IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS, VOL. 10, NO. 1, FEBRUARY 2014
399
An Effective Control Method for Quasi-Z-Source
Cascade Multilevel Inverter-Based Grid-Tie
Single-Phase Photovoltaic Power System
Yushan Liu, Student Member, IEEE, Baoming Ge, Member, IEEE, Haitham Abu-Rub, Senior Member, IEEE,
and Fang Z. Peng, Fellow, IEEE
Abstract—An effective control method, including system-level
control and pulsewidth modulation for quasi-Z-source cascade
multilevel inverter (qZS-CMI) based grid-tie photovoltaic (PV)
power system is proposed. The system-level control achieves the
grid-tie current injection, independent maximum power point
tracking (MPPT) for separate PV panels, and dc-link voltage balance for all quasi-Z-source H-bridge inverter (qZS-HBI) modules.
The complete design process is disclosed. A multilevel space vector
modulation (SVM) for the single-phase qZS-CMI is proposed
to fulfill the synthetization of the step-like voltage waveforms.
Simulation and experiment based on a seven-level prototype are
carried out to validate the proposed methods.
Index Terms—Cascade multilevel inverter (CMI), photovoltaic
(PV) power system, quasi-Z-source inverter, space vector modulation (SVM).
I. INTRODUCTION
A
recent upsurge in the study of photovoltaic (PV) power
generation emerges, since they directly convert the solar
radiation into electric power without hampering the environment. However, the stochastic fluctuation of solar power is inconsistent with the desired stable power injected to the grid,
owing to variations of solar irradiation and temperature. To fully
exploit the solar energy, extracting the PV panels’ maximum
power and feeding them into grids at unity power factor become the most important. The contributions have been made by
the cascade multilevel inverter (CMI) [1], [2]. Nevertheless, the
H-bridge inverter (HBI) module lacks boost function so that the
Manuscript received October 17, 2012; revised January 31, 2013; accepted
August 20, 2013. Date of publication August 29, 2013; date of current version
December 12, 2014. This work was supported by the Qatar National Research
Fund, a member of Qatar Foundation, under Grant NPRP-EP X-033-2-007.
Paper no. TII-12-0726.
Y. Liu is with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China, and also with the Department of Electrical and
Computer Engineering, Texas A&M University at Qatar, Doha 23874, Qatar
(e-mail: yushan.liu@qatar.tamu.edu).
B. Ge is with the School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China, and also with the Department of Electrical and
Computer Engineering, Michigan State University, East Lansing, MI 48824
USA (e-mail: gebaoming@tsinghua.org.cn; bm-ge@263.net).
H. Abu-Rub is with the Department of Electrical and Computer Engineering, Texas A&M University at Qatar, Doha 23874, Qatar (e-mail:
haitham.abu-rub@qatar.tamu.edu).
F. Z. Peng is with the Department of Electrical and Computer Engineering,
Michigan State University, East Lansing, MI 48824 USA (e-mail: fzpeng@egr.
msu.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TII.2013.2280083
inverter KVA rating requirement has to be increased twice with
a PV voltage range of 1:2; and the different PV panel output
voltages result in imbalanced dc-link voltages. The extra dc–dc
boost converters were coupled to PV panel and HBI of the CMI
to implement separate maximum power point tracking (MPPT)
and dc-link voltage balance [3], [4]. However, each HBI module
is a two-stage inverter, and many extra dc–dc converters not
only increase the complexity of the power circuit and control
and the system cost, but also decrease the efficiency.
Recently, the Z-source/quasi-Z-source cascade multilevel
inverter (ZS/qZS-CMI)-based PV systems were proposed in
[5]–[8]. They possess the advantages of both traditional CMI
and Z-source topologies. For example, the ZS/qZS-CMI: 1)
has high-quality staircase output voltage waveforms with
lower harmonic distortions, and reduces/eliminates output filter
requirements for the compliance of grid harmonic standards;
2) requires power semiconductors with a lower rating, and
greatly saves the costs; 3) shows modular topology that each
inverter has the same circuit topology, control structure and
modulation [1], [2]; 4) most important of all, has independent dc-link voltage compensation with the special voltage
step-up/down function in a single-stage power conversion of
Z-source/quasi-Z-source network, which allows an independent
control of the power delivery with high reliability [9]–[11]; and
5) can fulfill the distributed MPPT [6], [8].
In order to properly operate the ZS/qZS-CMI, the power
injection, independent control of dc-link voltages, and the
pulsewidth modulation (PWM) are necessary. The work in
[5] and [7] focused on the parameter design of the ZS/qZS
networks and the analysis of efficiency. The work in [8] presented the whole control algorithm, i.e., the MPPT control of
separate quasi-Z-source H-bridge inverter (qZS-HBI) module,
and the grid-injected power control, whereas the phase-shifted
sinewave PWM (PS-SPWM) is the only existing PWM technique for the single-phase ZS/qZS-CMI. The PS-SPWM
consumes more resources to achieve the shoot-through states
because two more references are compared with the carrier
waveform. Additionally, the ZS/qZS-CMI based grid-tie
PV system has never been modeled in detail to design the
controllers.
The main contributions of this paper include: 1) a novel multilevel space vector modulation (SVM) technique for the singlephase qZS-CMI is proposed, which is implemented without additional resources; 2) a grid-connected control for the qZS-CMI
based PV system is proposed, where the all PV panel voltage
references from their independent MPPTs are used to control
the grid-tie current; the dual-loop dc-link peak voltage control
1551-3203 © 2013 IEEE
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is employed in every qZS-HBI module to balance the dc-link
voltages; 3) the design process of regulators is completely presented to achieve fast response and good stability; and 4) simulation and experimental results verify the proposed PWM algorithm and control scheme.
This paper is organized as follows. An overview of the
whole system with control strategy is presented in Section II.
Section III focuses on the system modeling and grid-connected
control. Section IV addresses the proposed multilevel SVM
technique. Section V designs the regulators; the proposed
strategy is verified by simulation and experimental results in
Section VI. Finally, a conclusion is given in Section VII. Note
that, in the derivations of the paper, all of the symbols with “ ”
denote the amplitude, and those with “ ” denote the average.
II. DESCRIPTION OF QZS-CMI-BASED GRID-TIE
PV POWER SYSTEM
Fig. 1 shows the discussed qZS-CMI-based grid-tie PV power
system. The total output voltage of the inverter is a series summation of qZS-HBI cell voltages. Each cell is fed by an independent PV panel. The individual PV power source is an array
composed of identical PV panels in parallel and series. A typical PV model in [12] is performed by considering both the solar
irradiation and the PV panel temperature.
A. qZS-CMI
The qZS-CMI combines the qZS network into each HBI
module. When the th qZS-HBI is in nonshoot-through states,
it will work as a traditional HBI. There are
(1)
while in shoot-through states, the qZS-HBI module does not
contribute voltage. There are
(2)
For the qZS-CMI, the synthesized voltage is
(3)
where
is the output voltage of the th PV array;
and
the dc-link voltage of the th qZS-HBI module;
represent the shoot-through duty ratio and boost factor of
th qZS-HBI, respectively,
is the output voltage of the
is the switching function of
module, and
th qZS-HBI.
is
the
th
the
B. Control Strategy
The control objectives of the qZS-CMI based grid-tie PV
system are: 1) the distributed MPPT to ensure the maximum
power extraction from each PV array; 2) the power injection
to the grid at unity power factor with low harmonic distortion;
3) the same dc-link peak voltage for all qZS-HBI modules. The
overall control scheme of Fig. 1 is proposed to fulfill these
purposes.
closed loops are
For achieving the first two goals, the
employed, as Fig. 1(a) shows.
Fig. 1. (a) qZS-CMI based grid-tie PV power system. (b) DC-link peak voltage
control.
1) Total PV array voltage loop adjusts the sum of PV array
voltages tracking the sum of PV array voltage references
by using a proportional and integral (PI) regulator
.
Each PV array voltage reference is from its MPPT control
independently.
2) Grid-tie current loop ensures a sinusoidal grid-injected current in phase with the grid voltage. The total PV array
voltage loop outputs the desired amplitude of grid-injected
current. A Proportional + Resonant (PR) regulator enforces
the actual grid current to track the desired grid-injected reference. The current loop output’s total modulation signal
subtracts the modulation signal sum of the second, third,
, and th qZS-HBI modules to get the first qZS-HBI
module’s modulation signal.
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401
Fig. 2. Block diagram of the proposed grid-tie control with the model for the qZS-CMI based PV system.
3) The
separate PV array voltage loops regulate the
PV array voltages to achieve their own MPPTs
other
PI regulators, such as
to
,
through the
respectively. With the total PV array voltage loop control, the PV arrays fulfill the distributed MPPT. In addition, the voltage feed forward control is used to generate
each qZS-HBI module’s modulation signal, which will reduce the regulators’ burden, achieve the fast dynamic
response, and minimize the grid voltage’s impact on the
grid-tie current.
For the third goal, the dc-link peak voltage is adjusted in terms
of its shoot-through duty ratio for each qZS-HBI module, as
Fig. 1(b) shows. A proportional ( ) regulator is employed in
current loop to improve the dynamic response,
the inductor
and a PI regulator of the dc-link voltage loop ensures the dc-link
peak voltage tracking the reference.
and shootFinally, the independent modulation signals
of the qZS-CMI,
,
through duty ratios
are combined into the proposed multilevel SVM to achieve the
desired purposes.
A PR regulator [13]
(7)
is employed to enforce the actual grid-injected current to track
the desired reference.
With a grid voltage feed forward control, the th qZS-HBI
module has the modulation signal
(8)
with
(9)
is the regulated modulation signal from the separate
where
voltage control of the th module, as Fig. 2 shows.
From (8) and (9), we have
(10)
III. SYSTEM MODELING AND CONTROL
Fig. 2 shows block diagram of the proposed grid-tie control with the system model for the qZS-CMI based PV power
system. The details will be explained as follows.
At the dc-link peak voltage balance control, all dc-link peak
voltages are the same. The qZS-HBI modules have the same
transfer function, and we assume
(11)
A. Grid-Tie Current Loop
The th qZS-HBI module has following dynamic:
Using (6)–(11), the grid-injected current will be
(4)
(12)
is the current of qZS inductor ,
is the th PV
where
is the capacitance of PV array terminal
array’s current, and
capacitor.
The qZS-CMI based grid-tie PV system has
Then, the current loop of Fig. 2 is simplified to Fig. 3, and the
open-loop transfer function can be obtained as
(5)
is the grid voltage, is the grid-injected current,
where
is the filter inductance, and
is its parasitic resistance. The
transfer function of the grid-injected current can be
(6)
(13)
With the compensation of the PR regulator, the transfer function becomes
(14)
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Fig. 3. Simplified block diagram of the grid-current closed loop.
Fig. 4. Block diagram of total PV voltage loop.
Consequently, the closed-loop transfer function of grid-tie current control can be obtained in (15), shown at the bottom of the
page.
B. PV Voltage Loop
From (4), we have
Fig. 5. Block diagram of separate PV voltage loop.
(16)
In addition, the output power of each qZS-HBI module
equals to its input power in the nonshoot-through state, the th
qZS-HBI module has the power equation
If
is considered as disturbance, with (20) and Fig. 4, the
transfer function of the total PV array voltage loop is given by
(21), shown at the bottom of the page, where the coefficients
and
are
(17)
where
is the average current of inductor
in noncan be solved as
shoot-through state. Using (1),
(22)
(18)
In the shoot-through state, the average current of inductor
can be expressed as
is applied to track
The PI regulator
the total reference voltage coming from MPPT algorithm. Thus,
the open-loop transfer function of total PV voltage loop after
compensation can be obtained by
(19)
Combining (18) and (19), the average current of inductor
(23)
is
where
(20)
Then, the block diagrams of total and separate PV voltage loops
can be obtained in Figs. 4 and 5.
(15)
(21)
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403
Fig. 6. Block diagram of the th module’s dc-link peak voltage control.
The closed-loop transfer function is
(24)
where
Fig. 7. Proposed multilevel SVM for the single-phase qZS-CMI. (a) Switching
pattern of one qZS-HBI module. (b) Synthetization of voltage vectors for the
qZS-CMI.
and
.
Similarly, from Fig. 5, the transfer function of the
, is
qZS-HBI module’s PV voltage loop,
th
and the closed-loop transfer function
(30)
(25)
which is compensated by PI regulator
. Then, the resultant open-loop transfer function of the
th qZS-HBI module’s PV voltage loop becomes
IV. PROPOSED MULTILEVEL SVM FOR QZS-CMI
As the qZS network is embedded to the HBI module, the
SVM for each qZS-HBI can be achieved by modifying the SVM
technique for the traditional single-phase inverter [15]. Using
the first qZS-HBI module of Fig. 1 as an example, the voltage
is created through the two vectors
and
vector reference
, by
(31)
(26)
Also, the closed-loop transfer function is obtained as
(27)
C. DC-Link Voltage Control
The independent dc-link peak voltage control based on the inductor- current and the capacitor- voltage is performed for
each qZS-HBI module, as Fig. 1(b) shows. From [14], the th
qZS-HBI module’s transfer functions from the shoot-through
, and from the
duty ratio to the dc-link peak voltage,
shoot-through duty ratio to the inductor- current,
,
can be obtained, respectively.
With the employed proportional regulator at the coefficient
for the inductor current loop, as the block diagram of
Fig. 6 shows, the closed-loop transfer function of inductor
current can be obtained by
(28)
A PI regulator with the transfer function of
is cascaded to the inductor current loop for
controlling the dc-link peak voltage, as shown in Fig. 6. Therefore, the th qZS-HBI module’s dc-link peak voltage control
has the open-loop transfer function
(29)
where
and
is the carrier frequency; the time interval is the duration of active vectors, and is the duration
of traditional zero voltage space vectors. Thus, the switching
times for the left and right bridge legs in traditional HBI are
. However, the shoot-through
states are required for the independent qZS-HBI module.
For this purpose, a delay of the switching times for upper
switches or a lead of the switching times for lower switches
are employed at the transition moments, as Fig. 7(a) shows.
of shoot-through
During each control cycle, the total time
zero state is equally divided into four parts. The time intervals
and
remain unof
and
changed;
are the modified times to generate the shoot-through states;
and
are the switching control signals for the upper switches,
and
are that for the lower switches,
.
In this way, the shoot-through states are distributed into the
qZS-HBI module without additional switching actions, losses,
and resources.
To generate the step-like ac output voltage waveform from
phase difference, in which
is the
the qZS-CMI, a
number of reference voltage vectors in each cycle, is employed
between any two adjacent voltage vectors, as Fig. 7(b) shows.
is composed of reference vectors
The total voltage vector
from the qZS-HBI modules.
V. CONTROL PARAMETER DESIGN
The prototype specifications of qZS-CMI based PV power
system are shown in Table I. For the grid-connected current
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TABLE I
PROTOTYPE SPECIFICATIONS
Fig. 9. Bode diagrams of (a)
.
and
; and (b)
and
TABLE II
CONTROL PARAMETERS
Fig. 10. Bode diagrams of (a)
and
.
Fig. 8. Bode diagrams of
and
.
loop, the PR regulator parameters are designed to get a fast dynamic and zero-steady state error at the grid frequency [13].
The fast dynamic response and stable steady-state performance
are taken into account to design the control parameters for total
PV voltage control loop, separate PV voltage control loop, and
dc-link voltage control loop. The design results are shown in
Table II, and all of the Bode plots are shown in Figs. 8–10.
Fig. 8 shows the Bode plots of the grid-tie current loop
and
, which are before and
transfer functions
is the corner
after compensation, respectively. The symbol
frequency of
, which equals
from (6);
is the
resonant frequency of the PR regulator, i.e., grid frequency of
provides a large gain
314 rad/s. After compensation,
inside its bandpass region, making the crossover frequency almost tenfold the corner frequency . Thus, the grid-connected
fast response is greatly enhanced without loss of stability,
which can be obtained from the bode diagram of closed-loop
.
transfer function
and
and (b)
Fig. 9(a) shows the Bode plots of total PV voltage control
and
, which corloop transfer functions
respond to before and after compensation, respectively. The
39.1-dB gain margin and 90.5 phase margin show an un. By using the zero-pole assignment of
,
stable
presents stable
the compensated transfer function
features, which is also verified from the Bode plots of the closed.
loop transfer function
Similarly, the Bode plots of separate PV voltage control are
shown in Fig. 9(b). From Fig. 9(b) and (25), we know that
is not stable. Compensated by the PI regulator
the
, an 87.5 phase margin is shown in
. The
also confirms its stable
closed-loop transfer function
feature.
Fig. 10 shows the Bode plots of transfer functions for each
module’s dc-link peak voltage control loop. When using a pro, the inductor
current shows a faster
portional gain
response without loss of the stability, as shown in Fig. 10(a).
From Fig. 10(b), the dc-link peak voltage closed-loop’s stability
is greatly improved by decreasing the crossover frequency. As
presents a
a result, the closed-loop transfer function
fast and robust characteristic.
VI. SIMULATION AND EXPERIMENTAL VERIFICATIONS
A seven-level qZS-CMI for grid-connected PV power system
is prototyped. Two Agilent E4360A Solar Array Simulators
(SAS) are used to emulate the electrical behavior of PV arrays.
Each SAS has two channel outputs, and each channel is with
)
maximum 120-V maximum power point (MPP) voltage (
and 5-A MPP current (
). Simulation and experimental
results are shown in Figs. 11–15.
LIU et al.: EFFECTIVE CONTROL METHOD FOR qZS-CMI-BASED GRID-TIE SINGLE-PHASE PHOTOVOLTAIC POWER SYSTEM
405
Fig. 11. Simulation results of qZS-CMI at different PV array voltages.
A. DC-Link Voltage Balance Test
The different PV array voltages are performed for the three
qZS-HBI modules. The second module’s PV voltage
is set
to 70 V and the others are at 90 V. A 50- resistor is used as ac
load in this test. All of the voltages in experimental results are
100 V/div.
From (1), the 136-V dc-link voltage of qZS-HBI module is
required to support the 230-V grid. Fig. 11 shows the simulation results, where the second module’s dc-link peak voltage is
boosted to the same voltage value when compared with other
modules, but with a longer shoot-through time interval. Also,
the qZS-CMI outputs the seven-level voltage with equal voltage
step from one level to another level.
Fig. 12 shows the experimental results. We can find that the
same qZS-CMI output voltages and currents are achieved in
Fig. 11 (or Fig. 12), which is derived from the designed dc-link
peak voltage control.
Fig. 12. Experimental results of qZS-CMI at different PV array voltages.
(a) Two modules’ PV array voltages and dc-link voltages. (b) Two PV array
voltages, seven-level output voltage, and load current.
B. Grid-Tie Investigation
The qZS-CMI is connected to the grid in order to test the
proposed grid-tie control. Fig. 13 shows the PV array’s powervoltage characteristics. The measured PV array voltage and current of each module are used to calculate the actual PV power
and the MPPT algorithm searches for the PV voltage reference
at the MPP, which is refreshed every 0.05 s. Here, the perturbation and observation (P&O) MPPT strategy is applied in considering the excellent tracking efficiency and easy implementation
[16].
At first, the three modules are all working at 900 W/m , and
all of the initial voltage references of MPPT algorithms are
given at 105 V from Fig. 13. The second module’s irradiation
decreases to 700 W/m from 1 to 2 s in simulation. Fig. 14 shows
the simulation results. In the experiments, the same test conditions of irradiation and temperature can be implemented by setting the curves of Agilent SAS. Fig. 15 shows the experimental
results.
Fig. 14(a) shows the total PV voltage (sum of three PV panel
voltages) and reference, PV panel voltages and references of
modules 2 and 3, respectively.
Fig. 14(b) is the enlarged detail of Fig. 14(a). It can be seen
that the excellent tracking performance is achieved during 0–1 s;
Fig. 13. PV array power–voltage characteristic.
even though the second module’s PV irradiation changes after
still tracks the reference very well after a very short
1 s, the
transient.
Fig. 14(c) and (d) shows that the grid-injected current is
exactly in phase with the grid voltage even at the irradiation
changing moment. The solar irradiation does not affect the
seven-level staircase output voltage of qZS-CMI, but the lower
irradiation makes the grid-injected current reduced.
The identical experimental results are shown in Fig. 15. As
in Fig. 15(a), the lower solar irradiation reduces the second
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Fig. 15. Experimental results at the grid-tie case. (a) Three PV panel currents.
(b) Second module’s PV panel voltage, qZS-CMI output voltage, grid voltage,
and the grid-injected current. (c) Results zoomed in when the second module’s
PV irradiation changes from 900 to 700 W/m .
The second module’s low irradiation causes the system power
reduced, so the grid-injected current decreases, as Fig. 15(c)
shows. No matter the solar irradiation changes or not, the
qZS-CMI always outputs consistent voltage, which verifies
the voltage balance ability. In simulation and experiments, the
irradiation change may be derived from the shading of cloud
or other objects. Figs. 14 and 15 validate the proposed control
methods.
Fig. 14. Simulation results at the grid-tie case. (a), (b) For PV voltages at
MPPT. (c), (d) For qZS-CMI output voltage, grid voltage, and current.
module’s PV panel current, the first and third modules’ PV
panel currents are not changed due to their constant irradiations.
VII. CONCLUSION
This paper proposed a control method for qZS-CMI based
single-phase grid-tie PV system. The grid-injected power was
fulfilled at unity power factor, all qZS-HBI modules separately
achieved their own maximum power points tracking even if
LIU et al.: EFFECTIVE CONTROL METHOD FOR qZS-CMI-BASED GRID-TIE SINGLE-PHASE PHOTOVOLTAIC POWER SYSTEM
some modules’ PV panels had different conditions. Moreover,
the independent dc-link voltage closed-loop control ensured all
qZS-HBI modules have the balanced voltage, which provided
the high quality output voltage waveform to the grid. The control parameters were well designed to ensure system stability
and fast response. A multilevel SVM integrating with shootthrough states was proposed to synthesize the staircase voltage
waveform of the single-phase qZS-CMI.
The simulation and experiment were carried out on the
seven-level qZS-CMI prototype. The qZS-CMI based grid-tie
PV system was tested. The simulation and experimental results
verified the proposed qZS-CMI based grid-tie PV power system
and the proposed control method.
In principle, the proposed system can work with the weak
grid, even though this paper did not address this topic. In future
work, we will focus on the application to the weak grid, and the
detailed analysis and experimental results will be disclosed in
the next paper.
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Yushan Liu (S’12) received the B.Sc. degree in
automation from the Beijing Institute of Technology,
Beijing, China, in 2008. She is currently working
toward the Ph.D. degree in electrical engineering
at the School of Electrical Engineering, Beijing
Jiaotong University, Beijing.
She is also currently a Research Assistant with the
Department of Electrical and Computer Engineering,
Texas A&M University at Qatar, Doha, Qatar. Her
research interests include modeling and control of
Z-source inverters, cascade multilevel inverters, PV
power generation, and battery energy storage.
Baoming Ge (M’11) received the Ph.D. degree in
electrical engineering from Zhejiang University,
Hangzhou, China, in 2000.
He was a Postdoctoral Researcher with the Department of Electrical Engineering, Tsinghua University,
Beijing, China, from 2000 to 2002, was a Visiting
Scholar with the Department of Electrical and Computer Engineering, University of Coimbra, Coimbra,
Portugal, from 2004 to 2005, and was a Visiting Professor with the Department of Electrical and Computer Engineering (ECE), Michigan State University
(MSU), East Lansing, MI, USA, from 2007 to 2008. He is currently with the
ECE of MSU as well as a Professor with the School of Electrical Engineering,
Beijing Jiaotong University, Beijing, which he joined in 2002. His research interests include renewable energy power generation, electrical machines and control, power electronics systems, and control theories and applications.
Haitham Abu-Rub (M’99–SM’07) received the
M.Sc. degree in electrical engineering from Gdynia
Marine Academy, Gdynia, Poland, in 1990, and
the Ph.D. degree from the Gdansk University of
Technology, Gdansk, Poland, in 1995.
For eight years, he was with Birzeit University,
Birzeit, Palestine, where he was first an Assistant
Professor and then an Associate Professor and was
the Chairman of the Electrical Engineering Department for four years. He is currently a Full Professor
with the Department of Electrical and Computer
Engineering, Texas A&M University at Qatar, Doha, Qatar. His main research
interests are the electrical machine drives and power electronics.
Dr. Abu-Rub was a recipient of many international prestigious awards, such
as the American Fulbright Scholarship (at Texas A&M University, College Station), the German Alexander von Humboldt Fellowship (at Wuppertal University, Wuppertal, Germany), the German DAAD Scholarship (at Ruhr University
Bochum, Bochum, Germany), and the British Royal Society Scholarship (at the
University of Southampton, Southampton, U.K.).
Fang Z. Peng, photograph and biography not available at the time of
publication.