Electrical Power and Energy Systems 43 (2012) 418–426
Contents lists available at SciVerse ScienceDirect
Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
Application of subsynchronous damping controller (SSDC) to STATCOM
Amir Ghorbani a,⇑, Babak Mozaffari a, A.M. Ranjbar b
a
b
Department of Electrical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Department of Electrical Engineering, Sharif University of Technology, Tehran, Iran
a r t i c l e
i n f o
Article history:
Received 17 October 2010
Received in revised form 31 May 2012
Accepted 2 June 2012
Available online 4 July 2012
Keywords:
Eigenvalue analysis
Subsynchronous resonance (SSR)
STATic synchronous COMpensator
(STATCOM)
Subsynchronous damping controller (SSDC)
a b s t r a c t
In this paper a novel supplementary subsynchronous damping controller (SSDC) is proposed for the
STATic synchronous COMpensator (STATCOM) which is capable of damping out subsynchronous oscillations in power system with series compensated transmission lines. An auxiliary subsynchronous damping controller (SSDC) for a STATCOM using the generator rotor speed deviation signal as the stabilizing
signal has been designed to damp subsynchronous oscillations. Eigenvalue analysis and transient simulations of detailed nonlinear system are considered to investigate the performance of the controller.
Robustness of the controller has been analyzed by facing the system with disturbances leading to significant changes in generator operating point. This paper deals with a cascaded multilevel converter model,
which is a 48-pulse (three levels) source converter. The IEEE Second Benchmark (SBM) model is considered for the analysis and the complete digital simulation of the STATCOM within the power system is performed in the MATLAB/Simulink environment.
Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction
Series capacitors have been used extensively since 1950 as a
very effective means of increasing the power transfer capability
of a power system that has long (150 miles or more) transmission
lines. Series capacitors significantly increase transient and steadystate stability limits, in addition to being a near perfect means of
Var and voltage control. Until about 1971, it was generally believed
that up to 70% series compensation could be used in any transmission line with little or no concern. However, when in 1970, and
again in 1971, a 750 MW cross compound Mohave turbinegenerator in southern Nevada experienced shaft damage it is
learned that series capacitors can create an adverse interaction between the series compensated electrical system and the springmass mechanical system of the turbine-generators. This effect is
called subsynchronous resonance (SSR) since it is the result of a
resonant condition, which has a natural frequency below the fundamental frequency of the power system [1–3]. Numerous papers
have been published about damping the SSR phenomenon however, in general most of the papers fall into two different categories: the first is using Flexible AC Transmission Systems (FACTSs)
and the second is using generator excitation system and Power
System Stabilizer (PSS). Successful application of FACTS controllers
has been reported in past to mitigate subsynchronous resonance.
In [4] the effectiveness of an auxiliary signal designated as Computed Internal Angle (CIA), which modulates the voltage reference
⇑ Corresponding author.
E-mail address: amirghorbani@stud.pwut.ac.ir (A. Ghorbani).
0142-0615/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.ijepes.2012.06.020
of STATCOM, is investigated. In [5] a SSDC is designed and added to
STATCOM to enhance the torsional mode damping of the system.
The SSDC in [5] uses the thevenin voltage signal to modulate the
reactive current reference of STATCOM. The thevenin voltage signal
is derived from the locally available STATCOM bus voltage and
reactive current signals. In [6] supplementary subsynchronous
damping controller (SSDC) is proposed for the generator excitation
system and the offered controller uses generator rotor speed signal
which is practically available.
The recent advances in WAM technologies using Phasor Measurement Units (PMUs) can deliver synchronous phasors and control signals at a high speed of about a 30 Hz sampling rate [7–9].
Dedicated fiber-optic communication lines are used to transmit
these measured states to the control centre. This information of
the entire power system network is used to design Power System
Stabilizers (PSSs) and FACTS controllers to damp inter-area oscillations [10]. It has been reported in [11] that through a dedicated
fiber-optic link the generator speed can be transmitted to the location of the FACTS controller to damp inter-area oscillations in a
large interconnected system.
In this paper, the main idea is that, in modern technologies,
remote signals are utilized for coordinating FACTS equipments installed in transmission lines and the output power of these equipments are controlled using these signals. In this paper, it is
illustrated that those signals could be used for SSR control besides,
in other words, the SSDC designed in this paper will utilize a signal
which was already available in STATCOM and no extra equipment
is needed. In this paper a pure derivative controller (D) is proposed
which is capable of damping all subsynchronous modes. Generator
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A. Ghorbani et al. / Electrical Power and Energy Systems 43 (2012) 418–426
V1
Generator Vt
~
V2
Xc
EB
Line 1
T
GEN
VS
X2/2
Line 2
EXC
R1
X1
Bc
HP
LP
X2/2
R2/2
R2/2
Xsys
Rsys
IS
ZS
Turbine
STATCOM
Vdc
bc
Fig. 1. Schematic representation of IEEE SBM system-1 model with STATCOM.
Remote signal(Δω)
VRef
+_
Voltage Regulator
Vmeas
Is
Phase-Locked
Loop (PLL)
Vs
_
Vdc
+
Vdc_Ref
KP+K I /S
θ=ωt
Dalpha
Dalpha
KP+KI /S
SSDC
I qRef
Positive
Sequence
Voltage
Measurement
+
+ +
+
+_
KP+K I /S
α
Iq
α
θ*
Gate Pattern
Logic
48-Pulse
VSC
Fig. 2. Control block diagram of STATCOM with SSDC.
rotor speed deviation signal which is measurable in practice is
used as the input signal of the SSDC controller in STATCOM. The
STATCOM based on a full model comprising a 48-pulse Gate
Turn-Off thyristor voltage source converter for combined reactive
power compensation and voltage stabilization of the electric grid
network [12,13]. Simplicity and ease of implementation are advantages of the proposed method. The offered controller covers a wide
range of series compensation ratios and can improve damping ratios of all modes. The performance of the designed controller is
shown both with linear analysis and both transient simulations
considering nonlinear model of the system. Robustness of the controller has been analyzed by facing the system with disturbances
leading to significant changes in generator operating point.
2. Model system
The IEEE SBM system-1 model [14] with STATCOM is considered as the SSR studying system which is shown in Fig. 1. It
ZS
VS ∠θ
ISD + j ISQ
~
E∠θ + α
Fig. 3. Equivalent circuit of STATCOM.
consists of a synchronous generator connected through a transformer and two parallel transmission lines to a very large network
approximated by an infinite bus. One of the lines is compensated
by series capacitors (Line 1). The mechanical system is modelled
by 3-masses: mass 1 = generator; mass 2 = low pressure turbine
(LP) and mass 3 = high pressure turbine (HP). An IEEE Committee
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A. Ghorbani et al. / Electrical Power and Energy Systems 43 (2012) 418–426
Mode 1
0.3
Mode 2
Real Parts of Torsional Modes
0.2
Mode 3
0.1
Mode 0
0
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
0
10
20
30
40
50
60
70
80
90
100
Compensation Percentage
Fig. 4. Real parts of torsional modes for different ratios of series compensation.
5
x 10
Mag (% of Fundamental)
2
X: 24.83
Y: 1.789e+005
1.5
1
X: 50.6
Y: 6.619e+004
X: 32.43
Y: 2.378e+004
0.5
0
0
5
10
15
20
25
30
35
40
45
50
55
Frequency (Hz)
Fig. 5. FFT analysis of Dx.
Fig. 6. Block diagram of the designed SSDC.
Report (1992) has described the modeling of hydraulic turbine and
turbine control model for dynamic studies [15].
Automatic Voltage Regulator (AVR), Excitation System Stabilizer (ESS) and Power System Stabilizer (PSS) have been included
to make the system closer to practical excitation systems. The
parameters of the system is described in [6,16].
The analysis is carried out based on the following initial operating condition and assumptions [5]:
(1) The generator delivers 1 p.u. power to the transmission system and the magnitude of the generator and infinite bus
voltages are set at 1.00 p.u.
(2) The compensation level provided by the series capacitor is
set at 52% of the reactance X1.
(3) In order to effectively utilize the capability of STATCOM a
fixed shunt capacitor is also used at the STATCOM bus (middle of the line 2). For the case studies without STATCOM, the
value of fixed shunt capacitor (BC) is selected such that, the
midpoint voltage is set at 1 p.u. in steady state (shunt capacitor provides required power of 160.37 M var to maintain
magnitude of voltage 1 p.u.).
(4) For the case studies with STATCOM, shunt capacitor provides 100 M var and the STATCOM supplies additional reactive power required to maintain the magnitude of midpoint
voltage 1 p.u. The rating of STATCOM is selected as
±100 M var.
(5) A step decrease of 10% mechanical input torque applied at
0.5 s and removed at 1 s is considered.
3. Model STATCOM
The STATCOM is a shunt device of the FACTS family using power
electronics. It regulates voltage by generating or absorbing reactive
power. The voltage source converter described in this paper is a
harmonic neutralized, 48-pulse GTO converter. It consists of four
three-phase, three-level inverters and four phase-shifting transformers. In the 48-pulse voltage source converter, the dc bus Vdc
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A. Ghorbani et al. / Electrical Power and Energy Systems 43 (2012) 418–426
Real Parts of Torsional Mode
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
Mode 0 (Without SSDC)
Mode 0 (With SSDC & Filter)
-1.2
Mode 0 (With SSDC & Without Filter)
0
10
20
30
40
50
60
70
80
90
100
Compensation Percentage
Fig. 7. Behaviour of mode-0 for Kp = 6.
0.05
Real Part of Torsional Modes
0
-0.05
-0.1
-0.15
Mode1(KP=6)
-0.2
Mode2(KP=6)
Mode3(KP=6)
-0.25
0
10
20
30
40
50
60
70
80
90
100
Compensation Percentage
Fig. 8. Real parts of SSR modes for different ratios of series compensation after adding the SSDC.
LP - GEN Torque (p.u)
4
3
2
1
0
-1
-2
0
1
2
3
4
5
6
7
8
9
10
Time (sec)
Fig. 9. Variation of LP-Gen section torque for pulse change in input mechanical torque (STATCOM with voltage control and without SSDC).
is connected to the four three-phase inverters. The four voltages by
the inverters are applied to secondary windings of four zig-zag
phase-shifting transformers connected in Y or D. The 48-pulse
converter model comprises four identical 12-pulse GTO converters
interlinked by four 12-pulse transformers with phase-shifted
windings [12,13].
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15000
2 - 4 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
15000
10000
5000
4 - 6 Sec
10000
5000
0
0
0
10
20
30
40
50
60
0
10
Frequency (Hz)
15000
30
40
50
60
15000
6 - 8 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
20
Frequency (Hz)
10000
5000
8 - 10 Sec
10000
5000
0
0
0
10
20
30
40
50
60
0
10
Frequency (Hz)
20
30
40
50
60
Frequency (Hz)
Fig. 10. FFT analysis of Dx (STATCOM without SSDC).
LP - GEN Torque (p.u)
(a)
2
With SSDC
Without SSDC
1.5
1
0.5
0
0
1
2
3
4
5
6
7
8
9
6
7
8
9
10
Time (sec)
(b)
80
QSTATCOM (Mvar)
70
60
50
40
30
20
1
2
3
4
5
10
Time (sec)
Fig. 11. Variation of LP-GEN section torque (a) and STATCOM reactive power (b) for pulse change in input mechanical torque (STATCOM with SSDC (KP = 2)).
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A. Ghorbani et al. / Electrical Power and Energy Systems 43 (2012) 418–426
1.1
KP=2
KP=5
LP - GEN Torque (p.u)
1.05
1
0.95
0.9
0.85
0
1
2
3
4
5
6
7
8
9
10
Time (sec)
Fig. 12. Variation of LP-GEN section torque for pulse change in input mechanical torque (STATCOM with SSDC (KP = 5 and KP = 2)).
x 104
5
5
x 104
4 - 6 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
2 - 4 Sec
4
3
2
1
0
4
3
2
1
0
0
10
20
30
40
50
60
0
10
x 104
5
6 - 8 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
5
4
3
2
1
0
20
30
40
50
60
Frequency (Hz)
Frequency (Hz)
x 104
8 - 10 Sec
4
3
2
1
0
0
10
20
30
40
50
60
Frequency (Hz)
0
10
20
30
40
50
60
Frequency (Hz)
Fig. 13. FFT analysis of Dx signal (STATCOM with SSDC (KP = 5)).
4. STATCOM control system
The implemented control system of STATCOM with SSDC is
shown in Fig. 2. It is based on a full-decoupled current control
strategy using both direct and quadrature current components of
the STATCOM ac current. A phase locked loop (PLL) synchronizes
on the positive sequence component of the three-phase terminal
voltage at interface point. The output of the PLL is the angle (h) that
is used to measure the direct axis and quadrature axis component
of the ac three-phase voltage and current. The regulation loop
comprising the ac voltage regulator provides the reference current
(IqRef) for the current regulator that is always in quadrature with
the terminal voltage to control the reactive power. The PLL system
generates the basic synchronizing-signal that is the phase angle h
of the transmission system voltage Vs (middle of the line 2). To
enhance the dynamic performance of the full 48-pulse STATCOM
device model, a supplementary regulator loop is added using the
dc capacitor voltage. The main concept is to detect any rapid variation in the dc capacitor voltage. The strategy of the supplementary damping regulator is to correct the phase angle of the
STATCOM device voltage h, with respect to the positive or negative
sign of the dc voltage variation. If DVdc > 0, the dc capacitor is
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4
x 10
10
x 104
2 - 4 Sec
4 - 6 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
10
8
6
4
2
0
0
10
20
30
40
50
8
6
4
2
0
60
0
10
Frequency (Hz)
x 104
10
30
40
50
60
x 104
8 - 10 Sec
6 - 8 Sec
Mag (% of Fundamental)
Mag (% of Fundamental)
10
20
Frequency (Hz)
8
6
4
2
8
6
4
2
0
0
0
10
20
30
40
50
0
60
10
20
Frequency (Hz)
30
40
50
60
Frequency (Hz)
Fig. 14. FFT analysis of Dx signal (STATCOM with SSDC (without high-pass filters, KP = 6)).
LP - GEN Torque (p.u)
1.1
1.05
1
0.95
0.9
0.85
0.8
0
1
2
3
4
5
6
7
8
9
10
Time (sec)
Fig. 15. Variation of LP-GEN section torque for pulse change in input mechanical torque (STATCOM with SSDC (with high-pass filters, KP = 6)).
charging very fast. This happens when the STATCOM converter
voltage lag behind the ac system voltage; in this way, the converter
absorbs a small amount of real power from the ac system to compensate for any internal losses and keeps the capacitor voltage at
the desired level. The same technique can be used to increase or
decrease the capacitor voltage and, thus, the amplitude of the converter output voltage to control the var generation or absorption.
This supplementary loop reduces ripple content in charging or discharging the capacitor and improves fast controllability of the
STATCOM. STATCOM output current is composed of two factors:
reactive (Iq) and active (Id) current. Reactive current of is compared
with reference reactive current IqRef. The resulting error between
the two signals after an appropriate amplification results in the a
angle. This angle defines the necessary phase shift between the
output voltage of the converter and the ac system voltage needed
for charging (or discharging) the storage capacitor to the dc voltage
level required. So, the a angle is added to h angle to form the a + h
angle which represents the desired synchronizing signal for the
converter to satisfy the reactive current reference [12,13].
5. Eigenvalue analysis and SSDC design
To have a better understanding of controller design procedure,
eignvalue analysis of the system is provided in this section. When
switching functions are approximated by their fundamental
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A. Ghorbani et al. / Electrical Power and Energy Systems 43 (2012) 418–426
6
With SSDC
LP - GEN Torque (p.u)
Without SSDC
4
2
0
-2
-4
0
1
2
3
4
5
6
7
Time (Sec)
Fig. 16. Variation of LP-Gen section torque for a–g fault.
frequency components neglecting harmonics, STATCOM can be
modelled by transforming the three-phase voltages and currents
to D–Q variables using Kron’s transformation [5,17]. The equivalent circuit representation of the STATCOM in D-Q reference frame
is shown in Fig. 3. The state space equations of STATCOM in D-Q
reference frame can be written as [18]:
½X_ s ¼ ½As X s þ ½Bs U s
ð1Þ
where:
mdc t
X s ¼ ½iSD iSQ
U s ¼ ½mSD
ð2Þ
mSQ t
ð3Þ
The matrices [AS] and [BS] are defined below:
2
6
As ¼ 6
4
RsXxs B
x0
x0
xB
k
sinð
a þ hÞ
bc
RsXxs B
2 xB
o
Xs
6
Bs ¼ 4 0
Xs
bc
k cosða þ hÞ
3
7
xX sB k cosða þ hÞ 7
5
ð4Þ
bxc RBp
3
xB 7
0
xB
xX sB k sinða þ hÞ
5
ð5Þ
0
ðS2 þ 48:64Þ
2
ðS þ 0:9862S þ 48:64Þ
0:9862S
where
pffiffiffi
6 48
k¼
p 6
h ¼ tan1
stabilizing signal. It is found by Fast Fourier Transform (FFT) analysis with MATLAB that modes exist in the generator rotor speed
deviation (Dx) signal and the torque signals of various turbine
stages (Fig. 5). The first idea in controller design was using a pure
derivative (D) controller. Generator rotor speed deviation (Dx) is
fed back and after passing through the D controller, added to the
voltage regulator output signal (Fig. 2).
Eignvalue analysis of the system after adding subsynchronous
damping controller (SSDC) shows that the included SSDC can damp
all torsional modes except mode-0. In other words increasing
derivative gain (KP) of the controller moves mode-0 towards instability. In order to solve this problem the corresponding frequency
(mode-0) has been eliminated from rotor speed deviation signal
by using a band-stop filter. Finally, to increase stability of mode0, its frequency is extracted from rotor speed deviation signal using
a band-pass filter and amplified in the adverse direction. Complete
structure of the designed SSDC after adding filters is shown in
Fig. 6.
Transfer functions of the band-stop and band-pass filters are as
follows, respectively:
ðS2 þ 0:9862S þ 48:64Þ
ð6Þ
mSD
mSQ
Z s ¼ Rs þ jX s
ð7Þ
ð8Þ
The resistance Rp represents the losses in the capacitor. Fig. 4
shows the real parts of torsional modes considering all compensation ratios; which are obtained after linearizing the system at the
aforementioned operating point. It can be observed that for 52%
compensation ratio, mode-1 and for 35% compensation ratio
mode-2 have the worst behaviour. It is supposed that a good controller can improve dynamics of all modes for all compensations
ratios.
The different signals generally considered as the input signals to
the auxiliary controller are line real power flow, line current magnitude, bus frequency, bus voltage magnitude, etc. [19]. In this paper, the remote generator rotor speed deviation signal as the
ð9Þ
ð10Þ
Fig. 7 shows the behavior of mode-0 for all compensation ratios
and Kp = 6. The result after adding the designed filters is also contained for comparison. As shown in the Fig. 7, using filtered input
signal the controller can damp mode-0, too. Real parts of all SSR
modes are shown in Fig. 8 after adding the SSDC with filtered input. Comparing Figs. 4 and 8 it can be observed that the designed
SSDC stabilizes the unstable torsional modes.
6. Simulation results
The results from transient simulation of the nonlinear system
including the designed SSDC are shown in this section. All the simulations are carried out in MATLAB-SIMULINK environment for 52%
compensation ratio of line1. The simulation results for 10% decrease in the input mechanical torque applied at 0.5 s and removed
at 1 s with STATCOM with voltage control and without SSDC is
shown in Fig. 9. It is clear from Fig. 9 that, the system is unstable
as the oscillations in LP-GEN section torque grows with time.
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The eignvalue analysis shows that for 52% compensation ratio
of line 1 the torsional mode-1 unstable, however the other modes
are stable. To validate the results of linear analysis and justify the
use of the filters in the SSDC, the Fast Fourier Transform (FFT)
analysis is applied to the system. The FFT analysis of the generator rotor speed deviation signal is performed among 2–10 s with
the time spread of 2 s. The results of FFT analysis are shown in
Fig. 10. As shown in the Fig. 10 all the torsional modes except
mode-1 are damped in time. The amplitude of torsional mode1 increases in time and leads to the system instability. This result
is completely consistent with the one obtained from linear
analysis.
Simulation results, when SSDC is implementing to STATCOM
are shown in Figs. 11. As it demonstrated in figures, system is stable and oscillation of LP-GEN section torque is damped in a few
seconds (The result without SSDC is also contained for comparison). Also as it was expected, for regulating the voltage of installation place in 1.00 p.u, the injected reactive power by STATCOM
becomes 60 M var.
As it was said (eigenvalue analysis), the mechanical modes become more stable by increase in amplitude of KP. Increment of stability can be seen in Fig. 12 where LP-GEN section torque is
demonstrated in the voltage control mode and KP = 5. By comparing results for KP = 5 and KP = 2 it can be seen that by bigger KP,
the damping rate of oscillations increases. Fig. 13 shows the FFT
analysis on the Dx signal of generator when KP = 5. It can be seen
that after seconds the amplitude of mechanical modes decrease
and become smaller than previous sections which shows system
stability. According eigenvalue analysis more increment in amplitude of KP, makes the mechanical damping rates increase but zero
mode damping rate declines (while SSDC without filter). FFT analysis on the Dx signal of generator when KP = 6 (Fig. 14) shows this
matter explicitly. As it is shown in Fig. 14, in time steps, amplitude
of mechanical modes decrease but amplitude of zero mode increases. Also comparing Figs. 13 and 14, shows that damping rate
of mechanical modes (except zero mode), when KP = 6 is bigger
than the state which KP = 5. LP-GEN section torque when the filter
is used in SSDC and KP = 6 is shown in Fig. 15. From the results in
the Fig. 15, it can be seen when filters applied to the SSDC, system
is stable and oscillation of LP-GEN section torque is damped in a
few seconds.
7. Robustness verification
In the next step robustness of the designed controller is investigated by considering a large disturbance in the transmission line.
A good controller should have a satisfactory performance when the
operating conditions change. The designed controller has been
simulated in some new operating conditions to be sure about its
robustness.
Serious faults occurred in the transmission lines cause a significant change in the operating conditions. The system has also been
faced with this type of disturbances to verify performance of the
designed controller. It is assumed that a single-line-to ground (a–
g) fault is occurred at the beginning of the line 2 at t = 0.5 s and
cleared at 0.64 s. If there was not any supplementary controller
the system would obviously become unstable. The variation of
LP-Gen section torque, is shown in Fig. 16 with the previously designed SSDC. As shown in the Fig. 16 the designed SSDC have successfully stabilized the system even when the large disturbance
affected the system.
8. Conclusions
A simple controller has been proposed for STATCOM to damp
subsynchronous oscillations. The performance of the designed controller has been verified using several testing scenarios. Some of
the main results from the simulations are listed below:
The designed controller has been applied successfully to damping the all unstable torsional modes.
A wide range of compensation ratios is covered by using the
offered SSDC.
Only one signal that is easily measurable is used in control
design.
Performance of the designed SSDC is validated using eignvalue
analysis as well as the nonlinear transient simulations.
The proposed controller uses an unsophisticated and easy to
implement idea to cope with the SSR phenomenon.
Simplicity and practicality of the proposed controller with its
excellent performance make it ideal to be implemented in real
power plants.
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