/div).
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the proposed SVPWM scheme I after 0.2 ms when the reference voltage is located in Sector I (from the top to the bottom) (Horizontal axis: 20us/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/div).
In
Fig. 10
and
Fig. 11
, half of the eight switches are in the switching state during every period. Compared with the normal PWM scheme, the switching losses of the SVPWM scheme I are reduced to half of the normal amount of losses. In every period, four of the eight PWM channels keep a constant output, which is identical with the previous principle analysis.
 3.2 Proposed PWM scheme II
Another PWM scheme is proposed to synthesize the reference voltage vector with reduced switching losses, which differs from PWM scheme I. The time duration,
T_{B}
, is fixed to a constant zero, which keeps one of the PWM channels constant in the cycle. The principle of the proposed PWM scheme II is shown in
Fig. 12
.
The switching patterns and duty cycles in Sector I for the proposed SVPWM scheme II
In
Fig. 12
, four PWM channels generate the PWM waveforms with a symmetric pattern in Sector I using four comparative values (
T_{B}
,
T_{A}
,
T_{B}
+
T_{1}
, and
T_{A}
) in the digital signal processor. Only one channel produces a changeless switching state of PWM1 and PWM2 in each cycle. Two zero vectors are inserted at the middle position of all of the PWM waveforms, and two basic vectors (
V_{1}
and
V_{2}
) are distributed symmetrically on both sides. The time durations in
Fig. 8
are given as follows:
Above all, the switching patterns of the proposed PWM scheme II in the eight sectors are derived as in
Fig. 13
.
Spacevector PWM based symmetric switching pattern II of a twophase full bridge inverter in eight sectors
In the proposed switching pattern II illustrated in
Fig. 13
, the PWM arrangement in each period is summarized as (
V_{1}
,
V_{2}
,
V_{00}
,
V_{00}
,
V_{2}
,
V_{1}
) with the following properties:

1. One of four PWM channels stays constant while the others switch twice for every PWM period unless the duty cycle is 0% or 100%;

2. The dead zones are inserted between the complimentary pairs of the PWM channels to avoid shootthrough faults;

3. Zero voltage vectors (V00) are inserted at the middle position of the PWM pattern in each PWM period. The amount of zero vectors is half of the number of basic voltage vectors in each PWM period.
To verify the proposed SVPWM scheme II, the experimental results of all of the switching patterns in each of the eight sectors are illustrated in
Figs. 14
and
Fig. 15
.
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the proposed SVPWM scheme II after 50 ms (Horizontal axis: 5ms/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/div).
The experimental results of the PWM signals of four switches S1, S3, S5, and S7 for the proposed SVPWM scheme II after 0.2 ms when the reference voltage is located in Sector I (Horizontal axis: 20 us/div; Vertical axis: 1) PWM1: 5V/div, 2) PWM3: 5V/div, 3) PWM5: 5V/div, 4) PWM7: 5V/div).
In
Figs. 14
and
Fig. 15
, the proposed SVPWM II also achieves lower switching losses, while two of the eight switches keep a constant output for every period. Compared with the normal SVPWM scheme, the proposed SVPWM scheme II has only threequarter of the normal switching losses.
Therefore, compared with the normal SVPWM scheme and two proposed SVPWM schemes for twophase PMSM drives, the switching frequency of the inverter is derived as in
Table 3
.
The frequency and the switching number per cycle of the normal SVPWM and two proposed schemes for twophase PMSM drives
The frequency and the switching number per cycle of the normal SVPWM and two proposed schemes for twophase PMSM drives
In
Table 3
, f
_{PWM}
represents the switching frequency using the normal SVPWM scheme in a twophase motor drive.
4. Experiment Results
To verify the proposed SVPWM schemes, a hardware drive with a digital signal processor (DSP) was developed to drive a twophase PMSM, as shown in
Fig. 16
. The parameters of the PMSM and the DSP controller are listed in
Table 4
.
The configuration of a twophase PMSM drive using the proposed SVPWM schemes
The main parameters of the used PMSM in the drive
The main parameters of the used PMSM in the drive
The related parameters of the drive are given by
Table 5
.
The parameters of the proposed control system in the drive
The parameters of the proposed control system in the drive
The block diagram of the designed experimental system is shown in
Fig. 16
.
As shown in
Fig. 16
, the system is composed of five parts including a twophase eightswitch inverter, an Infineon XE164based DSP controller, a twophase PMSM, a PC, and an oscilloscope. The main circuits of the twophase inverter contain eight insulated gate bipolar transistors (IGBTs) and a singlephase bridge rectifier with four diodes fed by an AC power input. The hardware of the DSP controller consists mainly of an Infineon XE164based DSP chip, signal adjustment circuits, and filter circuits. The motor is supplied by the four ends a, x, b, and y from the inverter, and two hall sensor signals from the motor are input into the DSP controller to calculate the speed and rotor position. Two stator currents, I
_{a}
and I
_{b}
, are detected by the signal adjustment circuit in the DSP controller. The source code with the SVPWM algorithm in the computer is compiled and downloaded to the DSP to generate eight PWM trigger signals for the eight IGBTs of the inverter through the Controller Area Network (CAN) communication port of the DSP controller. The state variables of the drive, such as the stator currents, speed, rotor position, and torque, etc., can be displayed in an oscilloscope through a filter circuit of the DSP controller.
In
Fig. 17
, the system for a twophase PMSM achieves a steady performance. Three responses of rotor position (Theta), two PWM time durations (Ta and Tb) are shown in the figures. During every period of the rotor position, two projections of the reference voltage vector in the twophase stationary frame are a sinusoidal waveform with a 90° phase shift. In
Fig. 18
, the PWM generation module produces the time durations of two adjacent vectors of the reference voltage vector with a triangular waveform. As shown in
Fig. 2
, there are two amplitudes of
V_{dc}
and 1.414
V_{dc}
among the eight voltage vectors, which causes the difference in the time durations of the two projection vectors.
The experiment results of the rotor position and two projections of the reference voltage vector in a two phase stationary frame using the normal and proposed PWM schemes (Horizontal axis: 10ms/ div; Vertical axis: 1) Theta: 5V/div, 2) Va: 2V/div, 3) Vb: 2V/div).
The experiment results of the rotor position, time duration of T1 and T2 in the equations of 1, 2, 3, and 4 using the normal and proposed PWM scheme (Horizontal axis: 10ms/div; Vertical axis: 1) Theta: 5V/div, 2) Ta: 2V/div, 3) Tb: 2V/div).
Fig. 19
shows the steady responses of the PWM1, rotor position (Theta), and two trigger time durations for PWM channels 1 and 2 (CmpA and CmpB), and the error of two time durations (CmpACmpB) using the normal SVPWM and two proposed SVPWM schemes. During every period of the rotor position, a different switching pattern among the eight sectors causes the special trigger time waveforms. Subsequently, two windings of the twophase PMSM in the drive are fed by two H switch bridges, respectively. In the experimental results, two trigger time durations are used to control two legs of one switch bridge and generate two output voltages to two ends of one winding of the PMSM. The error of the two trigger time durations of the two PWM channels is sinusoidal, which denotes that one winding of the PMSM is fed by a synthesized sinusoid voltage of any H bridge. In the proposed SVPWM schemes of
Fig. 19(b)
and
19(c)
, the trigger time duration with part of one period constant can effectively decrease the switching losses compared to the normal SVPWM scheme. From the experimental results of the system, SVPWM scheme II achieves a better steady performance than SVPWM scheme I.
The experiment results of the steady responses of the PWM1, rotor position, two trigger time durations for PWM channels 1 and 2, and the error of the two trigger time using the normal and two proposed PWM schemes (Horizontal axis: 20ms/div; Vertical axis: 1) PWM1: 5V/div, 2) Theta: 5V/div, 3) CmpA: 2V/div, 4) CmpB: 2V/div, 5) CmpACmpB: 5V/div).
Fig. 20
shows the dynamic responses of the PWM1, rotor speed (Speed), rotor position (Theta) and phase A current (Ia) using the normal SVPWM and two proposed SVPWM schemes. During the starting operation, the motor is initially at rest, and the speed of the motor gradually increase holding to 800rpm in 0.8 second. Experimental results indicate that the speed, the position and phase current responses quickly to supply voltage change. Two proposed SVPWM schemes both achieve better dynamic performance during the process of starting operation, the same as that of the normal one. It is clear that the PWM waveforms of the proposed two SVPWM schemes can reduce part of switching losses compared with the normal one. The proposed SVPWM schemes are effective for twophase motor drive.
The experiment results of the dynamic responses of the PWM1, speed, rotor position, phase A current using the normal and two proposed PWM schemes (Horizontal axis: 1s/div; Vertical axis: 1) PWM1: 5V/div, 2) Speed:2V/div, 3) Theta: 2V/div, 4) Ia: 2V/div).
Fig. 21
shows PWM1, the phase A current (Ia) and its frequency spectrum plot (FFT of Ia) using the normal and proposed PWM schemes. It is shown that the switching frequency (10 kHz and 20 KHz) harmonics also have significant magnitude in addition to the fundamental frequency. The proposed SVPWM scheme I has been proven to produce lower current harmonics than the normal one. Meanwhile, the proposed SVPWM scheme II achieve higher current harmonics that the normal one. The magnitude of the fundamental frequency of the proposed two schemes are lower. From the experimental results of the system, SVPWM scheme II achieves a better steady performance than SVPWM scheme I.
The experiment results of PWM1, phase A current and its frequency spectrum using the normal and two proposed PWM schemes (Horizontal axis: 20ms/div; Vertical axis: 1) PWM1: 5V/div, 2) Ia:5V/div, 3) FFT of Ia:20dB/div).
4. Conclusion
Two SVPWM schemes of a vector control based twophase PMSM drive with a twophase eightswitch inverter are investigated in the paper. In the normal SVPWM of a twophase motor drive, the PWM waveforms used to trigger the switches have to be changed twice in each PWM period, which causes a higher PWM frequency and big noise in the drive. Based on the normal SVPWM scheme, two new SVPWM techniques are proposed by the rearrangements of four comparative values to produce new PWM patterns, which can be used to reduce the switching frequency. The principles of the normal and proposed SVPWM schemes are analyzed to show their differences in detail. The experimental results demonstrate that two proposed PWM methods are effective at achieving a low switching loss.
Acknowledgements
This work was supported by BK21PLUS program through the National Research Foundation of Korea funded by the Ministry of Education and the Fundamental Research Funds for the Central Universities of China (2013G1321043).
BIO
Hai Lin obtained his B.S. degree in Industry Automation from Xi’an Petroleum University, China, and his M.S. and Ph.D. degrees in Control Theory and Control Engineering and in Weapon Science and Technology from Northwestern Polytechnical University, China. He is currently with Chang’an University, China. His research interests are multilevel inverters and motor drives.
Fei Zhao received the B.S. degree from Harbin Institute of Technology, Harbin, China, in 2010. She is currently a Ph.D. student in the department of Electronic Systems Engineering at Hanyang University, Ansan, Korea. Her fields of interest are the electric machine design, theoretical analysis and structure optimization.
ByungIl Kwon obtained his B.S. and M.S. degrees in Electrical Engineering from Hanyang University, Korea, and his Ph.D. degree in Electrical Engineering from Tokyo University, Japan. He is currently a Professor at Hanyang University. His research interests are linear drive systems, numerical analysis of machines, and motor control.
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