This article has been accepted for publication in a future issue of this journal, but has not been

fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TIE.2015.2410761, IEEE Transactions on Industrial Electronics

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

Three-Phase AC-AC Converter With Controllable

Phase and Amplitude
Youjun Zhang and Xinbo Ruan, Senior Member, IEEE

Abstract—Based on single-phase AC-AC converter with essence are equivalent to regulating the line impedance and
controllable phase and amplitude (ACCPA), a three-phase current and then controlling active power flow, but they are
ACCPA without third harmonic trap was proposed for power not able to control active and reactive power respectively
transmission control in grid by adopting symmetrical and simultaneously.
relationship of three-phase. The three-phase ACCPA is
comprised of two parts which are used to adjust the phase and
Being different from series var compensation device,
amplitude of three-phase output voltage respectively and shunt var compensation device controls reactive power flow
continuously. Its front-part is made up of 3 Buck type AC in grid and has advantages of stabilizing grid voltage,
converters, and the back-part is a three-phase Boost type AC improving transmission capacity, reducing active power loss,
converter. The operation principle of three-phase ACCPA, the providing voltage support for power system and then
adjustable ranges of the phase and amplitude of the front-part, improving system security, in essence it is as var source or
and the calculation formulas of control parameters under ideal var load. At present the widely used dynamic shunt var
conditions were studied and deduced in detail. Further more, compensation device is static var compensator (SVC), which
the control accuracy of the phase angle was discussed for has fast dynamic response speed and can adjust output
three-phase ACCPA with digital control, and then the method
to select close-loop control parameters was obtained. The
reactive power continuously [16]-[18]. Static synchronous
control strategy of three-phase ACCPA was presented and a compensator (STATCOM), in structure equaling a voltage
prototype was fabricated. The experimental waveforms and source inverter and a commutation reactance in series, is an
testing results verified the correctness of the theoretical analysis advanced shunt var compensation device and has better
and the feasibility of the control strategy. performance than SVC in dynamic compensation [19]-[23].
Although shunt var compensation device is mature in
Index Term—AC-AC converter with controllable phase and
amplitude (ACCPA), power transmission control, control technology, it can not control the current in individual
parameter, phase regulation, control accuracy of phase angle. branches and the active power flow in meshed systems
effectively.
I. INTRODUCTION United power flow controller (UPFC) is hitherto the most
powerful flexible AC transmission system (FACTS) device

I N meshed systems or a system with a plurality of

transmission lines in parallel, the line which is the first to
reach the maximum transmission current (thermal limit) will
[24]-[28]. It is made up of two voltage source inverters with
one shared capacitor and is similar to the combination of a
series SSSC and a shunt STATCOM. UPFC can separately
limit the power transmission capability of the entire power or simultaneously realize functions of shunt compensation,
grid, even if the flow capacity of other transmission lines series compensation and phase shifting, and control active
have not been fully utilized [1]-[2]. and reactive power flow respectively. Although UPFC,
With applications of series var compensation, it can SSSC and STATCOM have reached a high level of maturity,
effectively improve the power transmission capacity of grid their market penetration is not significant for the factor of
and the utilization of power system, control the power price. In addition, the adoption of big volume DC energy
distribution between lines in parallel, and enhance power storage element leads to high failure rate and short life cycle.
system transient stability [3]. Dynamic series var Actually, it is known that the active and reactive power
compensation devices, mainly include static synchronous flow through an AC transmission line is a function of the
series compensator (SSSC) [3]-[7], thyristor controlled line impedance, the amplitudes of the sending-end voltage
series capacitor (TCSC) [8]-[11], GTO controlled series and the receiving-end voltage, and the phase difference
capacitor (GCSC) [12], thyristor switched series capacitor between the two voltages [29]. Without adjusting the line
(TSSC) [13], distributed series impedance (DSI) [14] and impedance, if the phase and amplitude of the sending-end
current limiting conductor (CLiC) [15], whose functions in voltage are regulated independently, the active and reactive
power transmission in a grid could be controlled
simultaneously and separately. In order to obtain a kind of
Manuscript received June 8, 2014; revised August 23, 2014 and
December 28, 2014; accepted February 8, 2015.
device without big volume DC energy storage element,
Copyright (c) 2015 IEEE. Personal use of this material is permitted. which does not only have the functions of both voltage
However, permission to use this material for any other purposes must be step-up and step-down, but also can adjust the phase of the
obtained from the IEEE by sending a request to pubs-permissions output voltage lead or lag with respect to the input, an
@ieee.org.
This work was supported in part by the Natural Science Foundation of
improved topology with appropriate control algorithm
China under Award 51477107, by the Postdoctoral Science Foundation of should be developed. Though matrix converter does not
Jiangsu Province, China, under Award 1402107C, and by Open Research contain bulky DC energy storage element, its
Fund of Jiangsu Key Laboratory of Spectral Imaging & Intelligent Sense, maximum voltage transfer ratio is only 0.866 [30]-[34]. By
Jiangsu Province, China, under Award 3092014012200410.
Y. Zhang is with the College of Mechanical and Electric Engineering,
introducing the concept of virtual quadrature source (VQS)
Soochow University, Suzhou 215021, China, and also with the School of [35], literature 36 presented a novel method for power
Computer science & Technology, Soochow University, Suzhou 215021, transmission control ⎯ AC-AC converter with controllable
China (e-mail: zhangyoujun@suda.edu.cn). phase and amplitude (ACCPA), which is based on Buck and
X. Ruan is with the Aero-Power Sci-tech Center, the College of
Automation Engineering, Nanjing University of Aeronautics and Boost AC-AC converter [37]-[38].
Astronautics, Nanjing 210016, China (e-mail: ruanxb@nuaa.edu.cn). ACCPA has two control variables and be able to
1
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TIE.2015.2410761, IEEE Transactions on Industrial Electronics

IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

continuously regulate the phase and amplitude of output
voltage respectively. Compared with UPFC, STATCOM and
SSSC, ACCPA does not have DC energy storage element,
thereby it could reduce the failure rate and maintenance cost
and extend equipment life cycle. The voltage stresses of
power switching devices in its front-part and back-part are
low and equal to the maximum values of input voltage and
output voltage respectively. Moreover, ACCPA is sensitive
to dynamic response for employing high frequency control,
and has a direct power transmission path between its input
and output, which would result in high efficiency. In
single-phase ACCPA, a third harmonic trap is introduced to
filter out third harmonic voltage component. The third
harmonic trap is bulky and heavy, and its line resistance
Fig. 1. Three-phase ACCPA group.
would greatly weaken the effect of filtering out third
harmonic voltage. =2πf, is the angular frequency and f is the frequency of uix.
By adopting symmetrical relationship of three-phase, If the front-part duty ratios d1x of three-phase ACCPA
three-phase ACCPA without third harmonic trap was group were kept constant and equal to each other, the output
proposed for power transmission control in grid, which phase voltages uo1x of 3 single-phase Buck type AC
could regulate the phase and amplitude of three-phase output converters (the front-part of three-phase ACCPA group)
voltage respectively and continuously. Its front-part is were also sinusoidal and in phase with uix respectively.
comprised of 3 Buck type AC converters, and the back-part In order to obtain desired output voltages whose phase
is a three-phase Boost type AC converter. The operation angles are shifted with respect to the input, it is necessary to
principle of three-phase ACCPA, the adjustable ranges of the add cosine components in uo1x. So the concept of VQS
phase and amplitude of the front-part, and the calculation proposed by D.Divan is adopted [35].
formulas of control parameters under ideal conditions were Adding AC components of double frequency into the duty
studied and deduced in detail. The control accuracy ratios d1x, and taking into account phase relationship, one
of phase angle was discussed for three-phase ACCPA with knows that there is a difference of 120º in negative sequence
digital control, and then the method to select dynamic between the initial phase angles of d1x, that is
close-loop control parameters was obtained. For verifying ⎧ d1a = k0 + k 2 sin(2ω t + β 2 )
the correctness of theoretical analysis and the feasibility of ⎪ d = k + k sin(2(ω t − 120°) + β )
control strategy, a prototype of three-phase ACCPA was ⎪ 1b 0 2 2
⎪
fabricated. ⎨ = k0 k 2 sin(2ω t β 2 120 )
+ + + ° (2)
⎪ d = k + k sin(2(ω t + 120°) + β )
II. TOPOLOGY STRUCTURE AND OPERATIONAL PRINCIPLE OF ⎪ 1c 0 2 2

⎪⎩ = k0 + k 2 sin(2ω t + β 2 − 120°)
THREE-PHASE ACCPA
where coefficient k0 is the DC component of d1x, coefficient
A. Three-phase ACCPA group k2 and β2 are the amplitude and initial phase angle of the AC
As shown in Fig. 1, 3 single-phase ACCPAs can constitute component of d1a respectively.
a three-phase ACCPA group. Every single-phase ACCPA Coefficient k0 and k2 are nonnegative. Because the range
comprises of a Buck type AC converter, a Boost type AC of d1x is among [0, 1], k0 and k2 should satisfy the following
converter and a third harmonic trap which is made up of a relationship
transformer (TR) and a capacitor (C3), or an inductor with a ⎪⎧ k2 ≤ k0 , 0 ≤ k0 ≤ 0.5
capacitor in parallel [36]. ⎨ (3)
⎪⎩ k2 ≤ 1 − k0 , 0.5 ≤ k0 ≤ 1
Because each single-phase ACCPA is independent of each
other, by adjusting the front-part duty ratio d1x (x=a, b, c, x is Multiplying items of (1) with those of (2) respectively,
the name of phase at lowercase state) and the back-part duty one can obtain the output phase voltages uo1x of 3
ratio D2x of each single-phase ACCPA, the three-phase single-phase Buck type AC converters (the front-part of
ACCPA group is able to transform an asymmetrical three-phase ACCPA group). The voltage uo1x contains a
three-phase AC voltage source into a symmetrical one, fundamental voltage component u1x and a third harmonic
whose phase angle and amplitude could be regulated voltage component u3x. u1x is obtained across the capacitor
independently and continuously. Cf1 after u3x is filtered out by the third harmonic trap. uo1x,
For the simplicity of analysis, one should assume all u1x and u3x are as follows:
circuit components are ideal and same in every phase circuit, ⎧uo1a = U1m sin(ω t + ϕ1 ) + U 3m sin(3ω t + ϕ3 )
ignore low frequency voltages dropped across the ⎪
⎪ = u1a + u3a
inductance Lf1 and Lf2 and the fundamental voltage dropped ⎪⎪uo1b = U1m sin(ω t + ϕ1 − 120°) + U 3m sin(3ωt + ϕ3 )
across the third harmonic trap, and assume three-phase ⎨ (4)
input phase voltages uix are sinusoidal and symmetrical in ⎪ = u1b + u3b
positive sequence as below. ⎪uo1c = U1m sin(ω t + ϕ1 + 120°) + U 3m sin(3ωt + ϕ3 )
⎧uia = U im ⋅ sin ωt ⎪
⎪⎩ = u1c + u3c
⎪
⎨uib = U im ⋅ sin(ωt − 120°) (1) where U1m is the amplitude of u1x, ϕ1 is the initial phase
⎪u = U ⋅ sin(ωt + 120°)
⎩ ic im angle of u1a, U3m is the amplitude of u3x, and ϕ3 is the initial
where Uim is the amplitude of input phase voltages uix, ω phase angle of u3x. According to (1), (2), and (4), U1m, ϕ1,

2
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS

U3m and ϕ3 can be expressed with control parameter k0, k2

and β2.
⎧ k2
⎪U1m = U im 2 − k0 k2 sin β 2 + k02
⎪ 4
⎨ (5)
⎪ϕ1 = arctan k2 cos β 2
⎪⎩ 2k0 − k2 sin β 2

Load
⎧⎪ k
U 3m = 2 U im
⎨ 2 (6)
⎪⎩ϕ3 = β 2 − 90°

B. Three-phase ACCPA
It is known from (4) that fundamental voltage u1a, u1b and Fig. 2. Three-phase ACCPA.
u1c have equal amplitude, and there is a phase difference of
120º in positive sequence between them. Third harmonic uox of three-phase ACCPA (dropped across the capacitors Cf2
voltage u3a, u3b and u3c have equal amplitude and same phase in Fig. 2), as shown in (9), do not contain third harmonic
angle, namely u3a=u3b=u3c. So output line voltage uo1ab, uo1bc component, but only fundamental one.
and uo1ca of 3 Buck type AC converters are derived as (the ⎧ U1m
voltages between point A2, B2 and C2. Only point A2 is ⎪uoa = sin(ω t + ϕ1 )
⎪ 1 − D2
shown in Fig. 1)
⎪⎪ U1m
⎧uo1ab = uo1a − uo1b = u1a − u1b ⎨uob = sin(ωt + ϕ1 − 120°) (9)
⎪ ⎪ 1 − D2
⎪ = 3U1m sin(ω t + ϕ1 + 30°)
⎪ U
⎪u ⎪uoc = 1m sin(ω t + ϕ1 + 120°)
⎪ o1bc = uo1b − uo1c = u1b − u1c ⎪⎩ 1 − D2
⎨ (7)
⎪ = 3U1m sin(ω t + ϕ1 − 90°) Known from (1), (4), (7)~(9), in comparison with input
⎪u = u − u = u − u voltage, the phase shift ϕs and the amplitude gain kg of
⎪ o1ca o1c o1a 1c 1a

⎪⎩ three-phase ACCPA are as same as those of single-phase

= 3U1m sin(ω t + ϕ1 + 150°)
ACCPA [36]. Their expressions are shown in (10), where
It is obvious that uo1ab, uo1bc and uo1ca have no third Uom is the amplitude of uox and equal to U1m/(1- D2).
harmonic voltage component, but only fundamental voltage k2 cos β 2
⎧
component. uo1ab, uo1bc and uo1ca are sinusoidal and ⎪ϕs = ϕ1 = arctan 2k − k sin β
symmetrical in positive sequence, and equal to the voltages ⎪ 0 2 2

between point A3, B3 and C3 respectively (only point A3 is ⎨ 2

(10)
⎪ U om 1 k2
shown in Fig. 1). So the three-phase ACCPA group does not ⎪kg = U = 1 − D − k0 k2 sin β 2 + k0
2

need third harmonic trap. If without third harmonic trap, ⎩ im 2 4

while the back-part duty ratio D2a, D2b and D2c, are equal to It is known from (10) that the phase angle (ϕs=ϕ1) of the
each other and be constant within a fundamental cycle, the output voltage could be controlled by controlling the duty
output line voltages of the back-part of three-phase ACCPA ratio d1x of the front-part, and the amplitude of the output
group are also sinusoidal and symmetrical in positive voltage could be controlled by controlling the duty ratio D2
sequence, but the output phase voltages of the back-part of the back-part according to d1x. Thereby the phase angle
contain third harmonic voltage component. and amplitude of the output voltage of three-phase ACCPA
Replacing the back-part (3 Boost type AC converters in can be regulated independently and continuously.
Fig. 1) with a three-phase Boost type AC converter, and For the load which is float and not connected to ground, it
getting rid of 3 third harmonic traps in the front-part (namely could be directly connected with the output of three-phase
point X2 and X3 are combined into one point, X=A, B, C, X ACCPA. At this situation, load triangle connection (Δ type)
is the name of phase at capital state), one could obtain the is recommendable instead of Y type connection in Fig. 2.
circuit topology structure of three-phase ACCPA without For Y type connection, the phase voltage across load is
third harmonic trap, as shown in Fig. 2. asymmetrical with unbalance load. However, as for the load
If the duty ratio D2 of the three-phase Boost type AC which is not float but connected to ground, a three-phase
converter (the back-part in Fig. 2) is constant, the output line transformer must be needed to provide isolation. If the
voltages of three-phase ACCPA are output is connected to a Δ/Y transformer, a steady load
⎧ uo1ab 3U1m neutral point could be obtained and the phase voltage across
⎪uoab = = sin(ωt + ϕ1 + 30°) load is symmetrical even if with unbalance load.
⎪ 1 − D2 1 − D2
⎪
⎪ uo1bc 3U1m III. ADJUSTABLE RANGES AND CONTROL ACCURACY
⎨uobc = = sin(ω t + ϕ1 − 90°) (8)
1 − D2 1 − D2 ANALYSIS
⎪
⎪ A. Adjustable ranges of the phase angle and amplitude of
⎪uoca = uo1ca = 3U1m sin(ω t + ϕ1 + 150°) the front-part
⎪⎩ 1 − D2 1 − D2
Because there is no conduction path for third harmonic Obtaining dϕ1/dβ2 from (5) or (10) and making it equal to
component in the three-phase Boost type AC converter (the zero, one knows that under extremum of ϕ1 control
back-part of three-phase ACCPA), the output phase voltages parameter k0, k2 and β2 should satisfy

3
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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k2 maximum of U1m are

sin β 2 = ≥0 (11)
2 k0 ⎧⎪U1m min = U im (k0 − k2 / 2)
⎨ (14)
Obviously, in the range of 0°~360°, β2∈[0°, 180°]. ⎪⎩U1m max = U im (k0 + k2 / 2)
Substituting (10) with (11), then (12) is obtained. When k0 Taking (3) with equality and substituting it into (14), one
and k2 are fixed values and β2∈[0°, 90°], ϕ1 is maximum can obtain the relationship of minimum and maximum
and equal to β2. When k0 and k2 are fixed values and U1m/Um (U1m*) with changing k0, shown as curve 1 and 2 in
β2∈(90°, 180°], ϕ1 is minimum and equal to β2-180°. Fig. 4. While 0≤k0≤0.5 and k2 changes, the minimum and
⎧ k2 maximum of U1m/Uim equal to k0/2 and 3k0/2 respectively.
⎪ϕ1max = arcsin 2k = β 2 β 2 ∈ [0°, 90°] While 0.5≤k0≤1 and k2 changes, the minimum and maximum
⎪ 0
⎨ (12) of U1m/Uim equal to 3k0/2−0.5 and k0/2+0.5 respectively.
⎪ϕ k2
= − arcsin = β −180° β ∈ (90°, 180° ] B. Calculation of control parameters under ideal condition
⎪⎩ 1min 2k0
2 2

Known from (12), for a fixed k0, ϕ1 is maximum or Similarly, from (5) one can obtain
minimum under maximum k2 (taking (3) with equality). dU1m U m (2k0 − k2 sin β 2 )
= >0
While 0≤k0≤0.5 (0≤k2≤ k0), the adjustable range of ϕ1 is dk0 k22 (15)
[−30°, 30°]. While 0.5≤k0≤1 (0≤k2≤1−k0), the adjustable 2 − k0 k2 sin β 2 + k0
2

4
range of ϕ1 minishes with increasing k0, as shown in (13).
Equation (15) shows that U1m is an increasing function of
⎧ 1 − k0 k0 and increases with increasing k0.
⎪⎪ϕ1max = arcsin 2k After meeting the required values of the phase and
⎨ 0 when k2 = 1 − k0 (13)
1 − k0 amplitude of output voltage, U3m (the amplitude of third
⎪ϕ1min = − arcsin
⎪⎩ 2 k0 harmonic voltage in the front-part) should be as small as
From (11)~(13), one can obtain the relationship of possible, and U1m (the amplitude of fundamental voltage in
the front-part) should be as high as possible. Known from
extremum ϕ1 with changing k0, shown as curve A and B in
(6), U3m is proportionate to k2. If the smaller U3m is expected,
Fig. 3. The variation ranges of maximum and minimum ϕ1
it requires the smaller k2. From (15) one knows that the
are [0°, 30°] and [−30°, 0°] respectively, corresponding greater k0 will be required if the greater U1m is expected. In
ranges of β2 are [0°, 30°] and [150°, 180°]. other words, the smaller k2 and the greater k0 are required
When k0 and k2 are fixed values, U1m is minimum as β2 here, it means the requirement of the smaller k2/k0. Known
equals to 90º, or maximum as β2 to 270º. The minimum and from (12), the smaller k2/k0 leads to smaller adjustable scope
45º of the phase angle ϕ1. It can be seen in Fig. 3 that the
corresponding k2/k0 is smallest when the expected ϕ1 is
ϕ1max
30º extreme. Therefore, control parameter k0 should be taken
A among the scope [0.5, 1] according to the curve A or B in
15º Fig. 3, that is
1
0º
k0 = ϕ1_ ref ∈ [−30°, 30°] (16)
1 + 2 sin ϕ1_ ref

15º where ϕ1_ref is the phase angle reference of output voltage.

The curve of k0 with changing ϕ1_ref is shown in Fig. 5(a)
B (namely the combination of curves under k0∈[0.5, 1] in Fig.
30º
ϕ1min 3), and control parameter k2 is taken as 1-k0.
45º Know from (11) and (12), 0≤sinβ2≤0.5 when ϕ1 is taken
0 0.25 0.5 0.75 1.0 as extremum, then β2∈[0°, 30°] or [150°, 180°]. At
k0 extremum of ϕ1, From (11), (12) and (13) one can obtain
Fig. 3. Curve of the extremum of ϕ1 with changing k0. ⎧⎪ϕ1_ ref (0° ≤ ϕ1_ref ≤ 30°)
β2 = ⎨ (17)
1.0 ⎪⎩ϕ1_ ref +180° (−30° ≤ ϕ1_ref < 0°)
maximun of U1m* The curve of β2 with changing ϕ1_ref is shown in Fig. 5(b).
After control parameter k0, k2 and β2 are confirmed by the
0.75
2 phase angle reference ϕ1_ref, the front-part duty ratios d1x of
three-phase ACCPA are obtained from (2), and then the
0.5
back-part duty ratio D2 can be calculated with the reference
of amplitude gain kg_ref.
1
1 D2 = 1 − 3k02 + 2k0 − 1 (18)
0.25 2kg_ref
minimun of U1m*
Substituting (11) into (5), we have
0 U1m = U im k02 − k22 / 4 (19)
0 0.25 0.5 0.75 1.0
Taking into account k2 restricted by k0, and according to
k0
(6), (11) and (19), when the control parameters of the
Fig. 4. Curve of the extremum of U1m* with changing k0. front-part are determined as above, curves of U1m/Uim (U1m*)
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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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and U3m/Uim (U3m*) following k0 can be obtained at C. Control accuracy analysis and selection of close-loop
extremum of ϕ1, as shown in Fig. 6 with curve 1 and 2 control parameters
respectively. Curve 2 also represents that of maximum U3m*.
The controlled objects of three-phase ACCPA are the
A special situation should be illustrated here. It is
phase angle and amplitude of its output voltage. It is a
necessary to select control parameters again when the
multi-variable system and there are coupling relationship
amplitude reference of output line voltage of three-phase
among the variables. The circuit for phase control would be
ACCPA, UoLm_ref, is less than 3 U1m. Then making D2=0, very complicated if it is implemented by using analog circuit.
causing the back-part of three-phase ACCPA direct So digital control method is adopted to realize the phase
conduction. β2 is still selected according to (17), keeping control circuit which is based on DSP chip TMS320F2812.
k2/k0=2|sinϕ1_ref|, decreasing k2 and k0 with same proportion Because the control parameter of digital circuit is changed
until 3 U1m=UoLm_ref. In this paper, the special situation according to its step, and can not change smoothly as that of
analog circuit. It will bring errors and affect the control
would not be further discussed.
accuracy of system.
1
Considering the clock frequency of DSP, the relationship
of three-phase, and switch frequency, setting 450 points
0.9 within a sine cycle of double frequency, so the step of β2 is
0.8º. Taking the curve in Fig. 5(b) as an example, when the
0.8 phase angle reference ϕ1_ref varies among [0º, 30º] or [-30º，
0º], β2 can each have 38 values for being selected. That
k0

means the curve in Fig. 5(b) is made up of 76 discrete points.

0.7
Because at extremum of ϕ1 the value of β2 is determined by
ϕ1 (ϕ1=ϕ1_ref under ideal condition), the curve in Fig. 5(a) is
0.6 also made up of another 76 discrete points (2 points
coincides at k0=1 and ϕ1_ref=0º). Because of the nonlinear
0.5 relationship of the curve, the intervals of k0 are not equal to
30º 15º 0º 15º 30º each other (all are larger than its step).
ϕ1_ ref
Obviously, by using digital control and without
(a) considering other error factors, when three-phase ACCPA
adopts open-loop control according to curves in Fig. 5, only
75 points among [-29.6 º, 29.6 º] with interval of 0.8º can be
controlled precisely, and other phase angles among
[-30º, 30º] can be controlled approximately.
For an actual work system, many factors, such as
inductive impedance and variation in grid frequency or load,
would bring errors. So close-loop control should be adopted
β2

for accurate regulation of phase angle. In the close-loop

control of the phase, the phase angle reference ϕ1_ref is
compared with the feedback signal of ϕ1, then the phase
error signal is obtained, and 3 control parameters of the
front-part (k0, k2, and β2) are adjusted continuously.
In order to improve the stability of close-loop control
system, and reduce excessive oscillation caused by much
ϕ1_ ref
variation of control parameters, the initial control parameters
(b) of close-loop control should coincide with those of
Fig. 5. Curve of k0 and β2 with changing ϕ1_ref. (a) Curve of k0. (b) Curve of open-loop control under ideal conditions. When ϕ1_ref varies
β2 . among the scope of [-30º, 30º], due to 0.8º step of β2, there
1.0
are 76 groups of control parameter that can be adopted as
initial control parameters (having 2 groups at ϕ1_ref=0º).
When ϕ1_ref is not one of 75 points among [-30º, 30º] with
0.75 0.8º interval (-29.6º, -28.8º, ……, 0º, ……, 28.8º, 29.6º),
U1m* 1 matching ϕ1_ref with these 75 points and choosing initial
control parameters according to the nearest point.
0.5 Caused by dynamic variation of close-loop control
parameters, the step length of phase regulation (Δϕ1) is
dϕ dϕ dϕ
Δϕ1 = 1 Δk0 + 1 Δk2 + 1 Δβ 2 (20)
0.25 dk0 dk2 d β2
U3m*
2 Know from (20), in order to reduce the error of close-loop
0
phase adjustment, it is necessary to reduce Δϕ1, namely
0.5 0.6 0.7 0.8 0.9 1.0 Δk0, Δk2 and Δβ2 should be as small as possible.
k0 In the implementation of close-loop feedback control of
phase angle, the error signal of phase is obtained after its
Fig. 6. Curves of U1m* and U3m* at extremum of ϕ1.
feedback result is compared with its reference, and then
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dynamic control parameters (k0, k2 and β2) are adjusted uk1a_a

continuously. Sample
uP1_a
uia uk1b_a
Two methods were presented for selecting close-loop
control parameters dynamically. GND uN1_a
Method 1: According to the error signal of phase, Fig. 5(b)
d1a uk2b_a
and (12), β2 would be adjusted contrarily around its initial
value, and k0 is selected by β2 according to (12), (13) and rising 1-d1a uk2a_a
Fig. 5(a), retaking k2=1−k0. edge
In method 1, the dynamic control parameters are selected of d1b uk1a_b
according to the curves in Fig. 5. Because of k2=1-k0 and uia
uk1b_b
dϕ1/dβ2=0, Δϕ1 is Sample uP1_b
dϕ DSP uib uN1_b
Δϕ1 = 1 Δk0 (21) uk2b_b
dk0 rising GND
edge
where dϕ1/dk0 is as follows while k0∈[0.5，1]: 1-d1b uk2a_b
of
⎧ dϕ1 −1 uoab
⎪ dk = (0° ≤ ϕ1 ≤ 30°) d1c uk1a_c
⎪ 0 k0 4k0 − (1 − k0 )
2 2

⎨ dϕ (22) uk1b_c
⎪ 1= 1 1-d1c
(−30° ≤ ϕ1 < 0°)
⎪ dk0 k 4k − (1 − k ) 2
2
Sample
uN1_c
⎩ 0 0 0 uP1_c
uic uk2b_c
While 0°≤ϕ1≤30°, dϕ1/dk0 ∈ [-132.32° ， -28.65°]. while
-30°≤ϕ1<0°, dϕ1/dk0 ∈ (28.65° ， 132.32°]. For extremum GND comparator uk2a_c
curve A and B in Fig. 3 (or Fig. 5(a)), k0 can take 38 values Fig. 7. Phase angle control strategy of three-phase ACCPA.
within [0.5, 1] with average interval more than 0.0135. It is
derived that Δϕ1 equals to Δβ2, which is 0.8º, the step length angle of its output voltage. The phase angle close-loop
of β2. control strategy of three-phase ACCPA is shown in Fig. 7.
Clearly, Δϕ1 of 0.8º is too large to realize accurate phase Sampling input phase voltages uix respectively, generating
regulation. For obtaining smaller Δϕ1, an improved method their positive signals uP1_x by use of zero-crossing
(method 2) was proposed to select dynamic close-loop comparators, reversing uP1_x and getting their negative
control parameters. signals uN1_x. After detecting the rising edge of uia and that of
Method 2: β2 is kept to be its initial value. According to uoab (or uo1ab), a DSP controller calculates out the phase
the error signal of phase, only adjusting k0 contrarily, and angle ϕ1 between input and output voltages, and compares it
retaking k2=1−k0. with reference phase angle ϕ1_ref which is preset in DSP, then
Taking into account the fact that the difference is not large contrarily adjusts control parameters according to method 2,
between initial control parameter and dynamic one in and generates duty ratio signals of d1x and (1-d1x) of the
close-loop control, so we can keep β2 remain unchanged front-part. Signals uP1_x and uN1_x are modulated with d1x and
(1-d1x) in logical OR mode, and control signals uk1a_x, uk1b_x,
(being its initial value, that means Δβ2=0), and adjust k0 with
uk2a_x and uk2b_x are obtained for controlling switches S1a_x,
a smaller step. Here we take Δk0=0.001 and k2=1-k0, then
S1b_x, S2a_x and S2b_x.
Δϕ1 is still expressed by (21). It shows that a smaller Δϕ1
can be obtained because of a smaller Δk0. Known from (22) B. Amplitude close-loop control of three-phase ACCPA
and (21), at initial control parameter, the variation range of
The back-part of three-phase ACCPA is a three-phase
Δϕ1 is among [0.02865°, 0.13232°] (shown with positive Boost type AC converter, and is used to regulate the
value) and is far less than 0.8º in method 1. amplitude of its output voltage. The amplitude close-loop
As mentioned above, in the close-loop control of phase control strategy of three-phase ACCPA is shown in Fig. 8.
angle ϕ1, by adopting method 1 to select dynamic close-loop Sampling output phase voltages u oa , u ob and u oc ,
control parameters according to extremum of ϕ1 (curves in
Fig. 5), it needs to adjust 2 independent control parameters, uoa + ukab
usa
uks3
k0 and β2 (there is nonlinear relationship between them, and uob unab
-
k2=1-k0). The step length of phase regulation in method 1 is
usb
large (Δϕ1=0.8º while in digital control). However, by uob + ukbc uks4
adopting method 2 which is improved on the basis of uoc - unbc
method 1, it only needs to adjust k0 as dynamic close-loop usc
uoc + ukca uks5
control parameter (Δβ2=0, k2=1-k0). In method 2 the step
uoa - unca
length of phase regulation is small
(Δϕ1∈[0.02865°, 0.13232°] while Δk0=0.001). Compared Triangular uks8
Feedback
with method 1, method 2 is simple, easy to implement and carrier
signal of
has high stability and high control accuracy of phase angle. Uoabm - up uks6
- voltage + unp
IV. I MPLEMENTATION OF CONTROL S TRATEGY UoLm_ref ╳
+ regulator ue comparator uks7
A. Phase close-loop control of three-phase ACCPA
The front-part of three-phase ACCPA controls the phase Fig. 8. Amplitude control strategy of three-phase ACCPA.

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
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comparing them with each other and obtaining control phase voltage of three-phase ACCPA. uoab is leading uoa for
signals ukab, ukbc and ukca, reversing them respectively and 30º.
getting negative signals unab, unbc and unca. Signals ukab, ukbc By using a DSP emulator and the function of CCS (Code
and ukca are modulated with unbc, unca and unab respectively in Composer Studio) software to watch variables, we can
logical AND mode, and control signals usb, usc and usa are observe dynamic phase angle ϕ1 (equal to the phase
obtained to indicate which output phase voltage is minimum. difference between the input and output voltages)
Feedback signal of output line voltage amplitude Uoabm (or stochastically under close-loop control. Table I shows
Uobcm, Uocam) is compared with reference voltage amplitude random observation results of ϕ1 at steady state,
UoLm_ref and its error signal ue is obtained from voltage corresponding to ϕ1_ref being -25°, -15°, -5°, 5°, 15° and 25°
regulator (such as PI type). After ue is compared with respectively. Each has 10 measure data. Subtracting each
triangular carrier, PWM control signal up with duty ratio D2 datum with corresponding ϕ1_ref, taking absolute value and
is gained and its reversing signal is unp. Signals up and unp obtaining its phase angle error. Obviously, for each ϕ1_ref in
are modulated with usa, usb and usc respectively in logical OR Table I, there are maximum (Δmax), minimum (Δmin) and
mode, and control signals uks3, uks4, uks5, uks6, uks7 and uks8 are average (Δave) of phase angle error.
obtained for controlling switches S3, S4, S5, S6, S7 and S8. As shown in Table I, Δmax has its maximum (0.242°) and
minimum (0.152°) while ϕ1_ref is 25° and 5° respectively.
V. EXPERIMENTAL RESULTS Similarly, Δave has its maximum (0.146°) and minimum
In order to verify the analysis above, a prototype of (0.059°) while ϕ1_ref is 25° and -5° respectively. Δmax and
three-phase ACCPA is fabricated and tested in the lab, which Δave all increase with increasing |ϕ1_ref|. Δmin is very small,
is shown in Fig. 9. its maximum is 0.014° and its minimum is only 0.002°.
The specifications of the prototype are as follows: Taking into account the dynamic response speed of
1) amplitude of input line voltage: 200 2 V (Uim= system and the slight variation of other error factors, such as
the fluctuation of grid frequency, the zero crossing distortion
115 2 ); of grid voltage and the small amount of harmonic voltage in
2) fundamental frequency: f=50 Hz; grid, it can be seen in Table I that Δmax, Δmin and Δave
3) Rated amplitude of output line voltage: 200 2 V (especially) are consistent with the theoretical analysis of
(Uom=115 2 ); Δϕ1 (the step length of phase regulation). Δmax, Δmin and
4) Rated output capacity: 1200 VA; Δave in Table I reflect that the control system has small
5) switching frequency: fs=22.5 kHz; adjustment error and high control accuracy of phase angle.
6) IGBT power switch: HGTG20N60B3D; In Fig. 11, curves 1~10 show conversion efficiency of
7) inductor: Lf1=Lf2=0.5 mH; three-phase ACCPA, corresponding to ϕ1_ref being -5°, 5°,
8) capacitor: Cf1=4.4 μF, Cf2=6.6 μF; -10°, 10°, -15°, 15°, -20°, 20°, -25° and 25° respectively.
9) control IC of DSP: TMS320F2812. Known from Fig. 11(a), at heavy load, while ϕ1_ref is
Fig. 10 shows experimental waveforms of close-loop negative, the smaller |ϕ1_ref|, the higher efficiency. Similarly
control of three-phase ACCPA without third harmonic trap. for curves in Fig. 10(b), while ϕ1_ref is positive, also the
Fig. 10(a) shows the front-part output phase voltage uo1a, smaller |ϕ1_ref|, the higher efficiency.
uo1b and uo1c. They all contain third harmonic voltage Comparing Figs. 11(a) and 11(b), it is seen that the
component and have equal amplitude with a phase efficiency of negative ϕ1_ref is higher than that of positive
difference of 120º in positive fundamental sequence. ϕ1_ref. This is because the filter capacitor, inductance and line
Fig. 10(b) shows the waveforms of uo1a and uo1ab, which is impedance have lag effect for resistance load. Control
the output line voltage of the front-part and has only parameter k0 of the front-part at negative ϕ1_ref is more than
fundamental voltage component. that at positive ϕ1_ref. The larger k0, the higher efficiency and
Fig. 10(c) shows the waveforms of control signals usb, usc amplitude of the front-part. The efficiency of the back-part is
and usa, which indicate the minimum output phase voltage of affected to be higher by the higher amplitude of the
the back-part in different time spans. In a fundamental cycle, front-part, then the much higher efficiency of three-phase
usb, usc and usa each occupy a third period in positive ACCPA.
sequence with a phase difference of 120º.
Fig. 10(d) shows the waveforms of uCE_S6, uCE_S7 and
uCE_S8, the voltages between collector and emitter of
switches S6, S7 and S8. They are also in positive
fundamental sequence with a phase difference of 120º. The
voltage stresses of power switching devices in the back-part
are low and equal to the maximum value of the output line
voltage of three-phase ACCPA.
Fig. 10(e) shows the waveforms of the input line voltage
uiab, the output line voltage uoab and the front-part output line
voltage uo1ab. uoab and uo1ab are in same phase and have
evident phase difference with respect to uiab.
Fig. 10(f) shows the waveforms of uoab, uobc and uoca, the
output line voltages of three-phase ACCPA. They are
sinusoidal and symmetrical in positive sequence with a
phase difference of 120º.
Fig. 10(g) shows the waveforms of uoab and uoa, the output Fig. 9. Prototype of three-phase ACCPA.

7
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uo1a [40V/div] uo1b [40V/div] uo1ab [100V/div] uiab [100V/div]

uo1c [40V/div] uoab [100V/div]

t [5ms/div] t [5ms/div]
(a) (e)

uoca [100V/div] uoab [100V/div]

uo1ab [100V/div]

uo1a [100V/div]

uobc [100V/div]
t [5ms/div] t [5ms/div]
(b) (f)

usa [10V/div] uoab [100V/div]

usb [10V/div]

usc [10V/div]

uoa [100V/div]
t [5ms/div] t [5ms/div]
(c) (g)
Fig. 10. Experimental waveforms of close-loop control of three-phase
ACCPA. (a) uo1a, uo1b and uo1c. (b) uo1a and uo1ab. (c) usa, usb and usc. (d) uCE_S6,
uCE_S7 and uCE_S8. (e) uiab, uo1ab and uoab. (f) uoab, uobc and uoca. (g) uoab and uoa.

On the one hand, the cascaded topology structure of

uCE_S6 [200V/div] three-phase ACCPA adds a big degree of freedom in control,
where the front-part controls the phase angle and the
back-part controls the amplitude. On the other hand,
corresponding power losses are increased inevitably for the
uCE_S7 [200V/div] cascaded structure. Although the efficiency of three-phase
ACCPA at large |ϕ1_ref| is dissatisfactory, it is acceptable
especially at small |ϕ1_ref|. In practical application of power
transmission, a small change of phase angle is enough and
uCE_S8 [200V/div] would lead to a huge amount variation of power flow [36].
t [5ms/div]
(d)

8
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TABLE I harmonic trap for filtering out third harmonic voltage.
MEASUREMENT RESULTS OF ϕ1 IN THREE-PHASE ACCPA Based on three-phase ACCPA group, three-phase
ϕ1_ref /° -25 -15 -5 5 15 25
ACCPA without third harmonic trap was proposed for
power transmission control in grid. Its front-part is
Mea. 1 -25.101 -15.130 -5.008 4.966 14.976 24.803 comprised of 3 Buck type AC converters, and the
Mea. 2 -25.174 -14.950 -4.880 5.046 15.066 24.813 back-part is a three-phase Boost type AC converter. By
controlling duty ratios d 1x of front-part and the duty ratio
Mea. 3 -25.014 -14.992 -4.954 4.902 14.806 25.011
D2 of back-part, three-phase ACCPA could regulate the
Mea. 4 -24.858 -14.963 -4.979 5.002 15.034 24.758 phase and amplitude of three-phase output voltage
Mea. 5 -24.861 -14.816 -4.998 5.107 14.944 25.216 respectively and continuously.
Mea. 6 -24.986 -15.040 -4.934 5.053 14.960 24.826
For the method to select dynamic close-loop control
parameters according to extremum of ϕ1 , it is necessary to
Mea. 7 -24.842 -15.021 -5.082 4.973 15.197 25.184
adjust two independent control parameters k0 and β2, while
Mea. 8 -24.771 -14.931 -4.829 5.059 15.014 24.998 the improved method only needs to adjust k0 as dynamic
Mea. 9 -25.146 -15.034 -5.040 5.152 14.784 25.066 close-loop control parameter. So compared with the former
Mea.10 -25.219 -15.197 -4.976 4.977 15.056 24.819 method, the latter is simple, easy to implement and has high
stability. A prototype of three-phase ACCPA was fabricated.
Δmax 0.229 0.197 0.171 0.152 0.216 0.242
Its experimental waveforms verified the correctness of the
Δmin 0.014 0.008 0.002 0.002 0.014 0.002 theory and the feasibility of the control strategy, and the
Δave 0.134 0.077 0.059 0.060 0.090 0.146 measured data showed the control system has small
adjustment error and high control accuracy of phase angle.
95
REFERENCES
1
90 [1] D. Divan, H. Johal, “A smarter grid for improving system reliability
3
and asset utilization,” in Proc. CES/IEEE 5th International Power
5 Electronics and Motion Control Conference (IPEMC), Aug. 2006, pp.
85 16-22.
η /%

7 [2] Divan D, Sastry J, “Controllable network transformers,” in Proc. 2008

IEEE Power Electron. Spec. Conf., Jun. 2008, pp. 2340-2345.
80 [3] F. Zhang, Z. Xu, “Study on control and characteristics of static
-5º
-10º 9 synchronous series compensator,” Proceedings of the CSEE, vol. 28,
no. 19, pp. 75-80, Jul. 2008, in Chinese.
75 -15º [4] L. Gyugyi, C. D. Scauder, K. K. Sen, “Static synchronous series
-20º compensator: a solid-state approach to the series compensation of
-25º transmission lines,” IEEE Trans. Power Dli., vol. 12, no. 1, pp.
70 241-246, Jan. 1997.
0 200 400 600 800 1000 1200 1400
Po/W [5] F. A. Jowder, “Influence of mode of operation of the SSSC on the
small disturbance and transient stability of a radial power system,”
(a) IEEE Trans. Power Sys., vol. 20, no. 2, pp. 935-941, May, 1997.
[6] K. K. Sen, “SSSC-static synchronous series compensator: theory,
95 modeling, and application,” IEEE Trans. Power Dli., vol. 13, no. 1, pp.
241-246, Jan. 1998.
[7] W. Qiao, G. K. Venayagamoorthy, R. G. Harley,
90 “Missing-sensor-fault-tolerant control for SSSC FACTS device with
2
real-time implementation,” IEEE Trans. Power Del., vol. 24, no. 2, pp.
4 740-750, Apr. 2009.
85 [8] P. S. Dolan, J. R. Smith, W. A. Mittelstadt. “A study of TCSC optimal
6
damping control parameters for different operating conditions,” IEEE
Trans. Power sys., vol. 10, no. 4. pp. 1972-1978, Nov. 1995.
80 8 [9] P. J. Piwko, C. A. Wegner, S. J. Kinney, J. D. Eden, “Subsynchronous
5º
10º resonance performance tests of the SLATT thyristor-controlled series
15º 10 capacitor,” IEEE Trans. Power Del., vol. 11, no. 2, pp. 1112-1119, Apr.
75 1996.
20º
[10] A. Daneshpooy, A. M. Gole, “Frequency response of the thyristor
25º controlled series capacitor,” IEEE Trans. Power Del., vol. 16, no. 1, pp.
70
0 200 400 600 800 1000 1200 1400 53-58, Jan. 2001.
Po/W [11] P. Kumkratug, “The effect of thyristor controlled series capacitor on
transient stability of single machine infinite bus system with the exact
(b)
short transmission line model,” American Journal of Applied Sciences,
Fig. 11. Conversion efficiency curves of three-phase ACCPA at different vol. 9, no. 3, pp. 425-428, Mar. 2012.
ϕ1_ref. (a) -5°, -10°, -15°, -20° and -25°. (b) 5°, 10°, 15°, 20° and 25°. [12] L. F. W. De Souza, E. H. Watanabe, M. Aredes, “GTO controlled
series capacitors: multi-module and multi-pulse arrangements,” IEEE
Trans. Power Del., vol. 15, no. 2, pp. 725-731, Apr. 2001.
VI. CONCLUSIONS [13] N. Johansson, L. Angquist, H. P. Nee, “An adaptive controller for
power system stability improvement and power flow control by means
Three single-phase ACCPAs can constitute a of a thyristor switched series capacitor (TSSC),” IEEE Trans. Power
three-phase ACCPA group. By adopting symmetrical Sys., vol. 25, no. 1, pp. 381-391, Feb. 2010.
relationship of three-phase, third harmonic voltages in [14] D. Divan, H. Johal, “Distributed FACTS — a new concept for
the three-phase ACCPA group can offset each other, and realizing grid power flow control,” in Proc. 36th IEEE Power Electron.
Spec. Conf., Jun. 2005, pp. 8-14.
its three-phase output line voltages do not contain third [15] H. Johal, D. Divan, “Current limiting conductors: a distributed
harmonic voltage component, but only fundamental one. approach for increasing T&D system capacity and enhancing
Then three-phase ACCPA group does not need third reliability,” in Proc. IEEE Power Engineering Society Transmission
and Distribution Conf., May, 2006, pp. 1127-1133.

9
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http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI
10.1109/TIE.2015.2410761, IEEE Transactions on Industrial Electronics

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[16] L. Gyugyi, “Power electronics in electric utilities: static var Youjun Zhang was born in Anhui Province, China,
compensators, ” in Proc. IEEE, vol. 76, no. 4, pp. 483-494, Apr. 1988. in 1970. He received the B.S. and M.S. degrees in
[17] H. K. Tyll, G. Huesmann, K. Habur, K. Stump, W. H. Elliott, F. E. electrical engineering from Southwest Jiaotong
Trujillo, “Design consideration for the eddy county static var University, Chengdu, China, in 1992, and Nanjing
compensator,” IEEE Trans. Power Del., vol. 9, no. 2, pp. 757-763, Apr. University of Aeronautics and Astronautics
1994. (NUAA), Nanjing, China, in 2002, respectively,
[18] J. H. Chen, W. J. Lee, M. S. Chen. “Using a static var compensator to where he received the Ph.D. degree in electrical
balance a distribution system,” IEEE Trans. Ind. Appl., vol. 35, no. 2, engineering in 2014. In 2004, he joined the
pp. 298-304, Mar/Apr. 1999. College of Mechanical and Electric Engineering,
[19] K. V. Patil, J. Senthil, J. Jiang, R. M. Mathur, “Application of Soochow University, where he became an
STATCOM for damping torsional oscillations in series compensated associate professor in 2006. He has been a visiting researcher for Jiangsu
AC systems,” IEEE Trans. Energy Conversion, vol. 13, no. 3, pp. Key Laboratory of Spectral Imaging & Intelligent Sense, Jiangsu Province,
237-241, Sept. 1998. China since 2014.
[20] M. H. Baker, B. D. Gemmell, C. Horwill, D. J. Hanson, “STATCOM His main research interests include ac/ac converters for power flow
helps to guarantee a stable system,” in Proc. IEEE/PES Transmission control, ac/dc converters especially focusing on adaptors and its issue of
and Distribution Conference and Exposition, Oct/Nov. 2001, pp. low standby power, and dc/ac converters.
1129-1132.
[21] B. Cultekin, C. O. Gercek, T. Atalik, et al, “Design and
implementation of a 154-kV ± 50-Mvar transmission STATCOM Xinbo Ruan (M’97-SM’02) received the B.S. and
based on 21-level cascaded multilevel converter,” IEEE Trans. Ind. Ph.D. degrees in electrical engineering from
Appl., vol. 48, no. 3, pp. 1030-1045, May/Jun. 2012. Nanjing University of Aeronautics and Astronautics
[22] C. D. Townsend, T. J. Summers, R. E. Betz, “Multigoal heuristic (NUAA), Nanjing, China, in 1991 and 1996,
model predictive control technique applied to a cascaded H-bridge respectively.
STATCOM,” IEEE Trans. Power Electron., vol. 27, no. 3, pp. In 1996, he joined the College of Automation
1191-1199, Mar. 2012. Engineering, NUAA, where he became a Professor
[23] B. Cultekin, M. Ermis, “Cascaded multilevel converter-based in 2002. He is the author or co-author of six books
transmission STATCOM: system design methodology and and more than 200 technical papers published in
development of a 12 kV ±12-Mvar power stage,” IEEE Trans. Power journals and conferences. His main research
Electron., vol. 28, no. 11, pp. 4930-4949, Nov. 2013. interests include soft-switching power electronics
[24] M. H. Namin, “Using UPFC in order to power flow control,” in Proc. converters, power electronics system integration and renewable energy
IEEE International Conf. on Industrial Technology, Dec. 2006, pp: generation system.
1486-1491. From 2005 to 2013, he served as Vice President of the China Power
[25] A. S. Mehraban, A. Edris, C. D. Schauder, “Installation, Supply Society. He has been an Associate Editor for the IEEE Transactions
commissioning, and operation of the world's first UPFC on the AEP on Industrial Electronics and the IEEE Journal of Emerging and Selected
system,” in Proc. IEEE International Conf. on Power System Topics on Power Electronics since 2011 and 2013, respectively.
Technology, Aug. 1998, pp. 323-327.
[26] S. T. Kalyani, G. T. Das, “Control and performance of UPFC
connected to a transmission line,” in Proc. 8th IEEE International
Power Engineering Conf., 2007, pp. 302-307.
[27] K. Deepak, G. S. Ilango, C. Nagamani, K. S. Swarup, “Performance of
UPFC on system behavior under fault conditions ,” in Proc. IEEE
Indicon 2005 Conf., Dec. 2005, pp. 505-509.
[28] N. K. Sharma, P. P. Jagtapr, “Modelling and application of unified
power flow controller (UPFC),” in Proc. 3rd International Conf. on
Emerging Trends in Engineering and Technology, 2010, pp. 350-355.
[29] K. K. Sen, M. L. Sen, “Introducing the family of transformers: A set
of power flow controlling transformers,” IEEE Trans. Power Del., vol.
18, no. 1, pp. 149-157, Jan. 2003.
[30] J. Rodriguez, M. Rivera, J.W. Kolar, P.W. Wheeler, " A Review of
Control and Modulation Methods for Matrix Converters ," IEEE Trans.
Ind. Electron., vol. 59, no. 1, pp. 58-70, Jan. 2012.
[31] T.D. Nguyen, Hong-Hee Lee, " Modulation Strategies to Reduce
Common-Mode Voltage for Indirect Matrix Converters ," IEEE Trans.
Ind. Electron., vol. 59, no. 1, pp. 129-140, Jan. 2012.
[32] A. Dasgupta, P. Sensarma, " Filter Design of Direct Matrix Converter
for Synchronous Applications ," IEEE Trans. Ind. Electron., vol. 61,
no. 12, pp. 6483-6493 , Dec. 2014.
[33] J. Espina, C. Ortega, L. de Lillo, L. Empringham, J. Balcells, A.
Arias, " Reduction of Output Common Mode Voltage Using a Novel
SVM Implementation in Matrix Converters for Improved Motor
Lifetime ," IEEE Trans. Ind. Electron., vol. 61, no. 11, pp. 5903-5911 ,
Nov. 2014.
[34] Changliang Xia, Jiaxin Zhao, Yan Yan, Tingna Shi, " A Novel Direct
Torque Control of Matrix Converter-Fed PMSM Drives Using Duty
Cycle Control for Torque Ripple Reduction ," IEEE Trans. Ind.
Electron., vol. 61, no. 6, pp. 2700-2713 , June 2014.
[35] D. Divan, J. Sastry, “Voltage synthesis using dual Virtual quadrature
sources — A new concept in AC power conversion,” IEEE Trans.
Power Electron., vol. 23, no. 6, pp. 3004-3013, Nov. 2008.
[36] Y. J. Zhang, X. B. Ruan, “AC-AC converter with controllable phase
and amplitude,” IEEE Trans. Power Electron., vol. 29, no. 11, pp.
6235-6244, Nov. 2014.
[37] B. H. Kwon, B. D. Min, J. H. Kim, “Novel topologies of AC choppers,”
in Proc. IEE of Electric Power Applications, vol. 143, no. 4, pp.
323-330, July, 1996.
[38] Lei Li, Dongcai Tang, " Cascade Three-Level AC/AC Direct
Converter ," IEEE Trans. Ind. Electron., vol. 59, no. 1, pp. 27-34, Jan.
2012.

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