In this paper, a new continuously and linearly controlled capacitive static VAR compensator is proposed for the automatic power factor correction of inductive single phase loads in 220V 50Hz power system networks. The compensator is constructed of a harmonicsuppressed TCR equipped with a new adaptive current controller. The harmonicsuppressed TCR is a new configuration that includes a thyristor controlled reactor (TCR) shunted by a passive third harmonic filter. In addition, the parallel configuration is connected to an AC source via a series first harmonic filter. The harmonicsuppressed TCR is designed so that negligible harmonic current components are injected into the AC source. The compensator is equipped with a new adaptive closed loop current controller, which responds linearly to reactive current demands. The no load operating losses of this compensator are negligible when compared to its capacitive reactive current rating. The proposed system is validated on PSpice which is very close in terms of performance to real hardware.
I. INTRODUCTION
Poor power factor is a challenging issue facing power quality achievement. It causes extra losses in transmission systems and power generation stations. In addition, it may restrict the transmission capability of transmission systems. Therefore, power factor correction is an effective remedy for this issue. The benefits of power factor correction include energy savings, transmission loss reductions, and the feasibility of operating transmission lines closer to their thermal limits. Effective tools used to achieve power factor correction include static VAR compensators such as fixed capacitor thyristor controlled reactors, thyristor switched capacitors (TSC), static synchronous compensators (statcom), and power converter based static VAR compensators
[1]

[8]
. The traditional thyristor controller reactor (TCR) is simply a reactor connected in series to two antiparallel thyristors where the series combination is supplied by the phase or line to line voltage of the AC power system network. It is controlled continuously by the symmetric firing angles of its thyristors. It releases significant amounts of odd current harmonics. As a result, it requires the installation of harmonic filters at its location
[9]

[11]
. TCRs are considered to be an important application of what is known as Flexible Alternative of Current Transmission Systems (FACTS) devices, which represent the recent application of power electronics in transmission systems
[12]

[16]
. FACTS devices are designed to satisfy the real time demands of power systems. A TSC is constructed of a capacitor connected in series to two antiparallel thyristors where the series combination is supplied by the phase or line to line voltage of an AC source. A compensator constructed of several TSCs is characterized by a stepwise capacitive reactive power response
[17]

[19]
. In the design of TCRs, and TSC based static VAR compensators, naturally commutated thyristors are usually employed. These kinds of compensators are commonly referred to as traditional static VAR compensators.
Power converter based static VAR compensators are constructed of either voltage source inverter (VSI) or current source inverter (CSI)
[20]

[22]
. They are designed to exchange real power and reactive power with the AC networks through certain impedances. They can be adjusted to exchange reactive power and active power with the AC power system networks by changing the phases of the triggering signals of their solidstate switching devices. These kinds of compensators are usually supported by energy storage devices in order to stabilize their DC voltages. A statcom is an application based on the power conversion principles. It is either a voltage source inverter shunted by a DC capacitor
[23]
or a current source inverter shunted by a DC reactor
[24]
. Both categories can exchange capacitive or inductive reactive power with the AC network through, to some extent, small series impedances (usually small reactors). Statcoms can be used to control both real power and reactive power. They are built with different topologies in order to satisfy the requirements of being employed in applications requiring higher voltage and current ratings in addition to treating the current harmonics associated with their compensating currents
[25]

[27]
. Static VAR compensators built on the basis of power conversion are usually denoted by advanced static VAR compensators.
In this paper, a modified harmonicfree configuration constructed with a TCR and two passive circuits is presented as a reliable replacement for a fixed capacitor thyristor controlled reactor shunted by high power harmonic filters. This configuration represents a continuously and linearly controlled capacitive static VAR compensator. The capacitive current of this compensator is controlled by a new adaptive closed loop current controller, which forces the compensator to respond linearly to the reactive current demand.
II. SCHEMATIC DESIGN OF THE PROPOSED AUTOMATIC POWER FACTOR CORRECTION SYSTEM
The layout of the proposed system is shown in
Fig. 1
. The compensator power circuit is built with a traditional TCR and two filtering circuits.
L_{X}
and
R_{X}
are the selfinductance and resistance of the TCR reactor. The first filtering circuit is represented by the series circuit
C_{F1}L_{F1}R_{F1}
, which is tuned at the AC source fundamental angular frequency
ω
.
R_{F1}
is the selfresistance of
L_{F1}
. The second circuit is formed with
C_{F2}L_{F2}R_{F2}
and it is tuned at 3
ω
.
R_{F2}
is the selfresistance of
L_{F2}
.
The actual waveform of the TCR current
i_{X}
at a certain firing angle
α
is shown in
Fig. 2
. In this figure,
v_{X}
represents the AC voltage exerted across the TCR terminals, and
α
is the angle measured from the positive peak point of
v_{X}
to its next negative slope zerocrossing point. This angle varies in the range of 0≤
α
≤π/2. The absolute fundamental and nth harmonic current components of the TCR current are given by
[1]
:
Layout of the proposed automatic power factor correction system.
The TCR current waveform.
Where,
V_{m}
is the amplitude of
v_{X}
, and
n
is a positive odd integer greater than unity.
Since the first and second filtering circuits are tuned at
ω
and 3
ω
, respectively, the following can be written:
Where,
X_{F1}
and
X_{F2}
are the characteristic impedances of the first and second filtering impedances, respectively, at the corresponding resonance frequencies of
ω
and 3
ω
. At the fundamental angular frequency
ω
of the AC source, these impedances can be expressed as follows:
Where,
Z_{F1}(ω)
and
Z_{F2}(ω)
are the impedances of the first and second filtering circuits at the AC source fundamental. In Equation (6), the selfresistance
R_{F2}
is neglected because it is very small when compared to the imaginary part of
Z_{F2}(ω)
.
The second filtering circuit and the TCR circuit are designed so that the parallel combination draws zero reactive current during zero reactive current demand. This implies that:
Since
R_{X}
is negligible when compared to
ωL_{X}
, Equation (7) can be closely approximated to:
At the nth harmonic frequency, the impedances of the first and second filtering circuits can be expressed as follows:
To make this compensator suppress all of the current harmonics with orders higher than the 9
^{th}
harmonic, the nth harmonic current component flowing through the AC source side should be at least one tenth the component released by the TCR. This implies that:
Substituting Equation (9) and (10) into (11) gives the following closely approximated equation:
Equations (8) and (12) are the basic design equations of the proposed harmonicsuppressed TCR. Using these equations, the passive elements of the harmonicsuppressed TCR can be expressed in terms of its reactor inductance as follows:
III. SCHEMATIC DESIGN OF THE NEW ADAPTIVE CONTROLLER
The controlling scheme of the proposed compensator is shown in
Fig. 3
. The inputs to this controller are the instantaneous AC source voltage
v_{AC}
, a voltage signal proportional to the instantaneous compensator current
K_{I}i_{C}
, and a voltage signal proportional to the instantaneous load current
K_{I}i_{L}
. Where,
K_{I}
is a constant depending on the current transformer turn ratio and the parameters of its circuitry. The voltage
v_{AC}
is exerted to a stepdown voltage transformer in order to produce the analogue voltage
K_{V}v_{AC}
. Where, the
K_{V}
constant stands for the primary to secondary turn ratio of the voltage transformer. The analogue voltage
K_{V}v_{AC}
is zerocrossed and then delayed by 5ms to produce the voltage waveforms
v_{S1}
and
v_{S2}
. A third voltage waveform
v_{S3}
is produced through the XOR operation of
v_{S1}
and
v_{S2}
. The waveform
v_{S3}
is exerted on a sawtooth generator to produce the signal
v_{ST}
which has an amplitude of 4V and runs at a frequency of 2
f
. Where,
f
is the frequency of the AC source (
f
=
ω
/2π).
The new adaptive controlling scheme.
The voltage waveforms of the new adaptive controller of the proposed compensator.
The voltage waveform
v_{ST}
is subtracted from a DC voltage of 4V to produce the reference voltage waveform
v_{REF}
which is used together with the output of the current controller to determine the TCR firing angle
α
. The inputs of the current controller are the analogue voltages
K_{I}i_{C}
and
K_{I}i_{L}
. In this controller, a closed loop strategy is adopted so that its output
v_{CX}
settles when the reactive current components of the inductive load and the compensator current cancel each other out. The analogue signal controlling the firing angle of the TCR is obtained by comparing the output of the current controller
v_{CX}
with the reference voltage waveform
v_{REF}
. The latter waveform varies in the range of 0 to +4V. The waveforms of the new adaptive controlling scheme are shown in
Fig. 4
. By examining this figure, it can be seen that the TCR firing angle can be related to the voltage
v_{CX}
as follows:
The instantaneous fundamental current of the TCR (
i_{X1}
) can expressed as follows:
The instantaneous fundamental current of the third harmonic filter (
i_{Y1}
) can expressed as follows:
Since this compensator is designed so that negligible harmonic current components are permitted to flow into the AC source side, its instantaneous current (
i_{C}
) contains only the fundamental current components of the third harmonic filter and the TCR. Consequently,
i_{C}
can determined as follows:
Substituting Equations (18), (19), and (8) into (20) gives:
Substituting Equation (17) into (21) gives:
Equation (22) indicates that the compensator current is purely capacitive and can be directly controlled by the voltage
v_{CX}
. If
v_{CX}
is zero, then the compensator will generate its maximum reactive current. On the other hand, its current will be zero if
v_{CX}
is +4V. The instantaneous current of the inductive load can be defined by:
Where,
I_{Lm}
and
φ
are the amplitude and power factor angle of the inductive load, respectively. The automatic power factor correction system is designed so that the compensator current cancels the reactive current component of the inductive load. Consequently, the following can be written:
Equation (24) is directly governed by
v_{CX}
. A closed loop control strategy is adopted in this paper to make Equation (24) settle to zero within a short time.
The new adaptive current controller of the proposed compensator is shown in
Fig. 5
. The actual current of the harmonicsuppressed TCR
i_{C}
is detected by a current transformer and converted to the analogue voltage
K_{I}i_{C}
. Where,
K_{I}
is a constant depending on the current transformer turn ratio and the parameters of its circuitry. The load current is detected by a similar current transformer and converted to the analogue voltage
K_{I}i_{L}
. The analogue voltage signal
K_{I}i_{C}
is sampled and held at
ωt
=2
k
π and
ωt
=(1+
k
)π in order to detect
K_{I}I_{Cm}
and 
K_{I}I_{Cm}
. Where,
k
=0, 1, 2, 3, ... and
I_{Cm}
is the actual amplitude of the compensator current
i_{C}
. The two sampled signals are treated through a difference amplifier for obtaining the mean of
K_{I}I_{Cm}
. The latter signal is proportional to the compensator capacitive reactive current. The analogue voltage signal
K_{I}i_{L}
is sampled and held at
ωt
=2
k
π for obtaining the analogue voltage signal –
K_{I}I_{Lm}sin(φ)
, which is proportional to the inductive load reactive current component.
The voltage across capacitor
C_{X}
represents the controller output voltage
v_{CX}
. This voltage directly controls the triggering circuits of the thyristors employed in the compensator design. If the error signal becomes zero, then the charging and discharging processes will cease and the capacitor will sustain its final voltage as long as the error signal is not effective. Therefore, the steady state operation is reached when the error signal continues having zero values.
The TCR controlling signal
v_{X}
is produced by comparing
v_{Cx}
with
v_{REF}
. The voltage signal
v_{X}
is logically multiplied by
v_{S2}
and its complement to obtain the TCR thyristor triggering signals
v_{X1}
and
v_{X2}
, as shown in
Fig. 4
. The triggering signals
v_{X1}
and
v_{X2}
can be defined by:
A validation system for the proposed automatic power factor correction system is designed on Pspice, as shown in
Fig. 6
. The system is designed so that it has a reactive current rating of 110A (peak) in a 220V 50Hz power system network.
The new adaptive current controller of proposed compensator.
The reference waveform generator is shown in
Fig. 7
. This generator produces the voltage signal
v_{REF}
illustrated in
Fig. 4
.
A circuit diagram of the new adaptive current controller is shown in
Fig. 8
. This figure represents a circuit diagram that stands for the schematic design shown in
Fig. 5
.
The PSpice validation system of proposed automatic power factor correction system.
The reference waveform generator.
The circuit diagram of the adaptive current controller.
According to the specified reactive current rating, the inductance of the TCR reactor
L_{X}
is calculated to be (311V/110A)=9mH. 311V stands for the rms value of 220V. According to this value of
L_{X}
and using the design Equations (13) to (16), the following design values are obtained:
L_{F1}
=10.125mH,
C_{F1}
=1000μF,
L_{F2}
=1.125mH, and
C_{F2}
=1000μF. The selfresistances of the reactors are chosen so that the resistance to inductance ratio is 10Ω/H in order to reduce their losses and to make them behave, to some extent, as pure reactances.
Two identical current transformers are used in this design. The primary to secondary ratio of each transformer is 1:100. The thyristors used are T627121574DNs. These thyristors have continuous voltage and current ratings of 2200V and 300A, respectively.
The
npn
transistors used in the new adaptive controller design are Q2N2222As. These transistors have continuous voltage and current ratings of 75V and 800mA, respectively. Their forward current gain
β
is 256.
IV. RESULTS AND DISCUSSION
The automatic power factor correction system depicted in
Fig. 6
was tested in PSpice at rated load currents with different lagging power factors. The PSpice tests involve the transient and steady state performance of the compensation system. The transient performance started from the first plug in instant of the compensator to the AC power system network and ended once the compensator current was completely settled. The steady state performance started from the instant at which the compensator current was completely settled. Therefore, it is appropriate to reveal the transient and steady state performance results together to show the instants at which the steady state performance started. Then the steady state performance results are revealed to demonstrate the potency of the compensator in power factor correction and harmonic cancellation.
 A. Transient and Steady State Performance
The automatic power factor correction system in this paper is proposed to correct to unity the power factor of a singlephase inductive load in a 220V 50Hz power system network. During the PSpice test, a load of a 2Ω impedance was chosen. According to the design capability of the compensation system, a lagging power factor of 0.707 of the above load can be corrected to unity. If the power factor is lower than 0.707, a partial power factor improvement can be expected. Firstly, the compensation system was tested at the rated resistive load (2Ω).
Fig. 9
shows the performance results of this test.
Fig. 9
a shows that the adaptive current controller approached steady performance at
t
=200ms. This is deduced from the error signal
K_{I}
Δ
I
which attained a zero value at this time and sustained it.
Fig. 9
a shows that the current drawn from the AC source
i_{AC}
approached zero at
t
=160ms. Consequently, it can be said that the steady state performance in this figure started at
t
=200ms. The voltage
v_{CX}
attained a value of +5V, which corresponded to the zero firing angle of the TCR. Therefore, the TCR was running at its maximum inductive current rating, which cancelled the capacitive current generated by the third harmonic filter.
Transient and steady state performance during rated resistive load: (a) current controller, (b) the whole compensator.
Fig. 10
,
Fig. 11
, and
Fig. 12
show the transient and steady state performance results of the automatic power factor correction system during the compensation of inductive rated loads at 0.9, 0.8, and 0.707 lagging power factors, respectively. In
Fig. 10
(a), the error signal of the current controller settled to the zero value at
t
=200ms. At this time, the voltage
v_{X}
is about 2.5V. This value of
v_{X}
corresponds to a firing angle of 0.98 radians (56
^{0}
). According to Equation (25), the zero error signal means that the compensator capacitive current and the load reactive current components are equal in magnitude and out of phase by 180
^{0}
. This situation corresponds to unity power factor correction.
In
Fig. 11
(a), the current error signal settled to the zero value before
t
=200ms while
v_{X}
settled to the steady state value at the same time. In this figure,
v_{X}
is slightly less than 2V. This value of
v_{X}
corresponds to a firing angle of slightly less than π/4.
In
Fig. 12
(a), the current error signal settled to the zero value before
t
=200ms while
v_{X}
settled to the zero value at the same time. This value of
v_{X}
corresponds to a firing angle of π/2, which in turn corresponds to the zero TCR current.
Fig. 12
(b) shows the zero reactive current absorbed by the TCR.
Transient and steady state performance results during rated load at 0.9 lagging power factor: (a) current controller, (b) the whole compensator.
Transient and steady state performance results during rated load at 0.8 lagging power factor: (a) current controller, (b) the whole compensator.
Transient and steady state performance results during rated load at 0.707 lagging power factor: (a) current controller, (b) the whole compensator.
 B. steady State Performance
The steady state performance started at about
t
=200ms after the first plug in of the compensator to the power system network. However, for better evaluation of the harmonic contents, the steady state performance tests were carried out beyond
t
=300ms.
Fig. 13
shows the steady state performance of the adaptive current controller during a resistive load.
Steady state performance results of the adaptive current controller during rated resistive load.
Fig. 14
(a),
Fig. 14
(b), and
Fig. 14
(c) show the steady state performance results of the adaptive current controller corresponding to the loading conditions specified in
Fig. 10
(a),
Fig. 11
(a), and
Fig. 12
(a), respectively.
Fig. 13
and
Fig. 14
show that the voltage signals
K_{I}I_{Cm}
and
K_{I}I_{Lm}sinφ
are equal in magnitude and having different signs. Therefore, the error signal Δ
I
is zero. In addition, these figures show a constant
v_{X}
during steady state performance. This guaranties a fixed firing angle.
Steady state performance of the current controller during rated loads at lagging power factor of: (a) 0.9, (b) 0.8, (c) 0.707.
Fig. 15
,
Fig. 16
,
Fig. 17
, and
Fig. 18
show the steady state performance of the compensation process corresponding to the loading conditions specified in
Fig. 9
(b),
Fig. 10
(b),
Fig. 11
(b), and
Fig. 12
(b), respectively.
Fig. 15
corresponds to the rated resistive load. Since the reactive current component is zero, the compensator current should also be zero according to Equation (25). The figure shows that the AC source
i_{AC}
and the load current
i_{L}
are coinciding with each other.
Fig. 16
corresponds to a rated inductive load at a 0.9 lagging power factor. The reactive current component of this current is 68A (peak value). Therefore, the compensator should generate a reactive current of 68A (peak value) in order to achieve a unity power factor correction to
i_{AC}
. The unity power factor correction is obvious in this figure.
Fig. 17
and
Fig. 18
correspond to rated inductive loads at 0.8 and 0.707 lagging power factors, respectively. The reactive current components of these currents are 93A and 110A (peak values), respectively. The compensator was able to compensate the above load reactive current components and the compensation processes resulted in a unity power factor correction to
i_{AC}
as shown in these two figures.
In
Fig. 15
to
Fig. 18
, no sign of current harmonics beyond the fundamental component are noticeable on the compensator current frequency spectrum
F(i_{C})
, the AC source current frequency spectrum
F(i_{AC})
, or the load current frequency spectrum
F(i_{L})
. Consequently, this automatic power factor correction system is harmonicfree.
In
Fig. 15
, the instantaneous TCR current
i_{X}
and the third harmonic filter current
i_{Y}
are pure sinusoidal, equal in magnitude, and out of phase by 180
^{0}
. Therefore, they cancel each other out and result in almost zero compensating current
i_{C}
. Consequently, the linearly and continuously controlled capacitive compensator used in this compensation system and represented by the harmonicsuppressed TCR is a pure reactive device having negligible no load operating losses.
The compensator steady state performance during rated resistive load.
The compensator steady state performance during rated inductive load at 0.9 lagging power factor.
The compensator steady state performance during rated inductive load at 0.8 lagging power factor.
The compensator steady state performance during rated inductive load at 0.707 lagging power factor.
The TCR current frequency spectrum
F(i_{X})
and the third harmonic filter current frequency spectrum
F(i_{Y})
coincide with each other in
Fig. 15
to
Fig. 18
. The fact that they coincide verifies that this compensation system is harmonicfree.
The above applied tests show that the new adaptive current controller approaches its steady state performance within a time of about 200ms. This time is very small when compared to those achieved by the phase shift current controller in
[2]
, the microprocessor based power factor controller in
[4]
, the hysteresis current controller depicted in
[5]
, and the SVC current controller with a Fuzzy ranking system in
[7]
. For instance, the steady state performance time for the hysteresis current controller
[5]
is about one second. This is approximately five times the transient time of the new current controller adopted in this paper.
The frequency spectrums of the steady state current of the harmonicsuppressed TCR demonstrate its efficiency as a linear harmonicfree capacitive static VAR compensator. It reveals excellent harmonic cancellation when compared to traditional static VAR compensators such as the power factor compensator and harmonic suppresser in
[2]
. In addition, it exhibits competitive compensation and harmonic cancellation efficiencies when compared to the advanced static compensators depicted in
[6]
,
[11]
,
[13]
,
[22]
.
V. CONCLUSIONS
There are three types of control schemes used to govern the susceptances of static VAR compensators. The first scheme is dependent on direct computations of the VAR demands to specify the firing triggering signals of the switching devices of static VAR compensators. This type of control is referred to as open loop control. The second type depends on feedback control to govern the current of the static VAR compensator. However, this type of control requires undistorted compensating currents in order to settle accurately and rapidly to the steady state operation. The third controlling scheme mixes these two approaches of control. Traditionally, TCR control is usually realized by the first control scheme through look up tables, programmable controlling schemes, direct analogue computations, and analogue simulation of the TCR current fundamental. This is because the TCR current waveform is not sinusoidal. In this paper, an adaptive closed loop controlling strategy for a TCR is presented. This is done because all of the harmonic current components released by the TCR are not permitted to be injected into the AC source side. Consequently, the harmonicsuppressed TCR based capacitive static VAR compensator becomes a harmonicfree pure reactive device that can be controlled using closed loop strategies. The perfect unity power factor correction handled by the proposed automatic power factor correction system validates its design methodology and reveals it potency in energy saving for generation stations and the reduction of transmission losses.
BIO
Abdulkareem Mokif Obais was born in Iraq, in 1960. He received his B.S. and M.S. degrees in Electrical Engineering from the University of Baghdad, Baghdad, Iraq, in 1982 and 1987, respectively, and his Ph.D. degree in Electrical Engineering from the Universiti Tewnaga Nasional, Kajang, Malaysia, in 2013. He joined Alkufa University, Kufa, Iraq, as an Assistant Lecturer, in 1988, and then joined Babylon University, Babylon, Iraq, in 1991. He was promoted to Lecturer and Assistant Professor, in 1996 and 2000, respectively. In 2008, he was promoted to Professor in the Department of Electrical Engineering, College of Engineering, Babylon University. He has supervised and examined a number of postgraduate students. He has published many papers in Iraqi academic and international Journals.
Jagadeesh Pasupuleti was born in Vadamalapeta, India. He received his B.S. degree in Electrical and Electronics Engineering from Acharya Nagarjuna University, Guntur, India, in 1986, and his M.S. and Ph.D. degrees in Electrical and Electronics Engineering with a specialization in power system operation and control from Sri Venkateswara University, Tirupati, India, in 1988 and 2002, respectively. He has published a number of papers in international conference proceedings and international journals in the fields of power system operation and control as well as renewable energy. His current research interests include power system operation and control, applications of power electronics and renewable energy. Dr. Pasupuleti is a Senior Member of IEEE, and a Member of IET and ISTE.
Gyugyi L.
1988
“Power electronics in electric utilities: static Var compensators”
inProc. the IEEE
76
(4)
483 
494
DOI : 10.1109/5.4433
Moran L. T.
,
Ziogas P. D.
,
Joos G.
1989
“Analysis and design of a novel 3ϕ solidstate power factor compensator and harmonic suppressor system”
IEEE Trans. Ind. Appl.
25
(4)
609 
619
DOI : 10.1109/28.31237
Raonic D.
,
Cyganski D.
1989
“Power factor compensation at busses with slightly distorted voltage due to random harmonics”
IEEE Trans. Power Del.
4
(1)
502 
507
DOI : 10.1109/61.19240
AlBolok H. M.
,
Masoud M. E.
,
Mahmoud M. M.
1990
“A microprocessorbased adaptive power factor corrector for nonlinear loads”
IEEE Trans. Ind. Electron.
37
(1)
77 
81
DOI : 10.1109/41.45846
Hirve S.
,
Chatterjee K.
,
Fernandes B. G.
,
Imayavaramban M.
,
Drawi S.
2007
“PLLless active power filter based on onecycle control for compensating unbalanced loads in threephase fourwire system”
IEEE Trans. Power Del.
22
(4)
2457 
2465
DOI : 10.1109/TPWRD.2007.893450
Singh B.
,
Jayaprakash P.
,
Somayajulu T. R.
,
Kothari D. P.
2009
“Reduced rating VSC with a zigzag transformer for current compensation in a threephase fourwire distribution system”
IEEE Trans. Power Del.
24
(1)
249 
259
DOI : 10.1109/TPWRD.2008.2005398
Kulkarni D. B.
,
Udupi G. R.
2010
“ANNbased SVC switching at distribution level for minimalinjected harmonics”
IEEE Trans. Power Del.
25
(3)
1978 
1985
DOI : 10.1109/TPWRD.2010.2040293
Xu Y.
,
Tolbert L. M.
,
Kuek J. D.
,
Rizy D. T.
2010
“Voltage and current unbalance compensation using a static VAR compensator”
IET Power Electron.
3
(6)
977 
988
DOI : 10.1049/ietpel.2008.0094
IEEE PES Harmonic Working Group
2001
“Characteristics and modeling of harmonic sourcespower electronic devices”
IEEE Trans. Power Del.
16
(4)
791 
800
DOI : 10.1109/61.956771
Alves J. E. R.
,
Pilotto L. A. S.
,
Watanabe E. H.
2008
“Thyristorcontrolled reactors nonlinear and linear dynamic analytical models”
IEEE Trans. Power Del.
23
(1)
338 
346
DOI : 10.1109/TPWRD.2007.911131
Luo A.
,
Shuai Zhikang
,
Zhu Wenji
,
Shen Z. John
2009
“Combined system for harmonic suppression and reactive power compensation”
IEEE Trans. Ind. Electron.
56
(2)
418 
428
DOI : 10.1109/TIE.2008.2008357
Ooi B. T.
,
Kazerani M.
,
Marceau R.
,
Wolanski Z.
,
Galiana F. D.
,
McGillis D.
,
Joos G.
1997
“Midpoint siting of FACTS devices in transmission lines”
IEEE Trans. Power Del.
12
(4)
1717 
1722
DOI : 10.1109/61.634196
Strivastava K. N.
,
Strivastava S.C
1998
“Elimination of dynamic bifurcation and chaos in power systems using FACTS devices”
IEEE Trans. Circuits and Syst. I Fundam. Theory Appl.
45
(1)
72 
78
DOI : 10.1109/81.660759
Pourbeik P.
,
Gibbard M.J.
1998
“Simultaneous coordination of power system stabilizers and FACTS device stabilizers in a multimachine power system for enhancing dynamic performance”
IEEE Trans. Power Syst.
13
(2)
473 
479
DOI : 10.1109/59.667371
Tan W. L.
,
Wang Y.
1998
“Effects of FACTS controller line compensation on power system stability”
IEEE Power Eng. Rev.
55 
56
DOI : 10.1109/39.691726
Haque M. H.
2008
“Evaluation of first swing stability of a large power system with various FACTS devices”
IEEE Trans. Power Syst.
23
(3)
1144 
1151
DOI : 10.1109/TPWRS.2008.926095
Chakravorti A. K.
,
Emanuel A.E.
1994
“A current regulated switched capacitor static volt ampere reactive compensator”
IEEE Trans. Ind. Appl.
30
(4)
986 
997
DOI : 10.1109/28.297916
Nandi S.
,
Biswas P.
,
Nandakumar V. N.
,
Hedge R. K.
1997
“Two novel schemes suitable for static switching of threephase deltaconnected capacitor banks with minimum surge current”
IEEE Trans. Ind. Appl.
33
(5)
1348 
1354
DOI : 10.1109/28.633816
Dixon J.
,
Moran L.
,
Rodriguez J.
,
Domke R.
2005
“Reactive power compensation technologies: stateofart review”
inProc. The IEEE
93
(12)
2144 
2164
DOI : 10.1109/JPROC.2005.859937
Gupta R.
,
Ghosh A.
,
Joshi A
2008
“Switching characterization of cascaded multilevelinvertercontrolled systems”
IEEE Trans. Ind. Electron.
55
(3)
1047 
1058
DOI : 10.1109/TIE.2007.896274
Wen J.
,
Smedley K. M.
2008
“Synthesis of multilevel converters based on single and or threephase converter building blocks”
IEEE Trans. Power Electron.
23
(3)
1247 
1256
DOI : 10.1109/TPEL.2008.921175
Hamadi A.
,
Rahmani S.
,
Al K.
2010
“A Hybrid passive filter configuration for VAR control and harmonic compensation”
IEEE Trans. Ind. Electron.
57
(7)
2419 
2434
DOI : 10.1109/TIE.2009.2035460
Sumi Y.
,
Hanunoto Y.
,
Hasegawa T.
,
Yano M.
,
Ikeda K.
,
Matsuura T.
1981
“New Static VAR control using forcedcommutated inverter”
IEEE Trans. Power App. Syst.
PAS100
(9)
4216 
4224
DOI : 10.1109/TPAS.1981.316973
Ye Y.
,
Kazerani M.
,
Quintana V. H.
2005
“Currentsource converter based STATCOM: modeling and control”
IEEE Trans. Power Del.
20
(2)
795 
800
DOI : 10.1109/TPWRD.2004.837838
Barrena J. A.
,
Marroyo L.
,
Vidal M. A. R.
,
Apraiz J. R. T.
2008
“Individual voltage balancing strategy for PWM cascaded Hbridge converterbased STATCOM”
IEEE Trans. Ind. Electron.
55
(1)
21 
29
DOI : 10.1109/TIE.2007.906127
Song Q.
,
Liu W.
2009
“Control of a cascade STATCOM with star configuration under unbalanced conditions”
IEEE Trans. Power Electron.
24
(1)
45 
57
DOI : 10.1109/TPEL.2008.2009172
Mohammadi H. P.
,
Bina M.T.
2011
“A transformerless mediumvoltage STATCOM topology based on extended modular multilevel converters”
IEEE Trans. Power Electron.
26
(5)
1534 
1545
DOI : 10.1109/TPEL.2010.2085088